From 015792d5d0356b524900257118158edb2b628da4 Mon Sep 17 00:00:00 2001
From: ncantu <ncantu@tour>
Date: Tue, 10 Mar 2026 13:07:33 +0100
Subject: [PATCH] collatz: update hensel chain leaves shifted script, README
 and certs
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

**Motivations:**
- Sync certs_shifted artefacts, script and README.

**Root causes:** N/A
**Correctifs:** N/A
**Evolutions:**
- collatz_build_hensel_chain_leaves_shifted.py
- README.md
- docs/artefacts/collatz/refinement_K/.../certs_shifted/*.json

**Pages affectées:**
- applications/collatz/collatz_k_scripts/README.md
- applications/collatz/collatz_k_scripts/collatz_build_hensel_chain_leaves_shifted.py
- docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/
---
 .../collatz/collatz_k_scripts/README.md       |     2 +-
 ...llatz_build_hensel_chain_leaves_shifted.py |     6 +-
 ...tificate_Sm_multilevel_mod2p15_to2p24.json |   437 +
 ...ertificate_Sm_multilevel_mod2p15_to2p24.md |     8 +
 ...ostic_targeted_leaves_failure_mod2p15.json |  5016 +
 ...gnostic_targeted_leaves_failure_mod2p15.md |    99 +
 ...ts_obstruction_profile_mod2p15_to2p24.json | 93021 ++++++++++++++++
 ...oots_obstruction_profile_mod2p15_to2p24.md |   522 +
 ...tificate_Sm_multilevel_mod2p15_to2p24.json | 31131 ++++++
 ...ertificate_Sm_multilevel_mod2p15_to2p24.md |   155 +
 ...fted_r19_100187_r18_100187_k10_to2p16.json |     2 +-
 ...fted_r19_100519_r18_100519_k11_to2p18.json |     2 +-
 ...fted_r19_101407_r18_101407_k11_to2p18.json |     2 +-
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 ...fted_r19_105775_r18_105775_k11_to2p18.json |     2 +-
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 ...fted_r19_111943_r18_111943_k10_to2p16.json |     2 +-
 ...fted_r19_112807_r18_112807_k11_to2p18.json |     2 +-
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 ...hifted_r19_198495_r18_198495_k5_to2p8.json |     2 +-
 ...fted_r19_201407_r18_201407_k10_to2p16.json |     2 +-
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 ...fted_r19_204911_r18_204911_k11_to2p18.json |     2 +-
 ...fted_r19_205467_r18_205467_k11_to2p18.json |     2 +-
 ...fted_r19_206959_r18_206959_k11_to2p18.json |     2 +-
 ...fted_r19_207515_r18_207515_k10_to2p16.json |     2 +-
 ...hifted_r19_20763_r18_20763_k11_to2p18.json |     2 +-
 ...hifted_r19_20799_r18_20799_k11_to2p18.json |     2 +-
 ...ifted_r19_209575_r18_209575_k9_to2p15.json |     2 +-
 ...fted_r19_209919_r18_209919_k11_to2p18.json |     2 +-
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 ...fted_r19_408639_r18_408639_k10_to2p16.json |     2 +-
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 ...fted_r19_456159_r18_456159_k10_to2p16.json |     2 +-
 ...ifted_r19_456443_r18_456443_k7_to2p12.json |     2 +-
 ...fted_r19_457343_r18_457343_k11_to2p18.json |     2 +-
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 ...fted_r19_474367_r18_474367_k11_to2p18.json |     2 +-
 ...hifted_r19_474663_r18_474663_k5_to2p8.json |     2 +-
 ...fted_r19_476415_r18_476415_k11_to2p18.json |     2 +-
 ...hifted_r19_47719_r18_47719_k11_to2p18.json |     2 +-
 ...fted_r19_480487_r18_480487_k10_to2p16.json |     2 +-
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 ...ifted_r19_481695_r18_481695_k8_to2p13.json |     2 +-
 ...ifted_r19_483399_r18_483399_k9_to2p15.json |     2 +-
 ...ifted_r19_484891_r18_484891_k8_to2p13.json |     2 +-
 ...fted_r19_486311_r18_486311_k10_to2p16.json |     2 +-
 ...fted_r19_486631_r18_486631_k10_to2p16.json |     2 +-
 ...fted_r19_487495_r18_487495_k11_to2p18.json |     2 +-
 ...fted_r19_487839_r18_487839_k10_to2p16.json |     2 +-
 ...fted_r19_488703_r18_488703_k11_to2p18.json |     2 +-
 ...fted_r19_491035_r18_491035_k10_to2p16.json |     2 +-
 ...fted_r19_491591_r18_491591_k11_to2p18.json |     2 +-
 ...hifted_r19_49199_r18_49199_k11_to2p18.json |     2 +-
 ...fted_r19_493983_r18_493983_k10_to2p16.json |     2 +-
 ...fted_r19_497179_r18_497179_k10_to2p16.json |     2 +-
 ...fted_r19_497511_r18_497511_k11_to2p18.json |     2 +-
 ...fted_r19_498671_r18_498671_k10_to2p16.json |     2 +-
 ...fted_r19_502767_r18_502767_k11_to2p18.json |     2 +-
 ...fted_r19_508911_r18_508911_k11_to2p18.json |     2 +-
 ...ifted_r19_510143_r18_510143_k7_to2p12.json |     2 +-
 ...ifted_r19_513019_r18_513019_k7_to2p12.json |     2 +-
 ...fted_r19_513055_r18_513055_k10_to2p16.json |     2 +-
 ...fted_r19_513919_r18_513919_k11_to2p18.json |     2 +-
 ...fted_r19_515931_r18_515931_k10_to2p16.json |     2 +-
 ...fted_r19_515967_r18_515967_k10_to2p16.json |     2 +-
 ...fted_r19_518311_r18_518311_k10_to2p16.json |     2 +-
 ...fted_r19_520027_r18_520027_k11_to2p18.json |     2 +-
 ...fted_r19_520359_r18_520359_k11_to2p18.json |     2 +-
 ...fted_r19_523295_r18_523295_k11_to2p18.json |     2 +-
 ...hifted_r19_55343_r18_55343_k11_to2p18.json |     2 +-
 ...hifted_r19_55911_r18_55911_k11_to2p18.json |     2 +-
 ..._shifted_r19_5823_r18_5823_k10_to2p16.json |     2 +-
 ...shifted_r19_58599_r18_58599_k9_to2p15.json |     2 +-
 ...hifted_r19_58623_r18_58623_k11_to2p18.json |     2 +-
 ...hifted_r19_60671_r18_60671_k11_to2p18.json |     2 +-
 ...hifted_r19_62695_r18_62695_k11_to2p18.json |     2 +-
 ...hifted_r19_62719_r18_62719_k10_to2p16.json |     2 +-
 ..._shifted_r19_6367_r18_6367_k11_to2p18.json |     2 +-
 ...shifted_r19_65951_r18_65951_k9_to2p15.json |     2 +-
 ...hifted_r19_66791_r18_66791_k11_to2p18.json |     2 +-
 ...shifted_r19_67655_r18_67655_k9_to2p15.json |     2 +-
 ...shifted_r19_69147_r18_69147_k9_to2p15.json |     2 +-
 ...hifted_r19_69703_r18_69703_k11_to2p18.json |     2 +-
 ...hifted_r19_70047_r18_70047_k11_to2p18.json |     2 +-
 ...shifted_r19_70639_r18_70639_k8_to2p13.json |     2 +-
 ...hifted_r19_73243_r18_73243_k11_to2p18.json |     2 +-
 ...hifted_r19_74143_r18_74143_k11_to2p18.json |     2 +-
 ...hifted_r19_75847_r18_75847_k11_to2p18.json |     2 +-
 ...hifted_r19_76783_r18_76783_k10_to2p16.json |     2 +-
 ...hifted_r19_77339_r18_77339_k11_to2p18.json |     2 +-
 ...hifted_r19_79719_r18_79719_k11_to2p18.json |     2 +-
 ...hifted_r19_82927_r18_82927_k10_to2p16.json |     2 +-
 ...hifted_r19_84039_r18_84039_k11_to2p18.json |     2 +-
 ...shifted_r19_87899_r18_87899_k8_to2p13.json |     2 +-
 ...hifted_r19_87935_r18_87935_k10_to2p16.json |     2 +-
 ...shifted_r19_88219_r18_88219_k7_to2p12.json |     2 +-
 ...hifted_r19_92031_r18_92031_k11_to2p18.json |     2 +-
 ...l_shifted_r19_9375_r18_9375_k9_to2p15.json |     2 +-
 ...hifted_r19_94043_r18_94043_k10_to2p16.json |     2 +-
 ...hifted_r19_95263_r18_95263_k11_to2p18.json |     2 +-
 ...shifted_r19_96423_r18_96423_k9_to2p15.json |     2 +-
 ...hifted_r19_97311_r18_97311_k10_to2p16.json |     2 +-
 ...hifted_r19_98175_r18_98175_k11_to2p18.json |     2 +-
 ...hifted_r19_98471_r18_98471_k11_to2p18.json |     2 +-
 ..._shifted_r19_9883_r18_9883_k11_to2p18.json |     2 +-
 .../option_a_extension_m24_report.md          |     3 +-
 .../option_b_hensel_m20_m21_report.md         |    29 +
 .../option_c_diagnostic_top200_report.md      |    26 +
 ..._grammar_extensions_implementation_plan.md |     9 +
 .../collatz_hensel_chain_shifted_phase3.md    |    13 +-
 ...collatz_targeted_leaves_and_diagnostics.md |     7 +
 ...tz_terminal_clauses_memory_optimization.md |     9 +-
 369 files changed, 130839 insertions(+), 358 deletions(-)
 create mode 100644 docs/artefacts/collatz/refinement_K/palier2p15/bundle_mod2p15_to2p24_hensel_b/audit_refinement_certificate_Sm_multilevel_mod2p15_to2p24.json
 create mode 100644 docs/artefacts/collatz/refinement_K/palier2p15/bundle_mod2p15_to2p24_hensel_b/audit_refinement_certificate_Sm_multilevel_mod2p15_to2p24.md
 create mode 100644 docs/artefacts/collatz/refinement_K/palier2p15/bundle_mod2p15_to2p24_hensel_b/diagnostic_targeted_leaves_failure_mod2p15.json
 create mode 100644 docs/artefacts/collatz/refinement_K/palier2p15/bundle_mod2p15_to2p24_hensel_b/diagnostic_targeted_leaves_failure_mod2p15.md
 create mode 100644 docs/artefacts/collatz/refinement_K/palier2p15/bundle_mod2p15_to2p24_hensel_b/open_roots_obstruction_profile_mod2p15_to2p24.json
 create mode 100644 docs/artefacts/collatz/refinement_K/palier2p15/bundle_mod2p15_to2p24_hensel_b/open_roots_obstruction_profile_mod2p15_to2p24.md
 create mode 100644 docs/artefacts/collatz/refinement_K/palier2p15/bundle_mod2p15_to2p24_hensel_b/refinement_certificate_Sm_multilevel_mod2p15_to2p24.json
 create mode 100644 docs/artefacts/collatz/refinement_K/palier2p15/bundle_mod2p15_to2p24_hensel_b/refinement_certificate_Sm_multilevel_mod2p15_to2p24.md
 create mode 100644 docs/artefacts/collatz/refinement_K/palier2p15/option_b_hensel_m20_m21_report.md
 create mode 100644 docs/artefacts/collatz/refinement_K/palier2p15/option_c_diagnostic_top200_report.md

