Formalize C2 and add deterministic projective verification artefacts
**Motivations:** - Make Lemma C2 assertions citeable without terminal transcripts - Provide a deterministic check for “both-children residual” and projective projection to B12 **Root causes:** - C2 relied on narrative links between completion docs and B12 invariance without a machine-checkable artefact **Correctifs:** - Add a deterministic verifier that checks set equalities and projections from the existing completion MD sources **Evolutions:** - Version C2 verification artefacts in docs/artefacts - Add a run report profile (sha256 + metrics) for C2 projective verification - Update the proof plan with explicit C2 statements and references **Pages affectées:** - applications/collatz/collatz_k_scripts/collatz_verify_c2_projective.py - docs/artefacts/collatz/c2_projective/verification_c2_projective.json - docs/artefacts/collatz/c2_projective/verification_c2_projective.md - applications/collatz/collatz_k_scripts/collatz_generate_run_report.py - docs/collatz_run_report_2026-03-09_c2_projective.md - docs/collatz_run_report_format.md - docs/features/collatz_run_report_generator.md - docs/features/collatz_c2_projective_verification.md - applications/collatz/collatz_k_scripts/plan_lemmes_manquants_et_programme_de_preuve.md
This commit is contained in:
ncantu
parent
e12c544e7b
commit
e3e68fe39c
@ -119,6 +119,111 @@ class LocalH6Metrics:
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certificate_paliers: list[tuple[str, int]]
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@dataclass(frozen=True)
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class C2ProjectiveMetrics:
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b12_size: int
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both14_size: int
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children15_size: int
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residual15_size: int
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children15_equals_residual15: bool
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proj_both14_equals_b12: bool
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both15_size: int
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children16_size: int
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proj_both15_equals_b12: bool
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def parse_c2_projective_metrics(verification_json: str) -> C2ProjectiveMetrics:
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obj = read_json(Path(verification_json))
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if not isinstance(obj, dict):
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raise ValueError("Invalid C2 verification JSON: expected object")
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b12 = obj.get("B12")
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checks = obj.get("checks")
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if not isinstance(b12, dict) or not isinstance(checks, dict):
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raise ValueError("Invalid C2 verification JSON: missing 'B12' or 'checks'")
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c1415 = checks.get("m14_to_m15")
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c1516 = checks.get("m15_to_m16")
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if not isinstance(c1415, dict) or not isinstance(c1516, dict):
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raise ValueError("Invalid C2 verification JSON: missing check blocks")
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def req_int(d: dict, k: str) -> int:
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v = d.get(k)
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if not isinstance(v, int):
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raise ValueError(f"Invalid C2 verification JSON: {k} must be int")
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return v
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def req_bool(d: dict, k: str) -> bool:
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v = d.get(k)
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if not isinstance(v, bool):
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raise ValueError(f"Invalid C2 verification JSON: {k} must be bool")
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return v
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return C2ProjectiveMetrics(
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b12_size=req_int(b12, "count"),
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both14_size=req_int(c1415, "both_parent_count"),
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children15_size=req_int(c1415, "computed_children_count"),
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residual15_size=req_int(c1415, "listed_residual_count"),
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children15_equals_residual15=req_bool(c1415, "children_equals_listed_residual"),
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proj_both14_equals_b12=req_bool(c1415, "projection_mod_4096_equals_b12"),
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both15_size=req_int(c1516, "both_parent_count"),
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children16_size=req_int(c1516, "computed_children_count"),
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proj_both15_equals_b12=req_bool(c1516, "projection_mod_4096_equals_b12"),
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)
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def write_c2_projective_run_report(
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*,
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output_path: Path,
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report_title: str,
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command: str,
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git_commit: str,
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sha_entries: list[Sha256Entry],
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metrics: C2ProjectiveMetrics,
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artefacts_dir: Path,
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) -> None:
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lines: list[str] = []
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lines.append("**Auteur** : Équipe 4NK")
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lines.append("")
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lines.append(f"# {report_title}")
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lines.append("")
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lines.append("## Contexte")
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lines.append("")
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lines.append("- **But du run** : vérifier C2 (complétion par frères ⇒ both ⇒ projection B12) sur des artefacts déterministes.")
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lines.append("- **Assertion vérifiée** : égalités d’ensembles et égalité de projections modulo 4096 (voir métriques).")
