From 94280b93fd0f832f27210bcc1d28893647d04dea Mon Sep 17 00:00:00 2001 From: ncantu Date: Mon, 9 Mar 2026 03:26:07 +0100 Subject: [PATCH] collatz: extract and verify universal clause candidates (Option A) MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit **Motivations:** - Produce a deterministic bridge from C3 local witnesses to universal-clause candidates (D/F) usable in later H4/H5 formalization. **Root causes:** - Local witnesses (Lift(B12)-scoped) were not exportable into a versioned, machine-checkable clause artefact. **Correctifs:** - Add deterministic extraction with minimal stable modulus lifting for D_exact/F and local encoding for D_brother dependencies. - Add deterministic verifier checking arithmetic consistency, lifting stability, and brother↔mate relation. **Evolutions:** - Version universal clause artefacts (JSON/MD) under `docs/artefacts/collatz/universal_clauses/`. - Document the feature and reproduction steps in `docs/features/`. **Pages affectées:** - applications/collatz/collatz_k_scripts/collatz_extract_universal_clauses.py - applications/collatz/collatz_k_scripts/collatz_verify_universal_clauses.py - docs/artefacts/collatz/universal_clauses/* - docs/features/collatz_universal_clause_extraction_optionA.md --- .../collatz_extract_universal_clauses.py | 392 + .../collatz_verify_universal_clauses.py | 339 + .../clauses_universelles.json | 13360 ++++++++++++++++ .../universal_clauses/clauses_universelles.md | 414 + .../verification_universal_clauses.json | 17 + .../verification_universal_clauses.md | 22 + ...atz_universal_clause_extraction_optionA.md | 64 + 7 files changed, 14608 insertions(+) create mode 100644 applications/collatz/collatz_k_scripts/collatz_extract_universal_clauses.py create mode 100644 applications/collatz/collatz_k_scripts/collatz_verify_universal_clauses.py create mode 100644 docs/artefacts/collatz/universal_clauses/clauses_universelles.json create mode 100644 docs/artefacts/collatz/universal_clauses/clauses_universelles.md create mode 100644 docs/artefacts/collatz/universal_clauses/verification_universal_clauses.json create mode 100644 docs/artefacts/collatz/universal_clauses/verification_universal_clauses.md create mode 100644 docs/features/collatz_universal_clause_extraction_optionA.md diff --git a/applications/collatz/collatz_k_scripts/collatz_extract_universal_clauses.py b/applications/collatz/collatz_k_scripts/collatz_extract_universal_clauses.py new file mode 100644 index 0000000..f97d2ff --- /dev/null +++ b/applications/collatz/collatz_k_scripts/collatz_extract_universal_clauses.py @@ -0,0 +1,392 @@ +#!/usr/bin/env python3 +# -*- coding: utf-8 -*- +""" +collatz_extract_universal_clauses.py + +Option A (Lift(B12)-scoped): convert deterministic *local witnesses* from the C3 +verification artefact into *universal clause candidates* (D/F) by lifting each +witnessed residue to the minimal modulus that fixes its prefix of valuations. + +Inputs: +- docs/artefacts/collatz/c3_local_descent/verification_c3_local_descent.json + +Outputs (versionable, no transcripts): +- docs/artefacts/collatz/universal_clauses/clauses_universelles.json +- docs/artefacts/collatz/universal_clauses/clauses_universelles.md + +Notes: +- D_exact and F witnesses are lifted to modulus 2^(A+1) where A is the prefix sum. +- D_brother witnesses are preserved as *local* dependencies (mate_exact) at the + domain palier; they are not asserted as standalone universal reductions here. +""" + +from __future__ import annotations + +import argparse +import json +from dataclasses import dataclass +from pathlib import Path +from typing import Literal + +from collatz_k_core import prefix_data + + +ClauseKind = Literal["D_exact", "F", "D_brother_local"] + + +def _read_json(path: Path) -> object: + return json.loads(path.read_text(encoding="utf-8", errors="strict")) + + +def _display_path(path: Path, repo_root: Path) -> str: + try: + rel = path.resolve().relative_to(repo_root.resolve()) + return str(rel) + except ValueError: + return str(path) + + +@dataclass(frozen=True) +class ExtractedClause: + kind: ClauseKind + domain_palier: int + source_n: int + stable_modulus_power: int | None + stable_residue_mod_2p: int | None + # shared: prefix length + affine constants + k_or_t: int | None + A: int | None + C: int | None + word: tuple[int, ...] | None + # D + N0: int | None + # F + a: int | None + y: int | None + preimage_m: int | None + DeltaF: int | None + Nf: int | None + source_csv: str | None + # brother + mate_exact: int | None + + def to_json(self) -> dict[str, object]: + return { + "kind": self.kind, + "domain_palier": self.domain_palier, + "source_n": self.source_n, + "stable_modulus_power": self.stable_modulus_power, + "stable_residue_mod_2p": self.stable_residue_mod_2p, + "k_or_t": self.k_or_t, + "A": self.A, + "C": self.C, + "word": list(self.word) if self.word is not None else None, + "N0": self.N0, + "a": self.a, + "y": self.y, + "preimage_m": self.preimage_m, + "DeltaF": self.DeltaF, + "Nf": self.Nf, + "source_csv": self.source_csv, + "mate_exact": self.mate_exact, + } + + +def _lift_to_stable_residue( + *, + n0: int, + base_palier: int, + target_palier: int, + prefix_len: int, + expected_word: tuple[int, ...], +) -> int: + """ + Deterministically lift a residue from 2^base_palier to 2^target_palier by choosing, + at each step, the unique child (r or r+2^m) that preserves the expected prefix word. + """ + if target_palier < base_palier: + raise ValueError("target_palier must be >= base_palier") + if prefix_len < 1: + raise ValueError("prefix_len must be >= 1") + r = n0 + for m in range(base_palier, target_palier): + shift = 1 << m + c0 = r + c1 = r + shift + w0 = prefix_data(c0, prefix_len).word + w1 = prefix_data(c1, prefix_len).word + ok0 = w0 == expected_word + ok1 = w1 == expected_word + if ok0 and not ok1: + r = c0 + elif ok1 and not ok0: + r = c1 + else: + raise ValueError( + "Ambiguous lift (expected exactly one child to preserve the prefix word): " + f"m={m}, base_palier={base_palier}, target_palier={target_palier}, n0={n0}, ok0={ok0}, ok1={ok1}" + ) + return r + + +def _format_int_list(values: list[int], per_line: int = 16) -> list[str]: + lines: list[str] = [] + for i in range(0, len(values), per_line): + lines.append(", ".join(str(x) for x in values[i : i + per_line])) + return lines + + +def run(*, verification_json: Path, output_dir: Path, repo_root: Path) -> None: + obj = _read_json(verification_json) + if not isinstance(obj, dict): + raise ValueError("Invalid C3 verification JSON: expected object") + domain = obj.get("domain") + records = obj.get("records") + if not isinstance(domain, dict) or not isinstance(records, list): + raise ValueError("Invalid C3 verification JSON: missing domain/records") + palier = domain.get("palier") + if not isinstance(palier, int): + raise ValueError("Invalid C3 verification JSON: domain.palier must be int") + + extracted: list[ExtractedClause] = [] + for rec in records: + if not