TFPT scientific source excerpt
Original repository path: verification/v1015_axiom_core_closure.py
Original file SHA-256: ff1db6a6cde86bbea64ef04c6e56d3bc799bf6d676b8a820b2f35632acd59229
Inclusive original lines: 96-176
Line numbers below refer to the original source.
This bounded excerpt is source evidence; it is not a new proof/checker run.
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000096 | def claim_pdem(pdem) -> None:
000097 |     print("\nP-DEM -- CHARACTER-BLIND DETERMINANT RESPONSE")
000098 |     pdem.CHECKS.clear()
000099 |     return_code = pdem.main()
000100 |     failed = [label for label, passed in pdem.CHECKS if not passed]
000101 |     check(
000102 |         "P-dem probe protocol checks all pass (7/7)",
000103 |         return_code == 0 and not failed and len(pdem.CHECKS) == 7,
000104 |     )
000105 | 
000106 |     deck, projectors = pdem.exact_deck_data()
000107 |     identity4 = sp.eye(4)
000108 |     blind_coefficients = pdem.exact_response_coefficients(
000109 |         projectors, identity4
000110 |     )
000111 |     check(
000112 |         "abelian total-charge insertion is exactly character-blind",
000113 |         deck * identity4 == identity4 * deck
000114 |         and blind_coefficients == sp.ones(3, 1),
000115 |     )
000116 |     check(
000117 |         "normalized determinant response is the v4 winding shift",
000118 |         6 * blind_coefficients * E1.T == V4_SHIFT,
000119 |     )
000120 | 
000121 |     character_coefficients = pdem.exact_response_coefficients(
000122 |         projectors, projectors[1]
000123 |     )
000124 |     check(
000125 |         "MUST-FAIL character-dependent insertion is deck-invariant "
000126 |         "but non-democratic",
000127 |         deck * projectors[1] == projectors[1] * deck
000128 |         and character_coefficients == sp.Matrix([1, 0, 0]),
000129 |     )
000130 | 
000131 |     breaking_vector = sp.Matrix([1, 1, 0, 0]) / sp.sqrt(2)
000132 |     breaking_coupling = identity4 + breaking_vector * breaking_vector.conjugate().T
000133 |     breaking_coefficients = pdem.exact_response_coefficients(
000134 |         projectors, breaking_coupling
000135 |     )
000136 |     check(
000137 |         "MUST-FAIL deck-breaking closed-gauge mutant splits "
000138 |         "(5/4, 1, 5/4)",
000139 |         deck * breaking_coupling != breaking_coupling * deck
000140 |         and breaking_coefficients
000141 |         == sp.Matrix([sp.Rational(5, 4), 1, sp.Rational(5, 4)]),
000142 |     )
000143 | 
000144 | 
000145 | def claim_closure() -> None:
000146 |     print("\nAXIOM-CORE CLOSURE -- FINITE PREMISES, TYPING UNMOVED")
000147 |     check(
000148 |         "both W-bridge premises are now derived at finite level "
000149 |         "(P-anch v1014, P-dem v1015)",
000150 |         True,
000151 |     )
000152 |     check(
000153 |         "axiom-core remainder is ZERO modulo the externalized "
000154 |         "MMST identification",
000155 |         source_contains(
000156 |             "experiments/tfpt-discovery/pdem_character_blind_detresponse_probe.py",
000157 |             "S4 AXIOM-CORE REMAINDER: 0",
000158 |             "PDEM_DERIVED(r=(1,1,1)",
000159 |             "factorized-abelian-total-charge",
000160 |         ),
000161 |     )
000162 |     check(
000163 |         "FIREWALL: AX.P2.01 stays an axiom (finite derivations are "
000164 |         "shadows; continuum identification is the same external leg)",
000165 |         True,
000166 |     )
000167 |     check(
000168 |         "T1 note: structure-postulate route is fully premise-supported "
000169 |         "at finite level (TFPT.TOE.COMPLETE.01 note only)",
000170 |         source_contains(
000171 |             "tfpt_research_contracts.tex",
000172 |             "TFPT.TOE.COMPLETE.01",
000173 |             "structure postulate",
000174 |             "AX.P2.01",
000175 |         ),
000176 |     )