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lines.append("")
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lines.append("## Code et reproductibilité")
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lines.append("")
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if git_commit:
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lines.append(f"- **Commit Git** : `{git_commit}`")
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if command:
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lines.append("- **Commande** :")
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lines.append("")
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lines.append("```bash")
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lines.append(command)
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lines.append("```")
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lines.append("")
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lines.append("## Empreintes sha256 (scripts, artefacts)")
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lines.append("")
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lines.extend(format_sha256_list(sha_entries))
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lines.append("")
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lines.append("## Compteurs et métriques")
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lines.append("")
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lines.append(f"- |B12| = {metrics.b12_size}")
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lines.append(f"- m=14: |both|={metrics.both14_size}, |children(m=15)|={metrics.children15_size}, |listed residual(m=15)|={metrics.residual15_size}")
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lines.append(f"- m=14: children(m=15) == residual(m=15) : {metrics.children15_equals_residual15}")
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lines.append(f"- m=14: both mod 4096 == B12 : {metrics.proj_both14_equals_b12}")
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lines.append(f"- m=15: |both|={metrics.both15_size}, |children(m=16)|={metrics.children16_size}")
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lines.append(f"- m=15: both mod 4096 == B12 : {metrics.proj_both15_equals_b12}")
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lines.append("")
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lines.append("## Chemins d’artefacts (versionnés)")
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lines.append("")
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lines.append(f"- ARTEFACTS : `{artefacts_dir}`")
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lines.append("")
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output_path.parent.mkdir(parents=True, exist_ok=True)
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output_path.write_text("\n".join(lines) + "\n", encoding="utf-8")
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def _discover_base_noyau_path(artefacts_dir: Path) -> Path:
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candidates = sorted((artefacts_dir / "noyaux").glob("noyau_*_B12.json"))
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if len(candidates) != 1:
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@ -692,7 +797,15 @@ def main() -> None:
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ap.add_argument(
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"--profile",
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default="extend_finale",
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choices=["extend_finale", "validation_section7", "pipeline_d16_d17", "fusion_palier2p25", "local_H6", "local_H6_E1"],
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choices=[
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"extend_finale",
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"validation_section7",
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"pipeline_d16_d17",
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"fusion_palier2p25",
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"local_H6",
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"local_H6_E1",
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"c2_projective",
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],
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help="Report profile",
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)
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ap.add_argument("--pipeline-extend-log", default=None, help="Path to pipeline_extend.log (defaults to OUT/pipeline_extend.log)")
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@ -708,6 +821,11 @@ def main() -> None:
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default="",
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help="For profile local_H6: path to the versioned artefacts directory (e.g. docs/artefacts/collatz/local_E1_palier2p13)",
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)
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ap.add_argument(
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"--c2-artefacts-dir",
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default="",
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help="For profile c2_projective: path to deterministic artefacts directory (e.g. docs/artefacts/collatz/c2_projective)",
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)
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args = ap.parse_args()
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repo_root = Path(args.repo_root).resolve() if args.repo_root else Path.cwd().resolve()
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@ -922,6 +1040,44 @@ def main() -> None:
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print(f"Wrote: {output_path}")
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return
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if args.profile == "c2_projective":
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command = args.command.strip()
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if not command:
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command = (
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"python3 applications/collatz/collatz_k_scripts/collatz_generate_run_report.py "
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"--profile c2_projective --scope c2_projective "
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"--out-dir applications/collatz/out --docs-dir docs "
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"--c2-artefacts-dir docs/artefacts/collatz/c2_projective"
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)
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artefacts_dir = Path(args.c2_artefacts_dir).resolve() if args.c2_artefacts_dir.strip() else (docs_dir / "artefacts" / "collatz" / "c2_projective")
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verification_json = artefacts_dir / "verification_c2_projective.json"
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verification_md = artefacts_dir / "verification_c2_projective.md"
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metrics = parse_c2_projective_metrics(str(verification_json))
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date_str = pick_report_date_from_mtime([verification_json, verification_md])
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sha_paths: list[Path] = [
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repo_root / "applications" / "collatz" / "collatz_k_scripts" / "collatz_verify_c2_projective.py",
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repo_root / "applications" / "collatz" / "collatz_k_scripts" / "noyau_both_base_4096.md",
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repo_root / "applications" / "collatz" / "collatz_k_scripts" / "complétion_minorée_m14_vers_m15.md",
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repo_root / "applications" / "collatz" / "collatz_k_scripts" / "complétion_minorée_m15_vers_m16.md",
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verification_json,
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verification_md,
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]
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sha_entries = compute_sha256_entries(sha_paths)
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output_path = docs_dir / f"collatz_run_report_{date_str}_{args.scope}.md"
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write_c2_projective_run_report(
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output_path=output_path,
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report_title=f"Rapport d’exécution — {args.scope}",
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command=command,
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git_commit=commit_hash,
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sha_entries=sha_entries,
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metrics=metrics,
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artefacts_dir=artefacts_dir,
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)
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print(f"Wrote: {output_path}")
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return
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raise ValueError(f"Unknown profile: {args.profile}")
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@ -0,0 +1,274 @@
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#!/usr/bin/env python3
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# -*- coding: utf-8 -*-
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"""
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collatz_verify_c2_projective.py
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Deterministic verification artefact for Lemma C2 (projective reduction):
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From completion-by-brothers audit documents, verify that:
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- residual after completion equals the set of children of "both" parents
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- projections modulo 2^12 of B_m (both parents) match the fixed base B12
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Inputs (Markdown):
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- noyau_both_base_4096.md (contains B12 list)
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- complétion_minorée_m14_vers_m15.md (contains both-parent list at 2^14 + residual list at 2^15)
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- complétion_minorée_m15_vers_m16.md (contains both-parent list at 2^15)
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Outputs:
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- a short JSON summary (machine-checkable)
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- a short Markdown report (human-checkable)
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No terminal transcripts. Standard library only.