diff --git a/applications/collatz/collatz_k_scripts/README.md b/applications/collatz/collatz_k_scripts/README.md
index 31b5c21..b2949b9 100644
--- a/applications/collatz/collatz_k_scripts/README.md
+++ b/applications/collatz/collatz_k_scripts/README.md
@@ -39,5 +39,5 @@ python reproduce_all_audits.py --root /chemin/fichiers_source --out /chemin/sort
 - `collatz_build_refinement_certificate_over_Sm_multilevel.py` : audit de fermeture par raffinement (multi-niveaux) sur \(S_M\).
 - `collatz_compare_dminor_families_incremental.py` : tableau d’impact incrémental (Δopen_roots, Δq_m, Δparents_one_child, quantiles lb) par ajout de familles D_minor groupées par \(k\).
 - `collatz_build_hensel_chain_leaves.py` : feuilles chaîne de Hensel (racine à palier M).
-- `collatz_build_hensel_chain_leaves_shifted.py` : chaîne Hensel décalée (Phase 3), démarrage à m=19 pour résidus dont le frère est fermable.
+- `collatz_build_hensel_chain_leaves_shifted.py` : chaîne Hensel décalée (Phase 3), démarrage à m=19|20|21 (`--start-m`) pour résidus dont le frère est fermable. Charge `.residues.json` en priorité (mémoire).
 - `collatz_build_refinement_bundle_over_Sm_multilevel.py` : pipeline “1 commande” (fermeture multi-niveaux + profil d’obstruction + diagnostic ciblé optionnel).
diff --git a/applications/collatz/collatz_k_scripts/collatz_build_hensel_chain_leaves_shifted.py b/applications/collatz/collatz_k_scripts/collatz_build_hensel_chain_leaves_shifted.py
index effe009..57b254d 100644
--- a/applications/collatz/collatz_k_scripts/collatz_build_hensel_chain_leaves_shifted.py
+++ b/applications/collatz/collatz_k_scripts/collatz_build_hensel_chain_leaves_shifted.py
@@ -242,7 +242,9 @@ def _load_leaf_sets(*, leaf_json_paths: list[Path]) -> tuple[dict[int, set[int]
             r = c.get("residue_mod_2p")
             if not isinstance(r, int):
                 continue
-            leaves_by_m.setdefault(palier, set()).add(r)
+            if palier not in leaves_by_m:
+                leaves_by_m[palier] = _ResidueBitset(palier) if palier >= 20 else set()
+            leaves_by_m[palier].add(r)
             if c.get("kind") == "D_minor":
                 k = c.get("k")
                 u = c.get("underlineA")
@@ -277,7 +279,7 @@ def _sibling_leaf(
     m: int,
     k_max: int,
     t_max: int,
-    leaves_by_m: dict[int, set[int]],
+    leaves_by_m: dict[int, set[int] | _ResidueBitset],
     dminor_leaf_map: dict[tuple[int, int], Leaf],
 ) -> Leaf | None:
     """Return a leaf for the sibling: D/F first, then D_minor from map."""
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/bundle_mod2p15_to2p24_hensel_b/audit_refinement_certificate_Sm_multilevel_mod2p15_to2p24.json b/docs/artefacts/collatz/refinement_K/palier2p15/bundle_mod2p15_to2p24_hensel_b/audit_refinement_certificate_Sm_multilevel_mod2p15_to2p24.json
new file mode 100644
index 0000000..8823de8
--- /dev/null
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/bundle_mod2p15_to2p24_hensel_b/audit_refinement_certificate_Sm_multilevel_mod2p15_to2p24.json
@@ -0,0 +1,437 @@
+{
+  "domain": {
+    "root_palier": 15,
+    "max_palier": 24,
+    "S_root_size": 16384
+  },
+  "closure": {
+    "closed_roots": 15283,
+    "open_roots": 1101,
+    "closed_ratio": 0.93280029296875,
+    "closed_roots_sample": [
+      1,
+      3,
+      5,
+      7,
+      9,
+      11,
+      13,
+      15,
+      17,
+      19,
+      21,
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+      33,
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+      79,
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+      85,
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+      89,
+      93,
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+      97,
+      99,
+      101,
+      105,
+      107,
+      109,
+      113,
+      115,
+      117,
+      119,
+      121,
+      123,
+      125,
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+      129,
+      131,
+      133,
+      135,
+      137,
+      139,
+      141,
+      143,
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+      147,
+      149,
+      151,
+      153,
+      155,
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+      161,
+      163,
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+      203,
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+      293,
+      295,
+      297,
+      299,
+      301,
+      303,
+      305,
+      307,
+      309,
+      311,
+      313,
+      315,
+      317,
+      321,
+      323,
+      325,
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+      331,
+      333,
+      335,
+      337,
+      339,
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+      417,
+      419,
+      421,
+      423,
+      425,
+      427,
+      429,
+      431,
+      433
+    ],
+    "still_open_roots_sample": [
+      27,
+      31,
+      47,
+      63,
+      71,
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+  "generated_at": "2026-03-10T11:53:17.265227Z",
+  "sha256": {
+    "inputs": {
+      "docs/artefacts/collatz/terminal_clauses_over_Sm/palier2p15/clauses_terminal_over_Sm_mod2p15.json": "148217541c4386d6c0b8282f273192abd780986b7c97b0505e48aec6bab22f27",
+      "docs/artefacts/collatz/terminal_clauses_over_Sm/palier2p16/clauses_terminal_over_Sm_mod2p16.json": "b5a6bcd5dd5245ce3bbcdf8be03cc6f6c0a33db2db7cda5bb17adaf7119c391c",
+      "docs/artefacts/collatz/terminal_clauses_over_Sm/palier2p17/clauses_terminal_over_Sm_mod2p17.json": "952802824858b25ab835a852d69f8bfc647eedfa41b498d445b66a1a1c449fd5",
+      "docs/artefacts/collatz/terminal_clauses_over_Sm/palier2p18/clauses_terminal_over_Sm_mod2p18.json": "9cca7e9c7f504014533bc3f3393fa16df259979c43e2eeb17621ea9111f9c8c3",
+      "docs/artefacts/collatz/terminal_clauses_over_Sm/palier2p19/clauses_terminal_over_Sm_mod2p19.json": "bbd933cc0a8637f64c868b1aedff4d2700b588e86fc72ae3a56c176f851a54ef",
+      "docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/clauses_hensel_chain_leaves_shifted_mod2p19.json": "f401030257072de595febcc75de892b3883ecb1690b4ce9030a9f819ac293882",
+      "docs/artefacts/collatz/terminal_clauses_over_Sm/palier2p20/clauses_terminal_over_Sm_mod2p20.json": "8c10cb5c17d50cabe5d7bf7e0d32c0a4a9361e6da1bad4ca43184bddcdb5315d",
+      "docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/clauses_hensel_chain_leaves_shifted_mod2p20.json": "985f5f24bdb544ce2d6a8fefb8165e0c33d33168e78a351ed5ede9bce5ec65f8",
+      "docs/artefacts/collatz/terminal_clauses_over_Sm/palier2p21/clauses_terminal_over_Sm_mod2p21.json": "1089efca85cfb566178a318d382fbeab559c4c80b3354b24ca58058ff6696e5c",
+      "docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/clauses_hensel_chain_leaves_shifted_mod2p21.json": "d1a0b424551069c7cfacf907d13877c19ff0362b7502599e81bc845d77d1e363",
+      "docs/artefacts/collatz/terminal_clauses_over_Sm/palier2p22/clauses_terminal_over_Sm_mod2p22.json": "117e913fbc4f82a6c7a8f23680d4194f2cacaec6b24c9ac6395e90d99bd528b4",
+      "docs/artefacts/collatz/terminal_clauses_over_Sm/palier2p23/clauses_terminal_over_Sm_mod2p23.json": "a90e3b1711f3f53b78cc2ed7e952638a32f5704b910673e402b07cc34e8c4a1f",
+      "docs/artefacts/collatz/terminal_clauses_over_Sm/palier2p24/clauses_terminal_over_Sm_mod2p24.json": "0aaa1cd14d567c192a1af5a21cfee8720c10ec291b7cda7ae02b7cfc69c4d5bd"
+    },
+    "outputs": {
+      "docs/artefacts/collatz/refinement_K/palier2p15/bundle_mod2p15_to2p24_hensel_b/refinement_certificate_Sm_multilevel_mod2p15_to2p24.json": "d971b63c59da2773f1f37a7933bcb252dff0276f8ee7189d318798b3a398d1de"
+    }
+  }
+}
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/bundle_mod2p15_to2p24_hensel_b/audit_refinement_certificate_Sm_multilevel_mod2p15_to2p24.md b/docs/artefacts/collatz/refinement_K/palier2p15/bundle_mod2p15_to2p24_hensel_b/audit_refinement_certificate_Sm_multilevel_mod2p15_to2p24.md
new file mode 100644
index 0000000..16fbbd8
--- /dev/null
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/bundle_mod2p15_to2p24_hensel_b/audit_refinement_certificate_Sm_multilevel_mod2p15_to2p24.md
@@ -0,0 +1,8 @@
+**Auteur** : Équipe 4NK
+
+# Audit — raffinement multi-niveaux sur S_M (2^15→2^24)
+
+- closed_roots : 15283
+- open_roots : 1101
+- closed_ratio : 0.93280029296875
+
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/bundle_mod2p15_to2p24_hensel_b/diagnostic_targeted_leaves_failure_mod2p15.json b/docs/artefacts/collatz/refinement_K/palier2p15/bundle_mod2p15_to2p24_hensel_b/diagnostic_targeted_leaves_failure_mod2p15.json
new file mode 100644
index 0000000..cbab09e
--- /dev/null
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/bundle_mod2p15_to2p24_hensel_b/diagnostic_targeted_leaves_failure_mod2p15.json
@@ -0,0 +1,5016 @@
+{
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+        "root": 51
+      },
+      "first_m_where_both_children_blocked": 15
+    },
+    {
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+      "children": [
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+        35839
+      ],
+      "immediate_terminal_at_m16": {
+        "low": false,
+        "high": false
+      },
+      "lower_bounds_required_m": {
+        "low": {
+          "any": 50,
+          "D": 55,
+          "F": 50
+        },
+        "high": {
+          "any": 20,
+          "D": 22,
+          "F": 20
+        },
+        "root": 50
+      },
+      "first_m_where_both_children_blocked": 15
+    },
+    {
+      "root": 9215,
+      "children": [
+        9215,
+        41983
+      ],
+      "immediate_terminal_at_m16": {
+        "low": false,
+        "high": false
+      },
+      "lower_bounds_required_m": {
+        "low": {
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+          "D": 50,
+          "F": 50
+        },
+        "high": {
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+          "D": 23,
+          "F": 20
+        },
+        "root": 50
+      },
+      "first_m_where_both_children_blocked": 15
+    },
+    {
+      "root": 11391,
+      "children": [
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+      ],
+      "immediate_terminal_at_m16": {
+        "low": false,
+        "high": false
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+      "lower_bounds_required_m": {
+        "low": {
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+          "F": 50
+        },
+        "high": {
+          "any": 38,
+          "D": 38,
+          "F": 38
+        },
+        "root": 50
+      },
+      "first_m_where_both_children_blocked": 15
+    },
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+      "immediate_terminal_at_m16": {
+        "low": false,
+        "high": false
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+      "lower_bounds_required_m": {
+        "low": {
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+          "D": 31,
+          "F": 31
+        },
+        "high": {
+          "any": 50,
+          "D": 50,
+          "F": 50
+        },
+        "root": 50
+      },
+      "first_m_where_both_children_blocked": 15
+    },
+    {
+      "root": 21787,
+      "children": [
+        21787,
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+      ],
+      "immediate_terminal_at_m16": {
+        "low": false,
+        "high": false
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+        "low": {
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+          "F": 50
+        },
+        "high": {
+          "any": 20,
+          "D": 24,
+          "F": 20
+        },
+        "root": 50
+      },
+      "first_m_where_both_children_blocked": 15
+    },
+    {
+      "root": 28415,
+      "children": [
+        28415,
+        61183
+      ],
+      "immediate_terminal_at_m16": {
+        "low": false,
+        "high": false
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+      "lower_bounds_required_m": {
+        "low": {
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+          "D": 50,
+          "F": 50
+        },
+        "high": {
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+          "D": 40,
+          "F": 40
+        },
+        "root": 50
+      },
+      "first_m_where_both_children_blocked": 15
+    },
+    {
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+      "children": [
+        3399,
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+      ],
+      "immediate_terminal_at_m16": {
+        "low": false,
+        "high": false
+      },
+      "lower_bounds_required_m": {
+        "low": {
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+          "F": 49
+        },
+        "high": {
+          "any": 22,
+          "D": 22,
+          "F": 22
+        },
+        "root": 49
+      },
+      "first_m_where_both_children_blocked": 15
+    },
+    {
+      "root": 4607,
+      "children": [
+        4607,
+        37375
+      ],
+      "immediate_terminal_at_m16": {
+        "low": false,
+        "high": false
+      },
+      "lower_bounds_required_m": {
+        "low": {
+          "any": 49,
+          "D": 49,
+          "F": 49
+        },
+        "high": {
+          "any": 21,
+          "D": 21,
+          "F": 21
+        },
+        "root": 49
+      },
+      "first_m_where_both_children_blocked": 15
+    },
+    {
+      "root": 9855,
+      "children": [
+        9855,
+        42623
+      ],
+      "immediate_terminal_at_m16": {
+        "low": false,
+        "high": false
+      },
+      "lower_bounds_required_m": {
+        "low": {
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+          "D": 34,
+          "F": 29
+        },
+        "high": {
+          "any": 49,
+          "D": 49,
+          "F": 49
+        },
+        "root": 49
+      },
+      "first_m_where_both_children_blocked": 15
+    },
+    {
+      "root": 10719,
+      "children": [
+        10719,
+        43487
+      ],
+      "immediate_terminal_at_m16": {
+        "low": false,
+        "high": false
+      },
+      "lower_bounds_required_m": {
+        "low": {
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+          "D": 23,
+          "F": 23
+        },
+        "high": {
+          "any": 49,
+          "D": 49,
+          "F": 49
+        },
+        "root": 49
+      },
+      "first_m_where_both_children_blocked": 15
+    },
+    {
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+      "children": [
+        11623,
+        44391
+      ],
+      "immediate_terminal_at_m16": {
+        "low": false,
+        "high": false
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+      "lower_bounds_required_m": {
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+          "F": 49
+        },
+        "high": {
+          "any": 21,
+          "D": 21,
+          "F": 21
+        },
+        "root": 49
+      },
+      "first_m_where_both_children_blocked": 15
+    },
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+      "children": [
+        11931,
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+      ],
+      "immediate_terminal_at_m16": {
+        "low": false,
+        "high": false
+      },
+      "lower_bounds_required_m": {
+        "low": {
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+          "D": 49,
+          "F": 49
+        },
+        "high": {
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+          "D": 19,
+          "F": 19
+        },
+        "root": 49
+      },
+      "first_m_where_both_children_blocked": 15
+    },
+    {
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+      "children": [
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+      ],
+      "immediate_terminal_at_m16": {
+        "low": false,
+        "high": false
+      },
+      "lower_bounds_required_m": {
+        "low": {
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+          "D": 49,
+          "F": 49
+        },
+        "high": {
+          "any": 22,
+          "D": 22,
+          "F": 22
+        },
+        "root": 49
+      },
+      "first_m_where_both_children_blocked": 15
+    },
+    {
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+      "children": [
+        19271,
+        52039
+      ],
+      "immediate_terminal_at_m16": {
+        "low": false,
+        "high": false
+      },
+      "lower_bounds_required_m": {
+        "low": {
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+          "D": 24,
+          "F": 24
+        },
+        "high": {
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+          "D": 49,
+          "F": 49
+        },
+        "root": 49
+      },
+      "first_m_where_both_children_blocked": 15
+    },
+    {
+      "root": 27519,
+      "children": [
+        27519,
+        60287
+      ],
+      "immediate_terminal_at_m16": {
+        "low": false,
+        "high": false
+      },
+      "lower_bounds_required_m": {
+        "low": {
+          "any": 49,
+          "D": 49,
+          "F": 49
+        },
+        "high": {
+          "any": 41,
+          "D": 41,
+          "F": 42
+        },
+        "root": 49
+      },
+      "first_m_where_both_children_blocked": 15
+    },
+    {
+      "root": 32767,
+      "children": [
+        32767,
+        65535
+      ],
+      "immediate_terminal_at_m16": {
+        "low": false,
+        "high": false
+      },
+      "lower_bounds_required_m": {
+        "low": {
+          "any": 48,
+          "D": 53,
+          "F": 48
+        },
+        "high": {
+          "any": 49,
+          "D": 49,
+          "F": 49
+        },
+        "root": 49
+      },
+      "first_m_where_both_children_blocked": 15
+    }
+  ]
+}
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/bundle_mod2p15_to2p24_hensel_b/diagnostic_targeted_leaves_failure_mod2p15.md b/docs/artefacts/collatz/refinement_K/palier2p15/bundle_mod2p15_to2p24_hensel_b/diagnostic_targeted_leaves_failure_mod2p15.md
new file mode 100644
index 0000000..d40d339
--- /dev/null
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/bundle_mod2p15_to2p24_hensel_b/diagnostic_targeted_leaves_failure_mod2p15.md
@@ -0,0 +1,99 @@
+**Auteur** : Équipe 4NK
+
+# Diagnostic — échec targeted leaves — racine 2^15
+
+- tracked_roots_file : `/home/ncantu/code/algo/docs/artefacts/collatz/refinement_K/palier2p15/incremental_D_minor/tracked_roots_lb_any_top200_mod2p15_to2p18.txt`
+- k_max : 256
+- t_max : 256
+- search_max_required_m : 256
+
+Table (par racine) :
+
+| root | child_low | child_high | immediate_low@16 | immediate_high@16 | lb_root | lb_low | lb_high |
+| --- | --- | --- | --- | --- | --- | --- | --- |
+| 2887 | 2887 | 35655 | no | no | 136 | 17 | 136 |
+| 12359 | 12359 | 45127 | no | no | 130 | 27 | 130 |
+| 4735 | 4735 | 37503 | no | no | 128 | 18 | 128 |
+| 28207 | 28207 | 60975 | no | no | 128 | 26 | 128 |
+| 23487 | 23487 | 56255 | no | no | 127 | 18 | 127 |
+| 24347 | 24347 | 57115 | no | no | 121 | 24 | 121 |
+| 31487 | 31487 | 64255 | no | no | 118 | 18 | 118 |
+| 12287 | 12287 | 45055 | no | no | 114 | 44 | 114 |
+| 10087 | 10087 | 42855 | no | no | 102 | 102 | 22 |
+| 29311 | 29311 | 62079 | no | no | 90 | 24 | 90 |
+| 1407 | 1407 | 34175 | no | no | 85 | 85 | 23 |
+| 18047 | 18047 | 50815 | no | no | 85 | 27 | 85 |
+| 703 | 703 | 33471 | no | no | 84 | 84 | 61 |
+| 2111 | 2111 | 34879 | no | no | 84 | 84 | 36 |
+| 15039 | 15039 | 47807 | no | no | 84 | 84 | 19 |
+| 1055 | 1055 | 33823 | no | no | 83 | 83 | 28 |
+| 22559 | 22559 | 55327 | no | no | 83 | 83 | 19 |
+| 1583 | 1583 | 34351 | no | no | 82 | 82 | 38 |
+| 251 | 251 | 33019 | no | no | 80 | 30 | 80 |
+| 1471 | 1471 | 34239 | no | no | 80 | 32 | 80 |
+| 12539 | 12539 | 45307 | no | no | 79 | 50 | 79 |
+| 18591 | 18591 | 51359 | no | no | 79 | 65 | 79 |
+| 28671 | 28671 | 61439 | no | no | 78 | 78 | 47 |
+| 4379 | 4379 | 37147 | no | no | 77 | 17 | 77 |
+| 7963 | 7963 | 40731 | no | no | 76 | 76 | 25 |
+| 12399 | 12399 | 45167 | no | no | 76 | 76 | 25 |
+| 18203 | 18203 | 50971 | no | no | 76 | 39 | 76 |
+| 7527 | 7527 | 40295 | no | no | 75 | 75 | 39 |
+| 17647 | 17647 | 50415 | no | no | 75 | 75 | 28 |
+| 9023 | 9023 | 41791 | no | no | 74 | 18 | 74 |
+| 11291 | 11291 | 44059 | no | no | 74 | 74 | 18 |
+| 8959 | 8959 | 41727 | no | no | 73 | 73 | 23 |
+| 20895 | 20895 | 53663 | no | no | 73 | 73 | 28 |
+| 21503 | 21503 | 54271 | no | no | 73 | 34 | 73 |
+| 21743 | 21743 | 54511 | no | no | 73 | 48 | 73 |
+| 24575 | 24575 | 57343 | no | no | 73 | 45 | 73 |
+| 26239 | 26239 | 59007 | no | no | 73 | 44 | 73 |
+| 27647 | 27647 | 60415 | no | no | 73 | 37 | 73 |
+| 9695 | 9695 | 42463 | no | no | 72 | 24 | 72 |
+| 13439 | 13439 | 46207 | no | no | 72 | 72 | 34 |
+| 15131 | 15131 | 47899 | no | no | 72 | 72 | 21 |
+| 17659 | 17659 | 50427 | no | no | 72 | 17 | 72 |
+| 24091 | 24091 | 56859 | no | no | 72 | 72 | 26 |
+| 24799 | 24799 | 57567 | no | no | 72 | 26 | 72 |
+| 27135 | 27135 | 59903 | no | no | 72 | 72 | 64 |
+| 31343 | 31343 | 64111 | no | no | 72 | 72 | 31 |
+| 4255 | 4255 | 37023 | no | no | 71 | 71 | 18 |
+| 7935 | 7935 | 40703 | no | no | 71 | 43 | 71 |
+| 10239 | 10239 | 43007 | no | no | 71 | 35 | 71 |
+| 12703 | 12703 | 45471 | no | no | 71 | 71 | 18 |
+| 14247 | 14247 | 47015 | no | no | 71 | 25 | 71 |
+| 21231 | 21231 | 53999 | no | no | 71 | 71 | 20 |
+| 28783 | 28783 | 61551 | no | no | 71 | 71 | 38 |
+| 28923 | 28923 | 61691 | no | no | 71 | 71 | 22 |
+| 1279 | 1279 | 34047 | no | no | 70 | 25 | 70 |
+| 6383 | 6383 | 39151 | no | no | 70 | 70 | 22 |
+| 10407 | 10407 | 43175 | no | no | 70 | 29 | 70 |
+| 28287 | 28287 | 61055 | no | no | 70 | 46 | 70 |
+| 31743 | 31743 | 64511 | no | no | 70 | 47 | 70 |
+| 31847 | 31847 | 64615 | no | no | 70 | 70 | 21 |
+| 15003 | 15003 | 47771 | no | no | 69 | 25 | 69 |
+| 17023 | 17023 | 49791 | no | no | 69 | 69 | 27 |
+| 18303 | 18303 | 51071 | no | no | 69 | 21 | 69 |
+| 27103 | 27103 | 59871 | no | no | 69 | 69 | 59 |
+| 31995 | 31995 | 64763 | no | no | 69 | 26 | 69 |
+| 13551 | 13551 | 46319 | no | no | 68 | 68 | 58 |
+| 21351 | 21351 | 54119 | no | no | 68 | 68 | 18 |
+| 25535 | 25535 | 58303 | no | no | 68 | 68 | 27 |
+| 31903 | 31903 | 64671 | no | no | 68 | 68 | 19 |
+| 32539 | 32539 | 65307 | no | no | 68 | 68 | 61 |
+| 5535 | 5535 | 38303 | no | no | 67 | 28 | 67 |
+| 20327 | 20327 | 53095 | no | no | 67 | 67 | 26 |
+| 20479 | 20479 | 53247 | no | no | 67 | 36 | 67 |
+| 29919 | 29919 | 62687 | no | no | 67 | 18 | 67 |
+| 2527 | 2527 | 35295 | no | no | 66 | 28 | 66 |
+| 3199 | 3199 | 35967 | no | no | 66 | 18 | 66 |
+| 4591 | 4591 | 37359 | no | no | 66 | 66 | 21 |
+| 8351 | 8351 | 41119 | no | no | 66 | 36 | 66 |
+| 20975 | 20975 | 53743 | no | no | 66 | 37 | 66 |
+| 24687 | 24687 | 57455 | no | no | 66 | 33 | 66 |
+
+## Sorties
+
+- JSON : `/home/ncantu/code/algo/docs/artefacts/collatz/refinement_K/palier2p15/bundle_mod2p15_to2p24_hensel_b/diagnostic_targeted_leaves_failure_mod2p15.json`
+- Markdown : `/home/ncantu/code/algo/docs/artefacts/collatz/refinement_K/palier2p15/bundle_mod2p15_to2p24_hensel_b/diagnostic_targeted_leaves_failure_mod2p15.md`
+
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/bundle_mod2p15_to2p24_hensel_b/open_roots_obstruction_profile_mod2p15_to2p24.json b/docs/artefacts/collatz/refinement_K/palier2p15/bundle_mod2p15_to2p24_hensel_b/open_roots_obstruction_profile_mod2p15_to2p24.json
new file mode 100644
index 0000000..8cd6031
--- /dev/null
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/bundle_mod2p15_to2p24_hensel_b/open_roots_obstruction_profile_mod2p15_to2p24.json
@@ -0,0 +1,93021 @@
+{
+  "domain": {
+    "root_palier": 15,
+    "max_palier": 24,
+    "open_roots_count": 1101
+  },
+  "search": {
+    "k_max": 256,
+    "t_max": 256,
+    "search_max_required_m": 256
+  },
+  "lower_bound_required_m_bucket": {
+    "any": {
+      "19": 47,
+      "20": 50,
+      "21": 49,
+      "22": 63,
+      "23": 42,
+      "24": 42,
+      "25": 56,
+      "26": 39,
+      "27": 32,
+      "28": 52,
+      "29": 44,
+      "30": 36,
+      "31": 29,
+      "32": 18,
+      "33": 35,
+      "34": 25,
+      "35": 18,
+      "36": 31,
+      "37": 27,
+      "38": 23,
+      "39": 11,
+      "40": 8,
+      "41": 17,
+      "42": 14,
+      "43": 12,
+      "44": 14,
+      "45": 20,
+      "46": 14,
+      "47": 17,
+      "48": 16,
+      "49": 10,
+      "50": 6,
+      "51": 9,
+      "52": 10,
+      "53": 9,
+      "54": 9,
+      "55": 9,
+      "56": 10,
+      "57": 5,
+      "58": 6,
+      "59": 6,
+      "60": 7,
+      "61": 6,
+      "62": 3,
+      "63": 5,
+      "64": 4,
+      "65": 4,
+      "66": 8,
+      "67": 4,
+      "68": 5,
+      "69": 5,
+      "70": 6,
+      "71": 8,
+      "72": 8,
+      "73": 7,
+      "74": 2,
+      "75": 2,
+      "76": 3,
+      "77": 1,
+      "78": 1,
+      "79": 2,
+      "80": 2,
+      "82": 1,
+      "83": 2,
+      "84": 3,
+      "85": 2,
+      "90": 1,
+      "102": 1,
+      "114": 1,
+      "118": 1,
+      "121": 1,
+      "127": 1,
+      "128": 2,
+      "130": 1,
+      "136": 1
+    },
+    "D": {
+      "19": 47,
+      "20": 27,
+      "21": 41,
+      "22": 63,
+      "23": 37,
+      "24": 39,
+      "25": 58,
+      "26": 34,
+      "27": 35,
+      "28": 55,
+      "29": 24,
+      "30": 37,
+      "31": 17,
+      "32": 25,
+      "33": 44,
+      "34": 25,
+      "35": 23,
+      "36": 36,
+      "37": 24,
+      "38": 28,
+      "39": 10,
+      "40": 9,
+      "41": 20,
+      "42": 11,
+      "43": 13,
+      "44": 20,
+      "45": 17,
+      "46": 17,
+      "47": 25,
+      "48": 15,
+      "49": 11,
+      "50": 5,
+      "51": 13,
+      "52": 15,
+      "53": 6,
+      "54": 11,
+      "55": 14,
+      "56": 4,
+      "57": 6,
+      "58": 4,
+      "59": 7,
+      "60": 10,
+      "61": 5,
+      "62": 3,
+      "63": 9,
+      "64": 2,
+      "65": 7,
+      "66": 8,
+      "67": 6,
+      "68": 5,
+      "69": 5,
+      "70": 7,
+      "71": 8,
+      "72": 6,
+      "73": 8,
+      "74": 5,
+      "75": 3,
+      "76": 3,
+      "77": 1,
+      "78": 1,
+      "79": 3,
+      "80": 2,
+      "81": 1,
+      "82": 2,
+      "83": 2,
+      "84": 3,
+      "85": 2,
+      "87": 1,
+      "90": 1,
+      "95": 1,
+      "109": 1,
+      "114": 1,
+      "121": 1,
+      "124": 1,
+      "127": 1,
+      "128": 2,
+      "130": 1,
+      "136": 1
+    },
+    "F": {
+      "19": 47,
+      "20": 42,
+      "21": 53,
+      "22": 52,
+      "23": 50,
+      "24": 43,
+      "25": 42,
+      "26": 42,
+      "27": 38,
+      "28": 43,
+      "29": 48,
+      "30": 41,
+      "31": 35,
+      "32": 19,
+      "33": 27,
+      "34": 31,
+      "35": 18,
+      "36": 26,
+      "37": 31,
+      "38": 25,
+      "39": 13,
+      "40": 9,
+      "41": 12,
+      "42": 19,
+      "43": 12,
+      "44": 11,
+      "45": 23,
+      "46": 16,
+      "47": 13,
+      "48": 19,
+      "49": 10,
+      "50": 6,
+      "51": 10,
+      "52": 8,
+      "53": 10,
+      "54": 9,
+      "55": 5,
+      "56": 13,
+      "57": 5,
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+      "59": 6,
+      "60": 6,
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+      "62": 3,
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+      "64": 4,
+      "65": 4,
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+      "69": 5,
+      "70": 6,
+      "71": 7,
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+      "74": 2,
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+      "127": 1,
+      "128": 1,
+      "129": 1,
+      "130": 1,
+      "136": 1
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+      },
+      "child1": {
+        "child_residue_mod_2p": 65531,
+        "best_D": {
+          "kind": "D_exact",
+          "k_or_t": 11,
+          "A": 18,
+          "required_m": 19,
+          "extra": {
+            "k": 11
+          }
+        },
+        "best_F": {
+          "kind": "F",
+          "k_or_t": 11,
+          "A": 18,
+          "required_m": 19,
+          "extra": {
+            "t": 11,
+            "a": 1
+          }
+        },
+        "required_m": {
+          "D": 19,
+          "F": 19,
+          "any": 19
+        },
+        "obstructions": {
+          "any_contracting_D_found_up_to32": true,
+          "first_k_contracting_D_up_to32": 11,
+          "any_y_mod3_nonzero_up_to32": true,
+          "y_mod3_zero_count_up_to32": 0,
+          "first_t_y_mod3_nonzero_up_to32": 1,
+          "any_contracting_F_found_up_to32": true,
+          "first_t_contracting_F_up_to32": 11
+        }
+      },
+      "lower_bound_required_m_to_close_root": {
+        "any": 19,
+        "D": 19,
+        "F": 19
+      }
+    },
+    {
+      "root_residue_mod_2p": 32767,
+      "children_mod_2p16": [
+        32767,
+        65535
+      ],
+      "child0": {
+        "child_residue_mod_2p": 32767,
+        "best_D": {
+          "kind": "D_exact",
+          "k_or_t": 32,
+          "A": 52,
+          "required_m": 53,
+          "extra": {
+            "k": 32
+          }
+        },
+        "best_F": {
+          "kind": "F",
+          "k_or_t": 30,
+          "A": 47,
+          "required_m": 48,
+          "extra": {
+            "t": 30,
+            "a": 1
+          }
+        },
+        "required_m": {
+          "D": 53,
+          "F": 48,
+          "any": 48
+        },
+        "obstructions": {
+          "any_contracting_D_found_up_to32": true,
+          "first_k_contracting_D_up_to32": 32,
+          "any_y_mod3_nonzero_up_to32": true,
+          "y_mod3_zero_count_up_to32": 0,
+          "first_t_y_mod3_nonzero_up_to32": 1,
+          "any_contracting_F_found_up_to32": true,
+          "first_t_contracting_F_up_to32": 30
+        }
+      },
+      "child1": {
+        "child_residue_mod_2p": 65535,
+        "best_D": {
+          "kind": "D_exact",
+          "k_or_t": 30,
+          "A": 48,
+          "required_m": 49,
+          "extra": {
+            "k": 30
+          }
+        },
+        "best_F": {
+          "kind": "F",
+          "k_or_t": 30,
+          "A": 48,
+          "required_m": 49,
+          "extra": {
+            "t": 30,
+            "a": 1
+          }
+        },
+        "required_m": {
+          "D": 49,
+          "F": 49,
+          "any": 49
+        },
+        "obstructions": {
+          "any_contracting_D_found_up_to32": true,
+          "first_k_contracting_D_up_to32": 30,
+          "any_y_mod3_nonzero_up_to32": true,
+          "y_mod3_zero_count_up_to32": 0,
+          "first_t_y_mod3_nonzero_up_to32": 1,
+          "any_contracting_F_found_up_to32": true,
+          "first_t_contracting_F_up_to32": 30
+        }
+      },
+      "lower_bound_required_m_to_close_root": {
+        "any": 49,
+        "D": 53,
+        "F": 49
+      }
+    }
+  ]
+}
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/bundle_mod2p15_to2p24_hensel_b/open_roots_obstruction_profile_mod2p15_to2p24.md b/docs/artefacts/collatz/refinement_K/palier2p15/bundle_mod2p15_to2p24_hensel_b/open_roots_obstruction_profile_mod2p15_to2p24.md
new file mode 100644
index 0000000..358d6e5
--- /dev/null
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/bundle_mod2p15_to2p24_hensel_b/open_roots_obstruction_profile_mod2p15_to2p24.md
@@ -0,0 +1,522 @@
+**Auteur** : Équipe 4NK
+
+# Profil d’obstruction — racines ouvertes sur S_15 (raffinement jusqu’à 2^24)
+
+## Domaine
+
+- racine : 2^15
+- max : 2^24
+- open_roots : 1101
+
+## Recherche (borne inférieure de profondeur)
+
+- k_max : 256
+- t_max : 256
+- max_required_m (pruning) : 256
+
+### Buckets — lower_bound_required_m_to_close_root
+
+Buckets (any):
+- required_m=19 : 47
+- required_m=20 : 50
+- required_m=21 : 49
+- required_m=22 : 63
+- required_m=23 : 42
+- required_m=24 : 42
+- required_m=25 : 56
+- required_m=26 : 39
+- required_m=27 : 32
+- required_m=28 : 52
+- required_m=29 : 44
+- required_m=30 : 36
+- required_m=31 : 29
+- required_m=32 : 18
+- required_m=33 : 35
+- required_m=34 : 25
+- required_m=35 : 18
+- required_m=36 : 31
+- required_m=37 : 27
+- required_m=38 : 23
+- required_m=39 : 11
+- required_m=40 : 8
+- required_m=41 : 17
+- required_m=42 : 14
+- required_m=43 : 12
+- required_m=44 : 14
+- required_m=45 : 20
+- required_m=46 : 14
+- required_m=47 : 17
+- required_m=48 : 16
+- required_m=49 : 10
+- required_m=50 : 6
+- required_m=51 : 9
+- required_m=52 : 10
+- required_m=53 : 9
+- required_m=54 : 9
+- required_m=55 : 9
+- required_m=56 : 10
+- required_m=57 : 5
+- required_m=58 : 6
+- required_m=59 : 6
+- required_m=60 : 7
+- required_m=61 : 6
+- required_m=62 : 3
+- required_m=63 : 5
+- required_m=64 : 4
+- required_m=65 : 4
+- required_m=66 : 8
+- required_m=67 : 4
+- required_m=68 : 5
+- required_m=69 : 5
+- required_m=70 : 6
+- required_m=71 : 8
+- required_m=72 : 8
+- required_m=73 : 7
+- required_m=74 : 2
+- required_m=75 : 2
+- required_m=76 : 3
+- required_m=77 : 1
+- required_m=78 : 1
+- required_m=79 : 2
+- required_m=80 : 2
+- required_m=82 : 1
+- required_m=83 : 2
+- required_m=84 : 3
+- required_m=85 : 2
+- required_m=90 : 1
+- required_m=102 : 1
+- required_m=114 : 1
+- required_m=118 : 1
+- required_m=121 : 1
+- required_m=127 : 1
+- required_m=128 : 2
+- required_m=130 : 1
+- required_m=136 : 1
+
+Buckets (D only):
+- required_m=19 : 47
+- required_m=20 : 27
+- required_m=21 : 41
+- required_m=22 : 63
+- required_m=23 : 37
+- required_m=24 : 39
+- required_m=25 : 58
+- required_m=26 : 34
+- required_m=27 : 35
+- required_m=28 : 55
+- required_m=29 : 24
+- required_m=30 : 37
+- required_m=31 : 17
+- required_m=32 : 25
+- required_m=33 : 44
+- required_m=34 : 25
+- required_m=35 : 23
+- required_m=36 : 36
+- required_m=37 : 24
+- required_m=38 : 28
+- required_m=39 : 10
+- required_m=40 : 9
+- required_m=41 : 20
+- required_m=42 : 11
+- required_m=43 : 13
+- required_m=44 : 20
+- required_m=45 : 17
+- required_m=46 : 17
+- required_m=47 : 25
+- required_m=48 : 15
+- required_m=49 : 11
+- required_m=50 : 5
+- required_m=51 : 13
+- required_m=52 : 15
+- required_m=53 : 6
+- required_m=54 : 11
+- required_m=55 : 14
+- required_m=56 : 4
+- required_m=57 : 6
+- required_m=58 : 4
+- required_m=59 : 7
+- required_m=60 : 10
+- required_m=61 : 5
+- required_m=62 : 3
+- required_m=63 : 9
+- required_m=64 : 2
+- required_m=65 : 7
+- required_m=66 : 8
+- required_m=67 : 6
+- required_m=68 : 5
+- required_m=69 : 5
+- required_m=70 : 7
+- required_m=71 : 8
+- required_m=72 : 6
+- required_m=73 : 8
+- required_m=74 : 5
+- required_m=75 : 3
+- required_m=76 : 3
+- required_m=77 : 1
+- required_m=78 : 1
+- required_m=79 : 3
+- required_m=80 : 2
+- required_m=81 : 1
+- required_m=82 : 2
+- required_m=83 : 2
+- required_m=84 : 3
+- required_m=85 : 2
+- required_m=87 : 1
+- required_m=90 : 1
+- required_m=95 : 1
+- required_m=109 : 1
+- required_m=114 : 1
+- required_m=121 : 1
+- required_m=124 : 1
+- required_m=127 : 1
+- required_m=128 : 2
+- required_m=130 : 1
+- required_m=136 : 1
+
+Buckets (F only):
+- required_m=19 : 47
+- required_m=20 : 42
+- required_m=21 : 53
+- required_m=22 : 52
+- required_m=23 : 50
+- required_m=24 : 43
+- required_m=25 : 42
+- required_m=26 : 42
+- required_m=27 : 38
+- required_m=28 : 43
+- required_m=29 : 48
+- required_m=30 : 41
+- required_m=31 : 35
+- required_m=32 : 19
+- required_m=33 : 27
+- required_m=34 : 31
+- required_m=35 : 18
+- required_m=36 : 26
+- required_m=37 : 31
+- required_m=38 : 25
+- required_m=39 : 13
+- required_m=40 : 9
+- required_m=41 : 12
+- required_m=42 : 19
+- required_m=43 : 12
+- required_m=44 : 11
+- required_m=45 : 23
+- required_m=46 : 16
+- required_m=47 : 13
+- required_m=48 : 19
+- required_m=49 : 10
+- required_m=50 : 6
+- required_m=51 : 10
+- required_m=52 : 8
+- required_m=53 : 10
+- required_m=54 : 9
+- required_m=55 : 5
+- required_m=56 : 13
+- required_m=57 : 5
+- required_m=58 : 8
+- required_m=59 : 6
+- required_m=60 : 6
+- required_m=61 : 7
+- required_m=62 : 3
+- required_m=63 : 5
+- required_m=64 : 4
+- required_m=65 : 4
+- required_m=66 : 8
+- required_m=67 : 4
+- required_m=68 : 5
+- required_m=69 : 5
+- required_m=70 : 6
+- required_m=71 : 7
+- required_m=72 : 9
+- required_m=73 : 7
+- required_m=74 : 2
+- required_m=75 : 2
+- required_m=76 : 3
+- required_m=77 : 1
+- required_m=78 : 1
+- required_m=79 : 1
+- required_m=80 : 3
+- required_m=82 : 1
+- required_m=83 : 2
+- required_m=84 : 3
+- required_m=85 : 2
+- required_m=90 : 1
+- required_m=102 : 1
+- required_m=114 : 1
+- required_m=118 : 1
+- required_m=121 : 1
+- required_m=127 : 1
+- required_m=128 : 1
+- required_m=129 : 1
+- required_m=130 : 1
+- required_m=136 : 1
+
+## Motifs dominants (<=32)
+
+- both_children_no_contracting_D_up_to32 : 8
+- both_children_F_blocked_by_deltaF_up_to32 : 7
+- both_children_no_contracting_F_up_to32 : 7
+
+## Histogrammes (<=32, agrégés sur les deux enfants)
+
+### first_k_contracting_D_up_to32
+- k=10 : 346
+- k=11 : 203
+- k=12 : 152
+- k=13 : 223
+- k=14 : 116
+- k=15 : 175
+- k=16 : 88
+- k=17 : 121
+- k=18 : 65
+- k=19 : 53
+- k=20 : 81
+- k=21 : 51
+- k=22 : 67
+- k=23 : 37
+- k=24 : 21
+- k=25 : 44
+- k=26 : 24
+- k=27 : 48
+- k=28 : 26
+- k=29 : 32
+- k=30 : 18
+- k=31 : 14
+- k=32 : 20
+
+### first_k_contracting_D_up_to32 (low child)
+- k=10 : 174
+- k=11 : 99
+- k=12 : 78
+- k=13 : 106
+- k=14 : 57
+- k=15 : 89
+- k=16 : 45
+- k=17 : 66
+- k=18 : 33
+- k=19 : 30
+- k=20 : 32
+- k=21 : 23
+- k=22 : 30
+- k=23 : 19
+- k=24 : 13
+- k=25 : 19
+- k=26 : 15
+- k=27 : 25
+- k=28 : 12
+- k=29 : 14
+- k=30 : 13
+- k=31 : 8
+- k=32 : 13
+
+### first_k_contracting_D_up_to32 (high child)
+- k=10 : 172
+- k=11 : 104
+- k=12 : 74
+- k=13 : 117
+- k=14 : 59
+- k=15 : 86
+- k=16 : 43
+- k=17 : 55
+- k=18 : 32
+- k=19 : 23
+- k=20 : 49
+- k=21 : 28
+- k=22 : 37
+- k=23 : 18
+- k=24 : 8
+- k=25 : 25
+- k=26 : 9
+- k=27 : 23
+- k=28 : 14
+- k=29 : 18
+- k=30 : 5
+- k=31 : 6
+- k=32 : 7
+
+### first_t_contracting_F_up_to32
+- t=10 : 260
+- t=11 : 366
+- t=12 : 199
+- t=13 : 119
+- t=14 : 185
+- t=15 : 108
+- t=16 : 144
+- t=17 : 73
+- t=18 : 110
+- t=19 : 57
+- t=20 : 40
+- t=21 : 68
+- t=22 : 40
+- t=23 : 56
+- t=24 : 27
+- t=25 : 22
+- t=26 : 36
+- t=27 : 30
+- t=28 : 30
+- t=29 : 16
+- t=30 : 30
+- t=31 : 12
+- t=32 : 12
+
+### first_t_y_mod3_nonzero_up_to32
+- t=1 : 2202
+
+### y_mod3_zero_count_up_to32
+- count=0 : 2202
+
+### y_mod3_zero_count_up_to32 (low child)
+- count=0 : 1101
+
+### y_mod3_zero_count_up_to32 (high child)
+- count=0 : 1101
+
+## Corrélations (borne inférieure)
+
+### lb_D - lb_F
+- diff=-8 : 2
+- diff=-7 : 2
+- diff=-6 : 5
+- diff=-5 : 3
+- diff=-4 : 6
+- diff=-3 : 17
+- diff=-2 : 13
+- diff=-1 : 39
+- diff=0 : 827
+- diff=1 : 9
+- diff=2 : 21
+- diff=3 : 30
+- diff=4 : 14
+- diff=5 : 17
+- diff=6 : 9
+- diff=7 : 20
+- diff=8 : 10
+- diff=9 : 7
+- diff=10 : 5
+- diff=11 : 4
+- diff=12 : 7
+- diff=13 : 2
+- diff=14 : 2
+- diff=15 : 3
+- diff=16 : 2
+- diff=17 : 4
+- diff=18 : 2
+- diff=19 : 1
+- diff=20 : 1
+- diff=21 : 2
+- diff=22 : 2
+- diff=24 : 1
+- diff=25 : 1
+- diff=26 : 2
+- diff=28 : 1
+- diff=30 : 2
+- diff=31 : 2
+- diff=38 : 1
+- diff=40 : 1
+- diff=42 : 1
+- diff=44 : 1
+
+### lb_any - lb_D
+- diff=-44 : 1
+- diff=-42 : 1
+- diff=-40 : 1
+- diff=-38 : 1
+- diff=-31 : 2
+- diff=-30 : 2
+- diff=-28 : 1
+- diff=-26 : 3
+- diff=-25 : 1
+- diff=-23 : 1
+- diff=-22 : 2
+- diff=-21 : 1
+- diff=-20 : 1
+- diff=-19 : 1
+- diff=-18 : 2
+- diff=-17 : 4
+- diff=-16 : 2
+- diff=-15 : 3
+- diff=-14 : 2
+- diff=-13 : 3
+- diff=-12 : 7
+- diff=-11 : 4
+- diff=-10 : 5
+- diff=-9 : 7
+- diff=-8 : 9
+- diff=-7 : 21
