collatz: update scripts, conjoncture, hensel_b bundle and certs_shifted

**Motivations:**
- Sync refinement bundle script, hensel chain shifted, conjoncture and artefacts.

**Root causes:** N/A
**Correctifs:** N/A
**Evolutions:**
- collatz_build_hensel_chain_leaves_shifted.py
- collatz_build_refinement_bundle_over_Sm_multilevel.py
- README.md, conjoncture_collatz.md
- bundle_mod2p15_to2p24_hensel_b, certs_shifted

**Pages affectées:**
- applications/collatz/collatz_k_scripts/
- applications/collatz/conjoncture_collatz.md
- docs/artefacts/collatz/refinement_K/

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|20|21 (`--start-m`) pour résidus dont le frère est fermable. Charge `.residues.json` en priorité (mémoire).
+- `collatz_build_hensel_chain_leaves_shifted.py` : chaîne Hensel décalée (Phase 3), démarrage à m=19..24 (`--start-m`). Charge `.residues.json` et D_minor > 50 Mo en flux ; `--leaf-list-file` pour éviter CLI long.
-- `collatz_build_refinement_bundle_over_Sm_multilevel.py` : pipeline “1 commande” (fermeture multi-niveaux + profil d’obstruction + diagnostic ciblé optionnel).
+- `collatz_build_refinement_bundle_over_Sm_multilevel.py` : pipeline “1 commande” (fermeture multi-niveaux + profil d’obstruction + diagnostic ciblé optionnel). `--leaf-list-file` pour chemins depuis un fichier.

applications/collatz/collatz_k_scripts/collatz_build_hensel_chain_leaves_shifted.py

@@ -13,12 +13,16 @@ we try to build a Hensel chain from the other child to m_end. Output: leaves at
 from __future__ import annotations
 
 import argparse
+import gc
 import hashlib
 import json
 import re
 from dataclasses import dataclass
 from pathlib import Path
 
+# (k, u, Bk, Akm1, Ckm1, N0) - compact D_minor, Leaf created on demand
+_DMinorData = tuple[int, int, int, int, int, int]
+
 from collatz_k_core import (
     delta_D,
     delta_F,
@@ -206,36 +210,65 @@ def _load_residues_streaming(residues_path: Path, palier: int) -> set[int] | _Re
     return residues
 
 
-def _load_leaf_sets(*, leaf_json_paths: list[Path]) -> tuple[dict[int, set[int] | _ResidueBitset], dict[tuple[int, int], Leaf]]:
+_STREAM_THRESHOLD_MB = 50
-    """Load leaf sets and D_minor leaf map. Uses .residues.json when available for terminal clauses."""
-    leaves_by_m: dict[int, set[int] | _ResidueBitset] = {}
-    dminor_leaf_map: dict[tuple[int, int], Leaf] = {}
 
-    for p in leaf_json_paths:
+
-        residues_path = p.with_name(p.stem + ".residues.json")
+def _load_dminor_streaming(
-        if "clauses_terminal" in p.name and residues_path.exists():
+    path: Path,
-            with residues_path.open("rb") as f:
+    leaves_by_m: dict[int, set[int] | _ResidueBitset],
-                head = f.read(80)
+    dminor_leaf_map: dict[tuple[int, int], Leaf],
+) -> None:
+    """Stream-load large D_minor JSON to avoid OOM."""
+    try:
+        import ijson
+    except ImportError:
+        obj = _read_json(path)
+        _merge_dminor_obj(obj, leaves_by_m, dminor_leaf_map)
+        return
+    with path.open("rb") as f:
+        head = f.read(200)
     match = re.search(rb'"palier"\s*:\s*(\d+)', head)
-            if match:
+    palier = int(match.group(1)) if match else 0
-                palier = int(match.group(1))
+    if palier <= 0:
-                residues = _load_residues_streaming(residues_path, palier)
+        return
     if palier not in leaves_by_m:
         leaves_by_m[palier] = _ResidueBitset(palier) if palier >= 20 else set()
-                leaves_by_m[palier].update(residues)
+    f.seek(0)
+    for c in ijson.items(f, "clauses.item"):
+        if not isinstance(c, dict) or c.get("kind") != "D_minor":
             continue
-        obj = _read_json(p)
+        r = c.get("residue_mod_2p")
+        if not isinstance(r, int):
+            continue
+        k = c.get("k")
+        u = c.get("underlineA")
+        Bk = c.get("numerator_B_k")
+        Akm1 = c.get("A_km1")
+        Ckm1 = c.get("C_km1")
+        N0 = c.get("N0")
+        if not all(isinstance(x, int) for x in (k, u, Bk, Akm1, Ckm1, N0)):
+            continue
+        leaves_by_m[palier].add(r)
+        dminor_leaf_map[(palier, r)] = (k, u, Bk, Akm1, Ckm1, N0)
+
+
+def _merge_dminor_obj(
+    obj: object,
+    leaves_by_m: dict[int, set[int] | _ResidueBitset],
+    dminor_leaf_map: dict[tuple[int, int], Leaf | _DMinorData],
+) -> None:
+    """Merge D_minor object into leaves_by_m and dminor_leaf_map."""
     if not isinstance(obj, dict):
-            continue
+        return
     domain = obj.get("domain")
     if not isinstance(domain, dict):
-            continue
+        return
     palier = domain.get("palier")
     if not isinstance(palier, int):
-            continue
+        return
     clauses = obj.get("clauses")
     if not isinstance(clauses, list):
-            continue
+        return
     for c in clauses:
         if not isinstance(c, dict):
             continue
@@ -252,25 +285,47 @@ def _load_leaf_sets(*, leaf_json_paths: list[Path]) -> tuple[dict[int, set[int]
             Akm1 = c.get("A_km1")
             Ckm1 = c.get("C_km1")
             N0 = c.get("N0")
-                if (
+            if all(isinstance(x, int) for x in (k, u, Bk, Akm1, Ckm1, N0)):
-                    isinstance(k, int)
+                dminor_leaf_map[(palier, r)] = (k, u, Bk, Akm1, Ckm1, N0)
-                    and isinstance(u, int)
+
-                    and isinstance(Bk, int)
+
-                    and isinstance(Akm1, int)
+def _load_leaf_sets(*, leaf_json_paths: list[Path]) -> tuple[dict[int, set[int] | _ResidueBitset], dict[tuple[int, int], Leaf]]:
-                    and isinstance(Ckm1, int)
+    """Load leaf sets and D_minor leaf map. Uses .residues.json for terminal, streaming for large D_minor."""
-                    and isinstance(N0, int)
+    leaves_by_m: dict[int, set[int] | _ResidueBitset] = {}
-                ):
+    dminor_leaf_map: dict[tuple[int, int], Leaf] = {}
-                    leaf = Leaf(
+
+    for p in leaf_json_paths:
+        residues_path = p.with_name(p.stem + ".residues.json")
+        if "clauses_terminal" in p.name and residues_path.exists():
+            with residues_path.open("rb") as f:
+                head = f.read(80)
+            match = re.search(rb'"palier"\s*:\s*(\d+)', head)
+            if match:
+                palier = int(match.group(1))
+                residues = _load_residues_streaming(residues_path, palier)
+                if palier not in leaves_by_m:
+                    leaves_by_m[palier] = _ResidueBitset(palier) if palier >= 20 else set()
+                leaves_by_m[palier].update(residues)
+                continue
+        if "D_minor" in p.name and p.stat().st_size > _STREAM_THRESHOLD_MB * 1024 * 1024:
+            _load_dminor_streaming(p, leaves_by_m, dminor_leaf_map)
+            continue
+        obj = _read_json(p)
+        _merge_dminor_obj(obj, leaves_by_m, dminor_leaf_map)
+    return leaves_by_m, dminor_leaf_map
+
+
+def _dminor_data_to_leaf(m: int, r: int, data: _DMinorData) -> Leaf:
+    k, u, Bk, Akm1, Ckm1, N0 = data
+    return Leaf(
         kind="D_minor",
-                        m=palier,
+        m=m,
         r=r,
         k_or_t=k,
         A=None,
         threshold=N0,
         extra={"underlineA": u, "A_km1": Akm1, "C_km1": Ckm1, "B_k": Bk},
     )
-                    dminor_leaf_map[(palier, r)] = leaf
-    return leaves_by_m, dminor_leaf_map
 