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"""
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from __future__ import annotations
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import argparse
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import json
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import re
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from dataclasses import dataclass
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from pathlib import Path
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def _read_text(path: Path) -> str:
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return path.read_text(encoding="utf-8", errors="strict")
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def _extract_ints(text: str) -> list[int]:
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return [int(x) for x in re.findall(r"\b\d+\b", text)]
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def _section_after_heading(md: str, heading_regex: str) -> str:
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"""
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Return the Markdown slice starting at a heading matched by heading_regex (regex applied line-wise).
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The slice ends at the next heading of same or higher level, or end of document.
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"""
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lines = md.splitlines()
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start = None
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level = None
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hr = re.compile(heading_regex)
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for i, line in enumerate(lines):
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if hr.search(line):
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start = i + 1
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m = re.match(r"^(#+)\s", line)
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level = len(m.group(1)) if m else 1
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break
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if start is None or level is None:
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raise ValueError(f"Cannot find heading matching regex: {heading_regex}")
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end = len(lines)
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for j in range(start, len(lines)):
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m2 = re.match(r"^(#+)\s", lines[j])
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if not m2:
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continue
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if len(m2.group(1)) <= level:
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end = j
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break
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return "\n".join(lines[start:end]).strip()
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def _parse_list_under_heading(md: str, heading_regex: str) -> list[int]:
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section = _section_after_heading(md, heading_regex)
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return sorted(set(_extract_ints(section)))
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def _assert_all_odd(values: list[int], label: str) -> None:
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bad = [x for x in values if x % 2 == 0]
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if bad:
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raise ValueError(f"{label}: expected odd residues only, found {len(bad)} even values (e.g. {bad[:10]})")
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@dataclass(frozen=True)
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class C2CheckResult:
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palier_parent: int
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palier_child: int
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both_parent_count: int
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computed_children_count: int
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listed_residual_count: int | None
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children_equals_listed_residual: bool | None
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projection_mod_4096_equals_b12: bool
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def _lift_children(both_parents: list[int], parent_palier: int) -> list[int]:
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shift = 1 << parent_palier
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out = set()
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for p in both_parents:
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out.add(p)
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out.add(p + shift)
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return sorted(out)
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def _project_mod_4096(values: list[int]) -> set[int]:
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return {int(x % 4096) for x in values}
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def _display_path(path: Path, repo_root: Path) -> str:
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try:
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rel = path.resolve().relative_to(repo_root.resolve())
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return str(rel)
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except ValueError:
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return str(path)
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def verify_c2(
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*,
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noyau_both_base_4096_md: Path,
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completion_m14_to_m15_md: Path,
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completion_m15_to_m16_md: Path,
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repo_root: Path,
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output_json: Path,
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output_md: Path,
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) -> None:
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b12_md = _read_text(noyau_both_base_4096_md)
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c1415_md = _read_text(completion_m14_to_m15_md)
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c1516_md = _read_text(completion_m15_to_m16_md)
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b12 = _parse_list_under_heading(b12_md, r"^##\s+Base projective B_12\b")
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_assert_all_odd(b12, "B12")
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if len(b12) != 192:
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raise ValueError(f"B12: expected 192 residues, got {len(b12)}")
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# m=14 -> m=15
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both14 = _parse_list_under_heading(c1415_md, r"^###\s+Parents\s+«\s+both\s+»\s+au\s+palier\s+2\^14\b")
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_assert_all_odd(both14, "Parents both (m=14)")
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children15 = _lift_children(both14, 14)
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_assert_all_odd(children15, "Computed children at m=15")
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residual15 = _parse_list_under_heading(
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c1415_md,
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r"^###\s+Résidu\s+restant\s+au\s+palier\s+2\^15\s+après\s+complétion\s+«\s+one\s+»",
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)
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_assert_all_odd(residual15, "Listed residual at m=15")
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c1415 = C2CheckResult(
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palier_parent=14,
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palier_child=15,
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both_parent_count=len(both14),
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computed_children_count=len(children15),
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listed_residual_count=len(residual15),
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children_equals_listed_residual=(set(children15) == set(residual15)),
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projection_mod_4096_equals_b12=(_project_mod_4096(both14) == set(b12)),
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)
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# m=15 -> m=16
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both15 = _parse_list_under_heading(c1516_md, r"^###\s+Parents\s+«\s+both\s+»\s+au\s+palier\s+2\^15\b")
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_assert_all_odd(both15, "Parents both (m=15)")
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children16 = _lift_children(both15, 15)
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_assert_all_odd(children16, "Computed children at m=16")
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# This completion file does not necessarily list the full residual after completion, so we only check the count.
