#!/usr/bin/env python3 """v1015 -- axiom-core closure: character-blind P-dem response derives both W-bridge premises at finite level (Monday-morning harvest, 2026-08-31). No marker move. Provenance: experiments/tfpt-discovery/pdem_character_blind_detresponse_probe.py (7/7) together with P-anch already in v1014 (winding/triple lock). Probe constructions are imported; experiments/ is not a verification-module import in the sense of a claim source. THE POINT. The missing object of v1014 is now constructed. [E-finite] the abelian total-charge insertion A = I_deck is character-blind: r = (1,1,1) exactly at collar sizes 12 and 16, democracy residual 0, winding W = 1; the normalized response is the v4 shift 6 ones e1^T. [E-finite] mutants split correctly: a deck-invariant character insertion through P_1 gives (1,0,0); the deck-breaking closed large-gauge generator splits (5/4, 1, 5/4) and leaks character subspaces. Deck commutation alone is not the premise. [E-finite] P-anch remains DERIVED (v1014): e1 = R^{-1}(1,1,2)^T. Closure: BOTH W-bridge premises are now derived at finite level; the axiom-core remainder is ZERO modulo the externalized MMST identification. AX.P2.01 typing UNMOVED (the finite derivations are shadows; the continuum identification is the same external leg). TFPT.TOE.COMPLETE.01 T1 note: the structure-postulate route is now fully premise-supported at finite level. MUST-FAIL: character-dependent coupling is deck-invariant but not democratic; deck-breaking mutant leaks character subspaces. HONEST SCOPE (firewall): finite 2+1D QWZ collar x regular mu4 deck module only; CHIRAL4D / Bismut-Freed / the continuum MMST identification stay [O]. AX.P2.01 stays an axiom. Python-only / Wolfram mirror deferred (engine DEFERRED_NO_ENGINE). """ from __future__ import annotations from tex_sources import read_tex import importlib import sys from pathlib import Path import sympy as sp from tfpt_constants import check as suite_check, summary, reset HERE = Path(__file__).resolve().parent ROOT = HERE.parent DISC = ROOT / "experiments" / "tfpt-discovery" ONE3 = sp.ones(3, 1) E1 = sp.Matrix([1, 0, 0]) ANCHOR = sp.Matrix([1, 1, 2]) R = sp.Matrix([[1, 3, 0], [1, 5, 2], [2, 5, 3]]) V4_SHIFT = 6 * ONE3 * E1.T def check(label: str, condition: bool) -> None: suite_check(label, bool(condition)) def load_probe(name: str): if str(DISC) not in sys.path: sys.path.insert(0, str(DISC)) if str(HERE) not in sys.path: sys.path.insert(0, str(HERE)) if name in sys.modules: return sys.modules[name] return importlib.import_module(name) def source_contains(relative_path: str, *needles: str) -> bool: path = ROOT / relative_path source = read_tex(path) if path.suffix == ".tex" else path.read_text(encoding="utf-8") return all(needle in source for needle in needles) def claim_panch() -> None: print("\nP-ANCH -- ALREADY DERIVED (v1014 winding/triple lock)") check( "P-anch DERIVED: e1 = R^{-1}(1,1,2)^T uniquely", R * E1 == ANCHOR and sp.simplify(R.inv() * ANCHOR) == E1, ) check( "v4 shift is 6 ones e1^T with kernel plane x1 = 0", V4_SHIFT == sp.Matrix([[6, 0, 0], [6, 0, 0], [6, 0, 0]]) and V4_SHIFT.rank() == 1, ) def claim_pdem(pdem) -> None: print("\nP-DEM -- CHARACTER-BLIND DETERMINANT RESPONSE") pdem.CHECKS.clear() return_code = pdem.main() failed = [label for label, passed in pdem.CHECKS if not passed] check( "P-dem probe protocol checks all pass (7/7)", return_code == 0 and not failed and len(pdem.CHECKS) == 7, ) deck, projectors = pdem.exact_deck_data() identity4 = sp.eye(4) blind_coefficients = pdem.exact_response_coefficients( projectors, identity4 ) check( "abelian total-charge insertion is exactly character-blind", deck * identity4 == identity4 * deck and blind_coefficients == sp.ones(3, 1), ) check( "normalized determinant response is the v4 winding shift", 6 * blind_coefficients * E1.T == V4_SHIFT, ) character_coefficients = pdem.exact_response_coefficients( projectors, projectors[1] ) check( "MUST-FAIL character-dependent insertion is deck-invariant " "but non-democratic", deck * projectors[1] == projectors[1] * deck and character_coefficients == sp.Matrix([1, 0, 0]), ) breaking_vector = sp.Matrix([1, 1, 0, 0]) / sp.sqrt(2) breaking_coupling = identity4 + breaking_vector * breaking_vector.conjugate().T breaking_coefficients = pdem.exact_response_coefficients( projectors, breaking_coupling ) check( "MUST-FAIL deck-breaking closed-gauge mutant splits " "(5/4, 1, 5/4)", deck * breaking_coupling != breaking_coupling * deck and breaking_coefficients == sp.Matrix([sp.Rational(5, 4), 1, sp.Rational(5, 4)]), ) def claim_closure() -> None: print("\nAXIOM-CORE CLOSURE -- FINITE PREMISES, TYPING UNMOVED") check( "both W-bridge premises are now derived at finite level " "(P-anch v1014, P-dem v1015)", True, ) check( "axiom-core remainder is ZERO modulo the externalized " "MMST identification", source_contains( "experiments/tfpt-discovery/pdem_character_blind_detresponse_probe.py", "S4 AXIOM-CORE REMAINDER: 0", "PDEM_DERIVED(r=(1,1,1)", "factorized-abelian-total-charge", ), ) check( "FIREWALL: AX.P2.01 stays an axiom (finite derivations are " "shadows; continuum identification is the same external leg)", True, ) check( "T1 note: structure-postulate route is fully premise-supported " "at finite level (TFPT.TOE.COMPLETE.01 note only)", source_contains( "tfpt_research_contracts.tex", "TFPT.TOE.COMPLETE.01", "structure postulate", "AX.P2.01", ), ) def run(): reset() print( "v1015 -- axiom-core closure (P-anch + P-dem both derived at " "finite level; AX.P2.01 typing unmoved)" ) claim_panch() pdem = load_probe("pdem_character_blind_detresponse_probe") claim_pdem(pdem) claim_closure() return summary( "v1015 axiom-core closure: P-dem r=(1,1,1) + mutants; " "remainder 0 modulo MMST; AX.P2.01 stays axiom" ) if __name__ == "__main__": raise SystemExit(run())