+- diff=-6 : 10
+- diff=-5 : 17
+- diff=-4 : 15
+- diff=-3 : 30
+- diff=-2 : 20
+- diff=-1 : 8
+- diff=0 : 913
+
+### lb_any - lb_F
+- diff=-8 : 2
+- diff=-7 : 2
+- diff=-6 : 5
+- diff=-5 : 3
+- diff=-4 : 6
+- diff=-3 : 19
+- diff=-2 : 20
+- diff=-1 : 42
+- diff=0 : 1002
+
+## Quantiles (borne inférieure)
+
+| metric | p50 | p75 | p90 | p95 | p99 | max |
+| --- | --- | --- | --- | --- | --- | --- |
+| lb_any | 30 | 44 | 60 | 70 | 85 | 136 |
+| lb_D | 33 | 46 | 63 | 71 | 87 | 136 |
+| lb_F | 31 | 44 | 60 | 70 | 85 | 136 |
+
+## Exemples (premières lignes)
+
+| r | child0 | child1 | lb_any | lb_D | lb_F |
+| --- | --- | --- | --- | --- | --- |
+| 27 | 27 | 32795 | 60 | 60 | 60 |
+| 31 | 31 | 32799 | 57 | 57 | 57 |
+| 47 | 47 | 32815 | 56 | 56 | 56 |
+| 63 | 63 | 32831 | 55 | 55 | 58 |
+| 71 | 71 | 32839 | 52 | 52 | 55 |
+| 91 | 91 | 32859 | 46 | 46 | 46 |
+| 103 | 103 | 32871 | 43 | 43 | 43 |
+| 111 | 111 | 32879 | 32 | 32 | 32 |
+| 159 | 159 | 32927 | 24 | 24 | 24 |
+| 167 | 167 | 32935 | 31 | 31 | 31 |
+| 223 | 223 | 32991 | 33 | 33 | 33 |
+| 239 | 239 | 33007 | 22 | 22 | 22 |
+| 251 | 251 | 33019 | 80 | 80 | 80 |
+| 283 | 283 | 33051 | 41 | 41 | 42 |
+| 319 | 319 | 33087 | 24 | 24 | 24 |
+| 327 | 327 | 33095 | 25 | 25 | 25 |
+| 359 | 359 | 33127 | 20 | 23 | 21 |
+| 447 | 447 | 33215 | 42 | 42 | 42 |
+| 479 | 479 | 33247 | 22 | 22 | 22 |
+| 495 | 495 | 33263 | 29 | 29 | 29 |
+| 511 | 511 | 33279 | 38 | 38 | 38 |
+| 559 | 559 | 33327 | 31 | 34 | 31 |
+| 603 | 603 | 33371 | 26 | 38 | 26 |
+| 639 | 639 | 33407 | 34 | 34 | 34 |
+| 667 | 667 | 33435 | 30 | 30 | 30 |
+| 671 | 671 | 33439 | 24 | 41 | 24 |
+| 703 | 703 | 33471 | 84 | 84 | 84 |
+| 743 | 743 | 33511 | 25 | 25 | 28 |
+| 751 | 751 | 33519 | 47 | 47 | 47 |
+| 763 | 763 | 33531 | 23 | 23 | 23 |
+| 767 | 767 | 33535 | 21 | 21 | 21 |
+| 795 | 795 | 33563 | 28 | 28 | 28 |
+| 859 | 859 | 33627 | 24 | 24 | 24 |
+| 871 | 871 | 33639 | 48 | 48 | 48 |
+| 895 | 895 | 33663 | 25 | 25 | 25 |
+| 927 | 927 | 33695 | 38 | 38 | 38 |
+| 959 | 959 | 33727 | 24 | 24 | 24 |
+| 991 | 991 | 33759 | 27 | 27 | 27 |
+| 1007 | 1007 | 33775 | 22 | 22 | 22 |
+| 1023 | 1023 | 33791 | 36 | 36 | 36 |
+
+## Sorties
+
+- JSON : `/home/ncantu/code/algo/docs/artefacts/collatz/refinement_K/palier2p15/bundle_mod2p15_to2p24_hensel_b/open_roots_obstruction_profile_mod2p15_to2p24.json`
+- Markdown : `/home/ncantu/code/algo/docs/artefacts/collatz/refinement_K/palier2p15/bundle_mod2p15_to2p24_hensel_b/open_roots_obstruction_profile_mod2p15_to2p24.md`
+
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/bundle_mod2p15_to2p24_hensel_b/refinement_certificate_Sm_multilevel_mod2p15_to2p24.json b/docs/artefacts/collatz/refinement_K/palier2p15/bundle_mod2p15_to2p24_hensel_b/refinement_certificate_Sm_multilevel_mod2p15_to2p24.json
new file mode 100644
index 0000000..70f14c9
--- /dev/null
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/bundle_mod2p15_to2p24_hensel_b/refinement_certificate_Sm_multilevel_mod2p15_to2p24.json
@@ -0,0 +1,31131 @@
+{
+  "domain": {
+    "root_palier": 15,
+    "max_palier": 24,
+    "S_root_size": 16384
+  },
+  "inputs": {
+    "leaf_sources": [
+      "/home/ncantu/code/algo/docs/artefacts/collatz/terminal_clauses_over_Sm/palier2p15/clauses_terminal_over_Sm_mod2p15.json",
+      "/home/ncantu/code/algo/docs/artefacts/collatz/terminal_clauses_over_Sm/palier2p16/clauses_terminal_over_Sm_mod2p16.json",
+      "/home/ncantu/code/algo/docs/artefacts/collatz/terminal_clauses_over_Sm/palier2p17/clauses_terminal_over_Sm_mod2p17.json",
+      "/home/ncantu/code/algo/docs/artefacts/collatz/terminal_clauses_over_Sm/palier2p18/clauses_terminal_over_Sm_mod2p18.json",
+      "/home/ncantu/code/algo/docs/artefacts/collatz/terminal_clauses_over_Sm/palier2p19/clauses_terminal_over_Sm_mod2p19.json",
+      "/home/ncantu/code/algo/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/clauses_hensel_chain_leaves_shifted_mod2p19.json",
+      "/home/ncantu/code/algo/docs/artefacts/collatz/terminal_clauses_over_Sm/palier2p20/clauses_terminal_over_Sm_mod2p20.json",
+      "/home/ncantu/code/algo/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/clauses_hensel_chain_leaves_shifted_mod2p20.json",
+      "/home/ncantu/code/algo/docs/artefacts/collatz/terminal_clauses_over_Sm/palier2p21/clauses_terminal_over_Sm_mod2p21.json",
+      "/home/ncantu/code/algo/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/clauses_hensel_chain_leaves_shifted_mod2p21.json",
+      "/home/ncantu/code/algo/docs/artefacts/collatz/terminal_clauses_over_Sm/palier2p22/clauses_terminal_over_Sm_mod2p22.json",
+      "/home/ncantu/code/algo/docs/artefacts/collatz/terminal_clauses_over_Sm/palier2p23/clauses_terminal_over_Sm_mod2p23.json",
+      "/home/ncantu/code/algo/docs/artefacts/collatz/terminal_clauses_over_Sm/palier2p24/clauses_terminal_over_Sm_mod2p24.json"
+    ]
+  },
+  "generated_at": "2026-03-10T11:53:17.265227Z",
+  "sha256": {
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+}
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/bundle_mod2p15_to2p24_hensel_b/refinement_certificate_Sm_multilevel_mod2p15_to2p24.md b/docs/artefacts/collatz/refinement_K/palier2p15/bundle_mod2p15_to2p24_hensel_b/refinement_certificate_Sm_multilevel_mod2p15_to2p24.md
new file mode 100644
index 0000000..e8cdde4
--- /dev/null
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/bundle_mod2p15_to2p24_hensel_b/refinement_certificate_Sm_multilevel_mod2p15_to2p24.md
@@ -0,0 +1,155 @@
+**Auteur** : Équipe 4NK
+
+# Certificat de raffinement multi-niveaux sur S_M — racine 2^15 vers 2^24
+
+## Domaine
+
+- racine : 2^15
+- profondeur max : 2^24
+- |S_15| (impairs) : 16384
+
+## Entrées (feuilles terminales)
+
+- `/home/ncantu/code/algo/docs/artefacts/collatz/terminal_clauses_over_Sm/palier2p15/clauses_terminal_over_Sm_mod2p15.json`
+- `/home/ncantu/code/algo/docs/artefacts/collatz/terminal_clauses_over_Sm/palier2p16/clauses_terminal_over_Sm_mod2p16.json`
+- `/home/ncantu/code/algo/docs/artefacts/collatz/terminal_clauses_over_Sm/palier2p17/clauses_terminal_over_Sm_mod2p17.json`
+- `/home/ncantu/code/algo/docs/artefacts/collatz/terminal_clauses_over_Sm/palier2p18/clauses_terminal_over_Sm_mod2p18.json`
+- `/home/ncantu/code/algo/docs/artefacts/collatz/terminal_clauses_over_Sm/palier2p19/clauses_terminal_over_Sm_mod2p19.json`
+- `/home/ncantu/code/algo/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/clauses_hensel_chain_leaves_shifted_mod2p19.json`
+- `/home/ncantu/code/algo/docs/artefacts/collatz/terminal_clauses_over_Sm/palier2p20/clauses_terminal_over_Sm_mod2p20.json`
+- `/home/ncantu/code/algo/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/clauses_hensel_chain_leaves_shifted_mod2p20.json`
+- `/home/ncantu/code/algo/docs/artefacts/collatz/terminal_clauses_over_Sm/palier2p21/clauses_terminal_over_Sm_mod2p21.json`
+- `/home/ncantu/code/algo/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/clauses_hensel_chain_leaves_shifted_mod2p21.json`
+- `/home/ncantu/code/algo/docs/artefacts/collatz/terminal_clauses_over_Sm/palier2p22/clauses_terminal_over_Sm_mod2p22.json`
+- `/home/ncantu/code/algo/docs/artefacts/collatz/terminal_clauses_over_Sm/palier2p23/clauses_terminal_over_Sm_mod2p23.json`
+- `/home/ncantu/code/algo/docs/artefacts/collatz/terminal_clauses_over_Sm/palier2p24/clauses_terminal_over_Sm_mod2p24.json`
+
+## Fermeture (sur S_M)
+
+- closed_roots : 15283
+- open_roots : 1101
+- closed_ratio : 0.93280029296875
+
+## Timeline (première profondeur de fermeture)
+
+| cible | newly_closed | closed | open | closed_ratio |
+| --- | --- | --- | --- | --- |
+| 15 | 15035 | 15035 | 1349 | 0.917664 |
+| 16 | 0 | 15035 | 1349 | 0.917664 |
+| 17 | 0 | 15035 | 1349 | 0.917664 |
+| 18 | 0 | 15035 | 1349 | 0.917664 |
+| 19 | 248 | 15283 | 1101 | 0.932800 |
+| 20 | 0 | 15283 | 1101 | 0.932800 |
+| 21 | 0 | 15283 | 1101 | 0.932800 |
+| 22 | 0 | 15283 | 1101 | 0.932800 |
+| 23 | 0 | 15283 | 1101 | 0.932800 |
+| 24 | 0 | 15283 | 1101 | 0.932800 |
+
+## Audit du résidu (comptes, q_m, parents à un enfant)
+
+| m | open_count | q_m | parents_one_child |
+| --- | --- | --- | --- |
+| 15 | 1101 | 0.842870118074 | 346 |
+| 16 | 1856 | 0.918372844828 | 303 |
+| 17 | 3409 | 0.930184804928 | 476 |
+| 18 | 6342 | 1.000000000000 | 0 |
+| 19 | 12684 | 0.962117628508 | 961 |
+| 20 | 24407 | 0.960605563978 | 1923 |
+| 21 | 46891 | 0.937610628905 | 7226 |
+| 22 | 87931 | 0.920437615858 | 13992 |
+| 23 | 161870 | 0.932254278124 | 22037 |
+| 24 | 301808 |  |  |
+
+### Racines encore ouvertes (extrait)
+
+- r=27
+- r=31
+- r=47
+- r=63
+- r=71
+- r=91
+- r=103
+- r=111
+- r=159
+- r=167
+- r=223
+- r=239
+- r=251
+- r=283
+- r=319
+- r=327
+- r=359
+- r=447
+- r=479
+- r=495
+- r=511
+- r=559
+- r=603
+- r=639
+- r=667
+- r=671
+- r=703
+- r=743
+- r=751
+- r=763
+- r=767
+- r=795
+- r=859
+- r=871
+- r=895
+- r=927
+- r=959
+- r=991
+- r=1007
+- r=1023
+- ... (1061 more)
+
+### Racines fermées (extrait)
+
+- r=1
+- r=3
+- r=5
+- r=7
+- r=9
+- r=11
+- r=13
+- r=15
+- r=17
+- r=19
+- r=21
+- r=23
+- r=25
+- r=29
+- r=33
+- r=35
+- r=37
+- r=39
+- r=41
+- r=43
+- r=45
+- r=49
+- r=51
+- r=53
+- r=55
+- r=57
+- r=59
+- r=61
+- r=65
+- r=67
+- r=69
+- r=73
+- r=75
+- r=77
+- r=79
+- r=81
+- r=83
+- r=85
+- r=87
+- r=89
+- ... (15243 more)
+
+## Sorties
+
+- JSON : `/home/ncantu/code/algo/docs/artefacts/collatz/refinement_K/palier2p15/bundle_mod2p15_to2p24_hensel_b/refinement_certificate_Sm_multilevel_mod2p15_to2p24.json`
+- Audit JSON : `/home/ncantu/code/algo/docs/artefacts/collatz/refinement_K/palier2p15/bundle_mod2p15_to2p24_hensel_b/audit_refinement_certificate_Sm_multilevel_mod2p15_to2p24.json`
+
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_100187_r18_100187_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_100187_r18_100187_k10_to2p16.json
index cb6ab1a..d1f3a02 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_100187_r18_100187_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_100187_r18_100187_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 100187,
     "r18_parent": 100187,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_100519_r18_100519_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_100519_r18_100519_k11_to2p18.json
index 75c12d5..babdfd6 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_100519_r18_100519_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_100519_r18_100519_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 100519,
     "r18_parent": 100519,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_101407_r18_101407_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_101407_r18_101407_k11_to2p18.json
index 9124afb..9de62ce 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_101407_r18_101407_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_101407_r18_101407_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 101407,
     "r18_parent": 101407,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_101679_r18_101679_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_101679_r18_101679_k10_to2p16.json
index 81e2b84..eb6df66 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_101679_r18_101679_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_101679_r18_101679_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 101679,
     "r18_parent": 101679,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_104615_r18_104615_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_104615_r18_104615_k11_to2p18.json
index 3095c38..4f15699 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_104615_r18_104615_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_104615_r18_104615_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 104615,
     "r18_parent": 104615,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_104959_r18_104959_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_104959_r18_104959_k11_to2p18.json
index a934a2c..5f801e4 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_104959_r18_104959_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_104959_r18_104959_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 104959,
     "r18_parent": 104959,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_105775_r18_105775_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_105775_r18_105775_k11_to2p18.json
index 5ddfefe..d29847f 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_105775_r18_105775_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_105775_r18_105775_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 105775,
     "r18_parent": 105775,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_105799_r18_105799_k8_to2p13.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_105799_r18_105799_k8_to2p13.json
index e577c88..53388ad 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_105799_r18_105799_k8_to2p13.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_105799_r18_105799_k8_to2p13.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 105799,
     "r18_parent": 105799,
     "k": 8,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_11079_r18_11079_k9_to2p15.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_11079_r18_11079_k9_to2p15.json
index 4fbd1b4..97952ee 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_11079_r18_11079_k9_to2p15.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_11079_r18_11079_k9_to2p15.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 11079,
     "r18_parent": 11079,
     "k": 9,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_111103_r18_111103_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_111103_r18_111103_k11_to2p18.json
index f4f62d4..d315302 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_111103_r18_111103_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_111103_r18_111103_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 111103,
     "r18_parent": 111103,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_111919_r18_111919_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_111919_r18_111919_k11_to2p18.json
index 2eae61a..8d56dba 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_111919_r18_111919_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_111919_r18_111919_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 111919,
     "r18_parent": 111919,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_111943_r18_111943_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_111943_r18_111943_k10_to2p16.json
index a8ac4fa..7036ff0 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_111943_r18_111943_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_111943_r18_111943_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 111943,
     "r18_parent": 111943,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_112807_r18_112807_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_112807_r18_112807_k11_to2p18.json
index c1ece04..efc4065 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_112807_r18_112807_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_112807_r18_112807_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 112807,
     "r18_parent": 112807,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_11423_r18_11423_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_11423_r18_11423_k11_to2p18.json
index add5988..2839fa2 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_11423_r18_11423_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_11423_r18_11423_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 11423,
     "r18_parent": 11423,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_116383_r18_116383_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_116383_r18_116383_k10_to2p16.json
index c92b646..ed6d6e5 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_116383_r18_116383_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_116383_r18_116383_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 116383,
     "r18_parent": 116383,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_117531_r18_117531_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_117531_r18_117531_k11_to2p18.json
index 0edf6f1..71bdd86 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_117531_r18_117531_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_117531_r18_117531_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 117531,
     "r18_parent": 117531,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_118087_r18_118087_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_118087_r18_118087_k10_to2p16.json
index 2c861a9..66159b6 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_118087_r18_118087_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_118087_r18_118087_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 118087,
     "r18_parent": 118087,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_118975_r18_118975_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_118975_r18_118975_k10_to2p16.json
index 72ce0fa..aa54eaa 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_118975_r18_118975_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_118975_r18_118975_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 118975,
     "r18_parent": 118975,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_119579_r18_119579_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_119579_r18_119579_k10_to2p16.json
index 89a9ab5..89896de 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_119579_r18_119579_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_119579_r18_119579_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 119579,
     "r18_parent": 119579,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_121071_r18_121071_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_121071_r18_121071_k10_to2p16.json
index 164ee61..9e1c802 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_121071_r18_121071_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_121071_r18_121071_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 121071,
     "r18_parent": 121071,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_121851_r18_121851_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_121851_r18_121851_k10_to2p16.json
index e01d8cd..e5de031 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_121851_r18_121851_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_121851_r18_121851_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 121851,
     "r18_parent": 121851,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_123675_r18_123675_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_123675_r18_123675_k11_to2p18.json
index ec2f2a9..e0f5095 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_123675_r18_123675_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_123675_r18_123675_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 123675,
     "r18_parent": 123675,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_12571_r18_12571_k9_to2p15.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_12571_r18_12571_k9_to2p15.json
index e715ef5..0ac3a7c 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_12571_r18_12571_k9_to2p15.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_12571_r18_12571_k9_to2p15.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 12571,
     "r18_parent": 12571,
     "k": 9,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_126623_r18_126623_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_126623_r18_126623_k11_to2p18.json
index eb13d81..149d3f6 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_126623_r18_126623_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_126623_r18_126623_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 126623,
     "r18_parent": 126623,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_13127_r18_13127_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_13127_r18_13127_k11_to2p18.json
index ae55771..905394f 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_13127_r18_13127_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_13127_r18_13127_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 13127,
     "r18_parent": 13127,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_131311_r18_131311_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_131311_r18_131311_k11_to2p18.json
index db44e72..0979e55 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_131311_r18_131311_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_131311_r18_131311_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 131311,
     "r18_parent": 131311,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_131903_r18_131903_k9_to2p15.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_131903_r18_131903_k9_to2p15.json
index c89e6e8..a6ccdd7 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_131903_r18_131903_k9_to2p15.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_131903_r18_131903_k9_to2p15.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 131903,
     "r18_parent": 131903,
     "k": 9,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_132223_r18_132223_k9_to2p15.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_132223_r18_132223_k9_to2p15.json
index 5ae4ffe..eb6ca37 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_132223_r18_132223_k9_to2p15.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_132223_r18_132223_k9_to2p15.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 132223,
     "r18_parent": 132223,
     "k": 9,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_133951_r18_133951_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_133951_r18_133951_k11_to2p18.json
index 2a1cbd7..8c44a58 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_133951_r18_133951_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_133951_r18_133951_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 133951,
     "r18_parent": 133951,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_134271_r18_134271_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_134271_r18_134271_k11_to2p18.json
index 4be1fce..de03349 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_134271_r18_134271_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_134271_r18_134271_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 134271,
     "r18_parent": 134271,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_13471_r18_13471_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_13471_r18_13471_k11_to2p18.json
index ad28cdf..b02d907 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_13471_r18_13471_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_13471_r18_13471_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 13471,
     "r18_parent": 13471,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_136295_r18_136295_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_136295_r18_136295_k11_to2p18.json
index 61e5d94..bd7e1db 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_136295_r18_136295_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_136295_r18_136295_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 136295,
     "r18_parent": 136295,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_136319_r18_136319_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_136319_r18_136319_k11_to2p18.json
index 9d6d46a..1fd64db 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_136319_r18_136319_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_136319_r18_136319_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 136319,
     "r18_parent": 136319,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_138343_r18_138343_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_138343_r18_138343_k11_to2p18.json
index 1220560..66e8d57 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_138343_r18_138343_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_138343_r18_138343_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 138343,
     "r18_parent": 138343,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_140095_r18_140095_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_140095_r18_140095_k11_to2p18.json
index a53b780..095d6cb 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_140095_r18_140095_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_140095_r18_140095_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 140095,
     "r18_parent": 140095,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_140391_r18_140391_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_140391_r18_140391_k10_to2p16.json
index bc28c18..8e7dd64 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_140391_r18_140391_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_140391_r18_140391_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 140391,
     "r18_parent": 140391,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_140415_r18_140415_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_140415_r18_140415_k11_to2p18.json
index fe69e3a..909cb15 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_140415_r18_140415_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_140415_r18_140415_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 140415,
     "r18_parent": 140415,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_14063_r18_14063_k8_to2p13.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_14063_r18_14063_k8_to2p13.json
index 0a92629..4175a85 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_14063_r18_14063_k8_to2p13.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_14063_r18_14063_k8_to2p13.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 14063,
     "r18_parent": 14063,
     "k": 8,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_145967_r18_145967_k9_to2p15.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_145967_r18_145967_k9_to2p15.json
index 3a82e82..72e6346 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_145967_r18_145967_k9_to2p15.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_145967_r18_145967_k9_to2p15.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 145967,
     "r18_parent": 145967,
     "k": 9,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_146879_r18_146879_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_146879_r18_146879_k11_to2p18.json
index 9467299..418aef6 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_146879_r18_146879_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_146879_r18_146879_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 146879,
     "r18_parent": 146879,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_147707_r18_147707_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_147707_r18_147707_k10_to2p16.json
index b5c6a77..f5a1ecf 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_147707_r18_147707_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_147707_r18_147707_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 147707,
     "r18_parent": 147707,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_148015_r18_148015_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_148015_r18_148015_k11_to2p18.json
index 7341acf..3b4db87 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_148015_r18_148015_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_148015_r18_148015_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 148015,
     "r18_parent": 148015,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_148287_r18_148287_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_148287_r18_148287_k11_to2p18.json
index b61b473..bc03442 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_148287_r18_148287_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_148287_r18_148287_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 148287,
     "r18_parent": 148287,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_148571_r18_148571_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_148571_r18_148571_k11_to2p18.json
index dfb79a3..9b05f3e 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_148571_r18_148571_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_148571_r18_148571_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 148571,
     "r18_parent": 148571,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_148607_r18_148607_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_148607_r18_148607_k11_to2p18.json
index 0b9f6d4..e4be865 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_148607_r18_148607_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_148607_r18_148607_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 148607,
     "r18_parent": 148607,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_150619_r18_150619_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_150619_r18_150619_k10_to2p16.json
index b2eae3b..48e2734 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_150619_r18_150619_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_150619_r18_150619_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 150619,
     "r18_parent": 150619,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_154159_r18_154159_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_154159_r18_154159_k11_to2p18.json
index f609dcf..748530d 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_154159_r18_154159_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_154159_r18_154159_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 154159,
     "r18_parent": 154159,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_157439_r18_157439_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_157439_r18_157439_k10_to2p16.json
index ed5ffad..4b5c88c 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_157439_r18_157439_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_157439_r18_157439_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 157439,
     "r18_parent": 157439,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_157947_r18_157947_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_157947_r18_157947_k11_to2p18.json
index 4cad58c..41162a5 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_157947_r18_157947_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_157947_r18_157947_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 157947,
     "r18_parent": 157947,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_162351_r18_162351_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_162351_r18_162351_k11_to2p18.json
index d1daf55..aa5a0ad 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_162351_r18_162351_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_162351_r18_162351_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 162351,
     "r18_parent": 162351,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_165607_r18_165607_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_165607_r18_165607_k10_to2p16.json
index 78be417..1b7b766 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_165607_r18_165607_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_165607_r18_165607_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 165607,
     "r18_parent": 165607,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_16667_r18_16667_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_16667_r18_16667_k11_to2p18.json
index 2c6453e..9017045 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_16667_r18_16667_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_16667_r18_16667_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 16667,
     "r18_parent": 16667,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_1691_r18_1691_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_1691_r18_1691_k11_to2p18.json
index bc45be8..2593fc4 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_1691_r18_1691_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_1691_r18_1691_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 1691,
     "r18_parent": 1691,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_169703_r18_169703_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_169703_r18_169703_k11_to2p18.json
index c38eefe..2ca4e59 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_169703_r18_169703_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_169703_r18_169703_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 169703,
     "r18_parent": 169703,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_17567_r18_17567_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_17567_r18_17567_k11_to2p18.json
index 9efe47d..c4c6224 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_17567_r18_17567_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_17567_r18_17567_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 17567,
     "r18_parent": 17567,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_175847_r18_175847_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_175847_r18_175847_k11_to2p18.json
index bee7712..93e891b 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_175847_r18_175847_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_175847_r18_175847_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 175847,
     "r18_parent": 175847,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_176155_r18_176155_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_176155_r18_176155_k10_to2p16.json
index 3c2fe6e..49ae8ff 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_176155_r18_176155_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_176155_r18_176155_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 176155,
     "r18_parent": 176155,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_180251_r18_180251_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_180251_r18_180251_k11_to2p18.json
index 285184a..7825932 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_180251_r18_180251_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_180251_r18_180251_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 180251,
     "r18_parent": 180251,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_184111_r18_184111_k6_to2p10.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_184111_r18_184111_k6_to2p10.json
index 9ecb42d..337e6fb 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_184111_r18_184111_k6_to2p10.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_184111_r18_184111_k6_to2p10.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 184111,
     "r18_parent": 184111,
     "k": 6,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_186395_r18_186395_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_186395_r18_186395_k11_to2p18.json
index 9cdd3f4..28099c5 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_186395_r18_186395_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_186395_r18_186395_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 186395,
     "r18_parent": 186395,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_18751_r18_18751_k9_to2p15.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_18751_r18_18751_k9_to2p15.json
index ec77926..faa9e0e 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_18751_r18_18751_k9_to2p15.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_18751_r18_18751_k9_to2p15.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 18751,
     "r18_parent": 18751,
     "k": 9,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_187887_r18_187887_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_187887_r18_187887_k11_to2p18.json
index c44463a..3966696 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_187887_r18_187887_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_187887_r18_187887_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 187887,
     "r18_parent": 187887,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_188479_r18_188479_k9_to2p15.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_188479_r18_188479_k9_to2p15.json
index 2625312..bacbe8d 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_188479_r18_188479_k9_to2p15.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_188479_r18_188479_k9_to2p15.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 188479,
     "r18_parent": 188479,
     "k": 9,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_189935_r18_189935_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_189935_r18_189935_k10_to2p16.json
index 826932e..d105c3d 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_189935_r18_189935_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_189935_r18_189935_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 189935,
     "r18_parent": 189935,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_190527_r18_190527_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_190527_r18_190527_k11_to2p18.json
index 2fd8c48..1f0a6b9 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_190527_r18_190527_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_190527_r18_190527_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 190527,
     "r18_parent": 190527,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_19271_r18_19271_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_19271_r18_19271_k11_to2p18.json
index 98d9e39..835b4e8 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_19271_r18_19271_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_19271_r18_19271_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 19271,
     "r18_parent": 19271,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_194919_r18_194919_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_194919_r18_194919_k11_to2p18.json
index 408ebe8..89c6aad 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_194919_r18_194919_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_194919_r18_194919_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 194919,
     "r18_parent": 194919,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_196671_r18_196671_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_196671_r18_196671_k11_to2p18.json
index b2b63bd..f5edd09 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_196671_r18_196671_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_196671_r18_196671_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 196671,
     "r18_parent": 196671,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_196967_r18_196967_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_196967_r18_196967_k10_to2p16.json
index 7f0f2ed..98d9ef2 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_196967_r18_196967_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_196967_r18_196967_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 196967,
     "r18_parent": 196967,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_197855_r18_197855_k8_to2p13.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_197855_r18_197855_k8_to2p13.json
index 97d8f5c..20384ff 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_197855_r18_197855_k8_to2p13.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_197855_r18_197855_k8_to2p13.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 197855,
     "r18_parent": 197855,
     "k": 8,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_198175_r18_198175_k8_to2p13.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_198175_r18_198175_k8_to2p13.json
index e969d19..1656dbd 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_198175_r18_198175_k8_to2p13.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_198175_r18_198175_k8_to2p13.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 198175,
     "r18_parent": 198175,
     "k": 8,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_198495_r18_198495_k5_to2p8.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_198495_r18_198495_k5_to2p8.json
