ncantu bd529682bf collatz: add palier2p15/p16 artefacts and Sm refinement tooling

**Motivations:**
- Publish new Collatz palier runs and associated artefacts (C3 local descent, universal clauses, iteration protocol).
- Extend the scripts toolbox to generate/verify clauses and build refinement certificates over S_m.

**Root causes:**
- Universal clause witnesses were lifted to 2^(A+1) even when the witness is already fixed modulo the domain palier, leading to unstable or unnecessarily weak/ambiguous modulus choices.
- CSV palier inference in scission could mis-detect short column names (e.g. "m") by substring matching.

**Correctifs:**
- Lift D_exact/F witnesses to m_stable := max(m, A+1) in universal clause extraction and run reports.
- Make scission palier/m column detection exact-match to avoid false positives.
- Update C3 local descent verification/reporting to use strict fusion witness selection prioritizing lower modular stability and refreshed D/F metrics.
- Add a dedicated run report profile for per-palier universal clauses.

**Evolutions:**
- Add scripts for terminal clauses and minorated descent clauses over S_m, their deterministic verification, and multi-level refinement certificate building.
- Add modular tooling for register_K and incremental comparison of D_minor families.
- Add/update feature documentation for the new pipelines and generated reports.

**Pages affectées:**
- applications/collatz/collatz_k_scripts/README.md
- applications/collatz/collatz_k_scripts/collatz_extract_universal_clauses.py
- applications/collatz/collatz_k_scripts/collatz_generate_run_report.py
- applications/collatz/collatz_k_scripts/collatz_iterate_palier_protocol.py
- applications/collatz/collatz_k_scripts/collatz_scission.py
- applications/collatz/collatz_k_scripts/collatz_verify_c3_local_descent.py
- applications/collatz/collatz_k_scripts/collatz_verify_universal_clauses.py
- applications/collatz/collatz_k_scripts/*refinement*over_Sm*.py
- applications/collatz/collatz_k_scripts/collatz_generate_*clauses_over_Sm.py
- applications/collatz/collatz_k_scripts/collatz_verify_minorated_descent_clauses_over_Sm.py
- applications/collatz/collatz_k_scripts/collatz_build_register_K_modular.py
- applications/collatz/collatz_k_scripts/collatz_compare_dminor_families_incremental.py
- applications/collatz/*.md
- docs/features/*.md
- docs/artefacts/collatz/**
- docs/collatz_run_report_2026-03-09_*.md

2026-03-09 23:29:59 +01:00

3.5 KiB

Raw Blame History

Auteur : Équipe 4NK

Collatz — Refinement certificate at palier 2^M (instrumented domain L)

Objective

Provide a deterministic, versionable artefact that makes “decidability from a coarse observable” explicit.

At palier 2^M, the modular register K_M only retains clauses with stable_modulus_power <= M. When most witnesses require m_stable > M, an alternative is to keep M as the root observable and record a finite refinement path to a finer modulus where a terminal clause D/F applies.

This feature builds and audits such refinement paths on the instrumented finite domain L (the C3 witness domain), without claiming a global certificate on S_M.

Impacts

Adds new versioned artefacts under docs/artefacts/collatz/refinement_K/.
Does not change the extraction of terminal clauses (Option A); it reuses clauses_universelles.json.

Modifications

Script

applications/collatz/collatz_k_scripts/collatz_build_refinement_certificate_modular.py
- reads clauses_universelles.json (Option A) and the referenced C3 verification JSON,
- for each n in the C3 domain L, records a deterministic refinement path from n mod 2^M to the terminal stable residue at 2^{m_{stable}},
- produces a summary audit (depth buckets, max depth).

S_M variant (full odd residue space)

applications/collatz/collatz_k_scripts/collatz_build_refinement_certificate_over_Sm.py
- reads clauses_universelles.json (Option A),
- attempts to close the full refinement tree for each root residue in S_M using the finite set of terminal clauses, producing a closed/open partition of S_M.

S_M multilevel variant (root M to max M_max)

applications/collatz/collatz_k_scripts/collatz_generate_terminal_clauses_over_Sm.py
- generates terminal clauses directly decidable at 2^m (criterion A+1\le m) on the full S_m.
applications/collatz/collatz_k_scripts/collatz_build_refinement_certificate_over_Sm_multilevel.py
- closes roots in S_M by refinement up to 2^{M_{max}} using leaf sets provided at multiple levels.

Artefacts

For palier M:

docs/artefacts/collatz/refinement_K/palier2pM/refinement_certificate_mod2pM.json
docs/artefacts/collatz/refinement_K/palier2pM/refinement_certificate_mod2pM.md
docs/artefacts/collatz/refinement_K/palier2pM/audit_refinement_certificate_mod2pM.json
docs/artefacts/collatz/refinement_K/palier2pM/audit_refinement_certificate_mod2pM.md

For palier M (S_M variant):

docs/artefacts/collatz/refinement_K/palier2pM/refinement_certificate_Sm_mod2pM.json
docs/artefacts/collatz/refinement_K/palier2pM/refinement_certificate_Sm_mod2pM.md
docs/artefacts/collatz/refinement_K/palier2pM/audit_refinement_certificate_Sm_mod2pM.json
docs/artefacts/collatz/refinement_K/palier2pM/audit_refinement_certificate_Sm_mod2pM.md

For palier M (S_M multilevel variant):

docs/artefacts/collatz/terminal_clauses_over_Sm/palier2p<m>/clauses_terminal_over_Sm_mod2p<m>.{json,md}
docs/artefacts/collatz/refinement_K/palier2pM/refinement_certificate_Sm_multilevel_mod2pM_to2pMmax.{json,md}
docs/artefacts/collatz/refinement_K/palier2pM/audit_refinement_certificate_Sm_multilevel_mod2pM_to2pMmax.{json,md}

Deployment

No deployment. Local scripts only; artefacts are intended to be committed.

Analysis / Reproduction

Example for palier 2^{15}:

python3 applications/collatz/collatz_k_scripts/collatz_build_refinement_certificate_modular.py \
  --palier 15 \
  --repo-root /home/ncantu/code/algo

3.5 KiB Raw Blame History