isinstance(rec, dict): + raise ValueError("Invalid C3 record: expected object") + n = rec.get("n") + kind = rec.get("kind") + if not isinstance(n, int) or not isinstance(kind, str): + raise ValueError("Invalid C3 record: missing n/kind") + + if kind == "D_exact": + k = rec.get("k") + A_k = rec.get("A_k") + C_k = rec.get("C_k") + N0 = rec.get("N0") + if not all(isinstance(x, int) for x in [k, A_k, C_k, N0]): + raise ValueError(f"Invalid D_exact record for n={n}: missing k/A_k/C_k/N0") + pref = prefix_data(n, k) + if pref.A != A_k or pref.C != C_k: + raise ValueError(f"D_exact mismatch for n={n}: prefix_data differs from record") + m_stab = A_k + 1 + r_stab = _lift_to_stable_residue( + n0=n, + base_palier=palier, + target_palier=m_stab, + prefix_len=k, + expected_word=pref.word, + ) + pref_stab = prefix_data(r_stab, k) + if pref_stab.word != pref.word or pref_stab.A != pref.A or pref_stab.C != pref.C: + raise ValueError(f"D_exact lift check failed for n={n} at modulus 2^{m_stab}") + + extracted.append( + ExtractedClause( + kind="D_exact", + domain_palier=palier, + source_n=n, + stable_modulus_power=m_stab, + stable_residue_mod_2p=r_stab, + k_or_t=k, + A=A_k, + C=C_k, + word=pref.word, + N0=N0, + a=None, + y=None, + preimage_m=None, + DeltaF=None, + Nf=None, + source_csv=None, + mate_exact=None, + ) + ) + continue + + if kind == "F": + t = rec.get("t") + a = rec.get("a") + y = rec.get("y") + preimage_m = rec.get("preimage_m") + A_t = rec.get("A_t") + C_t = rec.get("C_t") + DeltaF = rec.get("DeltaF") + Nf = rec.get("Nf") + source_csv = rec.get("source_csv") + ints_ok = all(isinstance(x, int) for x in [t, a, y, preimage_m, A_t, C_t, DeltaF, Nf]) + if not ints_ok or not isinstance(source_csv, str): + raise ValueError(f"Invalid F record for n={n}: missing fields") + pref = prefix_data(n, t) + if pref.A != A_t or pref.C != C_t or pref.y != y: + raise ValueError(f"F mismatch for n={n}: prefix_data differs from record") + m_stab = A_t + 1 + r_stab = _lift_to_stable_residue( + n0=n, + base_palier=palier, + target_palier=m_stab, + prefix_len=t, + expected_word=pref.word, + ) + pref_stab = prefix_data(r_stab, t) + if pref_stab.word != pref.word or pref_stab.A != pref.A or pref_stab.C != pref.C or pref_stab.y != pref.y: + raise ValueError(f"F lift check failed for n={n} at modulus 2^{m_stab}") + + extracted.append( + ExtractedClause( + kind="F", + domain_palier=palier, + source_n=n, + stable_modulus_power=m_stab, + stable_residue_mod_2p=r_stab, + k_or_t=t, + A=A_t, + C=C_t, + word=pref.word, + N0=None, + a=a, + y=y, + preimage_m=preimage_m, + DeltaF=DeltaF, + Nf=Nf, + source_csv=source_csv, + mate_exact=None, + ) + ) + continue + + if kind == "D_brother": + k = rec.get("k") + A_k = rec.get("A_k") + C_k = rec.get("C_k") + mate = rec.get("mate_exact") + if not all(isinstance(x, int) for x in [k, A_k, C_k, mate]): + raise ValueError(f"Invalid D_brother record for n={n}: missing fields") + pref = prefix_data(n, k) + if pref.A != A_k or pref.C != C_k: + raise ValueError(f"D_brother mismatch for n={n}: prefix_data differs from record") + extracted.append( + ExtractedClause( + kind="D_brother_local", + domain_palier=palier, + source_n=n, + stable_modulus_power=None, + stable_residue_mod_2p=None, + k_or_t=k, + A=A_k, + C=C_k, + word=pref.word, + N0=None, + a=None, + y=None, + preimage_m=None, + DeltaF=None, + Nf=None, + source_csv=None, + mate_exact=mate, + ) + ) + continue + + raise ValueError(f"Unknown record kind in C3 verification JSON: {kind}") + + extracted = sorted(extracted, key=lambda c: (c.kind, c.source_n)) + max_stab = max([c.stable_modulus_power for c in extracted if c.stable_modulus_power is not None], default=None) + + out_json = output_dir / "clauses_universelles.json" + out_md = output_dir / "clauses_universelles.md" + output_dir.mkdir(parents=True, exist_ok=True) + + summary = { + "inputs": { + "verification_c3_local_descent_json": _display_path(verification_json, repo_root), + }, + "domain": {"palier": palier, "max_stable_modulus_power": max_stab}, + "counts": { + "total": len(extracted), + "D_exact": sum(1 for c in extracted if c.kind == "D_exact"), + "F": sum(1 for c in extracted if c.kind == "F"), + "D_brother_local": sum(1 for c in extracted if c.kind == "D_brother_local"), + }, + "clauses": [c.to_json() for c in extracted], + } + out_json.write_text(json.dumps(summary, indent=2, ensure_ascii=False) + "\n", encoding="utf-8") + + # Markdown output (short, human-checkable) + lines: list[str] = [] + lines.append("**Auteur** : Équipe 4NK") + lines.append("") + lines.append("# Clauses universelles extraites — Option A (Lift(B12))") + lines.append("") + lines.append("## Entrée") + lines.append("") + lines.append(f"- C3 vérification JSON : `{_display_path(verification_json, repo_root)}`") + lines.append("") + lines.append("## Domaine") + lines.append("") + lines.append(f"- palier (domaine des témoins) : 2^{palier}") + if max_stab is not None: + lines.append(f"- max(2^m_stable) observé : 2^{max_stab}") + lines.append("") + lines.append("## Compteurs") + lines.append("") + lines.append(f"- total : {summary['counts']['total']}") + lines.append(f"- D_exact : {summary['counts']['D_exact']}") + lines.append(f"- F : {summary['counts']['F']}") + lines.append(f"- D_brother_local : {summary['counts']['D_brother_local']}") + lines.append("") + lines.append("## Table (extrait)") + lines.append("") + header = ["kind", "source_n", "m_stable", "residue_mod_2^m", "k/t", "A", "N0/Nf", "mate_exact"] + lines.append("| " + " | ".join(header) + " |") + lines.append("| " + " | ".join(["---"] * len(header)) + " |") + for c in extracted: + m_st = "" if c.stable_modulus_power is None else str(c.stable_modulus_power) + r_st = "" if c.stable_residue_mod_2p is None else str(c.stable_residue_mod_2p) + kt = "" if c.k_or_t is None else str(c.k_or_t) + A = "" if c.A is None else str(c.A) + if c.kind == "D_exact": + thr = "" if c.N0 is None else f"N0={c.N0}" + elif c.kind == "F": + thr = "" if c.Nf is None else f"Nf={c.Nf}" + else: + thr = "" + mate = "" if c.mate_exact is None else str(c.mate_exact) + lines.append(f"| {c.kind} | {c.source_n} | {m_st} | {r_st} | {kt} | {A} | {thr} | {mate} |") + lines.append("") + lines.append("## Notes") + lines.append("") + lines.append("- `D_exact` et `F` sont relevées au module minimal \\(2^{A+1}\\) qui fige le mot de valuations du témoin.") + lines.append("- `D_brother_local` encode une dépendance locale (palier du domaine) vers un `mate_exact` ; elle n’est pas utilisée ici comme clause universelle autonome.") + lines.append("") + out_md.write_text("\n".join(lines) + "\n", encoding="utf-8") + + +def main() -> None: + ap = argparse.ArgumentParser(description="Extract universal clause candidates from deterministic C3 witnesses (Option A)") + ap.add_argument( + "--verification-json", + default="docs/artefacts/collatz/c3_local_descent/verification_c3_local_descent.json", + help="Path to deterministic C3 verification JSON", + ) + ap.add_argument( + "--output-dir", + default="docs/artefacts/collatz/universal_clauses", + help="Output directory for extracted clause artefacts (JSON + MD)", + ) + ap.add_argument( + "--repo-root", + default="", + help="Repository root used to display relative paths in outputs (defaults to current working directory)", + ) + args = ap.parse_args() + + repo_root = Path(args.repo_root).resolve() if args.repo_root.strip() else Path.cwd().resolve() + run( + verification_json=Path(args.verification_json).resolve(), + output_dir=Path(args.output_dir).resolve(), + repo_root=repo_root, + ) + + +if __name__ == "__main__": + main() + diff --git a/applications/collatz/collatz_k_scripts/collatz_verify_universal_clauses.py b/applications/collatz/collatz_k_scripts/collatz_verify_universal_clauses.py new file mode 100644 index 0000000..67f057f --- /dev/null +++ b/applications/collatz/collatz_k_scripts/collatz_verify_universal_clauses.py @@ -0,0 +1,339 @@ +#!