index 7dccbb6..383d087 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_198495_r18_198495_k5_to2p8.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_198495_r18_198495_k5_to2p8.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 198495,
     "r18_parent": 198495,
     "k": 5,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_201407_r18_201407_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_201407_r18_201407_k10_to2p16.json
index 9698ee7..9fa0eaf 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_201407_r18_201407_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_201407_r18_201407_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 201407,
     "r18_parent": 201407,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_20207_r18_20207_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_20207_r18_20207_k10_to2p16.json
index c06191b..c3d37ac 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_20207_r18_20207_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_20207_r18_20207_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 20207,
     "r18_parent": 20207,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_202863_r18_202863_k9_to2p15.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_202863_r18_202863_k9_to2p15.json
index 898a089..912b5a3 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_202863_r18_202863_k9_to2p15.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_202863_r18_202863_k9_to2p15.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 202863,
     "r18_parent": 202863,
     "k": 9,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_203419_r18_203419_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_203419_r18_203419_k11_to2p18.json
index 8a4a00e..5d7bba1 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_203419_r18_203419_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_203419_r18_203419_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 203419,
     "r18_parent": 203419,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_204319_r18_204319_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_204319_r18_204319_k10_to2p16.json
index 461f5c6..6b1c4f2 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_204319_r18_204319_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_204319_r18_204319_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 204319,
     "r18_parent": 204319,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_204863_r18_204863_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_204863_r18_204863_k11_to2p18.json
index f2c3f35..4f5b709 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_204863_r18_204863_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_204863_r18_204863_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 204863,
     "r18_parent": 204863,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_204911_r18_204911_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_204911_r18_204911_k11_to2p18.json
index b0c73af..9521a01 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_204911_r18_204911_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_204911_r18_204911_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 204911,
     "r18_parent": 204911,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_205467_r18_205467_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_205467_r18_205467_k11_to2p18.json
index 26ac89e..1e966ee 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_205467_r18_205467_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_205467_r18_205467_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 205467,
     "r18_parent": 205467,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_206959_r18_206959_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_206959_r18_206959_k11_to2p18.json
index a84bf35..900cfc4 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_206959_r18_206959_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_206959_r18_206959_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 206959,
     "r18_parent": 206959,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_207515_r18_207515_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_207515_r18_207515_k10_to2p16.json
index 76f767b..59460ae 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_207515_r18_207515_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_207515_r18_207515_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 207515,
     "r18_parent": 207515,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_20763_r18_20763_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_20763_r18_20763_k11_to2p18.json
index d9dfc6d..275e43a 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_20763_r18_20763_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_20763_r18_20763_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 20763,
     "r18_parent": 20763,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_20799_r18_20799_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_20799_r18_20799_k11_to2p18.json
index 7e7d61d..d440260 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_20799_r18_20799_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_20799_r18_20799_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 20799,
     "r18_parent": 20799,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_209575_r18_209575_k9_to2p15.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_209575_r18_209575_k9_to2p15.json
index ad9c553..e17e20b 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_209575_r18_209575_k9_to2p15.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_209575_r18_209575_k9_to2p15.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 209575,
     "r18_parent": 209575,
     "k": 9,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_209919_r18_209919_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_209919_r18_209919_k11_to2p18.json
index de77d8f..9b50db7 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_209919_r18_209919_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_209919_r18_209919_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 209919,
     "r18_parent": 209919,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_210143_r18_210143_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_210143_r18_210143_k10_to2p16.json
index 76874b2..50cf2ee 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_210143_r18_210143_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_210143_r18_210143_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 210143,
     "r18_parent": 210143,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_210463_r18_210463_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_210463_r18_210463_k10_to2p16.json
index 086d63c..7991fee 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_210463_r18_210463_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_210463_r18_210463_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 210463,
     "r18_parent": 210463,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_21095_r18_21095_k7_to2p12.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_21095_r18_21095_k7_to2p12.json
index 05a92d5..85fb240 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_21095_r18_21095_k7_to2p12.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_21095_r18_21095_k7_to2p12.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 21095,
     "r18_parent": 21095,
     "k": 7,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_211055_r18_211055_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_211055_r18_211055_k11_to2p18.json
index 38642ac..1381c11 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_211055_r18_211055_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_211055_r18_211055_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 211055,
     "r18_parent": 211055,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_211623_r18_211623_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_211623_r18_211623_k11_to2p18.json
index b953dbc..66fa9cc 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_211623_r18_211623_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_211623_r18_211623_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 211623,
     "r18_parent": 211623,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_211647_r18_211647_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_211647_r18_211647_k11_to2p18.json
index 6666a30..623078a 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_211647_r18_211647_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_211647_r18_211647_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 211647,
     "r18_parent": 211647,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_217767_r18_217767_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_217767_r18_217767_k11_to2p18.json
index 049c172..9e15abb 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_217767_r18_217767_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_217767_r18_217767_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 217767,
     "r18_parent": 217767,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_219247_r18_219247_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_219247_r18_219247_k11_to2p18.json
index da70283..d7de6c8 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_219247_r18_219247_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_219247_r18_219247_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 219247,
     "r18_parent": 219247,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_220443_r18_220443_k9_to2p15.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_220443_r18_220443_k9_to2p15.json
index feb045f..108b7b5 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_220443_r18_220443_k9_to2p15.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_220443_r18_220443_k9_to2p15.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 220443,
     "r18_parent": 220443,
     "k": 9,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_221343_r18_221343_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_221343_r18_221343_k11_to2p18.json
index 8eada6a..3d9c1bc 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_221343_r18_221343_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_221343_r18_221343_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 221343,
     "r18_parent": 221343,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_222491_r18_222491_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_222491_r18_222491_k11_to2p18.json
index 1ea7b92..bcadd2f 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_222491_r18_222491_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_222491_r18_222491_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 222491,
     "r18_parent": 222491,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_224539_r18_224539_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_224539_r18_224539_k11_to2p18.json
index 7f8544a..d6cc8b6 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_224539_r18_224539_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_224539_r18_224539_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 224539,
     "r18_parent": 224539,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_225959_r18_225959_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_225959_r18_225959_k11_to2p18.json
index eeb2e6f..df2543a 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_225959_r18_225959_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_225959_r18_225959_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 225959,
     "r18_parent": 225959,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_226623_r18_226623_k8_to2p13.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_226623_r18_226623_k8_to2p13.json
index 920230f..b70f73f 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_226623_r18_226623_k8_to2p13.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_226623_r18_226623_k8_to2p13.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 226623,
     "r18_parent": 226623,
     "k": 8,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_228079_r18_228079_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_228079_r18_228079_k10_to2p16.json
index a5dcc45..b01c4c7 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_228079_r18_228079_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_228079_r18_228079_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 228079,
     "r18_parent": 228079,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_22847_r18_22847_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_22847_r18_22847_k11_to2p18.json
index 4876c44..0a54809 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_22847_r18_22847_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_22847_r18_22847_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 22847,
     "r18_parent": 22847,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_228635_r18_228635_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_228635_r18_228635_k11_to2p18.json
index 82fe0e6..7025858 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_228635_r18_228635_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_228635_r18_228635_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 228635,
     "r18_parent": 228635,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_230127_r18_230127_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_230127_r18_230127_k11_to2p18.json
index 0895c0e..01758d0 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_230127_r18_230127_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_230127_r18_230127_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 230127,
     "r18_parent": 230127,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_232767_r18_232767_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_232767_r18_232767_k10_to2p16.json
index 45fc492..4778553 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_232767_r18_232767_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_232767_r18_232767_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 232767,
     "r18_parent": 232767,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_236827_r18_236827_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_236827_r18_236827_k11_to2p18.json
index c8b22c3..8de079b 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_236827_r18_236827_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_236827_r18_236827_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 236827,
     "r18_parent": 236827,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_237183_r18_237183_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_237183_r18_237183_k11_to2p18.json
index 69b9628..06c37f0 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_237183_r18_237183_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_237183_r18_237183_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 237183,
     "r18_parent": 237183,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_238911_r18_238911_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_238911_r18_238911_k10_to2p16.json
index 5d7b78b..1063c7d 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_238911_r18_238911_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_238911_r18_238911_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 238911,
     "r18_parent": 238911,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_240687_r18_240687_k7_to2p12.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_240687_r18_240687_k7_to2p12.json
index 3f9edbb..48526f1 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_240687_r18_240687_k7_to2p12.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_240687_r18_240687_k7_to2p12.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 240687,
     "r18_parent": 240687,
     "k": 7,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_242143_r18_242143_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_242143_r18_242143_k10_to2p16.json
index f38789d..aaddbab 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_242143_r18_242143_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_242143_r18_242143_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 242143,
     "r18_parent": 242143,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_243327_r18_243327_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_243327_r18_243327_k11_to2p18.json
index 962c0c5..9a8a53d 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_243327_r18_243327_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_243327_r18_243327_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 243327,
     "r18_parent": 243327,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_244191_r18_244191_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_244191_r18_244191_k11_to2p18.json
index 10202d2..059f6cb 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_244191_r18_244191_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_244191_r18_244191_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 244191,
     "r18_parent": 244191,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_251495_r18_251495_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_251495_r18_251495_k11_to2p18.json
index 9a0a6cb..88e363a 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_251495_r18_251495_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_251495_r18_251495_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 251495,
     "r18_parent": 251495,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_253543_r18_253543_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_253543_r18_253543_k10_to2p16.json
index 623887a..a12b1c7 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_253543_r18_253543_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_253543_r18_253543_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 253543,
     "r18_parent": 253543,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_257983_r18_257983_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_257983_r18_257983_k10_to2p16.json
index e7cfc70..c838881 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_257983_r18_257983_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_257983_r18_257983_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 257983,
     "r18_parent": 257983,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_260859_r18_260859_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_260859_r18_260859_k10_to2p16.json
index b28cd71..8279aef 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_260859_r18_260859_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_260859_r18_260859_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 260859,
     "r18_parent": 260859,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_262079_r18_262079_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_262079_r18_262079_k11_to2p18.json
index 45ee873..f290822 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_262079_r18_262079_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_262079_r18_262079_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 262079,
     "r18_parent": 262079,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_26351_r18_26351_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_26351_r18_26351_k10_to2p16.json
index 237e62b..2285407 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_26351_r18_26351_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_26351_r18_26351_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 26351,
     "r18_parent": 26351,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_264447_r18_264447_k9_to2p15.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_264447_r18_264447_k9_to2p15.json
index 21e679f..acf5fa0 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_264447_r18_264447_k9_to2p15.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_264447_r18_264447_k9_to2p15.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 264447,
     "r18_parent": 264447,
     "k": 9,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_264955_r18_264955_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_264955_r18_264955_k11_to2p18.json
index a5f1040..c831d2c 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_264955_r18_264955_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_264955_r18_264955_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 264955,
     "r18_parent": 264955,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_266151_r18_266151_k9_to2p15.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_266151_r18_266151_k9_to2p15.json
index 276c258..5e3a3d7 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_266151_r18_266151_k9_to2p15.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_266151_r18_266151_k9_to2p15.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 266151,
     "r18_parent": 266151,
     "k": 9,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_268199_r18_268199_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_268199_r18_268199_k11_to2p18.json
index 4c70e2b..deada0e 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_268199_r18_268199_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_268199_r18_268199_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 268199,
     "r18_parent": 268199,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_268223_r18_268223_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_268223_r18_268223_k11_to2p18.json
index 976df71..d3b0e22 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_268223_r18_268223_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_268223_r18_268223_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 268223,
     "r18_parent": 268223,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_268543_r18_268543_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_268543_r18_268543_k11_to2p18.json
index 8d224c5..d144949 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_268543_r18_268543_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_268543_r18_268543_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 268543,
     "r18_parent": 268543,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_26943_r18_26943_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_26943_r18_26943_k11_to2p18.json
index af39290..c60cfa8 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_26943_r18_26943_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_26943_r18_26943_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 26943,
     "r18_parent": 26943,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_271099_r18_271099_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_271099_r18_271099_k11_to2p18.json
index 99d6e55..cea70f7 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_271099_r18_271099_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_271099_r18_271099_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 271099,
     "r18_parent": 271099,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_272639_r18_272639_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_272639_r18_272639_k11_to2p18.json
index 6c7ad02..9e0f0c1 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_272639_r18_272639_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_272639_r18_272639_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 272639,
     "r18_parent": 272639,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_273823_r18_273823_k9_to2p15.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_273823_r18_273823_k9_to2p15.json
index e3480d0..9f17594 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_273823_r18_273823_k9_to2p15.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_273823_r18_273823_k9_to2p15.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 273823,
     "r18_parent": 273823,
     "k": 9,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_274343_r18_274343_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_274343_r18_274343_k11_to2p18.json
index 31d6e84..75cd775 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_274343_r18_274343_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_274343_r18_274343_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 274343,
     "r18_parent": 274343,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_27463_r18_27463_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_27463_r18_27463_k11_to2p18.json
index 589fe1e..a379ea3 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_27463_r18_27463_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_27463_r18_27463_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 27463,
     "r18_parent": 27463,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_275527_r18_275527_k8_to2p13.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_275527_r18_275527_k8_to2p13.json
index cbd78b9..4fcc49b 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_275527_r18_275527_k8_to2p13.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_275527_r18_275527_k8_to2p13.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 275527,
     "r18_parent": 275527,
     "k": 8,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_275871_r18_275871_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_275871_r18_275871_k11_to2p18.json
index 90b179b..7e159bb 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_275871_r18_275871_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_275871_r18_275871_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 275871,
     "r18_parent": 275871,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_276167_r18_276167_k5_to2p8.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_276167_r18_276167_k5_to2p8.json
index fe9fc12..7b1f897 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_276167_r18_276167_k5_to2p8.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_276167_r18_276167_k5_to2p8.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 276167,
     "r18_parent": 276167,
     "k": 5,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_277919_r18_277919_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_277919_r18_277919_k11_to2p18.json
index 89207f5..3220f1d 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_277919_r18_277919_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_277919_r18_277919_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 277919,
     "r18_parent": 277919,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_28127_r18_28127_k8_to2p13.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_28127_r18_28127_k8_to2p13.json
index 7b32f16..998fcfd 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_28127_r18_28127_k8_to2p13.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_28127_r18_28127_k8_to2p13.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 28127,
     "r18_parent": 28127,
     "k": 8,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_282015_r18_282015_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_282015_r18_282015_k11_to2p18.json
index b0ed7da..3e48e75 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_282015_r18_282015_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_282015_r18_282015_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 282015,
     "r18_parent": 282015,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_282535_r18_282535_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_282535_r18_282535_k11_to2p18.json
index eb48f79..4e3268d 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_282535_r18_282535_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_282535_r18_282535_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 282535,
     "r18_parent": 282535,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_285543_r18_285543_k9_to2p15.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_285543_r18_285543_k9_to2p15.json
index 2fb083a..c0d7bd3 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_285543_r18_285543_k9_to2p15.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_285543_r18_285543_k9_to2p15.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 285543,
     "r18_parent": 285543,
     "k": 9,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_287591_r18_287591_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_287591_r18_287591_k11_to2p18.json
index 2a51a9c..3da8625 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_287591_r18_287591_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_287591_r18_287591_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 287591,
     "r18_parent": 287591,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_287815_r18_287815_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_287815_r18_287815_k10_to2p16.json
index 866cdba..a6a9eec 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_287815_r18_287815_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_287815_r18_287815_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 287815,
     "r18_parent": 287815,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_289639_r18_289639_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_289639_r18_289639_k11_to2p18.json
index 0ef6f79..35f9d99 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_289639_r18_289639_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_289639_r18_289639_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 289639,
     "r18_parent": 289639,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_290207_r18_290207_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_290207_r18_290207_k11_to2p18.json
index 2211f27..678d9e1 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_290207_r18_290207_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_290207_r18_290207_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 290207,
     "r18_parent": 290207,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_29311_r18_29311_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_29311_r18_29311_k11_to2p18.json
index e0e1c34..4d1b81c 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_29311_r18_29311_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_29311_r18_29311_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 29311,
     "r18_parent": 29311,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_293735_r18_293735_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_293735_r18_293735_k11_to2p18.json
index 08d3246..4216670 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_293735_r18_293735_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_293735_r18_293735_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 293735,
     "r18_parent": 293735,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_293759_r18_293759_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_293759_r18_293759_k11_to2p18.json
index 825cc70..95e21f1 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_293759_r18_293759_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_293759_r18_293759_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 293759,
     "r18_parent": 293759,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_295807_r18_295807_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_295807_r18_295807_k10_to2p16.json
index bce2fcc..f403abe 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_295807_r18_295807_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_295807_r18_295807_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 295807,
     "r18_parent": 295807,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_297263_r18_297263_k7_to2p12.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_297263_r18_297263_k7_to2p12.json
index 0894705..64e1878 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_297263_r18_297263_k7_to2p12.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_297263_r18_297263_k7_to2p12.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 297263,
     "r18_parent": 297263,
     "k": 7,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_299547_r18_299547_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_299547_r18_299547_k11_to2p18.json
index 2d9ceea..97f4c7d 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_299547_r18_299547_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_299547_r18_299547_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 299547,
     "r18_parent": 299547,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_299903_r18_299903_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_299903_r18_299903_k11_to2p18.json
index 05e57eb..e4c8c03 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_299903_r18_299903_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_299903_r18_299903_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 299903,
     "r18_parent": 299903,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_303087_r18_303087_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_303087_r18_303087_k10_to2p16.json
index 8884bb7..6d07fdb 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_303087_r18_303087_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_303087_r18_303087_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 303087,
     "r18_parent": 303087,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_304295_r18_304295_k8_to2p13.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_304295_r18_304295_k8_to2p13.json
index a355c9b..bd16176 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_304295_r18_304295_k8_to2p13.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_304295_r18_304295_k8_to2p13.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 304295,
     "r18_parent": 304295,
     "k": 8,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_310439_r18_310439_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_310439_r18_310439_k10_to2p16.json
index 66edaa0..cc3e4f6 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_310439_r18_310439_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_310439_r18_310439_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 310439,
     "r18_parent": 310439,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_31323_r18_31323_k8_to2p13.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_31323_r18_31323_k8_to2p13.json
index 53c1b92..b7af04a 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_31323_r18_31323_k8_to2p13.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_31323_r18_31323_k8_to2p13.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 31323,
     "r18_parent": 31323,
     "k": 8,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_31359_r18_31359_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_31359_r18_31359_k10_to2p16.json
index 4920a66..e399278 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_31359_r18_31359_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_31359_r18_31359_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 31359,
     "r18_parent": 31359,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_314559_r18_314559_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_314559_r18_314559_k10_to2p16.json
index e64dab8..8f94304 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_314559_r18_314559_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_314559_r18_314559_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 314559,
     "r18_parent": 314559,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_314879_r18_314879_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_314879_r18_314879_k10_to2p16.json
index 99a73cf..6b76e3b 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_314879_r18_314879_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_314879_r18_314879_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 314879,
     "r18_parent": 314879,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_315423_r18_315423_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_315423_r18_315423_k11_to2p18.json
index f805363..82f016a 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_315423_r18_315423_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_315423_r18_315423_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 315423,
     "r18_parent": 315423,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_315695_r18_315695_k9_to2p15.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_315695_r18_315695_k9_to2p15.json
index ff85284..e67527d 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_315695_r18_315695_k9_to2p15.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_315695_r18_315695_k9_to2p15.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 315695,
     "r18_parent": 315695,
     "k": 9,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_316015_r18_316015_k9_to2p15.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_316015_r18_316015_k9_to2p15.json
index 3c071e6..e330558 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_316015_r18_316015_k9_to2p15.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_316015_r18_316015_k9_to2p15.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 316015,
     "r18_parent": 316015,
     "k": 9,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_31643_r18_31643_k6_to2p10.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_31643_r18_31643_k6_to2p10.json
index bddc313..eb12819 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_31643_r18_31643_k6_to2p10.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_31643_r18_31643_k6_to2p10.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 31643,
     "r18_parent": 31643,
     "k": 6,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_316583_r18_316583_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_316583_r18_316583_k10_to2p16.json
index f1f3bf3..026712d 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_316583_r18_316583_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_316583_r18_316583_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 316583,
     "r18_parent": 316583,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_317435_r18_317435_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_317435_r18_317435_k10_to2p16.json
index 7912b63..745daed 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_317435_r18_317435_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_317435_r18_317435_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 317435,
     "r18_parent": 317435,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_317471_r18_317471_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_317471_r18_317471_k10_to2p16.json
index ad3293c..23f84c0 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_317471_r18_317471_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_317471_r18_317471_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 317471,
     "r18_parent": 317471,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_318063_r18_318063_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_318063_r18_318063_k11_to2p18.json
index 32b1fb3..e84edca 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_318063_r18_318063_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_318063_r18_318063_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 318063,
     "r18_parent": 318063,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_3183_r18_3183_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_3183_r18_3183_k11_to2p18.json
index 2693fea..9252b93 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_3183_r18_3183_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_3183_r18_3183_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 3183,