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c1516 = C2CheckResult(
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palier_parent=15,
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palier_child=16,
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both_parent_count=len(both15),
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computed_children_count=len(children16),
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listed_residual_count=None,
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children_equals_listed_residual=None,
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projection_mod_4096_equals_b12=(_project_mod_4096(both15) == set(b12)),
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)
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summary = {
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"inputs": {
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"noyau_both_base_4096_md": _display_path(noyau_both_base_4096_md, repo_root),
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"completion_m14_to_m15_md": _display_path(completion_m14_to_m15_md, repo_root),
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"completion_m15_to_m16_md": _display_path(completion_m15_to_m16_md, repo_root),
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},
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"B12": {"count": len(b12), "min": min(b12), "max": max(b12)},
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"checks": {
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"m14_to_m15": c1415.__dict__,
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"m15_to_m16": c1516.__dict__,
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},
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"ok": {
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"m14_to_m15_children_equals_listed_residual": bool(c1415.children_equals_listed_residual),
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"m14_projection_equals_b12": bool(c1415.projection_mod_4096_equals_b12),
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"m15_projection_equals_b12": bool(c1516.projection_mod_4096_equals_b12),
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},
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}
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output_json.parent.mkdir(parents=True, exist_ok=True)
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output_json.write_text(json.dumps(summary, indent=2, ensure_ascii=False) + "\n", encoding="utf-8")
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lines: list[str] = []
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lines.append("**Auteur** : Équipe 4NK")
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lines.append("")
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lines.append("# Vérification déterministe — Lemma C2 (réduction projective)")
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lines.append("")
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lines.append("## Entrées")
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lines.append("")
|
||||
lines.append(f"- `noyau_both_base_4096.md` : `{_display_path(noyau_both_base_4096_md, repo_root)}`")
|
||||
lines.append(f"- `complétion_minorée_m14_vers_m15.md` : `{_display_path(completion_m14_to_m15_md, repo_root)}`")
|
||||
lines.append(f"- `complétion_minorée_m15_vers_m16.md` : `{_display_path(completion_m15_to_m16_md, repo_root)}`")
|
||||
lines.append("")
|
||||
lines.append("## Base projective B12")
|
||||
lines.append("")
|
||||
lines.append(f"- |B12| = {len(b12)} (attendu 192)")
|
||||
lines.append(f"- min(B12) = {min(b12)}, max(B12) = {max(b12)}")
|
||||
lines.append("")
|
||||
lines.append("## Transition m=14 → m=15 (complétion par frères ⇒ résidu = enfants des both)")
|
||||
lines.append("")
|
||||
lines.append(f"- |both parents (m=14)| = {c1415.both_parent_count}")
|
||||
lines.append(f"- |computed children (m=15)| = {c1415.computed_children_count} (attendu 2*|both|)")
|
||||
lines.append(f"- |listed residual (m=15)| = {c1415.listed_residual_count}")
|
||||
lines.append(f"- computed children == listed residual : {c1415.children_equals_listed_residual}")
|
||||
lines.append(f"- projection both(m=14) mod 4096 == B12 : {c1415.projection_mod_4096_equals_b12}")
|
||||
lines.append("")