/usr/bin/env python3 +# -*- coding: utf-8 -*- +""" +collatz_verify_universal_clauses.py + +Deterministic verifier for the extracted clause artefact produced by +collatz_extract_universal_clauses.py. + +Scope (Option A): +- check internal arithmetic consistency for each extracted D_exact / F clause + against the originating C3 witness record +- check deterministic lifting (stable residue) preserves the prefix word and + affine constants on the canonical representative +- check D_brother_local records point to an existing D_exact mate and match the + "sister" relation at the domain palier (xor 2^(m-1)) + +Outputs: +- docs/artefacts/collatz/universal_clauses/verification_universal_clauses.json +- docs/artefacts/collatz/universal_clauses/verification_universal_clauses.md +""" + +from __future__ import annotations + +import argparse +import json +from pathlib import Path + +from collatz_k_core import ( + N0_D, + Nf_F, + U_step, + delta_F, + fusion_choice_a, + prefix_data, + preimage_m, +) + + +def _read_json(path: Path) -> object: + return json.loads(path.read_text(encoding="utf-8", errors="strict")) + + +def _display_path(path: Path, repo_root: Path) -> str: + try: + rel = path.resolve().relative_to(repo_root.resolve()) + return str(rel) + except ValueError: + return str(path) + + +def _req_int(obj: dict[str, object], key: str) -> int: + v = obj.get(key) + if not isinstance(v, int): + raise ValueError(f"Expected int for {key}") + return v + + +def _opt_int(obj: dict[str, object], key: str) -> int | None: + v = obj.get(key) + if v is None: + return None + if not isinstance(v, int): + raise ValueError(f"Expected int|null for {key}") + return v + + +def _opt_str(obj: dict[str, object], key: str) -> str | None: + v = obj.get(key) + if v is None: + return None + if not isinstance(v, str): + raise ValueError(f"Expected str|null for {key}") + return v + + +def _opt_word(obj: dict[str, object], key: str) -> tuple[int, ...] | None: + v = obj.get(key) + if v is None: + return None + if not isinstance(v, list) or not all(isinstance(x, int) for x in v): + raise ValueError(f"Expected list[int]|null for {key}") + return tuple(v) + + +def run( + *, + verification_json: Path, + clauses_json: Path, + output_dir: Path, + repo_root: Path, +) -> None: + vobj = _read_json(verification_json) + if not isinstance(vobj, dict): + raise ValueError("Invalid C3 verification JSON: expected object") + domain = vobj.get("domain") + records = vobj.get("records") + if not isinstance(domain, dict) or not isinstance(records, list): + raise ValueError("Invalid C3 verification JSON: missing domain/records") + palier = domain.get("palier") + if not isinstance(palier, int): + raise ValueError("Invalid C3 verification JSON: domain.palier must be int") + + cobj = _read_json(clauses_json) + if not isinstance(cobj, dict): + raise ValueError("Invalid clauses JSON: expected object") + clauses = cobj.get("clauses") + if not isinstance(clauses, list) or not all(isinstance(x, dict) for x in clauses): + raise ValueError("Invalid clauses JSON: missing clauses list") + + by_source_n: dict[int, dict[str, object]] = {} + for c in clauses: + sn = c.get("source_n") + if not isinstance(sn, int): + raise ValueError("Invalid clause: missing source_n") + if sn in by_source_n: + raise ValueError(f"Duplicate source_n in clauses JSON: {sn}") + by_source_n[sn] = c + + by_record_n: dict[int, dict[str, object]] = {} + for r in records: + if not isinstance(r, dict): + raise ValueError("Invalid C3 record: expected object") + n = r.get("n") + if not isinstance(n, int): + raise ValueError("Invalid C3 record: missing n") + if n in by_record_n: + raise ValueError(f"Duplicate n in C3 records: {n}") + by_record_n[n] = r + + missing = sorted(set(by_record_n.keys()) - set(by_source_n.keys())) + if missing: + raise ValueError(f"Missing extracted clauses for {len(missing)} records (e.g. {missing[:20]})") + + ok_records = 0 + kind_counts: dict[str, int] = {"D_exact": 0, "F": 0, "D_brother_local": 0} + max_stable_mod: int | None = None + + for n, r in by_record_n.items(): + c = by_source_n[n] + kind = c.get("kind") + if not isinstance(kind, str): + raise ValueError(f"Invalid clause for n={n}: missing kind") + if kind not in kind_counts: + raise ValueError(f"Unknown clause kind for n={n}: {kind}") + kind_counts[kind] += 1 + + domain_palier = _req_int(c, "domain_palier") + if domain_palier != palier: + raise ValueError(f"Clause domain_palier mismatch for n={n}: {domain_palier} != {palier}") + + word = _opt_word(c, "word") + A = _opt_int(c, "A") + C = _opt_int(c, "C") + k_or_t = _opt_int(c, "k_or_t") + m_stab = _opt_int(c, "stable_modulus_power") + r_stab = _opt_int(c, "stable_residue_mod_2p") + if m_stab is not None: + max_stable_mod = m_stab if max_stable_mod is None else max(max_stable_mod, m_stab) + + if kind == "D_exact": + if r.get("kind") != "D_exact": + raise ValueError(f"Record kind mismatch for n={n}: expected D_exact") + k = _req_int(r, "k") + A_k = _req_int(r, "A_k") + C_k = _req_int(r, "C_k") + N0 = _req_int(r, "N0") + if k_or_t != k or A != A_k or C != C_k: + raise ValueError(f"D_exact clause params mismatch for n={n}") + if m_stab is None or r_stab is None or word is None: + raise ValueError(f"D_exact clause missing stability fields for n={n}") + if m_stab != A_k + 1: + raise ValueError(f"D_exact stable modulus mismatch for n={n}: {m_stab} != {A_k+1}") + pref = prefix_data(n, k) + if pref.word != word or pref.A != A_k or pref.C != C_k: + raise ValueError(f"D_exact prefix mismatch for n={n}") + pref_stab = prefix_data(r_stab, k) + if pref_stab.word != word or pref_stab.A != A_k or pref_stab.C != C_k: + raise ValueError(f"D_exact lift mismatch for n={n}") + N0_calc = N0_D(C_k, A_k, k) + if N0_calc != N0: + raise ValueError(f"D_exact N0 mismatch for n={n}: {N0_calc} != {N0}") + if n >= N0: + next_n = prefix_data(n, k).y + if not next_n < n: + raise ValueError(f"D_exact descent failed on representative for n={n}: U^k(n)={next_n} not < n") + ok_records += 1 + continue + + if kind == "F": + if