bd529682bf
**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
81 lines
3.5 KiB
Markdown
81 lines
3.5 KiB
Markdown
**Auteur** : Équipe 4NK
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# Collatz — Refinement certificate at palier 2^M (instrumented domain L)
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## Objective
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Provide a deterministic, versionable artefact that makes “decidability from a coarse observable” explicit.
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At palier \(2^M\), the modular register \(K_M\) only retains clauses with `stable_modulus_power <= M`.
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When most witnesses require `m_stable > M`, an alternative is to keep \(M\) as the *root observable*
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and record a finite refinement path to a finer modulus where a terminal clause \(D/F\) applies.
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This feature builds and audits such refinement paths on the instrumented finite domain \(L\)
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(the C3 witness domain), without claiming a global certificate on \(S_M\).
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## Impacts
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- Adds new versioned artefacts under `docs/artefacts/collatz/refinement_K/`.
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- Does not change the extraction of terminal clauses (Option A); it reuses `clauses_universelles.json`.
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## Modifications
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### Script
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- `applications/collatz/collatz_k_scripts/collatz_build_refinement_certificate_modular.py`
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- reads `clauses_universelles.json` (Option A) and the referenced C3 verification JSON,
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- for each `n` in the C3 domain \(L\), records a deterministic refinement path from \(n mod 2^M\)
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to the terminal stable residue at \(2^{m_{stable}}\),
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- produces a summary audit (depth buckets, max depth).
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### S_M variant (full odd residue space)
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- `applications/collatz/collatz_k_scripts/collatz_build_refinement_certificate_over_Sm.py`
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- reads `clauses_universelles.json` (Option A),
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- attempts to close the full refinement tree for each root residue in \(S_M\) using the finite
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set of terminal clauses, producing a closed/open partition of \(S_M\).
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### S_M multilevel variant (root M to max M_max)
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- `applications/collatz/collatz_k_scripts/collatz_generate_terminal_clauses_over_Sm.py`
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- generates terminal clauses directly decidable at \(2^m\) (criterion \(A+1\le m\)) on the full \(S_m\).
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- `applications/collatz/collatz_k_scripts/collatz_build_refinement_certificate_over_Sm_multilevel.py`
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- closes roots in \(S_M\) by refinement up to \(2^{M_{max}}\) using leaf sets provided at multiple levels.
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### Artefacts
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For palier \(M\):
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- `docs/artefacts/collatz/refinement_K/palier2pM/refinement_certificate_mod2pM.json`
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- `docs/artefacts/collatz/refinement_K/palier2pM/refinement_certificate_mod2pM.md`
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- `docs/artefacts/collatz/refinement_K/palier2pM/audit_refinement_certificate_mod2pM.json`
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- `docs/artefacts/collatz/refinement_K/palier2pM/audit_refinement_certificate_mod2pM.md`
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For palier \(M\) (S_M variant):
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- `docs/artefacts/collatz/refinement_K/palier2pM/refinement_certificate_Sm_mod2pM.json`
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- `docs/artefacts/collatz/refinement_K/palier2pM/refinement_certificate_Sm_mod2pM.md`
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- `docs/artefacts/collatz/refinement_K/palier2pM/audit_refinement_certificate_Sm_mod2pM.json`
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- `docs/artefacts/collatz/refinement_K/palier2pM/audit_refinement_certificate_Sm_mod2pM.md`
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For palier \(M\) (S_M multilevel variant):
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- `docs/artefacts/collatz/terminal_clauses_over_Sm/palier2p<m>/clauses_terminal_over_Sm_mod2p<m>.{json,md}`
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- `docs/artefacts/collatz/refinement_K/palier2pM/refinement_certificate_Sm_multilevel_mod2pM_to2pMmax.{json,md}`
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- `docs/artefacts/collatz/refinement_K/palier2pM/audit_refinement_certificate_Sm_multilevel_mod2pM_to2pMmax.{json,md}`
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## Deployment
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No deployment. Local scripts only; artefacts are intended to be committed.
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## Analysis / Reproduction
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Example for palier \(2^{15}\):
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```bash
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python3 applications/collatz/collatz_k_scripts/collatz_build_refinement_certificate_modular.py \
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--palier 15 \
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--repo-root /home/ncantu/code/algo
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```
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