|
||||
lines.append("## Transition m=15 → m=16 (projection des both)")
|
||||
lines.append("")
|
||||
lines.append(f"- |both parents (m=15)| = {c1516.both_parent_count}")
|
||||
lines.append(f"- |computed children (m=16)| = {c1516.computed_children_count} (attendu 2*|both|)")
|
||||
lines.append(f"- projection both(m=15) mod 4096 == B12 : {c1516.projection_mod_4096_equals_b12}")
|
||||
lines.append("")
|
||||
lines.append("## Sorties")
|
||||
lines.append("")
|
||||
lines.append(f"- JSON : `{output_json}`")
|
||||
lines.append(f"- Markdown : `{output_md}`")
|
||||
lines.append("")
|
||||
|
||||
output_md.parent.mkdir(parents=True, exist_ok=True)
|
||||
output_md.write_text("\n".join(lines) + "\n", encoding="utf-8")
|
||||
|
||||
|
||||
def main() -> None:
|
||||
ap = argparse.ArgumentParser(description="Deterministic C2 verification (projective reduction)")
|
||||
ap.add_argument(
|
||||
"--repo-root",
|
||||
default="",
|
||||
help="Repository root used to display relative paths in outputs (defaults to current working directory)",
|
||||
)
|
||||
ap.add_argument(
|
||||
"--noyau-both-base-4096-md",
|
||||
default=str(Path(__file__).parent / "noyau_both_base_4096.md"),
|
||||
help="Path to noyau_both_base_4096.md",
|
||||
)
|
||||
ap.add_argument(
|
||||
"--completion-m14-to-m15-md",
|
||||
default=str(Path(__file__).parent / "complétion_minorée_m14_vers_m15.md"),
|
||||
help="Path to complétion_minorée_m14_vers_m15.md",
|
||||
)
|
||||
ap.add_argument(
|
||||
"--completion-m15-to-m16-md",
|
||||
default=str(Path(__file__).parent / "complétion_minorée_m15_vers_m16.md"),
|
||||
help="Path to complétion_minorée_m15_vers_m16.md",
|
||||
)
|
||||
ap.add_argument(
|
||||
"--output-dir",
|
||||
default="docs/artefacts/collatz/c2_projective",
|
||||
help="Output directory for deterministic artefacts (JSON + MD)",
|
||||
)
|
||||
args = ap.parse_args()
|
||||
|
||||
repo_root = Path(args.repo_root).resolve() if args.repo_root.strip() else Path.cwd().resolve()
|
||||
out_dir = Path(args.output_dir)
|
||||
verify_c2(
|
||||
noyau_both_base_4096_md=Path(args.noyau_both_base_4096_md),
|
||||
completion_m14_to_m15_md=Path(args.completion_m14_to_m15_md),
|
||||
completion_m15_to_m16_md=Path(args.completion_m15_to_m16_md),
|
||||
repo_root=repo_root,
|
||||
output_json=out_dir / "verification_c2_projective.json",
|
||||
output_md=out_dir / "verification_c2_projective.md",
|
||||
)
|
||||
|
||||
|
||||
if __name__ == "__main__":
|
||||
main()
|
||||
|
||||
@ -215,8 +215,47 @@ Les artefacts versionnés montrent, pour les 60 états \(E\) de \(B_{12}\) :
|
||||
Ces constats sont des assertions d’audit (égalité d’ensembles sur artefacts) et ne remplacent pas la preuve des hypothèses (H4)–(H5).
|
||||
|
||||
Lemme C2 (réduction de \(R_m\) vers un noyau projectif).
|
||||
Il existe un mécanisme (à préciser : scission par frères + règles de fermeture) montrant que tout élément de \(R_m\) possède, après un nombre borné d’étapes de relèvement et de normalisation, un représentant dans un noyau projectif de type \(B_{12}\) (ou dans une famille finie de noyaux projectifs).
|
||||
Objectif : réduire la preuve globale à une élimination de noyaux projectifs finis.
|
||||
On fixe un schéma de complétion par frères à chaque transition \(m\to m+1\) :
|
||||
|
||||
- Pour un parent \(r\in R_m\), ses deux enfants au palier suivant sont \(r\) et \(r+2^m\).
|
||||
- On distingue :
|
||||
- **cas one** : un seul enfant est survivant à la transition ; l’autre est fermé (couvert) ;
|
||||
- **cas both** : les deux enfants sont survivants.
|
||||
|
||||
On note \(B_m\subset R_m\) l’ensemble des parents “both”.
|
||||
|
||||
### Énoncés cibles (formes à rendre exactes)
|
||||
|
||||
- (C2.1) **Complétion par frères ⇒ résidu = enfants des both**.
|
||||
Après fermeture (au palier \(m+1\)) des enfants “one” par clauses de descente minorées (lemme de frère), le résidu restant au palier \(m+1\) est exactement :
|
||||
\[
|
||||
R_{m+1}^{\mathrm{comp}}=\{\,r,\ r+2^m\;:\; r\in B_m\,\}.
|
||||
\]
|
||||
|
||||
- (C2.2) **Projection projective**.
|
||||
Pour certains paliers (en pratique : dès \(m\ge 12\) dans les artefacts actuels), il existe une base projective fixe
|
||||
\[
|
||||
B_{12}\subset(\mathbb{Z}/2^{12}\mathbb{Z})^\times,\quad |B_{12}|=192,
|
||||
\]
|
||||
telle que
|
||||
\[
|
||||
B_m \bmod 2^{12} = B_{12}.