r.get("kind") != "F": + raise ValueError(f"Record kind mismatch for n={n}: expected F") + t = _req_int(r, "t") + a = _req_int(r, "a") + y = _req_int(r, "y") + pre_m = _req_int(r, "preimage_m") + A_t = _req_int(r, "A_t") + C_t = _req_int(r, "C_t") + dF = _req_int(r, "DeltaF") + Nf = _req_int(r, "Nf") + src = r.get("source_csv") + if not isinstance(src, str): + raise ValueError(f"F record missing source_csv for n={n}") + + a2 = _opt_int(c, "a") + y2 = _opt_int(c, "y") + pre2 = _opt_int(c, "preimage_m") + dF2 = _opt_int(c, "DeltaF") + Nf2 = _opt_int(c, "Nf") + src2 = _opt_str(c, "source_csv") + if (k_or_t, A, C, a2, y2, pre2, dF2, Nf2, src2) != (t, A_t, C_t, a, y, pre_m, dF, Nf, src): + raise ValueError(f"F clause params mismatch for n={n}") + if m_stab is None or r_stab is None or word is None: + raise ValueError(f"F clause missing stability fields for n={n}") + if m_stab != A_t + 1: + raise ValueError(f"F stable modulus mismatch for n={n}: {m_stab} != {A_t+1}") + + pref = prefix_data(n, t) + if pref.word != word or pref.A != A_t or pref.C != C_t or pref.y != y: + raise ValueError(f"F prefix mismatch for n={n}") + pref_stab = prefix_data(r_stab, t) + if pref_stab.word != word or pref_stab.A != A_t or pref_stab.C != C_t or pref_stab.y != y: + raise ValueError(f"F lift mismatch for n={n}") + + a_calc = fusion_choice_a(y) + if a_calc is None or a_calc != a: + raise ValueError(f"F a mismatch for n={n}: fusion_choice_a(y)={a_calc} != {a}") + dF_calc = delta_F(A_t, t, a) + if dF_calc != dF: + raise ValueError(f"F DeltaF mismatch for n={n}: {dF_calc} != {dF}") + Nf_calc = Nf_F(C_t, A_t, t, a) + if Nf_calc != Nf: + raise ValueError(f"F Nf mismatch for n={n}: {Nf_calc} != {Nf}") + pre_calc = preimage_m(y, a) + if pre_calc != pre_m: + raise ValueError(f"F preimage mismatch for n={n}: {pre_calc} != {pre_m}") + um, _ = U_step(pre_m) + if um != y: + raise ValueError(f"F witness failed for n={n}: U(preimage_m)={um} != y={y}") + if n >= Nf and not (pre_m < n): + raise ValueError(f"F m= n") + ok_records += 1 + continue + + if kind == "D_brother_local": + if r.get("kind") != "D_brother": + raise ValueError(f"Record kind mismatch for n={n}: expected D_brother") + mate = _req_int(r, "mate_exact") + mate2 = _opt_int(c, "mate_exact") + if mate2 != mate: + raise ValueError(f"D_brother_local mate mismatch for n={n}") + shift = 1 << (palier - 1) + if (n ^ shift) != mate: + raise ValueError(f"D_brother_local mate relation mismatch for n={n}: n^2^(m-1) != mate_exact") + mate_rec = by_record_n.get(mate) + if not isinstance(mate_rec, dict) or mate_rec.get("kind") != "D_exact": + raise ValueError(f"D_brother_local mate is not a D_exact record for n={n}: mate={mate}") + ok_records += 1 + continue + + raise ValueError(f"Unhandled kind for n={n}: {kind}") + + output_dir.mkdir(parents=True, exist_ok=True) + out_json = output_dir / "verification_universal_clauses.json" + out_md = output_dir / "verification_universal_clauses.md" + + summary = { + "inputs": { + "verification_c3_local_descent_json": _display_path(verification_json, repo_root), + "clauses_universelles_json": _display_path(clauses_json, repo_root), + }, + "domain": {"palier": palier, "max_stable_modulus_power": max_stable_mod}, + "counts": {"ok_records": ok_records, **kind_counts}, + "ok": True, + } + out_json.write_text(json.dumps(summary, indent=2, ensure_ascii=False) + "\n", encoding="utf-8") + + lines: list[str] = [] + lines.append("**Auteur** : Équipe 4NK") + lines.append("") + lines.append("# Vérification déterministe — clauses universelles extraites (Option A)") + lines.append("") + lines.append("## Entrées") + lines.append("") + lines.append(f"- C3 vérification JSON : `{_display_path(verification_json, repo_root)}`") + lines.append(f"- clauses JSON : `{_display_path(clauses_json, repo_root)}`") + lines.append("") + lines.append("## Résultat") + lines.append("") + lines.append(f"- ok : {summary['ok']}") + lines.append(f"- palier (domaine) : 2^{palier}") + if max_stable_mod is not None: + lines.append(f"- max(2^m_stable) observé : 2^{max_stable_mod}") + lines.append("") + lines.append("## Compteurs") + lines.append("") + lines.append(f"- ok_records : {ok_records}") + lines.append(f"- D_exact : {kind_counts['D_exact']}") + lines.append(f"- F : {kind_counts['F']}") + lines.append(f"- D_brother_local : {kind_counts['D_brother_local']}") + lines.append("") + out_md.write_text("\n".join(lines) + "\n", encoding="utf-8") + + +def main() -> None: + ap = argparse.ArgumentParser(description="Verify extracted universal clauses (Option A)") + ap.add_argument( + "--verification-json", + default="docs/artefacts/collatz/c3_local_descent/verification_c3_local_descent.json", + help="Path to deterministic C3 verification JSON", + ) + ap.add_argument( + "--clauses-json", + default="docs/artefacts/collatz/universal_clauses/clauses_universelles.json", + help="Path to extracted clauses JSON", + ) + ap.add_argument( + "--output-dir", + default="docs/artefacts/collatz/universal_clauses", + help="Output directory for verification artefacts (JSON + MD)", + ) + ap.add_argument( + "--repo-root", + default="", + help="Repository root used to display relative paths in outputs (defaults to current working directory)", + ) + args = ap.parse_args() + + repo_root = Path(args.repo_root).resolve() if args.repo_root.strip() else Path.cwd().resolve() + run( + verification_json=Path(args.verification_json).resolve(), + clauses_json=Path(args.clauses_json).resolve(), + output_dir=Path(args.output_dir).resolve(), + repo_root=repo_root, + ) + + +if __name__ == "__main__": + main() + diff --git a/docs/artefacts/collatz/universal_clauses/clauses_universelles.json b/docs/artefacts/collatz/universal_clauses/clauses_universelles.json new file mode 100644 index 0000000..72a4bb4 --- /dev/null +++ b/docs/artefacts/collatz/universal_clauses/clauses_universelles.json @@ -0,0 +1,13360 @@ +{ + "inputs": { + "verification_c3_local_descent_json": "docs/artefacts/collatz/c3_local_descent/verification_c3_local_descent.json" + }, + "domain": { + "palier": 13, + "max_stable_modulus_power": 85 + }, + "counts": { + "total": 384, + "D_exact": 27, + "F": 330, + "D_brother_local": 27 + }, + "clauses": [ + { + "kind": "D_brother_local", + "domain_palier": 13, + "source_n": 127, + "stable_modulus_power": null, + "stable_residue_mod_2p": null, + "k_or_t": 8, + "A": 12, + "C": 6433, + "word": [ + 1, + 1, + 1, + 1, + 1, + 1, + 2, + 4 + ], + "N0": null, + "a": null, + "y": null, + "preimage_m": null, + "DeltaF": null, + "Nf": null, + "source_csv": null, + "mate_exact": 4223 + }, + { + "kind": "D_brother_local", + "domain_palier": 13, + "source_n": 359, + "stable_modulus_power": null, + "stable_residue_mod_2p": null, + "k_or_t": 8, + "A": 12, + "C": 7993, + "word": [ + 1, + 1, + 2, + 1, + 1, + 1, + 1, + 4 + ], + "N0": null, + "a": null, + "y": null, + "preimage_m": null, + "DeltaF": null, + "Nf": null, + "source_csv": null, + "mate_exact": 4455 + }, + { + "kind": "D_brother_local", + "domain_palier": 