 
 def _sibling_leaf(
@@ -280,14 +335,19 @@ def _sibling_leaf(
     k_max: int,
     t_max: int,
     leaves_by_m: dict[int, set[int] | _ResidueBitset],
-    dminor_leaf_map: dict[tuple[int, int], Leaf],
+    dminor_leaf_map: dict[tuple[int, int], Leaf | _DMinorData],
 ) -> Leaf | None:
     """Return a leaf for the sibling: D/F first, then D_minor from map."""
     leaf = _leaf_for_sibling(residue=residue, m=m, k_max=k_max, t_max=t_max)
     if leaf is not None:
         return leaf
     if residue in leaves_by_m.get(m, set()):
-        return dminor_leaf_map.get((m, residue))
+        val = dminor_leaf_map.get((m, residue))
+        if val is None:
+            return None
+        if isinstance(val, tuple):
+            return _dminor_data_to_leaf(m, residue, val)
+        return val
     return None
 
 
@@ -357,7 +417,10 @@ def run(
     lines.append("| --- | --- | --- | --- | --- | --- |")
 
     ok = 0
+    gc_interval = 1 << 18
     for r_parent in range(1, 1 << (start_m - 1), 2):
+        if r_parent > 1 and (r_parent - 1) % gc_interval == 0:
+            gc.collect()
         r_low = r_parent
         r_high = r_parent + step_parent
         low_in = r_low in leaf_set_19
@@ -482,6 +545,7 @@ def main() -> None:
     ap.add_argument("--repo-root", default=".", help="Repository root")
     ap.add_argument("--start-m", type=int, default=19)
     ap.add_argument("--leaf-json", action="append", default=[], help="Leaf JSON path (terminal + D_minor)")
+    ap.add_argument("--leaf-list-file", default="", help="File with one leaf JSON path per line (avoids long CLI)")
     ap.add_argument("--k-chain-max", type=int, default=80)
     ap.add_argument("--k-leaf-max", type=int, default=256)
     ap.add_argument("--t-leaf-max", type=int, default=256)
@@ -491,6 +555,13 @@ def main() -> None:
     repo_root = Path(args.repo_root).resolve()
     start_m = int(args.start_m)
     leaf_paths = [Path(p).resolve() for p in args.leaf_json] if args.leaf_json else []
+    if args.leaf_list_file:
+        list_path = Path(args.leaf_list_file).resolve()
+        if list_path.exists():
+            for line in list_path.read_text(encoding="utf-8").splitlines():
+                p = line.strip()
+                if p and not p.startswith("#"):
+                    leaf_paths.append(Path(p).resolve() if Path(p).is_absolute() else (repo_root / p).resolve())
     if not leaf_paths:
         base = repo_root / "docs" / "artefacts" / "collatz"
         leaf_paths = [

applications/collatz/collatz_k_scripts/collatz_build_refinement_bundle_over_Sm_multilevel.py