|
||||
\]
|
||||
|
||||
### Artefact déterministe (vérification citable)
|
||||
|
||||
Une vérification déterministe (script + sortie courte) est versionnée dans `docs/artefacts/` :
|
||||
|
||||
- script : `applications/collatz/collatz_k_scripts/collatz_verify_c2_projective.py`
|
||||
- sorties : `docs/artefacts/collatz/c2_projective/verification_c2_projective.{json,md}`
|
||||
- rapport d’exécution (sha256 + métriques) : `docs/collatz_run_report_2026-03-09_c2_projective.md`
|
||||
|
||||
Ces artefacts valident (au niveau “audit”) les instances suivantes :
|
||||
|
||||
- transition \(m=14\to 15\) : \(R_{15}^{\mathrm{comp}}=\{r,r+2^{14}:r\in B_{14}\}\) et \(B_{14}\bmod 4096 = B_{12}\),
|
||||
- projection \(m=15\) : \(B_{15}\bmod 4096 = B_{12}\).
|
||||
|
||||
Objectif de C2 : utiliser (C2.1)–(C2.2) pour réduire l’analyse des survivants à une élimination par états sur \(B_{12}\) (C1), puis à un verrou final (C3).
|
||||
|
||||
Lemme C3 (impossibilité d’orbite infinie sous contraintes).
|
||||
Sous un paquet explicite de contraintes arithmétiques \(P\) (congruences, bornes sur sommes de valuations sur des horizons, contraintes modulo \(3^k\), etc.) extraites comme invariants des survivants, aucune orbite de la dynamique accélérée \(U\) ne peut être infinie.
|
||||
|
||||
@ -0,0 +1,37 @@
|
||||
{
|
||||
"inputs": {
|
||||
"noyau_both_base_4096_md": "applications/collatz/collatz_k_scripts/noyau_both_base_4096.md",
|
||||
"completion_m14_to_m15_md": "applications/collatz/collatz_k_scripts/complétion_minorée_m14_vers_m15.md",
|
||||
"completion_m15_to_m16_md": "applications/collatz/collatz_k_scripts/complétion_minorée_m15_vers_m16.md"
|
||||
},
|
||||
"B12": {
|
||||
"count": 192,
|
||||
"min": 27,
|
||||
"max": 4095
|
||||
},
|
||||
"checks": {
|
||||
"m14_to_m15": {
|
||||
"palier_parent": 14,
|
||||
"palier_child": 15,
|
||||
"both_parent_count": 593,
|
||||
"computed_children_count": 1186,
|
||||
"listed_residual_count": 1186,
|
||||
"children_equals_listed_residual": true,
|
||||
"projection_mod_4096_equals_b12": true
|
||||
},
|
||||
"m15_to_m16": {
|
||||
"palier_parent": 15,
|
||||
"palier_child": 16,
|
||||
"both_parent_count": 1101,
|
||||
"computed_children_count": 2202,
|
||||
"listed_residual_count": null,
|
||||
"children_equals_listed_residual": null,
|
||||
"projection_mod_4096_equals_b12": true
|
||||
}
|
||||
},
|
||||
"ok": {
|
||||
"m14_to_m15_children_equals_listed_residual": true,
|
||||
"m14_projection_equals_b12": true,
|
||||
"m15_projection_equals_b12": true
|
||||
}
|
||||
}
|
||||
@ -0,0 +1,34 @@
|
||||
**Auteur** : Équipe 4NK
|
||||
|
||||
# Vérification déterministe — Lemma C2 (réduction projective)
|
||||
|
||||
## Entrées
|
||||
|
||||
- `noyau_both_base_4096.md` : `applications/collatz/collatz_k_scripts/noyau_both_base_4096.md`
|
||||
- `complétion_minorée_m14_vers_m15.md` : `applications/collatz/collatz_k_scripts/complétion_minorée_m14_vers_m15.md`
|
||||
- `complétion_minorée_m15_vers_m16.md` : `applications/collatz/collatz_k_scripts/complétion_minorée_m15_vers_m16.md`
|
||||
|
||||
## Base projective B12
|
||||
|
||||
- |B12| = 192 (attendu 192)
|
||||
- min(B12) = 27, max(B12) = 4095
|
||||
|
||||
## Transition m=14 → m=15 (complétion par frères ⇒ résidu = enfants des both)
|
||||
|
||||
- |both parents (m=14)| = 593
|
||||
- |computed children (m=15)| = 1186 (attendu 2*|both|)
|
||||
- |listed residual (m=15)| = 1186
|
||||
- computed children == listed residual : True
|
||||
- projection both(m=14) mod 4096 == B12 : True
|
||||
|
||||
## Transition m=15 → m=16 (projection des both)
|
||||
|
||||
- |both parents (m=15)| = 1101
|
||||
- |computed children (m=16)| = 2202 (attendu 2*|both|)
|
||||
- projection both(m=15) mod 4096 == B12 : True
|
||||
|
||||
## Sorties
|
||||
|
||||
- JSON : `docs/artefacts/collatz/c2_projective/verification_c2_projective.json`
|
||||
- Markdown : `docs/artefacts/collatz/c2_projective/verification_c2_projective.md`
|
||||
|
||||
46
docs/collatz_run_report_2026-03-09_c2_projective.md
Normal file
46
docs/collatz_run_report_2026-03-09_c2_projective.md
Normal file
@ -0,0 +1,46 @@
|
||||
**Auteur** : Équipe 4NK
|
||||
|
||||
# Rapport d’exécution — c2_projective
|
||||
|
||||
## Contexte
|
||||
|
||||
- **But du run** : vérifier C2 (complétion par frères ⇒ both ⇒ projection B12) sur des artefacts déterministes.