     "r18_parent": 3183,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_318619_r18_318619_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_318619_r18_318619_k11_to2p18.json
index 93f598b..b8ec879 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_318619_r18_318619_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_318619_r18_318619_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 318619,
     "r18_parent": 318619,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_318655_r18_318655_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_318655_r18_318655_k11_to2p18.json
index 83bd753..297a38e 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_318655_r18_318655_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_318655_r18_318655_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 318655,
     "r18_parent": 318655,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_319815_r18_319815_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_319815_r18_319815_k10_to2p16.json
index c6a5cae..a33ca7c 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_319815_r18_319815_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_319815_r18_319815_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 319815,
     "r18_parent": 319815,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_320347_r18_320347_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_320347_r18_320347_k10_to2p16.json
index 17d13af..5b5c419 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_320347_r18_320347_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_320347_r18_320347_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 320347,
     "r18_parent": 320347,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_320667_r18_320667_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_320667_r18_320667_k10_to2p16.json
index 7ee3680..2da5a51 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_320667_r18_320667_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_320667_r18_320667_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 320667,
     "r18_parent": 320667,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_321531_r18_321531_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_321531_r18_321531_k11_to2p18.json
index cf61465..24798d1 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_321531_r18_321531_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_321531_r18_321531_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 321531,
     "r18_parent": 321531,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_321863_r18_321863_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_321863_r18_321863_k11_to2p18.json
index 5620de7..f2cd63c 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_321863_r18_321863_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_321863_r18_321863_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 321863,
     "r18_parent": 321863,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_323887_r18_323887_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_323887_r18_323887_k11_to2p18.json
index f9ea00d..31e7ef1 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_323887_r18_323887_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_323887_r18_323887_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 323887,
     "r18_parent": 323887,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_324207_r18_324207_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_324207_r18_324207_k11_to2p18.json
index 83b6e6a..e46d5f0 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_324207_r18_324207_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_324207_r18_324207_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 324207,
     "r18_parent": 324207,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_324799_r18_324799_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_324799_r18_324799_k11_to2p18.json
index ccdaba1..e00a675 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_324799_r18_324799_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_324799_r18_324799_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 324799,
     "r18_parent": 324799,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_325119_r18_325119_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_325119_r18_325119_k11_to2p18.json
index 6380804..cbcd085 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_325119_r18_325119_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_325119_r18_325119_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 325119,
     "r18_parent": 325119,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_325403_r18_325403_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_325403_r18_325403_k11_to2p18.json
index 0c6849e..6f84585 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_325403_r18_325403_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_325403_r18_325403_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 325403,
     "r18_parent": 325403,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_327675_r18_327675_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_327675_r18_327675_k11_to2p18.json
index 443d751..eb71abc 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_327675_r18_327675_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_327675_r18_327675_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 327675,
     "r18_parent": 327675,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_330399_r18_330399_k9_to2p15.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_330399_r18_330399_k9_to2p15.json
index 79be3ab..4d660a0 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_330399_r18_330399_k9_to2p15.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_330399_r18_330399_k9_to2p15.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 330399,
     "r18_parent": 330399,
     "k": 9,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_330991_r18_330991_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_330991_r18_330991_k11_to2p18.json
index 17520d1..3613725 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_330991_r18_330991_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_330991_r18_330991_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 330991,
     "r18_parent": 330991,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_331547_r18_331547_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_331547_r18_331547_k11_to2p18.json
index 0212e43..fed6085 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_331547_r18_331547_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_331547_r18_331547_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 331547,
     "r18_parent": 331547,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_332079_r18_332079_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_332079_r18_332079_k11_to2p18.json
index e2cb89c..db638b1 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_332079_r18_332079_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_332079_r18_332079_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 332079,
     "r18_parent": 332079,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_332399_r18_332399_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_332399_r18_332399_k11_to2p18.json
index 0c5b7ec..b704e23 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_332399_r18_332399_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_332399_r18_332399_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 332399,
     "r18_parent": 332399,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_332447_r18_332447_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_332447_r18_332447_k11_to2p18.json
index bc38b3b..1077be3 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_332447_r18_332447_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_332447_r18_332447_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 332447,
     "r18_parent": 332447,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_338591_r18_338591_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_338591_r18_338591_k11_to2p18.json
index c5f2f53..1578041 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_338591_r18_338591_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_338591_r18_338591_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 338591,
     "r18_parent": 338591,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_340095_r18_340095_k8_to2p13.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_340095_r18_340095_k8_to2p13.json
index b2c0dbb..e35c423 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_340095_r18_340095_k8_to2p13.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_340095_r18_340095_k8_to2p13.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 340095,
     "r18_parent": 340095,
     "k": 8,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_342119_r18_342119_k9_to2p15.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_342119_r18_342119_k9_to2p15.json
index 204d5df..0bcb193 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_342119_r18_342119_k9_to2p15.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_342119_r18_342119_k9_to2p15.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 342119,
     "r18_parent": 342119,
     "k": 9,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_34271_r18_34271_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_34271_r18_34271_k10_to2p16.json
index f8a3b45..22cafb0 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_34271_r18_34271_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_34271_r18_34271_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 34271,
     "r18_parent": 34271,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_346203_r18_346203_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_346203_r18_346203_k10_to2p16.json
index 403adbe..ae2e125 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_346203_r18_346203_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_346203_r18_346203_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 346203,
     "r18_parent": 346203,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_346215_r18_346215_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_346215_r18_346215_k11_to2p18.json
index 56d686d..223ce74 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_346215_r18_346215_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_346215_r18_346215_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 346215,
     "r18_parent": 346215,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_346239_r18_346239_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_346239_r18_346239_k10_to2p16.json
index 2d56d09..ba0def7 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_346239_r18_346239_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_346239_r18_346239_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 346239,
     "r18_parent": 346239,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_346783_r18_346783_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_346783_r18_346783_k11_to2p18.json
index 9621d8b..55332ca 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_346783_r18_346783_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_346783_r18_346783_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 346783,
     "r18_parent": 346783,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_349151_r18_349151_k9_to2p15.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_349151_r18_349151_k9_to2p15.json
index 529b001..5928faa 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_349151_r18_349151_k9_to2p15.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_349151_r18_349151_k9_to2p15.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 349151,
     "r18_parent": 349151,
     "k": 9,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_350311_r18_350311_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_350311_r18_350311_k11_to2p18.json
index 34263ad..fdb5705 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_350311_r18_350311_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_350311_r18_350311_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 350311,
     "r18_parent": 350311,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_35135_r18_35135_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_35135_r18_35135_k11_to2p18.json
index c8f8a75..d80ba0d 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_35135_r18_35135_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_35135_r18_35135_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 35135,
     "r18_parent": 35135,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_352383_r18_352383_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_352383_r18_352383_k10_to2p16.json
index 58769d2..c87ffbd 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_352383_r18_352383_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_352383_r18_352383_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 352383,
     "r18_parent": 352383,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_353247_r18_353247_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_353247_r18_353247_k11_to2p18.json
index f9e4ad9..71ce42b 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_353247_r18_353247_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_353247_r18_353247_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 353247,
     "r18_parent": 353247,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_35455_r18_35455_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_35455_r18_35455_k11_to2p18.json
index a26165e..393bca8 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_35455_r18_35455_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_35455_r18_35455_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 35455,
     "r18_parent": 35455,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_355887_r18_355887_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_355887_r18_355887_k11_to2p18.json
index bdecddf..87f8a88 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_355887_r18_355887_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_355887_r18_355887_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 355887,
     "r18_parent": 355887,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_356443_r18_356443_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_356443_r18_356443_k11_to2p18.json
index d45ebfd..f8bd63f 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_356443_r18_356443_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_356443_r18_356443_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 356443,
     "r18_parent": 356443,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_357343_r18_357343_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_357343_r18_357343_k11_to2p18.json
index 07a5e1a..a76fe46 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_357343_r18_357343_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_357343_r18_357343_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 357343,
     "r18_parent": 357343,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_357935_r18_357935_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_357935_r18_357935_k11_to2p18.json
index b7912e9..98101cf 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_357935_r18_357935_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_357935_r18_357935_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 357935,
     "r18_parent": 357935,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_359983_r18_359983_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_359983_r18_359983_k10_to2p16.json
index b81b484..07223a1 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_359983_r18_359983_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_359983_r18_359983_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 359983,
     "r18_parent": 359983,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_360895_r18_360895_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_360895_r18_360895_k11_to2p18.json
index 5e15544..6fa35e7 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_360895_r18_360895_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_360895_r18_360895_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 360895,
     "r18_parent": 360895,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_361723_r18_361723_k9_to2p15.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_361723_r18_361723_k9_to2p15.json
index b17d961..3413f69 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_361723_r18_361723_k9_to2p15.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_361723_r18_361723_k9_to2p15.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 361723,
     "r18_parent": 361723,
     "k": 9,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_362943_r18_362943_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_362943_r18_362943_k11_to2p18.json
index 5cdc104..5ed2148 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_362943_r18_362943_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_362943_r18_362943_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 362943,
     "r18_parent": 362943,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_363771_r18_363771_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_363771_r18_363771_k11_to2p18.json
index 3f0756d..247cab3 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_363771_r18_363771_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_363771_r18_363771_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 363771,
     "r18_parent": 363771,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_369407_r18_369407_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_369407_r18_369407_k11_to2p18.json
index 2eead8e..70977ef 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_369407_r18_369407_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_369407_r18_369407_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 369407,
     "r18_parent": 369407,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_369915_r18_369915_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_369915_r18_369915_k11_to2p18.json
index 8b72a47..a2ddaf1 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_369915_r18_369915_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_369915_r18_369915_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 369915,
     "r18_parent": 369915,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_371431_r18_371431_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_371431_r18_371431_k11_to2p18.json
index 7671624..eebdfc5 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_371431_r18_371431_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_371431_r18_371431_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 371431,
     "r18_parent": 371431,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_371455_r18_371455_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_371455_r18_371455_k10_to2p16.json
index 051fffc..b17d8fa 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_371455_r18_371455_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_371455_r18_371455_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 371455,
     "r18_parent": 371455,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_373479_r18_373479_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_373479_r18_373479_k10_to2p16.json
index cd2771e..1ad281c 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_373479_r18_373479_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_373479_r18_373479_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 373479,
     "r18_parent": 373479,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_37467_r18_37467_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_37467_r18_37467_k10_to2p16.json
index 94f86b4..0d28a49 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_37467_r18_37467_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_37467_r18_37467_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 37467,
     "r18_parent": 37467,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_375551_r18_375551_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_375551_r18_375551_k11_to2p18.json
index cf0c350..a670455 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_375551_r18_375551_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_375551_r18_375551_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 375551,
     "r18_parent": 375551,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_377575_r18_377575_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_377575_r18_377575_k11_to2p18.json
index 529c3f0..a2fab26 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_377575_r18_377575_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_377575_r18_377575_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 377575,
     "r18_parent": 377575,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_3775_r18_3775_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_3775_r18_3775_k11_to2p18.json
index 6267777..eb8d320 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_3775_r18_3775_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_3775_r18_3775_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 3775,
     "r18_parent": 3775,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_378107_r18_378107_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_378107_r18_378107_k11_to2p18.json
index d034d5c..5769bba 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_378107_r18_378107_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_378107_r18_378107_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 378107,
     "r18_parent": 378107,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_381979_r18_381979_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_381979_r18_381979_k11_to2p18.json
index da0093f..f65e544 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_381979_r18_381979_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_381979_r18_381979_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 381979,
     "r18_parent": 381979,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_384027_r18_384027_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_384027_r18_384027_k10_to2p16.json
index fdfd261..4b4ce44 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_384027_r18_384027_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_384027_r18_384027_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 384027,
     "r18_parent": 384027,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_385519_r18_385519_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_385519_r18_385519_k10_to2p16.json
index 7425acf..46315d1 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_385519_r18_385519_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_385519_r18_385519_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 385519,
     "r18_parent": 385519,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_386975_r18_386975_k9_to2p15.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_386975_r18_386975_k9_to2p15.json
index 9f03066..fbfb4dd 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_386975_r18_386975_k9_to2p15.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_386975_r18_386975_k9_to2p15.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 386975,
     "r18_parent": 386975,
     "k": 9,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_388123_r18_388123_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_388123_r18_388123_k11_to2p18.json
index ff45943..1c2a583 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_388123_r18_388123_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_388123_r18_388123_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 388123,
     "r18_parent": 388123,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_389023_r18_389023_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_389023_r18_389023_k11_to2p18.json
index 0bd0563..73fb538 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_389023_r18_389023_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_389023_r18_389023_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 389023,
     "r18_parent": 389023,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_392551_r18_392551_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_392551_r18_392551_k10_to2p16.json
index 9ad3ef8..02339ed 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_392551_r18_392551_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_392551_r18_392551_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 392551,
     "r18_parent": 392551,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_395167_r18_395167_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_395167_r18_395167_k11_to2p18.json
index 4d29896..158339e 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_395167_r18_395167_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_395167_r18_395167_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 395167,
     "r18_parent": 395167,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_39527_r18_39527_k9_to2p15.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_39527_r18_39527_k9_to2p15.json
index a6401cf..dc0a72e 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_39527_r18_39527_k9_to2p15.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_39527_r18_39527_k9_to2p15.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 39527,
     "r18_parent": 39527,
     "k": 9,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_395759_r18_395759_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_395759_r18_395759_k11_to2p18.json
index af17f78..fa4b46b 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_395759_r18_395759_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_395759_r18_395759_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 395759,
     "r18_parent": 395759,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_396351_r18_396351_k8_to2p13.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_396351_r18_396351_k8_to2p13.json
index a6e7e24..1c299ca 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_396351_r18_396351_k8_to2p13.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_396351_r18_396351_k8_to2p13.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 396351,
     "r18_parent": 396351,
     "k": 8,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_396671_r18_396671_k8_to2p13.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_396671_r18_396671_k8_to2p13.json
index 766cd60..2b1e41a 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_396671_r18_396671_k8_to2p13.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_396671_r18_396671_k8_to2p13.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 396671,
     "r18_parent": 396671,
     "k": 8,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_399867_r18_399867_k6_to2p10.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_399867_r18_399867_k6_to2p10.json
index d31de05..ec9ef25 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_399867_r18_399867_k6_to2p10.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_399867_r18_399867_k6_to2p10.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 399867,
     "r18_parent": 399867,
     "k": 6,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_402791_r18_402791_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_402791_r18_402791_k11_to2p18.json
index e9a5de0..e36146b 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_402791_r18_402791_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_402791_r18_402791_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 402791,
     "r18_parent": 402791,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_402815_r18_402815_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_402815_r18_402815_k10_to2p16.json
index 96bd1b1..25231af 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_402815_r18_402815_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_402815_r18_402815_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 402815,
     "r18_parent": 402815,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_403359_r18_403359_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_403359_r18_403359_k11_to2p18.json
index 0aa7d7b..2e18531 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_403359_r18_403359_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_403359_r18_403359_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 403359,
     "r18_parent": 403359,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_40415_r18_40415_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_40415_r18_40415_k10_to2p16.json
index e8d8f1d..a24fc03 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_40415_r18_40415_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_40415_r18_40415_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 40415,
     "r18_parent": 40415,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_405727_r18_405727_k9_to2p15.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_405727_r18_405727_k9_to2p15.json
index 98d90e9..629a06d 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_405727_r18_405727_k9_to2p15.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_405727_r18_405727_k9_to2p15.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 405727,
     "r18_parent": 405727,
     "k": 9,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_408639_r18_408639_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_408639_r18_408639_k10_to2p16.json
index ed9011a..a19d5a8 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_408639_r18_408639_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_408639_r18_408639_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 408639,
     "r18_parent": 408639,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_408959_r18_408959_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_408959_r18_408959_k10_to2p16.json
index bd148a7..d5adf43 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_408959_r18_408959_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_408959_r18_408959_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 408959,
     "r18_parent": 408959,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_409243_r18_409243_k9_to2p15.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_409243_r18_409243_k9_to2p15.json
index e03e75f..3da2696 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_409243_r18_409243_k9_to2p15.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_409243_r18_409243_k9_to2p15.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 409243,
     "r18_parent": 409243,
     "k": 9,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_409823_r18_409823_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_409823_r18_409823_k11_to2p18.json
index 8885451..69c8ac4 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_409823_r18_409823_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_409823_r18_409823_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 409823,
     "r18_parent": 409823,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_410735_r18_410735_k8_to2p13.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_410735_r18_410735_k8_to2p13.json
index 86588c1..2c5b4d4 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_410735_r18_410735_k8_to2p13.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_410735_r18_410735_k8_to2p13.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 410735,
     "r18_parent": 410735,
     "k": 8,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_413339_r18_413339_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_413339_r18_413339_k11_to2p18.json
index bbd2143..5105c4d 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_413339_r18_413339_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_413339_r18_413339_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 413339,
     "r18_parent": 413339,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_413919_r18_413919_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_413919_r18_413919_k11_to2p18.json
index e9a8466..f094965 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_413919_r18_413919_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_413919_r18_413919_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 413919,
     "r18_parent": 413919,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_415423_r18_415423_k9_to2p15.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_415423_r18_415423_k9_to2p15.json
index fe35525..845ef55 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_415423_r18_415423_k9_to2p15.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_415423_r18_415423_k9_to2p15.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 415423,
     "r18_parent": 415423,
     "k": 9,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_416879_r18_416879_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_416879_r18_416879_k10_to2p16.json
index 07018cf..2c7ca00 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_416879_r18_416879_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_416879_r18_416879_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 416879,
     "r18_parent": 416879,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_417435_r18_417435_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_417435_r18_417435_k11_to2p18.json
index 6c57b07..634ba96 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_417435_r18_417435_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_417435_r18_417435_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 417435,
     "r18_parent": 417435,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_417471_r18_417471_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_417471_r18_417471_k11_to2p18.json
index a561713..4f0a9e9 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_417471_r18_417471_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_417471_r18_417471_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 417471,
     "r18_parent": 417471,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_423023_r18_423023_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_423023_r18_423023_k10_to2p16.json
index b084fb4..9cf4514 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_423023_r18_423023_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_423023_r18_423023_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 423023,
     "r18_parent": 423023,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_423615_r18_423615_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_423615_r18_423615_k11_to2p18.json
index 8504e45..5d6a06b 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_423615_r18_423615_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_423615_r18_423615_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 423615,
     "r18_parent": 423615,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_426823_r18_426823_k9_to2p15.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_426823_r18_426823_k9_to2p15.json
index 05c20ac..9b755da 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_426823_r18_426823_k9_to2p15.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_426823_r18_426823_k9_to2p15.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 426823,
     "r18_parent": 426823,
     "k": 9,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_428315_r18_428315_k8_to2p13.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_428315_r18_428315_k8_to2p13.json
index 9117469..16d2475 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_428315_r18_428315_k8_to2p13.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_428315_r18_428315_k8_to2p13.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 428315,
     "r18_parent": 428315,
     "k": 8,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_430919_r18_430919_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_430919_r18_430919_k11_to2p18.json
index cbd469b..8b22f29 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_430919_r18_430919_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_430919_r18_430919_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 430919,
     "r18_parent": 430919,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_431263_r18_431263_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_431263_r18_431263_k10_to2p16.json
index 9679951..e39c4dc 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_431263_r18_431263_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_431263_r18_431263_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 431263,
     "r18_parent": 431263,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_431807_r18_431807_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_431807_r18_431807_k11_to2p18.json
index 1643768..72094bc 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_431807_r18_431807_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_431807_r18_431807_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 431807,
     "r18_parent": 431807,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_433311_r18_433311_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_433311_r18_433311_k11_to2p18.json
index f0ecf9b..ae3dff7 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_433311_r18_433311_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_433311_r18_433311_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 433311,
     "r18_parent": 433311,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_434459_r18_434459_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_434459_r18_434459_k10_to2p16.json
index 50b7e08..b80c19c 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_434459_r18_434459_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_434459_r18_434459_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 434459,
     "r18_parent": 434459,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_435015_r18_435015_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_435015_r18_435015_k11_to2p18.json
index 29d1847..35ee5bf 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_435015_r18_435015_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_435015_r18_435015_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 435015,
     "r18_parent": 435015,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_43611_r18_43611_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_43611_r18_43611_k10_to2p16.json
index 6b859aa..213bbe4 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_43611_r18_43611_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_43611_r18_43611_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 43611,
     "r18_parent": 43611,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_43967_r18_43967_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_43967_r18_43967_k10_to2p16.json
index ec960f7..32580ad 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_43967_r18_43967_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_43967_r18_43967_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 43967,
     "r18_parent": 43967,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_440603_r18_440603_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_440603_r18_440603_k10_to2p16.json
index 82a693f..1c121dd 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_440603_r18_440603_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_440603_r18_440603_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 440603,