13, + "source_n": 763, + "stable_modulus_power": null, + "stable_residue_mod_2p": null, + "k_or_t": 8, + "A": 12, + "C": 11557, + "word": [ + 1, + 2, + 1, + 2, + 1, + 1, + 2, + 2 + ], + "N0": null, + "a": null, + "y": null, + "preimage_m": null, + "DeltaF": null, + "Nf": null, + "source_csv": null, + "mate_exact": 4859 + }, + { + "kind": "D_brother_local", + "domain_palier": 13, + "source_n": 831, + "stable_modulus_power": null, + "stable_residue_mod_2p": null, + "k_or_t": 8, + "A": 12, + "C": 7777, + "word": [ + 1, + 1, + 1, + 1, + 1, + 3, + 2, + 2 + ], + "N0": null, + "a": null, + "y": null, + "preimage_m": null, + "DeltaF": null, + "Nf": null, + "source_csv": null, + "mate_exact": 4927 + }, + { + "kind": "D_brother_local", + "domain_palier": 13, + "source_n": 1095, + "stable_modulus_power": null, + "stable_residue_mod_2p": null, + "k_or_t": 8, + "A": 12, + "C": 12377, + "word": [ + 1, + 1, + 2, + 2, + 1, + 2, + 2, + 1 + ], + "N0": null, + "a": null, + "y": null, + "preimage_m": null, + "DeltaF": null, + "Nf": null, + "source_csv": null, + "mate_exact": 5191 + }, + { + "kind": "D_brother_local", + "domain_palier": 13, + "source_n": 1275, + "stable_modulus_power": null, + "stable_residue_mod_2p": null, + "k_or_t": 8, + "A": 12, + "C": 11045, + "word": [ + 1, + 2, + 1, + 2, + 1, + 1, + 1, + 3 + ], + "N0": null, + "a": null, + "y": null, + "preimage_m": null, + "DeltaF": null, + "Nf": null, + "source_csv": null, + "mate_exact": 5371 + }, + { + "kind": "D_brother_local", + "domain_palier": 13, + "source_n": 1343, + "stable_modulus_power": null, + "stable_residue_mod_2p": null, + "k_or_t": 8, + "A": 12, + "C": 7265, + "word": [ + 1, + 1, + 1, + 1, + 1, + 3, + 1, + 3 + ], + "N0": null, + "a": null, + "y": null, + "preimage_m": null, + "DeltaF": null, + "Nf": null, + "source_csv": null, + "mate_exact": 5439 + }, + { + "kind": "D_brother_local", + "domain_palier": 13, + "source_n": 1775, + "stable_modulus_power": null, + "stable_residue_mod_2p": null, + "k_or_t": 8, + "A": 12, + "C": 7345, + "word": [ + 1, + 1, + 1, + 2, + 1, + 1, + 1, + 4 + ], + "N0": null, + "a": null, + "y": null, + "preimage_m": null, + "DeltaF": null, + "Nf": null, + "source_csv": null, + "mate_exact": 5871 + }, + { + "kind": "D_brother_local", + "domain_palier": 13, + "source_n": 2119, + "stable_modulus_power": null, + "stable_residue_mod_2p": null, + "k_or_t": 8, + "A": 12, + "C": 11353, + "word": [ + 1, + 1, + 2, + 2, + 1, + 2, + 1, + 2 + ], + "N0": null, + "a": null, + "y": null, + "preimage_m": null, + "DeltaF": null, + "Nf": null, + "source_csv": null, + "mate_exact": 6215 + }, + { + "kind": "D_brother_local", + "domain_palier": 13, + "source_n": 2651, + "stable_modulus_power": null, + "stable_residue_mod_2p": null, + "k_or_t": 8, + "A": 12, + "C": 10693, + 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"domain_palier": 13, + "source_n": 3163, + "stable_modulus_power": null, + "stable_residue_mod_2p": null, + "k_or_t": 8, + "A": 12, + "C": 10181, + "word": [ + 1, + 2, + 1, + 1, + 2, + 1, + 1, + 3 + ], + "N0": null, + "a": null, + "y": null, + "preimage_m": null, + "DeltaF": null, + "Nf": null, + "source_csv": null, + "mate_exact": 7259 + }, + { + "kind": "D_brother_local", + "domain_palier": 13, + "source_n": 3303, + "stable_modulus_power": null, + "stable_residue_mod_2p": null, + "k_or_t": 8, + "A": 12, + "C": 9145, + "word": [ + 1, + 1, + 2, + 1, + 1, + 2, + 2, + 2 + ], + "N0": null, + "a": null, + "y": null, + "preimage_m": null, + "DeltaF": null, + "Nf": null, + "source_csv": null, + "mate_exact": 7399 + }, + { + "kind": "D_brother_local", + "domain_palier": 13, + "source_n": 3815, + "stable_modulus_power": null, + "stable_residue_mod_2p": null, + "k_or_t": 8, + "A": 12, + "C": 8633, + "word": [ + 1, + 1, + 2, + 1, + 1, + 2, + 1, + 3 + ], + "N0": null, + "a": null, + "y": null, + 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"Nf": 1, + "source_csv": "docs/artefacts/collatz/local_E48_palier2p13/candidats/candidats_F9to11_E48_palier2p13.csv", + "mate_exact": null + }, + { + "kind": "F", + "domain_palier": 13, + "source_n": 8191, + "stable_modulus_power": 45, + "stable_residue_mod_2p": 8191, + "k_or_t": 27, + "A": 44, + "C": 8583644192699, + "word": [ + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 2, + 2, + 1, + 1, + 1, + 2, + 1, + 3, + 1, + 4, + 1, + 2, + 1, + 5, + 5 + ], + "N0": null, + "a": 1, + "y": 3551, + "preimage_m": 2367, + "DeltaF": 37525363163274, + "Nf": 1, + "source_csv": "docs/artefacts/collatz/local_E1_palier2p13/candidats/candidats_F9to36_E1_palier2p13.csv", + "mate_exact": null + } + ] +} diff --git a/docs/artefacts/collatz/universal_clauses/clauses_universelles.md b/docs/artefacts/collatz/universal_clauses/clauses_universelles.md new file mode 100644 index 0000000..6acd4ed --- /dev/null +++ b/docs/artefacts/collatz/universal_clauses/clauses_universelles.md @@ -0,0 +1,414 @@ +**Auteur** : Équipe 4NK + +# Clauses universelles extraites — Option A (Lift(B12)) + +## Entrée + +- C3 vérification JSON : `docs/artefacts/collatz/c3_local_descent/verification_c3_local_descent.json` + +## Domaine + +- palier (domaine des témoins) : 2^13 +- max(2^m_stable) observé : 2^85 + +## Compteurs + +- total : 384 +- D_exact : 27 +- F : 330 +- D_brother_local : 27 + +## Table (extrait) + +| kind | source_n | m_stable | residue_mod_2^m | k/t | A | N0/Nf | mate_exact | +| --- | --- | --- | --- | --- | --- | --- | --- | +| D_brother_local | 127 | | | 8 | 12 | | 4223 | +| D_brother_local | 359 | | | 8 | 12 | | 4455 | +| D_brother_local | 763 | | | 8 | 12 | | 4859 | +| D_brother_local | 831 | | | 8 | 12 | | 4927 | +| D_brother_local | 1095 | | | 8 | 12 | | 5191 | +| D_brother_local | 1275 | | | 8 | 12 | | 5371 | +| D_brother_local | 1343 | | | 8 | 12 | | 5439 | +| D_brother_local | 1775 | | | 8 | 12 | | 5871 | +| D_brother_local | 2119 | | | 8 | 12 | | 6215 | +| D_brother_local | 2651 | | | 8 | 12 | | 6747 | +| D_brother_local | 2719 | | | 8 | 12 | | 6815 | +| D_brother_local | 2983 | | | 8 | 12 | | 7079 | +| D_brother_local | 3163 | | | 8 | 12 | | 7259 | +| D_brother_local | 3303 | | | 8 | 12 | | 7399 | +| D_brother_local | 3815 | | | 8 | 12 | | 7911 | +| D_brother_local | 4007 | | | 8 | 12 | | 8103 | +| D_brother_local | 4351 | | | 8 | 12 | | 255 | +| D_brother_local | 4635 | | | 8 | 12 | | 539 | +| D_brother_local | 4775 | | | 8 | 12 | | 679 | +| D_brother_local | 5287 | | | 8 | 12 | | 1191 | +| D_brother_local | 5659 | | | 8 | 12 | | 1563 | +| D_brother_local | 6079 | | | 8 | 12 | | 1983 | +| D_brother_local | 6171 | | | 8 | 12 | | 2075 | +| D_brother_local | 6191 | | | 8 | 12 | | 2095 | +| D_brother_local | 6703 | | | 8 | 12 | | 2607 | +| D_brother_local | 7135 | | | 8 | 12 | | 3039 | +| D_brother_local | 7647 | | | 8 | 12 | | 3551 | +| D_exact | 255 | 14 | 255 | 8 | 13 | N0=4 | | +| D_exact | 539 | 14 | 539 | 8 | 13 | N0=7 | | +| D_exact | 679 | 14 | 679 | 8 | 13 | N0=6 | | +| D_exact | 1191 | 14 | 1191 | 8 | 13 | N0=6 | | +| D_exact | 1563 | 14 | 1563 | 8 | 13 | N0=6 | | +| D_exact | 1983 | 14 | 1983 | 8 | 13 | N0=5 | | +| D_exact | 2075 | 14 | 2075 | 8 | 13 | N0=6 | | +| D_exact | 2095 | 14 | 2095 | 8 | 13 | N0=6 | | +| D_exact | 2607 | 14 | 2607 | 8 | 13 | N0=6 | | +| D_exact | 3039 | 14 | 3039 | 8 | 13 | N0=6 | | +| D_exact | 3551 | 14 | 3551 | 8 | 13 | N0=5 | | +| D_exact | 4223 | 14 | 4223 | 8 | 13 | N0=4 | | +| D_exact | 4455 | 14 | 4455 | 8 | 13 | N0=5 | | +| D_exact | 4859 | 14 | 4859 | 8 | 13 | N0=8 | | +| D_exact | 4927 | 14 | 4927 | 8 | 13 | N0=5 | | +| D_exact | 5191 | 14 | 5191 | 8 | 13 | N0=8 | | +| D_exact | 5371 | 14 | 5371 | 8 | 13 | N0=7 | | +| D_exact | 5439 | 14 | 5439 | 8 | 13 | N0=5 | | +| D_exact | 5871 | 14 | 5871 | 8 | 13 | N0=5 | | +| D_exact | 6215 | 14 | 6215 | 8 | 13 | N0=7 | | +| D_exact | 6747 | 14 | 6747 | 8 | 13 | N0=7 | | +| D_exact | 6815 | 14 | 6815 | 8 | 13 | N0=5 | | +| D_exact | 7079 | 14 | 7079 | 8 | 13 | N0=8 | | +| D_exact | 7259 | 14 | 7259 | 8 | 13 | N0=7 | | +| D_exact | 7399 | 14 | 7399 | 8 | 13 | N0=6 | | +| D_exact | 7911 | 14 | 7911 | 8 | 13 | N0=6 | | +| D_exact | 8103 | 14 | 8103 | 8 | 13 | N0=7 | | +| F | 27 | 60 | 27 | 37 | 59 | Nf=2 | | +| F | 31 | 57 | 31 | 35 | 56 | Nf=2 | | +| F | 47 | 56 | 47 | 34 | 55 | Nf=1 | | +| F | 63 | 58 | 63 | 35 | 57 | Nf=1 | | +| F | 71 | 55 | 71 | 33 | 54 | Nf=1 | | +| F | 91 | 46 | 91 | 28 | 45 | Nf=16 | | +| F | 103 | 43 | 103 | 26 | 42 | Nf=8 | | +| F | 111 | 32 | 111 | 19 | 31 | Nf=4 | | +| F | 159 | 23 | 159 | 13 | 22 | Nf=1 | | +| F | 167 | 31 | 167 | 18 | 30 | Nf=2 | | +| F | 191 | 18 | 191 | 9 | 17 | Nf=1 | | +| F | 223 | 33 | 223 | 19 | 32 | Nf=1 | | +| F | 239 | 22 | 239 | 12 | 21 | Nf=1 | | +| F | 251 | 30 | 251 | 17 | 29 | Nf=1 | | +| F | 283 | 27 | 283 | 15 | 26 | Nf=1 | | +| F | 303 | 19 | 303 | 9 | 18 | Nf=1 | | +| F | 319 | 24 | 319 | 13 | 23 | Nf=1 | | +| F | 327 | 23 | 327 | 13 | 22 | Nf=1 | | +| F | 415 | 17 | 415 | 9 | 16 | Nf=1 | | +| F | 447 | 42 | 447 | 25 | 41 | Nf=1 | | +| F | 479 | 19 | 479 | 11 | 18 | Nf=15 | | +| F | 495 | 29 | 495 | 17 | 28 | Nf=1 | | +| F | 511 | 20 | 511 | 11 | 19 | Nf=1 | | +| F | 559 | 19 | 559 | 11 | 18 | Nf=14 | | +| F | 603 | 17 | 603 | 10 | 16 | Nf=2 | | +| F | 623 | 19 | 623 | 9 | 18 | Nf=1 | | +| F | 639 | 24 | 639 | 14 | 23 | Nf=1 | | +| F | 667 | 27 | 667 | 15 | 26 | Nf=1 | | +| F | 671 | 23 | 671 | 14 | 22 | Nf=4 | | +| F | 703 | 84 | 703 | 51 | 83 | Nf=1 | | +| F | 743 | 28 | 743 | 16 | 27 | Nf=1 | | +| F | 751 | 24 | 751 | 13 | 23 | Nf=1 | | +| F | 767 | 19 | 767 | 10 | 18 | Nf=1 | | +| F | 795 | 28 | 795 | 17 | 27 | Nf=3 | | +| F | 839 | 16 | 839 | 9 | 15 | Nf=6 | | +| F | 859 | 20 | 859 | 10 | 19 | Nf=1 | | +| F | 871 | 36 | 871 | 22 | 35 | Nf=2 | | +| F | 895 | 25 | 895 | 15 | 24 | Nf=2 | | +| F | 927 | 38 | 927 | 23 | 37 | Nf=28 | | +| F | 959 | 23 | 959 | 13 | 22 | Nf=1 | | +| F | 991 | 27 | 991 | 16 | 26 | Nf=10 | | +| F | 1007 | 22 | 1007 | 13 | 21 | Nf=2 | | +| F | 1023 | 21 | 1023 | 11 | 20 | Nf=1 | | +| F | 1051 | 20 | 1051 | 12 | 19 | Nf=3 | | +| F | 1055 | 83 | 1055 | 50 | 82 | Nf=1 | | +| F | 1115 | 24 | 1115 | 14 | 23 | Nf=6 | | +| F | 1127 | 23 | 1127 | 12 | 22 | Nf=1 | | +| F | 1135 | 16 | 1135 | 9 | 15 | Nf=1 | | +| F | 1151 | 18 | 1151 | 9 | 17 | Nf=1 | | +| F | 1179 | 20 | 1179 | 10 | 19 | Nf=1 | | +| F | 1183 | 17 | 1183 | 10 | 16 | Nf=1 | | +| F | 1215 | 16 | 1215 | 9 | 15 | Nf=1 | | +| F | 1247 | 20 | 1247 | 9 | 19 | Nf=1 | | +| F | 1255 | 21 | 1255 | 12 | 20 | Nf=3 | | +| F | 1263 | 27 | 1263 | 16 | 26 | Nf=6 | | +| F | 1279 | 25 | 1279 | 14 | 24 | Nf=1 | | +| F | 1307 | 35 | 1307 | 21 | 34 | Nf=1 | | +| F | 1327 | 21 | 1327 | 9 | 20 | Nf=1 | | +| F | 1351 | 15 | 1351 | 9 | 14 | Nf=5 | | +| F | 1383 | 43 | 1383 | 24 | 42 | Nf=1 | | +| F | 1407 | 85 | 1407 | 51 | 84 | Nf=1 | | +| F | 1439 | 22 | 1439 | 12 | 21 | Nf=1 | | +| F | 1471 | 32 | 1471 | 19 | 31 | Nf=1 | | +| F | 1503 | 25 | 1503 | 13 | 24 | Nf=1 | | +| F | 1519 | 18 | 1519 | 10 | 17 | Nf=2 | | +| F | 1535 | 20 | 1535 | 10 | 19 | Nf=1 | | +| F | 1567 | 20 | 1567 | 9 | 19 | Nf=1 | | +| F | 1583 | 82 | 1583 | 49 | 81 | Nf=1 | | +| F | 1639 | 37 | 1639 | 23 | 36 | Nf=25 | | +| F | 1663 | 18 | 1663 | 11 | 17 | Nf=7 | | +| F | 1691 | 22 | 1691 | 11 | 21 | Nf=1 | | +| F | 1695 | 34 | 1695 | 20 | 33 | Nf=1 | | +| F | 1727 | 20 | 1727 | 9 | 19 | Nf=1 | | +| F | 1767 | 20 | 1767 | 12 | 19 | Nf=3 | | +| F | 1791 | 19 | 1791 | 11 | 18 | Nf=1 | | +| F | 1819 | 62 | 1819 | 38 | 61 | Nf=1 | | +| F | 1883 | 20 | 1883 | 11 | 19 | Nf=2 | | +| F | 1895 | 26 | 1895 | 15 | 25 | Nf=2 | | +| F | 1919 | 24 | 1919 | 13 | 23 | Nf=1 | | +| F | 1951 | 18 | 1951 | 11 | 17 | Nf=12 | | +| F | 1959 | 28 | 1959 | 16 | 27 | Nf=1 | | +| F | 2043 | 20 | 2043 | 11 | 19 | Nf=2 | | +| F | 2047 | 59 | 2047 | 36 | 58 | Nf=1 | | +| F | 2079 | 17 | 2079 | 9 | 16 | Nf=1 | | +| F | 2111 | 84 | 2111 | 50 | 83 | Nf=1 | | +| F | 2139 | 21 | 2139 | 12 | 20 | Nf=1 | | +| F | 2151 | 42 | 2151 | 26 | 41 | Nf=7 | | +| F | 2159 | 21 | 2159 | 11 | 20 | Nf=1 | | +| F | 2175 | 21 | 2175 | 12 | 20 | Nf=1 | | +| F | 2207 | 31 | 2207 | 18 | 30 | Nf=1 | | +| F | 2215 | 45 | 2215 | 27 | 44 | Nf=2 | | +| F | 2271 | 17 | 2271 | 9 | 16 | Nf=1 | | +| F | 2287 | 54 | 2287 | 31 | 53 | Nf=1 | | +| F | 2299 | 17 | 2299 | 9 | 16 | Nf=1 | | +| F | 2303 | 19 | 2303 | 9 | 18 | Nf=1 | | +| F | 2331 | 17 | 2331 | 9 | 16 | Nf=1 | | +| F | 2367 | 18 | 2367 | 10 | 17 | Nf=1 | | +| F | 2375 | 29 | 2375 | 18 | 28 | Nf=49 | | +| F | 2407 | 18 | 2407 | 10 | 17 | Nf=1 | | +| F | 2463 | 23 | 2463 | 13 | 22 | Nf=2 | | +| F | 2495 | 17 | 2495 | 10 | 16 | Nf=1 | | +| F | 2527 | 28 | 2527 | 16 | 27 | Nf=1 | | +| F | 2543 | 30 | 2543 | 18 | 29 | Nf=59 | | +| F | 2559 | 41 | 2559 | 25 | 40 | Nf=1 | | +| F | 2663 | 16 | 2663 | 9 | 15 | Nf=1 | | +| F | 2671 | 20 | 2671 | 10 | 19 | Nf=1 | | +| F | 2687 | 18 | 2687 | 10 | 17 | Nf=1 | | +| F | 2715 | 34 | 2715 | 20 | 33 | Nf=1 | | +| F | 2727 | 16 | 2727 | 9 | 15 | Nf=5 | | +| F | 2751 | 44 | 2751 | 27 | 43 | Nf=3 | | +| F | 2791 | 19 | 2791 | 10 | 18 | Nf=1 | | +| F | 2799 | 17 | 2799 | 9 | 16 | Nf=1 | | +| F | 2811 | 19 | 2811 | 11 | 18 | Nf=2 | | +| F | 2815 | 15 | 2815 | 9 | 14 | Nf=3 | | +| F | 2843 | 25 | 2843 | 14 | 24 | Nf=1 | | +| F | 2879 | 18 | 2879 | 11 | 17 | Nf=10 | | +| F | 2887 | 17 | 2887 | 10 | 16 | Nf=3 | | +| F | 2919 | 18 | 2919 | 11 | 17 | Nf=10 | | +| F | 2943 | 30 | 2943 | 18 | 29 | Nf=36 | | +| F | 3007 | 23 | 3007 | 14 | 22 | Nf=5 | | +| F | 3055 | 31 | 3055 | 18 | 30 | Nf=1 | | +| F | 3067 | 18 | 3067 | 9 | 17 | Nf=1 | | +| F | 3071 | 50 | 3071 | 31 | 49 | Nf=3 | | +| F | 3099 | 20 | 3099 | 12 | 19 | Nf=3 | | +| F | 3103 | 20 | 3103 | 11 | 19 | Nf=1 | | +| F | 3135 | 21 | 3135 | 9 | 20 | Nf=1 | | +| F | 3175 | 43 | 3175 | 26 | 42 | Nf=11 | | +| F | 3183 | 22 | 3183 | 11 | 21 | Nf=1 | | +| F | 3199 | 18 | 3199 | 11 | 17 | Nf=7 | | +| F | 3227 | 41 | 3227 | 25 | 40 | Nf=3 | | +| F | 3231 | 24 | 3231 | 14 | 23 | Nf=3 | | +| F | 3239 | 15 | 3239 | 9 | 14 | Nf=5 | | +| F | 3263 | 20 | 3263 | 11 | 19 | Nf=1 | | +| F | 3311 | 27 | 3311 | 16 | 26 | Nf=9 | | +| F | 3323 | 44 | 3323 | 26 | 43 | Nf=2 | | +| F | 3327 | 19 | 3327 | 11 | 18 | Nf=1 | | +| F | 3355 | 25 | 3355 | 13 | 24 | Nf=1 | | +| F | 3375 | 20 | 3375 | 11 | 19 | Nf=1 | | +| F | 3391 | 30 | 3391 | 18 | 29 | Nf=61 | | +| F | 3399 | 49 | 3399 | 30 | 48 | Nf=3 | | +| F | 3431 | 37 | 3431 | 23 | 36 | Nf=17 | | +| F | 3455 | 21 | 3455 | 9 | 20 | Nf=1 | | +| F | 3487 | 17 | 3487 | 10 | 16 | Nf=2 | | +| F | 3519 | 25 | 3519 | 15 | 24 | Nf=2 | | +| F | 3567 | 31 | 3567 | 19 | 30 | Nf=4 | | +| F | 3583 | 20 | 3583 | 11 | 19 | Nf=1 | | +| F | 3611 | 17 | 3611 | 9 | 16 | Nf=1 | | +| F | 3615 | 21 | 3615 | 11 | 20 | Nf=1 | | +| F | 3631 | 29 | 3631 | 18 | 28 | Nf=37 | | +| F | 3687 | 19 | 3687 | 9 | 18 | Nf=1 | | +| F | 3711 | 38 | 3711 | 23 | 37 | Nf=1 | | +| F | 3739 | 41 | 3739 | 24 | 40 | Nf=1 | | +| F | 3743 | 16 | 3743 | 9 | 15 | Nf=1 | | +| F | 3775 | 22 | 3775 | 11 | 21 | Nf=1 | | +| F | 3823 | 26 | 3823 | 16 | 25 | Nf=10 | | +| F | 3839 | 37 | 3839 | 23 | 36 | Nf=10 | | +| F | 3867 | 25 | 3867 | 14 | 24 | Nf=1 | | +| F | 3931 | 27 | 3931 | 15 | 26 | Nf=1 | | +| F | 3943 | 46 | 3943 | 25 | 45 | Nf=1 | | +| F | 3967 | 20 | 3967 | 9 | 19 | Nf=1 | | +| F | 3999 | 20 | 3999 | 12 | 19 | Nf=2 | | +| F | 4031 | 17 | 4031 | 9 | 16 | Nf=1 | | +| F | 4079 | 18 | 4079 | 9 | 17 | Nf=1 | | +| F | 4091 | 16 | 4091 | 9 | 15 | Nf=2 | | +| F | 4095 | 52 | 4095 | 32 | 51 | Nf=2 | | +| F | 4123 | 15 | 4123 | 9 | 14 | Nf=5 | | +| F | 4127 | 43 | 4127 | 26 | 42 | Nf=2 | | +| F | 4143 | 15 | 4143 | 9 | 14 | Nf=5 | | +| F | 4159 | 18 | 4159 | 9 | 17 | Nf=1 | | +| F | 4167 | 21 | 4167 | 12 | 20 | Nf=4 | | +| F | 4187 | 18 | 4187 | 9 | 17 | Nf=1 | | +| F | 4199 | 18 | 4199 | 9 | 17 | Nf=1 | | +| F | 4207 | 38 | 4207 | 22 | 37 | Nf=1 | | +| F | 4255 | 71 | 4255 | 44 | 70 | Nf=2 | | +| F | 4263 | 58 | 4263 | 35 | 57 | Nf=1 | | +| F | 4287 | 20 | 4287 | 9 | 19 | Nf=1 | | +| F | 4319 | 17 | 4319 | 10 | 16 | Nf=2 | | +| F | 4335 | 18 | 4335 | 11 | 17 | Nf=12 | | +| F | 4347 | 48 | 4347 | 30 | 47 | Nf=138 | | +| F | 4379 | 17 | 4379 | 10 | 16 | Nf=2 | | +| F | 4399 | 34 | 4399 | 20 | 33 | Nf=1 | | +| F | 4415 | 29 | 4415 | 17 | 28 | Nf=3 | | +| F | 4423 | 24 | 4423 | 13 | 23 | Nf=1 | | +| F | 4511 | 21 | 4511 | 12 | 20 | Nf=2 | | +| F | 4543 | 15 | 4543 | 9 | 14 | Nf=3 | | +| F | 4575 | 39 | 4575 | 24 | 38 | Nf=4 | | +| F | 4591 | 66 | 4591 | 41 | 65 | Nf=4 | | +| F | 4607 | 49 | 4607 | 30 | 48 | Nf=1 | | +| F | 4655 | 16 | 4655 | 9 | 15 | Nf=4 | | +| F | 4699 | 23 | 4699 | 13 | 22 | Nf=1 | | +| F | 4719 | 26 | 4719 | 14 | 25 | Nf=1 | | +| F | 4735 | 18 | 4735 | 11 | 17 | Nf=7 | | +| F | 4763 | 26 | 4763 | 16 | 25 | Nf=10 | | +| F | 4767 | 24 | 4767 | 14 | 23 | Nf=5 | | +| F | 4799 | 17 | 4799 | 10 | 16 | Nf=1 | | +| F | 4839 | 20 | 4839 | 12 | 19 | Nf=4 | | +| F | 4847 | 23 | 4847 | 13 | 22 | Nf=1 | | +| F | 4863 | 36 | 4863 | 21 | 35 | Nf=1 | | +| F | 4891 | 45 | 4891 | 28 | 44 | Nf=22 | | +| F | 4935 | 24 | 4935 | 14 | 23 | Nf=6 | | +| F | 4955 | 17 | 4955 | 9 | 16 | Nf=2 | | +| F | 4967 | 26 | 4967 | 15 | 25 | Nf=3 | | +| F | 4991 | 18 | 4991 | 10 | 17 | Nf=1 | | +| F | 5023 | 18 | 5023 | 9 | 17 | Nf=1 | | +| F | 5055 | 24 | 5055 | 13 | 23 | Nf=1 | | +| F | 5087 | 15 | 5087 | 9 | 14 | Nf=5 | | +| F | 5103 | 18 | 5103 | 9 | 17 | Nf=1 | | +| F | 5119 | 39 | 5119 | 24 | 38 | Nf=2 | | +| F | 5147 | 36 | 5147 | 22 | 35 | Nf=3 | | +| F | 5151 | 34 | 5151 | 21 | 33 | Nf=7 | | +| F | 5211 | 22 | 5211 | 12 | 21 | Nf=1 | | +| F | 5223 | 18 | 5223 | 11 | 17 | Nf=11 | | +| F | 5231 | 16 | 5231 | 9 | 15 | Nf=1 | | +| F | 5247 | 23 | 5247 | 12 | 22 | Nf=1 | | +| F | 5275 | 17 | 5275 | 9 | 16 | Nf=2 | | +| F | 5279 | 24 | 5279 | 14 | 23 | Nf=1 | | +| F | 5311 | 16 | 5311 | 9 | 15 | Nf=1 | | +| F | 5343 | 21 | 5343 | 10 | 20 | Nf=1 | | +| F | 5351 | 30 | 5351 | 18 | 29 | Nf=2 | | +| F | 5359 | 23 | 5359 | 14 | 22 | Nf=4 | | +| F | 5375 | 19 | 5375 | 10 | 18 | Nf=1 | | +| F | 5403 | 22 | 5403 | 13 | 21 | Nf=2 | | +| F | 5423 | 20 | 5423 | 10 | 19 | Nf=1 | | +| F | 5447 | 28 | 5447 | 17 | 27 | Nf=3 | | +| F | 5479 | 26 | 5479 | 16 | 25 | Nf=8 | | +| F | 5503 | 42 | 5503 | 26 | 41 | Nf=11 | | +| F | 5535 | 28 | 5535 | 17 | 27 | Nf=2 | | +| F | 5567 | 37 | 5567 | 22 | 36 | Nf=1 | | +| F | 5599 | 18 | 5599 | 9 | 17 | Nf=1 | | +| F | 5615 | 17 | 5615 | 9 | 16 | Nf=1 | | +| F | 5631 | 16 | 5631 | 9 | 15 | Nf=1 | | +| F | 5663 | 21 | 5663 | 10 | 20 | Nf=1 | | +| F | 5679 | 21 | 5679 | 12 | 20 | Nf=1 | | +| F | 5735 | 25 | 5735 | 15 | 24 | Nf=3 | | +| F | 5759 | 36 | 5759 | 22 | 35 | Nf=2 | | +| F | 5787 | 17 | 5787 | 9 | 16 | Nf=1 | | +| F | 5791 | 33 | 5791 | 20 | 32 | Nf=2 | | +| F | 5823 | 24 | 5823 | 10 | 23 | Nf=1 | | +| F | 5863 | 19 | 5863 | 10 | 18 | Nf=1 | | +| F | 5887 | 27 | 5887 | 15 | 26 | Nf=1 | | +| F | 5915 | 45 | 5915 | 24 | 44 | Nf=1 | | +| F | 5979 | 16 | 5979 | 9 | 15 | Nf=2 | | +| F | 5991 | 29 | 5991 | 16 | 28 | Nf=1 | | +| F | 6015 | 23 | 6015 | 13 | 22 | Nf=1 | | +| F | 6047 | 17 | 6047 | 9 | 16 | Nf=1 | | +| F | 6055 | 19 | 6055 | 11 | 18 | Nf=14 | | +| F | 6139 | 20 | 6139 | 11 | 19 | Nf=1 | | +| F | 6143 | 51 | 6143 | 31 | 50 | Nf=1 | | +| F | 6175 | 17 | 6175 | 9 | 16 | Nf=1 | | +| F | 6207 | 18 | 6207 | 10 | 17 | Nf=2 | | +| F | 6235 | 18 | 6235 | 11 | 17 | Nf=12 | | +| F | 6247 | 18 | 6247 | 10 | 17 | Nf=2 | | +| F | 6255 | 17 | 6255 | 9 | 16 | Nf=1 | | +| F | 6271 | 15 | 6271 | 9 | 14 | Nf=3 | | +| F | 6303 | 29 | 6303 | 15 | 28 | Nf=1 | | +| F | 6311 | 37 | 6311 | 21 | 36 | Nf=1 | | +| F | 6367 | 23 | 6367 | 11 | 22 | Nf=1 | | +| F | 6383 | 70 | 6383 | 43 | 69 | Nf=2 | | +| F | 6395 | 23 | 6395 | 14 | 22 | Nf=6 | | +| F | 6399 | 19 | 6399 | 11 | 18 | Nf=1 | | +| F | 6427 | 25 | 6427 | 13 | 24 | Nf=1 | | +| F | 6463 | 25 | 6463 | 14 | 24 | Nf=1 | | +| F | 6471 | 51 | 6471 | 31 | 50 | Nf=1 | | +| F | 6503 | 16 | 6503 | 9 | 15 | Nf=4 | | +| F | 6559 | 16 | 6559 | 9 | 15 | Nf=1 | | +| F | 6591 | 45 | 6591 | 28 | 44 | Nf=8 | | +| F | 6623 | 28 | 6623 | 16 | 27 | Nf=2 | | +| F | 6639 | 18 | 6639 | 11 | 17 | Nf=12 | | +| F | 6655 | 42 | 6655 | 22 | 41 | Nf=1 | | +| F | 6759 | 16 | 6759 | 9 | 15 | Nf=1 | | +| F | 6767 | 20 | 6767 | 11 | 19 | Nf=1 | | +| F | 6783 | 16 | 6783 | 9 | 15 | Nf=3 | | +| F | 6811 | 29 | 6811 | 18 | 28 | Nf=45 | | +| F | 6823 | 38 | 6823 | 23 | 37 | Nf=18 | | +| F | 6847 | 21 | 6847 | 11 | 20 | Nf=1 | | +| F | 6887 | 58 | 6887 | 36 | 57 | Nf=4 | | +| F | 6895 | 22 | 6895 | 13 | 21 | Nf=1 | | +| F | 6907 | 17 | 6907 | 9 | 16 | Nf=1 | | +| F | 6911 | 48 | 6911 | 29 | 47 | Nf=1 | | +| F | 6939 | 29 | 6939 | 15 | 28 | Nf=1 | | +| F | 6975 | 15 | 6975 | 9 | 14 | Nf=4 | | +| F | 6983 | 18 | 6983 | 9 | 17 | Nf=1 | | +| F | 7015 | 15 | 7015 | 9 | 14 | Nf=4 | | +| F | 7039 | 18 | 7039 | 11 | 17 | Nf=8 | | +| F | 7103 | 17 | 7103 | 10 | 16 | Nf=1 | | +| F | 7151 | 23 | 7151 | 13 | 22 | Nf=2 | | +| F | 7163 | 20 | 7163 | 9 | 19 | Nf=1 | | +| F | 7167 | 34 | 