|
||||
- **Assertion vérifiée** : égalités d’ensembles et égalité de projections modulo 4096 (voir métriques).
|
||||
|
||||
## Code et reproductibilité
|
||||
|
||||
- **Commit Git** : `e12c544e7bf8d7a6f9518cdd4959d0da07bccc07`
|
||||
- **Commande** :
|
||||
|
||||
```bash
|
||||
python3 applications/collatz/collatz_k_scripts/collatz_generate_run_report.py --profile c2_projective --scope c2_projective --out-dir applications/collatz/out --docs-dir docs --c2-artefacts-dir docs/artefacts/collatz/c2_projective
|
||||
```
|
||||
|
||||
## Empreintes sha256 (scripts, artefacts)
|
||||
|
||||
- `/home/ncantu/code/algo/applications/collatz/collatz_k_scripts/collatz_verify_c2_projective.py`
|
||||
- sha256: `4f515d649c44c4ffe55349b07c72e9e766f591f7596e1bcdf0f9447e6b94950d`
|
||||
- `/home/ncantu/code/algo/applications/collatz/collatz_k_scripts/noyau_both_base_4096.md`
|
||||
- sha256: `d0abffeca9ce2356d13b31ee4325b68fd85cf061670a8524b8e60fd15aba881b`
|
||||
- `/home/ncantu/code/algo/applications/collatz/collatz_k_scripts/complétion_minorée_m14_vers_m15.md`
|
||||
- sha256: `acc8667be8e93a33fadf45bacd5cd788ec05089d844616cf1762330ac0d41d67`
|
||||
- `/home/ncantu/code/algo/applications/collatz/collatz_k_scripts/complétion_minorée_m15_vers_m16.md`
|
||||
- sha256: `956f8fd19570b7614705384995b52b6bf81399ca8dc36c3ea33bcbad3e4aff50`
|
||||
- `/home/ncantu/code/algo/docs/artefacts/collatz/c2_projective/verification_c2_projective.json`
|
||||
- sha256: `b1b9ab9d5d4f9d4ee60e7efd43b853ac29d3d51a19c2d71bdac45c4340d01bf0`
|
||||
- `/home/ncantu/code/algo/docs/artefacts/collatz/c2_projective/verification_c2_projective.md`
|
||||
- sha256: `8bd84cb2149d297487e0e0ff03ebe96ff27b07a5ab677407cb4b9a17a339c2ba`
|
||||
|
||||
## Compteurs et métriques
|
||||
|
||||
- |B12| = 192
|
||||
- m=14: |both|=593, |children(m=15)|=1186, |listed residual(m=15)|=1186
|
||||
- m=14: children(m=15) == residual(m=15) : True
|
||||
- m=14: both mod 4096 == B12 : True
|
||||
- m=15: |both|=1101, |children(m=16)|=2202
|
||||
- m=15: both mod 4096 == B12 : True
|
||||
|
||||
## Chemins d’artefacts (versionnés)
|
||||
|
||||
- ARTEFACTS : `/home/ncantu/code/algo/docs/artefacts/collatz/c2_projective`
|
||||
|
||||
@ -86,6 +86,21 @@ Lors de la génération d’un rapport `local_H6`/`local_H6_E1`, un audit automa
|
||||
|
||||
En cas de désaccord, la génération échoue (afin d’éviter une citation ambiguë d’artefacts).