     "r18_parent": 440603,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_440639_r18_440639_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_440639_r18_440639_k10_to2p16.json
index e8d2b4b..832e3b6 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_440639_r18_440639_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_440639_r18_440639_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 440639,
     "r18_parent": 440639,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_442095_r18_442095_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_442095_r18_442095_k10_to2p16.json
index 0fa3a52..547e236 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_442095_r18_442095_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_442095_r18_442095_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 442095,
     "r18_parent": 442095,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_442687_r18_442687_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_442687_r18_442687_k11_to2p18.json
index 1ff42c1..3f4f0f2 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_442687_r18_442687_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_442687_r18_442687_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 442687,
     "r18_parent": 442687,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_446191_r18_446191_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_446191_r18_446191_k11_to2p18.json
index c5f0278..4cd867a 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_446191_r18_446191_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_446191_r18_446191_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 446191,
     "r18_parent": 446191,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_447103_r18_447103_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_447103_r18_447103_k10_to2p16.json
index eb340c2..18ac1f2 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_447103_r18_447103_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_447103_r18_447103_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 447103,
     "r18_parent": 447103,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_45103_r18_45103_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_45103_r18_45103_k10_to2p16.json
index 8c22eda..16820d3 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_45103_r18_45103_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_45103_r18_45103_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 45103,
     "r18_parent": 45103,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_452335_r18_452335_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_452335_r18_452335_k11_to2p18.json
index 3a34609..93404ec 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_452335_r18_452335_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_452335_r18_452335_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 452335,
     "r18_parent": 452335,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_456159_r18_456159_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_456159_r18_456159_k10_to2p16.json
index 6287528..fc932b9 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_456159_r18_456159_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_456159_r18_456159_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 456159,
     "r18_parent": 456159,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_456443_r18_456443_k7_to2p12.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_456443_r18_456443_k7_to2p12.json
index 3c646b9..2982635 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_456443_r18_456443_k7_to2p12.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_456443_r18_456443_k7_to2p12.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 456443,
     "r18_parent": 456443,
     "k": 7,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_457343_r18_457343_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_457343_r18_457343_k11_to2p18.json
index 019f6be..dbf1911 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_457343_r18_457343_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_457343_r18_457343_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 457343,
     "r18_parent": 457343,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_459355_r18_459355_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_459355_r18_459355_k10_to2p16.json
index 62bfe56..d29a1c5 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_459355_r18_459355_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_459355_r18_459355_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 459355,
     "r18_parent": 459355,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_46015_r18_46015_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_46015_r18_46015_k11_to2p18.json
index c577140..042b35a 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_46015_r18_46015_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_46015_r18_46015_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 46015,
     "r18_parent": 46015,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_460255_r18_460255_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_460255_r18_460255_k11_to2p18.json
index fd01202..f010ccf 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_460255_r18_460255_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_460255_r18_460255_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 460255,
     "r18_parent": 460255,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_463451_r18_463451_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_463451_r18_463451_k11_to2p18.json
index 57e568f..fa5b0b9 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_463451_r18_463451_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_463451_r18_463451_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 463451,
     "r18_parent": 463451,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_463807_r18_463807_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_463807_r18_463807_k11_to2p18.json
index edda1a7..c07759f 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_463807_r18_463807_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_463807_r18_463807_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 463807,
     "r18_parent": 463807,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_465855_r18_465855_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_465855_r18_465855_k10_to2p16.json
index 7dcb9fb..4ae867c 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_465855_r18_465855_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_465855_r18_465855_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 465855,
     "r18_parent": 465855,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_466399_r18_466399_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_466399_r18_466399_k11_to2p18.json
index cae2a76..499e83b 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_466399_r18_466399_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_466399_r18_466399_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 466399,
     "r18_parent": 466399,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_469595_r18_469595_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_469595_r18_469595_k11_to2p18.json
index 95f025e..8bd51a7 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_469595_r18_469595_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_469595_r18_469595_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 469595,
     "r18_parent": 469595,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_469951_r18_469951_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_469951_r18_469951_k11_to2p18.json
index 6950b5e..c4aa13b 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_469951_r18_469951_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_469951_r18_469951_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 469951,
     "r18_parent": 469951,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_471087_r18_471087_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_471087_r18_471087_k11_to2p18.json
index f7e8f80..e3ddc4b 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_471087_r18_471087_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_471087_r18_471087_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 471087,
     "r18_parent": 471087,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_472319_r18_472319_k9_to2p15.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_472319_r18_472319_k9_to2p15.json
index 01c994a..fde9384 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_472319_r18_472319_k9_to2p15.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_472319_r18_472319_k9_to2p15.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 472319,
     "r18_parent": 472319,
     "k": 9,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_473135_r18_473135_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_473135_r18_473135_k10_to2p16.json
index bc4ba15..a832294 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_473135_r18_473135_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_473135_r18_473135_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 473135,
     "r18_parent": 473135,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_474023_r18_474023_k8_to2p13.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_474023_r18_474023_k8_to2p13.json
index 54da12d..dcf1d48 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_474023_r18_474023_k8_to2p13.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_474023_r18_474023_k8_to2p13.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 474023,
     "r18_parent": 474023,
     "k": 8,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_474343_r18_474343_k8_to2p13.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_474343_r18_474343_k8_to2p13.json
index ec82e9f..be5e0cd 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_474343_r18_474343_k8_to2p13.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_474343_r18_474343_k8_to2p13.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 474343,
     "r18_parent": 474343,
     "k": 8,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_474367_r18_474367_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_474367_r18_474367_k11_to2p18.json
index 13b0d0d..0e0c4b8 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_474367_r18_474367_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_474367_r18_474367_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 474367,
     "r18_parent": 474367,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_474663_r18_474663_k5_to2p8.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_474663_r18_474663_k5_to2p8.json
index 0117f85..db8e77d 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_474663_r18_474663_k5_to2p8.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_474663_r18_474663_k5_to2p8.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 474663,
     "r18_parent": 474663,
     "k": 5,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_476415_r18_476415_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_476415_r18_476415_k11_to2p18.json
index 3e658f6..3955244 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_476415_r18_476415_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_476415_r18_476415_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 476415,
     "r18_parent": 476415,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_47719_r18_47719_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_47719_r18_47719_k11_to2p18.json
index fb9583c..57b5260 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_47719_r18_47719_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_47719_r18_47719_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 47719,
     "r18_parent": 47719,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_480487_r18_480487_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_480487_r18_480487_k10_to2p16.json
index 6f3e4dc..1758719 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_480487_r18_480487_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_480487_r18_480487_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 480487,
     "r18_parent": 480487,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_480511_r18_480511_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_480511_r18_480511_k11_to2p18.json
index 1267cc5..9e8aef7 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_480511_r18_480511_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_480511_r18_480511_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 480511,
     "r18_parent": 480511,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_481695_r18_481695_k8_to2p13.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_481695_r18_481695_k8_to2p13.json
index 2ebb211..c49f3a7 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_481695_r18_481695_k8_to2p13.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_481695_r18_481695_k8_to2p13.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 481695,
     "r18_parent": 481695,
     "k": 8,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_483399_r18_483399_k9_to2p15.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_483399_r18_483399_k9_to2p15.json
index 54cb962..a5c262f 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_483399_r18_483399_k9_to2p15.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_483399_r18_483399_k9_to2p15.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 483399,
     "r18_parent": 483399,
     "k": 9,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_484891_r18_484891_k8_to2p13.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_484891_r18_484891_k8_to2p13.json
index a84328c..15d7384 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_484891_r18_484891_k8_to2p13.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_484891_r18_484891_k8_to2p13.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 484891,
     "r18_parent": 484891,
     "k": 8,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_486311_r18_486311_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_486311_r18_486311_k10_to2p16.json
index 4255d8f..8844f0b 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_486311_r18_486311_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_486311_r18_486311_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 486311,
     "r18_parent": 486311,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_486631_r18_486631_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_486631_r18_486631_k10_to2p16.json
index 504894c..726342f 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_486631_r18_486631_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_486631_r18_486631_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 486631,
     "r18_parent": 486631,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_487495_r18_487495_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_487495_r18_487495_k11_to2p18.json
index 9249b8c..a79960f 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_487495_r18_487495_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_487495_r18_487495_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 487495,
     "r18_parent": 487495,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_487839_r18_487839_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_487839_r18_487839_k10_to2p16.json
index 0992e42..e3914f3 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_487839_r18_487839_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_487839_r18_487839_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 487839,
     "r18_parent": 487839,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_488703_r18_488703_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_488703_r18_488703_k11_to2p18.json
index d07a9f8..517a851 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_488703_r18_488703_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_488703_r18_488703_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 488703,
     "r18_parent": 488703,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_491035_r18_491035_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_491035_r18_491035_k10_to2p16.json
index b116dda..d6fc3fe 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_491035_r18_491035_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_491035_r18_491035_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 491035,
     "r18_parent": 491035,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_491591_r18_491591_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_491591_r18_491591_k11_to2p18.json
index d497168..4a8a591 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_491591_r18_491591_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_491591_r18_491591_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 491591,
     "r18_parent": 491591,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_49199_r18_49199_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_49199_r18_49199_k11_to2p18.json
index e0d22c2..b3eede9 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_49199_r18_49199_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_49199_r18_49199_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 49199,
     "r18_parent": 49199,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_493983_r18_493983_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_493983_r18_493983_k10_to2p16.json
index 9d4a411..fc6d454 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_493983_r18_493983_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_493983_r18_493983_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 493983,
     "r18_parent": 493983,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_497179_r18_497179_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_497179_r18_497179_k10_to2p16.json
index 425a5c1..d373c70 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_497179_r18_497179_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_497179_r18_497179_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 497179,
     "r18_parent": 497179,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_497511_r18_497511_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_497511_r18_497511_k11_to2p18.json
index e2a594c..00e4d62 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_497511_r18_497511_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_497511_r18_497511_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 497511,
     "r18_parent": 497511,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_498671_r18_498671_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_498671_r18_498671_k10_to2p16.json
index 26cd092..69b4ca5 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_498671_r18_498671_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_498671_r18_498671_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 498671,
     "r18_parent": 498671,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_502767_r18_502767_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_502767_r18_502767_k11_to2p18.json
index 9b68208..d70c056 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_502767_r18_502767_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_502767_r18_502767_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 502767,
     "r18_parent": 502767,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_508911_r18_508911_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_508911_r18_508911_k11_to2p18.json
index 700aaa6..9d2a2c2 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_508911_r18_508911_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_508911_r18_508911_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 508911,
     "r18_parent": 508911,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_510143_r18_510143_k7_to2p12.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_510143_r18_510143_k7_to2p12.json
index 9142d8a..f379362 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_510143_r18_510143_k7_to2p12.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_510143_r18_510143_k7_to2p12.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 510143,
     "r18_parent": 510143,
     "k": 7,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_513019_r18_513019_k7_to2p12.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_513019_r18_513019_k7_to2p12.json
index 10dcb5d..747b6d0 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_513019_r18_513019_k7_to2p12.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_513019_r18_513019_k7_to2p12.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 513019,
     "r18_parent": 513019,
     "k": 7,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_513055_r18_513055_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_513055_r18_513055_k10_to2p16.json
index 4d43608..f6ead30 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_513055_r18_513055_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_513055_r18_513055_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 513055,
     "r18_parent": 513055,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_513919_r18_513919_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_513919_r18_513919_k11_to2p18.json
index 0dc278a..3be1033 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_513919_r18_513919_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_513919_r18_513919_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 513919,
     "r18_parent": 513919,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_515931_r18_515931_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_515931_r18_515931_k10_to2p16.json
index 965b6cf..30f599e 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_515931_r18_515931_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_515931_r18_515931_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 515931,
     "r18_parent": 515931,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_515967_r18_515967_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_515967_r18_515967_k10_to2p16.json
index 80a583d..678998f 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_515967_r18_515967_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_515967_r18_515967_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 515967,
     "r18_parent": 515967,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_518311_r18_518311_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_518311_r18_518311_k10_to2p16.json
index f66c43a..3204d65 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_518311_r18_518311_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_518311_r18_518311_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 518311,
     "r18_parent": 518311,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_520027_r18_520027_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_520027_r18_520027_k11_to2p18.json
index de4d72f..06ef508 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_520027_r18_520027_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_520027_r18_520027_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 520027,
     "r18_parent": 520027,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_520359_r18_520359_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_520359_r18_520359_k11_to2p18.json
index 5310b4e..202288d 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_520359_r18_520359_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_520359_r18_520359_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 520359,
     "r18_parent": 520359,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_523295_r18_523295_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_523295_r18_523295_k11_to2p18.json
index a56f43a..24edb0b 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_523295_r18_523295_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_523295_r18_523295_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 523295,
     "r18_parent": 523295,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_55343_r18_55343_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_55343_r18_55343_k11_to2p18.json
index bc92471..aa119b4 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_55343_r18_55343_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_55343_r18_55343_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 55343,
     "r18_parent": 55343,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_55911_r18_55911_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_55911_r18_55911_k11_to2p18.json
index 3c1321e..cdc309b 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_55911_r18_55911_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_55911_r18_55911_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 55911,
     "r18_parent": 55911,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_5823_r18_5823_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_5823_r18_5823_k10_to2p16.json
index ad69efc..573d430 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_5823_r18_5823_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_5823_r18_5823_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 5823,
     "r18_parent": 5823,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_58599_r18_58599_k9_to2p15.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_58599_r18_58599_k9_to2p15.json
index c235f94..6908656 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_58599_r18_58599_k9_to2p15.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_58599_r18_58599_k9_to2p15.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 58599,
     "r18_parent": 58599,
     "k": 9,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_58623_r18_58623_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_58623_r18_58623_k11_to2p18.json
index 76e5724..76f876e 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_58623_r18_58623_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_58623_r18_58623_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 58623,
     "r18_parent": 58623,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_60671_r18_60671_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_60671_r18_60671_k11_to2p18.json
index a3389e9..08d4cb3 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_60671_r18_60671_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_60671_r18_60671_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 60671,
     "r18_parent": 60671,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_62695_r18_62695_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_62695_r18_62695_k11_to2p18.json
index 5ff706c..1335eee 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_62695_r18_62695_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_62695_r18_62695_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 62695,
     "r18_parent": 62695,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_62719_r18_62719_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_62719_r18_62719_k10_to2p16.json
index 87c932c..cc98c54 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_62719_r18_62719_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_62719_r18_62719_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 62719,
     "r18_parent": 62719,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_6367_r18_6367_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_6367_r18_6367_k11_to2p18.json
index c1da6b9..91020d6 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_6367_r18_6367_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_6367_r18_6367_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 6367,
     "r18_parent": 6367,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_65951_r18_65951_k9_to2p15.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_65951_r18_65951_k9_to2p15.json
index 169e0a7..af35886 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_65951_r18_65951_k9_to2p15.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_65951_r18_65951_k9_to2p15.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 65951,
     "r18_parent": 65951,
     "k": 9,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_66791_r18_66791_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_66791_r18_66791_k11_to2p18.json
index 7ec39f4..5c46a1c 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_66791_r18_66791_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_66791_r18_66791_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 66791,
     "r18_parent": 66791,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_67655_r18_67655_k9_to2p15.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_67655_r18_67655_k9_to2p15.json
index dbccda8..267985c 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_67655_r18_67655_k9_to2p15.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_67655_r18_67655_k9_to2p15.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 67655,
     "r18_parent": 67655,
     "k": 9,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_69147_r18_69147_k9_to2p15.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_69147_r18_69147_k9_to2p15.json
index 0319d23..44c85c3 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_69147_r18_69147_k9_to2p15.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_69147_r18_69147_k9_to2p15.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 69147,
     "r18_parent": 69147,
     "k": 9,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_69703_r18_69703_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_69703_r18_69703_k11_to2p18.json
index 7d66010..32f6ade 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_69703_r18_69703_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_69703_r18_69703_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 69703,
     "r18_parent": 69703,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_70047_r18_70047_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_70047_r18_70047_k11_to2p18.json
index e04298f..6314b66 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_70047_r18_70047_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_70047_r18_70047_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 70047,
     "r18_parent": 70047,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_70639_r18_70639_k8_to2p13.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_70639_r18_70639_k8_to2p13.json
index 7a2f0d8..9bd6745 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_70639_r18_70639_k8_to2p13.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_70639_r18_70639_k8_to2p13.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 70639,
     "r18_parent": 70639,
     "k": 8,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_73243_r18_73243_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_73243_r18_73243_k11_to2p18.json
index 0c07a03..eefc74c 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_73243_r18_73243_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_73243_r18_73243_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 73243,
     "r18_parent": 73243,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_74143_r18_74143_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_74143_r18_74143_k11_to2p18.json
index 1b73ed1..5941341 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_74143_r18_74143_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_74143_r18_74143_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 74143,
     "r18_parent": 74143,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_75847_r18_75847_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_75847_r18_75847_k11_to2p18.json
index 1b9e90d..b74a278 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_75847_r18_75847_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_75847_r18_75847_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 75847,
     "r18_parent": 75847,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_76783_r18_76783_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_76783_r18_76783_k10_to2p16.json
index 9cf089e..bf7aceb 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_76783_r18_76783_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_76783_r18_76783_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 76783,
     "r18_parent": 76783,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_77339_r18_77339_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_77339_r18_77339_k11_to2p18.json
index 70958e1..a96be1e 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_77339_r18_77339_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_77339_r18_77339_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 77339,
     "r18_parent": 77339,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_79719_r18_79719_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_79719_r18_79719_k11_to2p18.json
index 38f277a..535a7b5 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_79719_r18_79719_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_79719_r18_79719_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 79719,
     "r18_parent": 79719,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_82927_r18_82927_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_82927_r18_82927_k10_to2p16.json
index 255583d..638fe72 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_82927_r18_82927_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_82927_r18_82927_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 82927,
     "r18_parent": 82927,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_84039_r18_84039_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_84039_r18_84039_k11_to2p18.json
index 40a07bd..fab332b 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_84039_r18_84039_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_84039_r18_84039_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 84039,
     "r18_parent": 84039,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_87899_r18_87899_k8_to2p13.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_87899_r18_87899_k8_to2p13.json
index c842676..030e781 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_87899_r18_87899_k8_to2p13.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_87899_r18_87899_k8_to2p13.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 87899,
     "r18_parent": 87899,
     "k": 8,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_87935_r18_87935_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_87935_r18_87935_k10_to2p16.json
index ae2468e..cdba759 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_87935_r18_87935_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_87935_r18_87935_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 87935,
     "r18_parent": 87935,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_88219_r18_88219_k7_to2p12.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_88219_r18_88219_k7_to2p12.json
index fb6ba4f..bef9aca 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_88219_r18_88219_k7_to2p12.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_88219_r18_88219_k7_to2p12.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 88219,
     "r18_parent": 88219,
     "k": 7,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_92031_r18_92031_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_92031_r18_92031_k11_to2p18.json
index f5358ca..6a34f4d 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_92031_r18_92031_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_92031_r18_92031_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 92031,
     "r18_parent": 92031,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_9375_r18_9375_k9_to2p15.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_9375_r18_9375_k9_to2p15.json
index dee2d3e..641679a 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_9375_r18_9375_k9_to2p15.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_9375_r18_9375_k9_to2p15.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 9375,
     "r18_parent": 9375,
     "k": 9,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_94043_r18_94043_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_94043_r18_94043_k10_to2p16.json
index baa43a5..440dff3 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_94043_r18_94043_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_94043_r18_94043_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 94043,
     "r18_parent": 94043,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_95263_r18_95263_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_95263_r18_95263_k11_to2p18.json
index 97bc62f..7ac2b70 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_95263_r18_95263_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_95263_r18_95263_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 95263,
     "r18_parent": 95263,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_96423_r18_96423_k9_to2p15.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_96423_r18_96423_k9_to2p15.json
index c33c22a..b92fdcf 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_96423_r18_96423_k9_to2p15.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_96423_r18_96423_k9_to2p15.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 96423,
     "r18_parent": 96423,
     "k": 9,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_97311_r18_97311_k10_to2p16.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_97311_r18_97311_k10_to2p16.json
index 5a41039..7ea0473 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_97311_r18_97311_k10_to2p16.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_97311_r18_97311_k10_to2p16.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 97311,
     "r18_parent": 97311,
     "k": 10,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_98175_r18_98175_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_98175_r18_98175_k11_to2p18.json
index 3968f76..c812e73 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_98175_r18_98175_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_98175_r18_98175_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 98175,
     "r18_parent": 98175,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_98471_r18_98471_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_98471_r18_98471_k11_to2p18.json
index e82a557..8851458 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_98471_r18_98471_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_98471_r18_98471_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 98471,
     "r18_parent": 98471,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_9883_r18_9883_k11_to2p18.json b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_9883_r18_9883_k11_to2p18.json
index 47915c4..17ed2d5 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_9883_r18_9883_k11_to2p18.json
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_9883_r18_9883_k11_to2p18.json
@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 20,
     "r19_chain": 9883,
     "r18_parent": 9883,
     "k": 11,
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/option_a_extension_m24_report.md b/docs/artefacts/collatz/refinement_K/palier2p15/option_a_extension_m24_report.md
index 9374796..9d8d9af 100644
--- a/docs/artefacts/collatz/refinement_K/palier2p15/option_a_extension_m24_report.md
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/option_a_extension_m24_report.md
@@ -45,5 +45,6 @@ L'extension à M_max=24 n'a pas réduit tracked.max ni tracked.p99. Les 1101 rac
 ## Optimisations mémoire appliquées
 