@@ -167,6 +167,7 @@ def main() -> None:
     ap.add_argument("--root-palier", type=int, default=15)
     ap.add_argument("--max-palier", type=int, default=18)
     ap.add_argument("--leaf-json", action="append", default=[], help="Leaf JSON path (repeatable). If omitted, uses terminal_clauses_over_Sm for M..Mmax.")
+    ap.add_argument("--leaf-list-file", default="", help="File with one leaf JSON path per line (relative to repo-root)")
     ap.add_argument("--bundle-dir", default="", help="Bundle output directory (defaults under docs/artefacts/...)")
     ap.add_argument("--k-max", type=int, default=256)
     ap.add_argument("--t-max", type=int, default=256)
@@ -188,9 +189,15 @@ def main() -> None:
     root_palier = int(args.root_palier)
     max_palier = int(args.max_palier)
 
-    if args.leaf_json:
+    leaf_json: list[Path] = [Path(p).resolve() for p in args.leaf_json] if args.leaf_json else []
-        leaf_json = [Path(p).resolve() for p in args.leaf_json]
+    if args.leaf_list_file:
-    else:
+        list_path = Path(args.leaf_list_file).resolve()
+        if list_path.exists():
+            for line in list_path.read_text(encoding="utf-8").splitlines():
+                p = line.strip()
+                if p and not p.startswith("#"):
+                    leaf_json.append((repo_root / p).resolve())
+    if not leaf_json:
         leaf_json = [
             repo_root
             / "docs"

applications/collatz/conjoncture_collatz.md

@@ -2621,7 +2621,7 @@ On étend la projection à \(\Pi_{(M,s)}: n\mapsto (n\bmod 2^M,\, n\bmod 3^s)\)
 
 **Indexation.** La conclusion est indexée par le choix de \(s\), le choix de la projection (2-adique vs 3-adique), et le protocole de raffinement (ordre des splits).
 
-**Statut.** Proposition de recherche ; aucune implémentation ni artefact déterministe n'existe à ce jour.
+**Statut.** Phase 2 exécutée : partition par \(n\bmod 3^s\) ne stabilise pas \(y\bmod 3\). Rapport : `docs/artefacts/collatz/refinement_K/palier2p15/phase2_y_mod3_analysis_report.md`.
 
 ### Piste 2 : Clauses \(D_{\underline{}}\) à horizon plus long et paliers plus profonds
 
@@ -2634,7 +2634,7 @@ On génère des clauses \(D_{\underline{}}\) pour des \((k,\underline A)\) avec
 
 **Indexation.** La conclusion est indexée par \(k_{\max}\), \(M_{\max}\), et les familles \((k,\underline A)\) effectivement générées.
 
-**Statut.** Extension mécanique : réutiliser `collatz_generate_minorated_descent_clauses_over_Sm.py` et `collatz_build_refinement_certificate_over_Sm_multilevel.py` avec des paramètres étendus.
+**Statut.** Phase 1 et Option A exécutées : M_max=24, D_minor m=22,23,24. open_roots=1101, tracked.max=136, tracked.p99=128 (inchangés). Rapport : `docs/artefacts/collatz/refinement_K/palier2p15/option_a_extension_m24_report.md`.
 
 ### Piste 3 : Règle de chaîne Hensel (compression linéaire)
 
@@ -2649,7 +2649,7 @@ On définit une règle de type « chaîne Hensel » : au lieu de raffiner binair
 
 **Indexation.** La conclusion est indexée par \(k\), \(u_{\min}(k)\), et la disponibilité effective des clauses pour les frères le long de la chaîne.
 
-**Statut.** Tentative implémentée (`collatz_build_hensel_chain_leaves.py`) ; échec sur la liste fixe (0 racines fermées) car les frères ne sont pas fermables aux niveaux intermédiaires.
+**Statut.** Chaîne Hensel décalée implémentée (`collatz_build_hensel_chain_leaves_shifted.py`, start_m=19|20|21) : 1373 résidus fermés à m=19, open_roots 1349→1101 (−248). tracked.max/p99 inchangés (racines fermées hors top 200). Rapports : `docs/features/collatz_hensel_chain_shifted_phase3.md`, `option_b_hensel_m20_m21_report.md`.
 
 ### Piste 4 : Clause « \(D\) partielle » ou borne sur \(A(n)\)
 

docs/artefacts/collatz/refinement_K/palier2p15/bundle_leaf_list_hensel_full.txt

@@ -0,0 +1,17 @@
+# Bundle: terminal 15..24 + Hensel 19,20,21,22,23,24
+docs/artefacts/collatz/terminal_clauses_over_Sm/palier2p15/clauses_terminal_over_Sm_mod2p15.json
+docs/artefacts/collatz/terminal_clauses_over_Sm/palier2p16/clauses_terminal_over_Sm_mod2p16.json
+docs/artefacts/collatz/terminal_clauses_over_Sm/palier2p17/clauses_terminal_over_Sm_mod2p17.json
+docs/artefacts/collatz/terminal_clauses_over_Sm/palier2p18/clauses_terminal_over_Sm_mod2p18.json
+docs/artefacts/collatz/terminal_clauses_over_Sm/palier2p19/clauses_terminal_over_Sm_mod2p19.json
+docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/clauses_hensel_chain_leaves_shifted_mod2p19.json
+docs/artefacts/collatz/terminal_clauses_over_Sm/palier2p20/clauses_terminal_over_Sm_mod2p20.json
+docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/clauses_hensel_chain_leaves_shifted_mod2p20.json
+docs/artefacts/collatz/terminal_clauses_over_Sm/palier2p21/clauses_terminal_over_Sm_mod2p21.json
+docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/clauses_hensel_chain_leaves_shifted_mod2p21.json
+docs/artefacts/collatz/terminal_clauses_over_Sm/palier2p22/clauses_terminal_over_Sm_mod2p22.json
+docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/clauses_hensel_chain_leaves_shifted_mod2p22.json
+docs/artefacts/collatz/terminal_clauses_over_Sm/palier2p23/clauses_terminal_over_Sm_mod2p23.json
+docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/clauses_hensel_chain_leaves_shifted_mod2p23.json
+docs/artefacts/collatz/terminal_clauses_over_Sm/palier2p24/clauses_terminal_over_Sm_mod2p24.json
+docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/clauses_hensel_chain_leaves_shifted_mod2p24.json

docs/artefacts/collatz/refinement_K/palier2p15/bundle_mod2p15_to2p24_hensel_b/audit_refinement_certificate_Sm_multilevel_mod2p15_to2p24.json