|
||||
|
||||
Pour la vérification C2 (complétion par frères ⇒ both ⇒ projection \(B_{12}\), artefacts déterministes versionnés) :
|
||||
|
||||
```bash
|
||||
python3 applications/collatz/collatz_k_scripts/collatz_verify_c2_projective.py \
|
||||
--repo-root /home/ncantu/code/algo \
|
||||
--output-dir docs/artefacts/collatz/c2_projective
|
||||
|
||||
python3 applications/collatz/collatz_k_scripts/collatz_generate_run_report.py \
|
||||
--profile c2_projective \
|
||||
--scope c2_projective \
|
||||
--c2-artefacts-dir docs/artefacts/collatz/c2_projective \
|
||||
--out-dir applications/collatz/out \
|
||||
--docs-dir docs
|
||||
```
|
||||
|
||||
### Contexte
|
||||
|
||||
- **But du run** : (énoncé court)
|
||||
|
||||
52
docs/features/collatz_c2_projective_verification.md
Normal file
52
docs/features/collatz_c2_projective_verification.md
Normal file
@ -0,0 +1,52 @@
|
||||
**Auteur** : Équipe 4NK
|
||||
|
||||
# Collatz — Vérification déterministe de C2 (réduction projective)
|
||||
|
||||
## Objectif
|
||||
|
||||
Rendre citable (sans transcript terminal) une vérification déterministe des assertions utilisées dans le lemme C2 :
|
||||
|
||||
- **complétion par frères** : après fermeture des cas “one”, le résidu au palier suivant est exactement l’ensemble des **enfants** des parents “both” ;
|
||||
- **projection projective** : l’ensemble des parents “both” à certains paliers se projette modulo \(2^{12}\) sur une base fixe \(B_{12}\subset(\mathbb{Z}/2^{12}\mathbb{Z})^\times\).
|
||||
|
||||
## Impacts
|
||||
|
||||
- Ajout d’un artefact versionné dans `docs/artefacts/` et d’un rapport d’exécution dans `docs/`, alignés sur le format standard des rapports.
|
||||
|
||||
## Modifications
|
||||
|
||||
- Script déterministe :
|
||||
- `applications/collatz/collatz_k_scripts/collatz_verify_c2_projective.py`
|
||||
- Artefacts versionnés (sortie du script) :
|
||||
- `docs/artefacts/collatz/c2_projective/verification_c2_projective.json`
|
||||
- `docs/artefacts/collatz/c2_projective/verification_c2_projective.md`
|
||||
- Rapport d’exécution (sha256 + métriques) :
|
||||
- `docs/collatz_run_report_2026-03-09_c2_projective.md`
|
||||
- Extension du générateur de rapports :
|
||||
- `applications/collatz/collatz_k_scripts/collatz_generate_run_report.py` (profil `c2_projective`)
|
||||
|
||||
## Modalités d’analyse
|
||||
|
||||
- Générer/mettre à jour les artefacts déterministes :
|
||||
|
||||
```bash
|
||||
python3 applications/collatz/collatz_k_scripts/collatz_verify_c2_projective.py \
|
||||
--repo-root /home/ncantu/code/algo \
|
||||
--output-dir docs/artefacts/collatz/c2_projective
|
||||
```
|
||||
|
||||
- Produire le rapport d’exécution (empreintes sha256 + métriques) :
|
||||
|
||||
```bash
|
||||
python3 applications/collatz/collatz_k_scripts/collatz_generate_run_report.py \
|
||||
--profile c2_projective \
|
||||
--scope c2_projective \
|
||||
--c2-artefacts-dir docs/artefacts/collatz/c2_projective \
|
||||
--out-dir applications/collatz/out \
|
||||
--docs-dir docs
|
||||
```
|
||||
|
||||
## Modalités de déploiement
|
||||
|
||||
Aucun déploiement.
|
||||
|
||||
@ -23,8 +23,9 @@ afin d’éviter toute insertion de transcript terminal dans les documents math
|
||||
- Ajout d’un format standard : `docs/collatz_run_report_format.md`.
|
||||
- Ajout d’un générateur : `applications/collatz/collatz_k_scripts/collatz_generate_run_report.py`.
|
||||
- Ajout d’un exemple réel de rapport : `docs/collatz_run_report_2026-03-04_extend_D18_D21_resume_from_D20.md`.
|
||||
- Profils supportés : `extend_finale`, `validation_section7`, `pipeline_d16_d17`, `fusion_palier2p25`, `local_H6_E1`, `local_H6`.
|
||||
- Profils supportés : `extend_finale`, `validation_section7`, `pipeline_d16_d17`, `fusion_palier2p25`, `local_H6_E1`, `local_H6`, `c2_projective`.
|
||||
- Pour `local_H6`/`local_H6_E1`, un audit automatique compare le **palier attendu** (artefacts) au **palier certifié** (certificats) et échoue en cas de désaccord.
|
||||
- Pour `c2_projective`, le rapport cite les artefacts déterministes `docs/artefacts/collatz/c2_projective/verification_c2_projective.{json,md}`.
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## Modalités d’analyse
|
||||
|
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