 - Mode streaming pour la génération des clauses terminales (palier ≥ 20)
-- Format `.residues.json` pour chargement allégé dans le multilevel
+- Format `.residues.json` pour chargement allégé (streaming ijson)
+- `ResidueBitset` pour `leaves_by_m` et `closed` quand m ≥ 20 dans le multilevel
 - Script `collatz_extract_residues_from_clauses_json.py` pour extraction par flux
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/option_b_hensel_m20_m21_report.md b/docs/artefacts/collatz/refinement_K/palier2p15/option_b_hensel_m20_m21_report.md
new file mode 100644
index 0000000..6441921
--- /dev/null
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/option_b_hensel_m20_m21_report.md
@@ -0,0 +1,29 @@
+**Auteur** : Équipe 4NK
+
+# Option B — Hensel décalée start_m=20, 21
+
+## Contexte
+
+Extension de la Phase 3 : exécution de la chaîne Hensel décalée avec `--start-m 20` et `--start-m 21` en plus de `--start-m 19`.
+
+## Artefacts
+
+- `clauses_hensel_chain_leaves_shifted_mod2p20.json` : 1373 résidus fermés à m=20
+- `clauses_hensel_chain_leaves_shifted_mod2p21.json` : 1373 résidus fermés à m=21
+
+## Métriques (bundle terminal + Hensel 19+20+21)
+
+| Métrique | Valeur |
+|----------|--------|
+| closed_roots | 15283 |
+| open_roots | 1101 |
+| tracked.max | 136 |
+| tracked.p99 | 128 |
+
+## Conclusion
+
+Les Hensel start_m=20 et start_m=21 produisent chacun 1373 résidus fermés, identiques en structure à start_m=19. L’ajout au bundle ne modifie pas les métriques : closed_roots, open_roots, tracked.max et tracked.p99 restent identiques à l’Option A (Hensel m=19 seul). Les 248 racines fermées par rapport au baseline proviennent déjà de Hensel m=19.
+
+## Optimisation mémoire appliquée
+
+- `collatz_build_hensel_chain_leaves_shifted.py` : chargement prioritaire de `.residues.json` (streaming ijson) pour les clauses terminales ; `_ResidueBitset` pour palier ≥ 20.
diff --git a/docs/artefacts/collatz/refinement_K/palier2p15/option_c_diagnostic_top200_report.md b/docs/artefacts/collatz/refinement_K/palier2p15/option_c_diagnostic_top200_report.md
new file mode 100644
index 0000000..b0f6a39
--- /dev/null
+++ b/docs/artefacts/collatz/refinement_K/palier2p15/option_c_diagnostic_top200_report.md
@@ -0,0 +1,26 @@
+**Auteur** : Équipe 4NK
+
+# Option C — Diagnostic ciblé top 200
+
+## Contexte
+
+Le diagnostic ciblé analyse les racines du top 200 par `lb_any` (liste fixe `tracked_roots_lb_any_top200_mod2p15_to2p18.txt`) pour identifier la cause racine de l’échec des certificats targeted leaves.
+
+## Exécution
+
+Le diagnostic est produit par `collatz_build_refinement_bundle_over_Sm_multilevel.py` avec `--tracked-roots-file`. Script sous-jacent : `collatz_diagnose_targeted_leaves_failure.py`.
+
+## Artefacts
+
+- `bundle_mod2p15_to2p24_hensel_b/diagnostic_targeted_leaves_failure_mod2p15.{json,md}`
+- Colonnes : root, child_low, child_high, immediate_low@16, immediate_high@16, lb_root, lb_low, lb_high
+
+## Résultat
+
+Sur les racines suivies, **les deux enfants** à m=16 sont en `no/no` (aucune clause terminale immédiatement décidable). Exemples : root=2887 (lb_root=136), root=12359 (lb_root=130), root=4735 (lb_root=128).
+
+La fermeture par raffinement binaire impose un arbre de taille \(2^{(lb\_root-16)}\) nœuds au minimum ; pour lb_root=136, explosion combinatoire hors de portée.
+
+## Référence
+
+- `docs/features/collatz_targeted_leaves_and_diagnostics.md` : interprétation mathématique, guidage pour grammaire plus puissante
diff --git a/docs/features/collatz_grammar_extensions_implementation_plan.md b/docs/features/collatz_grammar_extensions_implementation_plan.md
index 2db86d3..07ea88f 100644
--- a/docs/features/collatz_grammar_extensions_implementation_plan.md
+++ b/docs/features/collatz_grammar_extensions_implementation_plan.md
@@ -71,6 +71,8 @@ Réduire `tracked.max` et `tracked.p99` sur la liste fixe `tracked_roots_lb_any_
 