@@ -413,7 +413,7 @@
       5991
     ]
   },
-  "generated_at": "2026-03-10T11:53:17.265227Z",
+  "generated_at": "2026-03-10T12:09:45.606012Z",
   "sha256": {
     "inputs": {
       "docs/artefacts/collatz/terminal_clauses_over_Sm/palier2p15/clauses_terminal_over_Sm_mod2p15.json": "148217541c4386d6c0b8282f273192abd780986b7c97b0505e48aec6bab22f27",
@@ -427,11 +427,12 @@
       "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/refinement_K/palier2p15/hensel_chain_leaves/clauses_hensel_chain_leaves_shifted_mod2p22.json": "3f43ad299f0755835e22f54860e24df9f50e019fd6c5e6476c495b6d2c45b19c",
       "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"
+      "docs/artefacts/collatz/refinement_K/palier2p15/bundle_mod2p15_to2p24_hensel_b/refinement_certificate_Sm_multilevel_mod2p15_to2p24.json": "501b43e72e7ead48ef5fa36c4e9536320921c75f33574a9088bb5a09e80db212"
     }
   }
 }

docs/artefacts/collatz/refinement_K/palier2p15/bundle_mod2p15_to2p24_hensel_b/refinement_certificate_Sm_multilevel_mod2p15_to2p24.json

@@ -17,11 +17,12 @@
       "/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/refinement_K/palier2p15/hensel_chain_leaves/clauses_hensel_chain_leaves_shifted_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",
+  "generated_at": "2026-03-10T12:09:45.606012Z",
   "sha256": {
     "inputs": {
       "docs/artefacts/collatz/terminal_clauses_over_Sm/palier2p15/clauses_terminal_over_Sm_mod2p15.json": "148217541c4386d6c0b8282f273192abd780986b7c97b0505e48aec6bab22f27",
@@ -35,6 +36,7 @@
       "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/refinement_K/palier2p15/hensel_chain_leaves/clauses_hensel_chain_leaves_shifted_mod2p22.json": "3f43ad299f0755835e22f54860e24df9f50e019fd6c5e6476c495b6d2c45b19c",
       "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"
     }
@@ -457,7 +459,7 @@
       "19": 12684,
       "20": 24407,
       "21": 46891,
-      "22": 87931,
+      "22": 86558,
       "23": 161870,
       "24": 301808
     },
@@ -468,8 +470,8 @@
       "18": 1.0,
       "19": 0.962117628508357,
       "20": 0.9606055639775474,
-      "21": 0.9376106289053336,
+      "21": 0.9229702928067219,
-      "22": 0.9204376158578885,
+      "22": 0.9350377781372028,
       "23": 0.9322542781244209
     },
     "parents_one_child_by_palier": {
@@ -480,7 +482,7 @@
       "19": 961,
       "20": 1923,
       "21": 7226,
-      "22": 13992,
+      "22": 12619,
       "23": 22037
     }
   },

docs/artefacts/collatz/refinement_K/palier2p15/bundle_mod2p15_to2p24_hensel_b/refinement_certificate_Sm_multilevel_mod2p15_to2p24.md

@@ -21,6 +21,7 @@
 - `/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/refinement_K/palier2p15/hensel_chain_leaves/clauses_hensel_chain_leaves_shifted_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`
 
@@ -55,8 +56,8 @@
 | 18 | 6342 | 1.000000000000 | 0 |
 | 19 | 12684 | 0.962117628508 | 961 |
 | 20 | 24407 | 0.960605563978 | 1923 |
-| 21 | 46891 | 0.937610628905 | 7226 |
+| 21 | 46891 | 0.922970292807 | 7226 |
-| 22 | 87931 | 0.920437615858 | 13992 |
+| 22 | 86558 | 0.935037778137 | 12619 |
 | 23 | 161870 | 0.932254278124 | 22037 |
 | 24 | 301808 |  |  |
 

docs/artefacts/collatz/refinement_K/palier2p15/bundle_mod2p15_to2p24_hensel_full/audit_refinement_certificate_Sm_multilevel_mod2p15_to2p24.json

@@ -0,0 +1,440 @@
+{
+  "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,
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+      301,
+      303,
+      305,
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+      423,
+      425,
+      427,
+      429,
+      431,
+      433
+    ],
+    "still_open_roots_sample": [
+      27,
+      31,
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+      63,
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+      103,
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+      763,
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+      859,
+      871,
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+      1255,
+      1263,
+      1279,
+      1307,
+      1343,
+      1383,
+      1407,
+      1439,
+      1471,
+      1503,
+      1519,
+      1535,
+      1583,
+      1639,
+      1663,
+      1691,
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+      1767,
+      1791,
+      1819,
+      1883,
+      1895,
+      1919,
+      1951,
+      1959,
+      2043,
+      2047,
+      2111,
+      2139,
+      2151,
+      2159,
+      2175,
+      2207,
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+      2287,
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+      2375,
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+      2463,
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+      2527,
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+      5915,
+      5991
+    ]
+  },
+  "generated_at": "2026-03-10T15:03:40.057229Z",
+  "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/refinement_K/palier2p15/hensel_chain_leaves/clauses_hensel_chain_leaves_shifted_mod2p22.json": "3f43ad299f0755835e22f54860e24df9f50e019fd6c5e6476c495b6d2c45b19c",
+      "docs/artefacts/collatz/terminal_clauses_over_Sm/palier2p23/clauses_terminal_over_Sm_mod2p23.json": "a90e3b1711f3f53b78cc2ed7e952638a32f5704b910673e402b07cc34e8c4a1f",
+      "docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/clauses_hensel_chain_leaves_shifted_mod2p23.json": "b21377d6446f69048a51aef86caf079e48aabd377bc03f57999b7763986a1dbe",
+      "docs/artefacts/collatz/terminal_clauses_over_Sm/palier2p24/clauses_terminal_over_Sm_mod2p24.json": "0aaa1cd14d567c192a1af5a21cfee8720c10ec291b7cda7ae02b7cfc69c4d5bd",
+      "docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/clauses_hensel_chain_leaves_shifted_mod2p24.json": "e48c16d040c14d4949e174a1fcddae3ccb580ec62bfc1eb03018011d8dc5eb17"
+    },
+    "outputs": {
+      "docs/artefacts/collatz/refinement_K/palier2p15/bundle_mod2p15_to2p24_hensel_full/refinement_certificate_Sm_multilevel_mod2p15_to2p24.json": "f1816482ac0867a64b2ff6097f57798b0a56203e6d48ae5c21cf73d5df27b232"
+    }
+  }
+}