7167 | 21 | 33 | Nf=4 | | +| F | 7195 | 20 | 7195 | 12 | 19 | Nf=3 | | +| F | 7199 | 16 | 7199 | 9 | 15 | Nf=1 | | +| F | 7231 | 22 | 7231 | 11 | 21 | Nf=1 | | +| F | 7271 | 22 | 7271 | 12 | 21 | Nf=1 | | +| F | 7279 | 58 | 7279 | 36 | 57 | Nf=4 | | +| F | 7295 | 32 | 7295 | 19 | 31 | Nf=3 | | +| F | 7323 | 31 | 7323 | 17 | 30 | Nf=1 | | +| F | 7327 | 23 | 7327 | 14 | 22 | Nf=4 | | +| F | 7335 | 25 | 7335 | 15 | 24 | Nf=2 | | +| F | 7359 | 45 | 7359 | 27 | 44 | Nf=1 | | +| F | 7407 | 31 | 7407 | 13 | 30 | Nf=1 | | +| F | 7419 | 15 | 7419 | 9 | 14 | Nf=6 | | +| F | 7423 | 39 | 7423 | 23 | 38 | Nf=1 | | +| F | 7451 | 18 | 7451 | 11 | 17 | Nf=16 | | +| F | 7471 | 20 | 7471 | 11 | 19 | Nf=1 | | +| F | 7487 | 17 | 7487 | 9 | 16 | Nf=1 | | +| F | 7495 | 19 | 7495 | 9 | 18 | Nf=1 | | +| F | 7527 | 75 | 7527 | 46 | 74 | Nf=1 | | +| F | 7551 | 23 | 7551 | 11 | 22 | Nf=1 | | +| F | 7583 | 23 | 7583 | 12 | 22 | Nf=1 | | +| F | 7615 | 23 | 7615 | 12 | 22 | Nf=1 | | +| F | 7663 | 26 | 7663 | 16 | 25 | Nf=8 | | +| F | 7679 | 38 | 7679 | 23 | 37 | Nf=1 | | +| F | 7707 | 21 | 7707 | 12 | 20 | Nf=3 | | +| F | 7711 | 21 | 7711 | 11 | 20 | Nf=1 | | +| F | 7727 | 33 | 7727 | 20 | 32 | Nf=3 | | +| F | 7783 | 18 | 7783 | 9 | 17 | Nf=1 | | +| F | 7807 | 26 | 7807 | 13 | 25 | Nf=1 | | +| F | 7835 | 17 | 7835 | 10 | 16 | Nf=2 | | +| F | 7839 | 26 | 7839 | 15 | 25 | Nf=1 | | +| F | 7871 | 22 | 7871 | 11 | 21 | Nf=1 | | +| F | 7919 | 15 | 7919 | 9 | 14 | Nf=4 | | +| F | 7935 | 43 | 7935 | 25 | 42 | Nf=1 | | +| F | 7963 | 76 | 7963 | 45 | 75 | Nf=1 | | +| F | 8027 | 26 | 8027 | 16 | 25 | Nf=13 | | +| F | 8039 | 21 | 8039 | 12 | 20 | Nf=2 | | +| F | 8063 | 18 | 8063 | 9 | 17 | Nf=1 | | +| F | 8095 | 17 | 8095 | 10 | 16 | Nf=2 | | +| F | 8127 | 47 | 8127 | 27 | 46 | Nf=1 | | +| F | 8175 | 26 | 8175 | 15 | 25 | Nf=1 | | +| F | 8187 | 16 | 8187 | 9 | 15 | Nf=1 | | +| F | 8191 | 45 | 8191 | 27 | 44 | Nf=1 | | + +## Notes + +- `D_exact` et `F` sont relevées au module minimal \(2^{A+1}\) qui fige le mot de valuations du témoin. +- `D_brother_local` encode une dépendance locale (palier du domaine) vers un `mate_exact` ; elle n’est pas utilisée ici comme clause universelle autonome. + diff --git a/docs/artefacts/collatz/universal_clauses/verification_universal_clauses.json b/docs/artefacts/collatz/universal_clauses/verification_universal_clauses.json new file mode 100644 index 0000000..d1f04f6 --- /dev/null +++ b/docs/artefacts/collatz/universal_clauses/verification_universal_clauses.json @@ -0,0 +1,17 @@ +{ + "inputs": { + "verification_c3_local_descent_json": "docs/artefacts/collatz/c3_local_descent/verification_c3_local_descent.json", + "clauses_universelles_json": "docs/artefacts/collatz/universal_clauses/clauses_universelles.json" + }, + "domain": { + "palier": 13, + "max_stable_modulus_power": 85 + }, + "counts": { + "ok_records": 384, + "D_exact": 27, + "F": 330, + "D_brother_local": 27 + }, + "ok": true +} diff --git a/docs/artefacts/collatz/universal_clauses/verification_universal_clauses.md b/docs/artefacts/collatz/universal_clauses/verification_universal_clauses.md new file mode 100644 index 0000000..b7c03b4 --- /dev/null +++ b/docs/artefacts/collatz/universal_clauses/verification_universal_clauses.md @@ -0,0 +1,22 @@ +**Auteur** : Équipe 4NK + +# Vérification déterministe — clauses universelles extraites (Option A) + +## Entrées + +- C3 vérification JSON : `docs/artefacts/collatz/c3_local_descent/verification_c3_local_descent.json` +- clauses JSON : `docs/artefacts/collatz/universal_clauses/clauses_universelles.json` + +## Résultat + +- ok : True +- palier (domaine) : 2^13 +- max(2^m_stable) observé : 2^85 + +## Compteurs + +- ok_records : 384 +- D_exact : 27 +- F : 330 +- D_brother_local : 27 + diff --git a/docs/features/collatz_universal_clause_extraction_optionA.md b/docs/features/collatz_universal_clause_extraction_optionA.md new file mode 100644 index 0000000..d3d27f5 --- /dev/null +++ b/docs/features/collatz_universal_clause_extraction_optionA.md @@ -0,0 +1,64 @@ +**Auteur** : Équipe 4NK + +# Collatz — Extraction de clauses universelles (Option A : Lift(B12)) + +## Objectif + +Industrialiser la conversion « témoin local → clause universelle candidate » (H4/H5) dans le périmètre **Option A** : + +- domaine des témoins : une instance locale de clôture (C3) sur \(L=\mathrm{Lift}_{12\to 13}(B_{12})\) ; +- entrée standard : un artefact déterministe `verification_c3_local_descent.json` contenant, pour chaque \(n\in L\), un témoin \(D\) (exact / brother) ou \(F\) (fusion) ; +- sortie : un ensemble versionné de **clauses candidates** \(D/F\) relevées au module minimal \(2^{A+1}\) qui fige le préfixe de valuations, plus une vérification déterministe de cohérence. + +Le but est de rendre la notion « certificat ⇒ clause universelle utilisable dans une induction bien fondée » exploitable de manière répétable, sans transcript, et sans dépendre d’un seul représentant. + +## Impacts + +- Ajoute un format d’artefacts versionnés `docs/artefacts/collatz/universal_clauses/` pour stocker : + - clauses extraites (JSON + MD), + - vérification (JSON + MD). +- N’altère pas la pipeline de génération de certificats ; le flux est en lecture seule vis‑à‑vis des artefacts C3. + +## Modifications + +### Scripts + +- `applications/collatz/collatz_k_scripts/collatz_extract_universal_clauses.py` + - lit `docs/artefacts/collatz/c3_local_descent/verification_c3_local_descent.json`, + - pour chaque témoin `D_exact` ou `F`, calcule le module minimal \(2^{A+1}\) et relève le résidu au palier stable par un relèvement déterministe (choix unique du bon enfant à chaque palier), + - conserve `D_brother` sous forme de dépendance locale `D_brother_local` (référence `mate_exact`). + +- `applications/collatz/collatz_k_scripts/collatz_verify_universal_clauses.py` + - vérifie la cohérence arithmétique et la cohérence de relèvement avec le fichier source C3, + - vérifie aussi les dépendances `D_brother_local` (relation de sœur au palier de domaine, et existence du `mate_exact` en `D_exact`). + +### Artefacts + +- `docs/artefacts/collatz/universal_clauses/clauses_universelles.{json,md}` +- `docs/artefacts/collatz/universal_clauses/verification_universal_clauses.{json,md}` + +## Modalités de déploiement + +Pas de déploiement : scripts exécutés localement, artefacts versionnés. + +## Modalités d’analyse / reproduction + +Commande d’extraction : + +```bash +python3 applications/collatz/collatz_k_scripts/collatz_extract_universal_clauses.py --repo-root /home/ncantu/code/algo +``` + +Commande de vérification : + +```bash +python3 applications/collatz/collatz_k_scripts/collatz_verify_universal_clauses.py --repo-root /home/ncantu/code/algo +``` + +Entrée attendue : +- `docs/artefacts/collatz/c3_local_descent/verification_c3_local_descent.json` + +Sorties attendues : +- `docs/artefacts/collatz/universal_clauses/clauses_universelles.json` +- `docs/artefacts/collatz/universal_clauses/verification_universal_clauses.json` +