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

2.1 KiB

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Auteur : Équipe 4NK

Collatz — Modular register K_M and finite coverage audit (Option A)

Objective

Provide a deterministic, versionable materialization of the modular coverage obligation (H2)/(I1):

build a finite register \mathcal{K}_M containing only clauses decidable at palier 2^M (i.e. m(c)\le M);
run a finite coverage audit on the instrumented domain L (the C3 witness domain), producing an equality-of-sets style artefact (covered vs uncovered on L).

This does not claim a global coverage of S_M; it is an auditable step “indexed by artefacts”.

Impacts

Adds new versioned artefacts under docs/artefacts/collatz/register_K/.
Does not modify any existing certificates, C3 artefacts, or universal clause extraction logic.

Modifications

Script

applications/collatz/collatz_k_scripts/collatz_build_register_K_modular.py
- reads clauses_universelles.json (Option A extracted clauses),
- filters eligible clauses with stable_modulus_power <= M into \mathcal{K}_M,
- computes N^\*=\max_c N(c) on eligible clauses,
- audits coverage on the finite C3 domain L (record n values), producing covered/uncovered sets and diagnostics.

Artefacts

For each palier M:

docs/artefacts/collatz/register_K/palier2pM/register_K_mod2pM.json
docs/artefacts/collatz/register_K/palier2pM/register_K_mod2pM.md
docs/artefacts/collatz/register_K/palier2pM/audit_register_K_mod2pM.json
docs/artefacts/collatz/register_K/palier2pM/audit_register_K_mod2pM.md
docs/artefacts/collatz/register_K/palier2pM/non_eligible_clauses_mod2pM.json
docs/artefacts/collatz/register_K/palier2pM/non_eligible_clauses_mod2pM.md
docs/artefacts/collatz/register_K/palier2pM/manifest_register_K_mod2pM.json
docs/artefacts/collatz/register_K/palier2pM/manifest_register_K_mod2pM.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_register_K_modular.py \
  --palier 15 \
  --horizon-k 5 \
  --repo-root /home/ncantu/code/algo

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