docs/artefacts/collatz/refinement_K/palier2p15/bundle_mod2p15_to2p24_hensel_full/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
+

docs/artefacts/collatz/refinement_K/palier2p15/bundle_mod2p15_to2p24_hensel_full/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_full/diagnostic_targeted_leaves_failure_mod2p15.json`
+- Markdown : `/home/ncantu/code/algo/docs/artefacts/collatz/refinement_K/palier2p15/bundle_mod2p15_to2p24_hensel_full/diagnostic_targeted_leaves_failure_mod2p15.md`
+

docs/artefacts/collatz/refinement_K/palier2p15/bundle_mod2p15_to2p24_hensel_full/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_full/open_roots_obstruction_profile_mod2p15_to2p24.json`
+- Markdown : `/home/ncantu/code/algo/docs/artefacts/collatz/refinement_K/palier2p15/bundle_mod2p15_to2p24_hensel_full/open_roots_obstruction_profile_mod2p15_to2p24.md`
+

docs/artefacts/collatz/refinement_K/palier2p15/bundle_mod2p15_to2p24_hensel_full/refinement_certificate_Sm_multilevel_mod2p15_to2p24.md

@@ -0,0 +1,158 @@
+**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/refinement_K/palier2p15/hensel_chain_leaves/clauses_hensel_chain_leaves_shifted_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/refinement_K/palier2p15/hensel_chain_leaves/clauses_hensel_chain_leaves_shifted_mod2p23.json`
+- `/home/ncantu/code/algo/docs/artefacts/collatz/terminal_clauses_over_Sm/palier2p24/clauses_terminal_over_Sm_mod2p24.json`
+- `/home/ncantu/code/algo/docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/clauses_hensel_chain_leaves_shifted_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 | 0.922970292807 | 7226 |
+| 22 | 86558 | 0.927106679914 | 12619 |
+| 23 | 160497 | 0.935808769011 | 20664 |
+| 24 | 300389 |  |  |
+
+### 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_full/refinement_certificate_Sm_multilevel_mod2p15_to2p24.json`
+- Audit JSON : `/home/ncantu/code/algo/docs/artefacts/collatz/refinement_K/palier2p15/bundle_mod2p15_to2p24_hensel_full/audit_refinement_certificate_Sm_multilevel_mod2p15_to2p24.json`
+

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10000487_r18_1611879_k11_to2p18.json

@@ -0,0 +1,34 @@
+{
+  "domain": {
+    "start_m": 24,
+    "r19_chain": 10000487,
+    "r18_parent": 1611879,
+    "k": 11,
+    "m_end": 18
+  },
+  "params": {
+    "k_leaf_max": 256,
+    "t_leaf_max": 256,
+    "k_chain_max": 80
+  },
+  "chain": {
+    "u_min": 18,
+    "v2_L_r19": 24,
+    "steps": [],
+    "final": {
+      "kind": "D_minor",
+      "modulus_power": 18,
+      "residue_mod_2p": 10000487,
+      "k_or_t": 11,
+      "A": null,
+      "threshold": 4,
+      "extra": {
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+        "C_km1": 88577,
+        "B_k": 298499
+      }
+    }
+  }
+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_1001723_r18_1001723_k11_to2p18.json

@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 24,
     "r19_chain": 1001723,
     "r18_parent": 1001723,
     "k": 11,

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10017535_r18_1628927_k11_to2p18.json

@@ -0,0 +1,34 @@
+{
+  "domain": {
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+    "r19_chain": 10017535,
+    "r18_parent": 1628927,
+    "k": 11,
+    "m_end": 18
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+    "k_chain_max": 80
+  },
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+    "v2_L_r19": 24,
+    "steps": [],
+    "final": {
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+        "C_km1": 62377,
+        "B_k": 195323
+      }
+    }
+  }
+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10020091_r18_1631483_k11_to2p18.json

@@ -0,0 +1,34 @@
+{
+  "domain": {
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+    "r19_chain": 10020091,
+    "r18_parent": 1631483,
+    "k": 11,
+    "m_end": 18
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+    "t_leaf_max": 256,
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+    "steps": [],
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+        "C_km1": 119885,
+        "B_k": 392423
+      }
+    }
+  }
+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_1003239_r18_1003239_k9_to2p15.json

@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 24,
     "r19_chain": 1003239,
     "r18_parent": 1003239,
     "k": 9,

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10034203_r18_1645595_k11_to2p18.json

@@ -0,0 +1,34 @@
+{
+  "domain": {
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+    "r19_chain": 10034203,
+    "r18_parent": 1645595,
+    "k": 11,
+    "m_end": 18
+  },
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+    "t_leaf_max": 256,
+    "k_chain_max": 80
+  },
+  "chain": {
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+    "v2_L_r19": 24,
+    "steps": [],
+    "final": {
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+        "C_km1": 94253,
+        "B_k": 299143
+      }
+    }
+  }
+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10042727_r18_1654119_k11_to2p18.json