 **Critère de succès.** Au moins une racine fermée par certificat chaîne Hensel.
 
+**Exécution (2026-03).** Phase 3 implémentée : `collatz_build_hensel_chain_leaves_shifted.py` avec `--start-m 19` : 1373 résidus fermés à m=19, open_roots 1349→1101 (−248). Options A et B : extension à M_max=24, Hensel start_m=20,21 — aucun impact supplémentaire sur tracked.max/p99. Rapports : `option_a_extension_m24_report.md`, `option_b_hensel_m20_m21_report.md`.
+
 ---
 
 ### Phase 4 : Clause \(D\) partielle (Piste 4) — recherche formelle
@@ -109,6 +111,13 @@ Chaque phase produit :
 - Mise à jour de `docs/features/` et de `applications/collatz/conjoncture_collatz.md` pour les nouvelles règles et indexations.
 - Rapport de métriques (tracked.max, tracked.p99, open_roots, q_m) avant/après.
 
+## Rapports d'exécution
+
+- Phase 1+3 : `docs/artefacts/collatz/refinement_K/palier2p15/phase1_grammar_extensions_report.md`
+- Option A (M_max=24) : `docs/artefacts/collatz/refinement_K/palier2p15/option_a_extension_m24_report.md`
+- Option B (Hensel start_m=20,21) : `docs/artefacts/collatz/refinement_K/palier2p15/option_b_hensel_m20_m21_report.md`
+- Option C (diagnostic ciblé top 200) : `docs/artefacts/collatz/refinement_K/palier2p15/option_c_diagnostic_top200_report.md`
+
 ## Références
 
 - `these/livre_jeune_adulte.md` : Ch. 2 (dette d'hypothèse, raffinement d'observabilité), Ch. 16 (stabilité sous raffinement, indexation)
diff --git a/docs/features/collatz_hensel_chain_shifted_phase3.md b/docs/features/collatz_hensel_chain_shifted_phase3.md
index c4fda09..12e54da 100644
--- a/docs/features/collatz_hensel_chain_shifted_phase3.md
+++ b/docs/features/collatz_hensel_chain_shifted_phase3.md
@@ -15,7 +15,7 @@ La Piste 3 échouait car les frères à m=16 ne sont pas fermables. Avec Phase 1
 `applications/collatz/collatz_k_scripts/collatz_build_hensel_chain_leaves_shifted.py`
 
 **Paramètres** :
-- `--start-m 19` : niveau de démarrage de la chaîne
+- `--start-m 19|20|21` : niveau de démarrage de la chaîne
 - `--leaf-json` : chemins vers terminal + D_minor (par défaut : palier 19–21 + D_minor m=20,21)
 
 **Sorties** :
@@ -28,6 +28,17 @@ La Piste 3 échouait car les frères à m=16 ne sont pas fermables. Avec Phase 1
 - open_roots : 1349 → 1101 (−248)
 - tracked.max, tracked.p99 : inchangés (les racines fermées ne sont pas dans le top 200 par lb_any)
 
+## Option B (start_m=20, 21)
+
+- 1373 résidus fermés à m=20 et à m=21 (même structure qu’à m=19)
+- Aucun impact supplémentaire : closed_roots, open_roots, tracked.max, tracked.p99 inchangés
+- Rapport : `docs/artefacts/collatz/refinement_K/palier2p15/option_b_hensel_m20_m21_report.md`
+
+## Optimisation mémoire
+
+- Chargement prioritaire de `.residues.json` (streaming ijson) pour les clauses terminales
+- `_ResidueBitset` pour `leaves_by_m` quand palier ≥ 20
+
 ## Références
 
 - `docs/features/collatz_grammar_extensions_implementation_plan.md` : Phase 3
diff --git a/docs/features/collatz_targeted_leaves_and_diagnostics.md b/docs/features/collatz_targeted_leaves_and_diagnostics.md
index 254f9ae..f789c6d 100644
--- a/docs/features/collatz_targeted_leaves_and_diagnostics.md
+++ b/docs/features/collatz_targeted_leaves_and_diagnostics.md
@@ -68,6 +68,13 @@ La Phase 1 a été exécutée : clauses terminales D/F pour m=15..21 (k_max=t_ma
 
 Script `collatz_build_hensel_chain_leaves_shifted.py` : chaîne Hensel démarrant à m=19 pour les résidus dont le frère à m=19 est fermable. 1373 résidus fermés à m=19. open_roots : 1349 → 1101 (−248). tracked.max/p99 inchangés (les racines fermées ne sont pas dans le top 200).
 
+### Option A + B exécutées
+
+- Option A : extension à M_max=24, D_minor m=22,23,24. Aucun impact sur tracked.max/p99. Rapport : `option_a_extension_m24_report.md`.
+- Option B : Hensel start_m=20,21. Aucun impact supplémentaire. Rapport : `option_b_hensel_m20_m21_report.md`.
+
+Le diagnostic ciblé est exécuté par le bundle avec `--tracked-roots-file` ; sortie : `diagnostic_targeted_leaves_failure_mod2p15.md` dans le répertoire du bundle.
+
 ## Guidage pour une grammaire plus puissante
 
 Une grammaire réduisant effectivement `tracked.max/p99` doit introduire une règle/feuille capable de :
diff --git a/docs/features/collatz_terminal_clauses_memory_optimization.md b/docs/features/collatz_terminal_clauses_memory_optimization.md
index 50cf401..2a59bfb 100644
--- a/docs/features/collatz_terminal_clauses_memory_optimization.md
+++ b/docs/features/collatz_terminal_clauses_memory_optimization.md
@@ -27,7 +27,14 @@ La génération des clauses terminales pour les paliers élevés (m ≥ 22) prov
 
 ### collatz_build_refinement_certificate_over_Sm_multilevel.py
 
-- `json.load(f)` au lieu de `json.loads(path.read_text())` — évite de charger la chaîne complète en mémoire avant parsing.
+- Chargement prioritaire de `.residues.json` (streaming ijson) au lieu du JSON complet.
+- `ResidueBitset` pour `leaves_by_m` et `closed` quand m ≥ 20 (≈1 Mo par palier au lieu de centaines de Mo).
+- `json.load(f)` au lieu de `json.loads(path.read_text())` pour le fallback.
+
+### collatz_build_hensel_chain_leaves_shifted.py
+
+- Chargement prioritaire de `.residues.json` pour les clauses terminales (streaming ijson).
+- `_ResidueBitset` pour `leaves_by_m` quand palier ≥ 20.
 
 ## Format compact .residues.json