@@ -0,0 +1,34 @@
+{
+  "domain": {
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+    "r18_parent": 1654119,
+    "k": 11,
+    "m_end": 18
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+    "t_leaf_max": 256,
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+    "steps": [],
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+        "C_km1": 77057,
+        "B_k": 247555
+      }
+    }
+  }
+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10073791_r18_1685183_k11_to2p18.json

@@ -0,0 +1,34 @@
+{
+  "domain": {
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+    "r18_parent": 1685183,
+    "k": 11,
+    "m_end": 18
+  },
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+    "k_chain_max": 80
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+    "steps": [],
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+        "C_km1": 82409,
+        "B_k": 279995
+      }
+    }
+  }
+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10087239_r18_1698631_k10_to2p16.json

@@ -0,0 +1,34 @@
+{
+  "domain": {
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+    "r19_chain": 10087239,
+    "r18_parent": 1698631,
+    "k": 10,
+    "m_end": 16
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+        "C_km1": 35851,
+        "B_k": 123937
+      }
+    }
+  }
+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10094911_r18_1706303_k10_to2p16.json

@@ -0,0 +1,34 @@
+{
+  "domain": {
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+    "r19_chain": 10094911,
+    "r18_parent": 1706303,
+    "k": 10,
+    "m_end": 16
+  },
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+  },
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+    "steps": [],
+    "final": {
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+        "C_km1": 22819,
+        "B_k": 84841
+      }
+    }
+  }
+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10097279_r18_1708671_k11_to2p18.json

@@ -0,0 +1,34 @@
+{
+  "domain": {
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+    "r19_chain": 10097279,
+    "r18_parent": 1708671,
+    "k": 11,
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+        "C_km1": 61481,
+        "B_k": 200827
+      }
+    }
+  }
+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10103151_r18_1714543_k6_to2p10.json

@@ -0,0 +1,34 @@
+{
+  "domain": {
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+    "r19_chain": 10103151,
+    "r18_parent": 1714543,
+    "k": 6,
+    "m_end": 10
+  },
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+    "t_leaf_max": 256,
+    "k_chain_max": 80
+  },
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+    "steps": [],
+    "final": {
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+        "C_km1": 227,
+        "B_k": 745
+      }
+    }
+  }
+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_1011431_r18_1011431_k11_to2p18.json

@@ -1,6 +1,6 @@
 {
   "domain": {
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+    "start_m": 23,
     "r19_chain": 1011431,
     "r18_parent": 1011431,
     "k": 11,

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10116031_r18_1727423_k11_to2p18.json

@@ -0,0 +1,34 @@
+{
+  "domain": {
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+    "r19_chain": 10116031,
+    "r18_parent": 1727423,
+    "k": 11,
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+    "k_chain_max": 80
+  },
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+    "steps": [],
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+        "C_km1": 70889,
+        "B_k": 229051
+      }
+    }
+  }
+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10136487_r18_1747879_k11_to2p18.json

@@ -0,0 +1,34 @@
+{
+  "domain": {
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+    "r18_parent": 1747879,
+    "k": 11,
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+  },
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+        "C_km1": 124097,
+        "B_k": 388675
+      }
+    }
+  }
+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10140655_r18_1752047_k9_to2p15.json

@@ -0,0 +1,34 @@
+{
+  "domain": {
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+    "r19_chain": 10140655,
+    "r18_parent": 1752047,
+    "k": 9,
+    "m_end": 15
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+    "t_leaf_max": 256,
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+  },
+  "chain": {
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+    "steps": [],
+    "final": {
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+        "C_km1": 8113,
+        "B_k": 26387
+      }
+    }
+  }
+}

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": {
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+    "start_m": 22,
     "r19_chain": 101407,
     "r18_parent": 101407,
     "k": 11,

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10143591_r18_1754983_k11_to2p18.json

@@ -0,0 +1,34 @@
+{
+  "domain": {
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+    "r18_parent": 1754983,
+    "k": 11,
+    "m_end": 18
+  },
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+  },
+  "chain": {
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+    "final": {
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+        "C_km1": 74497,
+        "B_k": 227587
+      }
+    }
+  }
+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10144159_r18_1755551_k11_to2p18.json

@@ -0,0 +1,34 @@
+{
+  "domain": {
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+  },
+  "chain": {
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+    "steps": [],
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+        "C_km1": 85001,
+        "B_k": 271387
+      }
+    }
+  }
+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10149179_r18_1760571_k4_to2p7.json

@@ -0,0 +1,34 @@
+{
+  "domain": {
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+    "r19_chain": 10149179,
+    "r18_parent": 1760571,
+    "k": 4,
+    "m_end": 7
+  },
+  "params": {
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+    "t_leaf_max": 256,
+    "k_chain_max": 80
+  },
+  "chain": {
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+    "steps": [],
+    "final": {
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+        "C_km1": 23,
+        "B_k": 85
+      }
+    }
+  }
+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_1015835_r18_1015835_k11_to2p18.json

@@ -1,6 +1,6 @@
 {
   "domain": {
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+    "start_m": 24,
     "r19_chain": 1015835,
     "r18_parent": 1015835,
     "k": 11,

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10159407_r18_1770799_k8_to2p13.json

@@ -0,0 +1,34 @@
+{
+  "domain": {
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+    "r19_chain": 10159407,
+    "r18_parent": 1770799,
+    "k": 8,
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+  },
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+    "t_leaf_max": 256,
+    "k_chain_max": 80
+  },
+  "chain": {
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+    "steps": [],
+    "final": {
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+        "C_km1": 2939,
+        "B_k": 9841
+      }
+    }
+  }
+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10186399_r18_1797791_k10_to2p16.json

@@ -0,0 +1,34 @@
+{
+  "domain": {
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+    "r19_chain": 10186399,
+    "r18_parent": 1797791,
+    "k": 10,
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+  },
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+    "t_leaf_max": 256,
+    "k_chain_max": 80
+  },
+  "chain": {
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+    "v2_L_r19": 26,
+    "steps": [],
+    "final": {
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+      "k_or_t": 10,
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+        "C_km1": 21763,
+        "B_k": 73481
+      }
+    }
+  }
+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_1019623_r18_1019623_k11_to2p18.json

@@ -1,6 +1,6 @@
 {
   "domain": {
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+    "start_m": 24,
     "r19_chain": 1019623,
     "r18_parent": 1019623,
     "k": 11,

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_1020287_r18_1020287_k7_to2p12.json

@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 24,
     "r19_chain": 1020287,
     "r18_parent": 1020287,
     "k": 7,

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10212443_r18_1823835_k11_to2p18.json

@@ -0,0 +1,34 @@
+{
+  "domain": {
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+    "r19_chain": 10212443,
+    "r18_parent": 1823835,
+    "k": 11,
+    "m_end": 18
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+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10221819_r18_1833211_k11_to2p18.json

@@ -0,0 +1,34 @@
+{
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+        "B_k": 352487
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+    }
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+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10223335_r18_1834727_k8_to2p13.json

@@ -0,0 +1,34 @@
+{
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+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10257903_r18_1869295_k11_to2p18.json

@@ -0,0 +1,34 @@
+{
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+      }
+    }
+  }
+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_1026111_r18_1026111_k10_to2p16.json

@@ -1,6 +1,6 @@
 {
   "domain": {
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+    "start_m": 23,
     "r19_chain": 1026111,
     "r18_parent": 1026111,
     "k": 10,

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10275519_r18_1886911_k11_to2p18.json

@@ -0,0 +1,34 @@
+{
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+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10275769_r18_1887161_k11_to2p18.json

@@ -0,0 +1,34 @@
+{
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+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10279023_r18_1890415_k10_to2p16.json

@@ -0,0 +1,34 @@
+{
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+      }
+    }
+  }
+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10294555_r18_1905947_k11_to2p18.json

@@ -0,0 +1,34 @@
+{
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+      }
+    }
+  }
+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10296639_r18_1908031_k9_to2p15.json

@@ -0,0 +1,34 @@
+{
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+      }
+    }
+  }
+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10300143_r18_1911535_k11_to2p18.json

@@ -0,0 +1,34 @@
+{
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+      }
+    }
+  }
+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10306015_r18_1917407_k9_to2p15.json

@@ -0,0 +1,34 @@
+{
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+      }
+    }
+  }
+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10322399_r18_1933791_k11_to2p18.json

@@ -0,0 +1,34 @@
+{
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+      }
+    }
+  }
+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_1033119_r18_1033119_k11_to2p18.json

@@ -1,6 +1,6 @@
 {
   "domain": {
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     "r19_chain": 1033119,
     "r18_parent": 1033119,
     "k": 11,

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10336511_r18_1947903_k11_to2p18.json

@@ -0,0 +1,34 @@
+{
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+      }
+    }
+  }
+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10345887_r18_1957279_k11_to2p18.json

@@ -0,0 +1,34 @@
+{
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+      }
+    }
+  }
+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10381307_r18_1992699_k10_to2p16.json

@@ -0,0 +1,34 @@
+{
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+    }
+  }
+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10388315_r18_1999707_k11_to2p18.json

@@ -0,0 +1,34 @@
+{
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+      }
+    }
+  }
+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_1039039_r18_1039039_k9_to2p15.json

@@ -1,6 +1,6 @@
 {
   "domain": {
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+    "start_m": 24,
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     "r18_parent": 1039039,
     "k": 9,

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10404511_r18_2015903_k11_to2p18.json

@@ -0,0 +1,34 @@
+{
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+      }
+    }
+  }
+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_1041051_r18_1041051_k11_to2p18.json

@@ -1,6 +1,6 @@
 {
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     "r19_chain": 1041051,
     "r18_parent": 1041051,
     "k": 11,

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_1041383_r18_1041383_k6_to2p10.json

@@ -1,6 +1,6 @@
 {
   "domain": {
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+    "start_m": 22,
     "r19_chain": 1041383,
     "r18_parent": 1041383,
     "k": 6,

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10414171_r18_2025563_k11_to2p18.json

@@ -0,0 +1,34 @@
+{
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+      }
+    }
+  }
+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10420327_r18_2031719_k11_to2p18.json

@@ -0,0 +1,34 @@
+{
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+        "C_km1": 94721,
+        "B_k": 300547
+      }
+    }
+  }
+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_1043135_r18_1043135_k11_to2p18.json

@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 22,
     "r19_chain": 1043135,
     "r18_parent": 1043135,
     "k": 11,

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10437375_r18_2048767_k11_to2p18.json

@@ -0,0 +1,34 @@
+{
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+    "r19_chain": 10437375,
+    "r18_parent": 2048767,
+    "k": 11,
+    "m_end": 18
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+    "t_leaf_max": 256,
+    "k_chain_max": 80
+  },
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+    "v2_L_r19": 25,
+    "steps": [],
+    "final": {
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+        "C_km1": 60329,
+        "B_k": 197371
+      }
+    }
+  }
+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10457685_r18_2069077_k11_to2p18.json

@@ -0,0 +1,34 @@
+{
+  "domain": {
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+    "r19_chain": 10457685,
+    "r18_parent": 2069077,
+    "k": 11,
+    "m_end": 18
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+        "B_k": 42997673
+      }
+    }
+  }
+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10459631_r18_2071023_k11_to2p18.json

@@ -0,0 +1,34 @@
+{
+  "domain": {
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+    "r19_chain": 10459631,
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+    "k": 11,
+    "m_end": 18
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+        "C_km1": 75577,
+        "B_k": 259499
+      }
+    }
+  }
+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10462567_r18_2073959_k10_to2p16.json

@@ -0,0 +1,34 @@
+{
+  "domain": {
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+    "r19_chain": 10462567,
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+        "B_k": 83201
+      }
+    }
+  }
+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10463135_r18_2074527_k10_to2p16.json

@@ -0,0 +1,34 @@
+{
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+    "r18_parent": 2074527,
+    "k": 10,
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+        "C_km1": 27139,
+        "B_k": 97801
+      }
+    }
+  }
+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_1046639_r18_1046639_k10_to2p16.json

@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 22,
     "r19_chain": 1046639,
     "r18_parent": 1046639,
     "k": 10,

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_1047207_r18_1047207_k10_to2p16.json

@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 22,
     "r19_chain": 1047207,
     "r18_parent": 1047207,
     "k": 10,

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_1047231_r18_1047231_k11_to2p18.json

@@ -1,6 +1,6 @@
 {
   "domain": {
-    "start_m": 21,
+    "start_m": 23,
     "r19_chain": 1047231,
     "r18_parent": 1047231,
     "k": 11,

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10474879_r18_2086271_k11_to2p18.json

@@ -0,0 +1,34 @@
+{
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+    "r18_parent": 2086271,
+    "k": 11,
+    "m_end": 18
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+        "C_km1": 79145,
+        "B_k": 253819
+      }
+    }
+  }
+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10480751_r18_2092143_k9_to2p15.json

@@ -0,0 +1,34 @@
+{
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+    "r18_parent": 2092143,
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+        "C_km1": 7985,
+        "B_k": 26003
+      }
+    }
+  }
+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_1049599_r18_1049599_k11_to2p18.json

@@ -0,0 +1,34 @@
+{
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+    "r19_chain": 1049599,
+    "r18_parent": 1049599,
+    "k": 11,
+    "m_end": 18
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+        "C_km1": 58025,
+        "B_k": 182267
+      }
+    }
+  }
+}

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": {
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+    "start_m": 22,
     "r19_chain": 104959,
     "r18_parent": 104959,
     "k": 11,

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_1050735_r18_1050735_k11_to2p18.json

@@ -0,0 +1,34 @@
+{
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+    "k": 11,
+    "m_end": 18
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+        "B_k": 269867
+      }
+    }
+  }
+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10517119_r18_2128511_k10_to2p16.json

@@ -0,0 +1,34 @@
+{
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+        "B_k": 67625
+      }
+    }
+  }
+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10517403_r18_2128795_k6_to2p10.json

@@ -0,0 +1,34 @@
+{
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+    "r18_parent": 2128795,
+    "k": 6,
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+    "final": {
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+        "B_k": 925
+      }
+    }
+  }
+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_1054239_r18_1054239_k10_to2p16.json

@@ -0,0 +1,34 @@
+{
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+    "r19_chain": 1054239,
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+    "k": 10,
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+      }
+    }
+  }
+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_1055423_r18_1055423_k11_to2p18.json

@@ -0,0 +1,34 @@
+{
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+        "B_k": 276923
+      }
+    }
+  }
+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10554907_r18_2166299_k9_to2p15.json

@@ -0,0 +1,34 @@
+{
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+        "B_k": 31247
+      }
+    }
+  }
+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10573659_r18_2185051_k8_to2p13.json

@@ -0,0 +1,34 @@
+{
+  "domain": {
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+    "r19_chain": 10573659,
+    "r18_parent": 2185051,
+    "k": 8,
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+        "B_k": 11461
+      }
+    }
+  }
+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10582183_r18_2193575_k9_to2p15.json

@@ -0,0 +1,34 @@
+{
+  "domain": {
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+        "B_k": 28651
+      }
+    }
+  }
+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_1058975_r18_1058975_k11_to2p18.json

@@ -0,0 +1,34 @@
+{
+  "domain": {
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+    "r19_chain": 1058975,
+    "r18_parent": 1058975,
+    "k": 11,
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+  },
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+    "steps": [],
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+        "B_k": 196379
+      }
+    }
+  }
+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10591559_r18_2202951_k8_to2p13.json

@@ -0,0 +1,34 @@
+{
+  "domain": {
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+    "r19_chain": 10591559,
+    "r18_parent": 2202951,
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+  },
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+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10596863_r18_2208255_k11_to2p18.json

@@ -0,0 +1,34 @@
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+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10598567_r18_2209959_k11_to2p18.json

@@ -0,0 +1,34 @@
+{
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+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10617983_r18_2229375_k9_to2p15.json

@@ -0,0 +1,34 @@
+{
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+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_1062171_r18_1062171_k11_to2p18.json

@@ -0,0 +1,34 @@
+{
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+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10622055_r18_2233447_k11_to2p18.json

@@ -0,0 +1,34 @@
+{
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+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10634367_r18_2245759_k11_to2p18.json

@@ -0,0 +1,34 @@
+{
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+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10672155_r18_2283547_k11_to2p18.json

@@ -0,0 +1,34 @@
+{
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+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10674239_r18_2285631_k9_to2p15.json

@@ -0,0 +1,34 @@
+{
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+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10680679_r18_2292071_k11_to2p18.json

@@ -0,0 +1,34 @@
+{
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+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10683615_r18_2295007_k8_to2p13.json

@@ -0,0 +1,34 @@
+{
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+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10690623_r18_2302015_k11_to2p18.json

@@ -0,0 +1,34 @@
+{
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+    }
+  }
+}

docs/artefacts/collatz/refinement_K/palier2p15/hensel_chain_leaves/certs_shifted/hensel_shifted_r19_10693275_r18_2304667_k10_to2p16.json

@@ -0,0 +1,34 @@
+{
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+}