TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ROOT-FULL-HOM-DECK-CONTRACTION-CHECK.json
Original file SHA-256: 0063e7ac73702a2918386ffc0935a2a76052e465b235a694b51bb7e7fb4a1e56
Inclusive original lines: 1-42
Line numbers below refer to the original source.
This bounded excerpt is source evidence; it is not a new proof/checker run.
Conversation metadata and personal execution details are omitted where indicated.

000001 | {
000002 |   "original_deck_group": "(C2)^4",
000003 |   "q_nontrivial_characters": [
000004 |     1,
000005 |     2,
000006 |     3
000007 |   ],
000008 |   "p_nontrivial_characters": [
000009 |     4,
000010 |     8,
000011 |     12
000012 |   ],
000013 |   "mixed_characters": {
000014 |     "(0, 0)": 5,
000015 |     "(0, 1)": 9,
000016 |     "(0, 2)": 13,
000017 |     "(1, 0)": 6,
000018 |     "(1, 1)": 10,
000019 |     "(1, 2)": 14,
000020 |     "(2, 0)": 7,
000021 |     "(2, 1)": 11,
000022 |     "(2, 2)": 15
000023 |   },
000024 |   "duality": "Hom(Lqa,Lpb)=Lqa^dual tensor Lpb; original sign lines have L^dual=L",
000025 |   "bundle_identity": "K tensor Lqa tensor Lpb = K tensor Hom(Lqa,Lpb), using existing two-torsion pairings",
000026 |   "evaluation": "(K tensor Hom(Fq,Fp)) tensor Hom(Fp,Fq) -> K by composition and trace",
000027 |   "exact_deck_pair_checks": 144,
000028 |   "result": "all signs cancel under dual Hom contraction",
000029 |   "scope": "Existing bundle/section evaluation, not selection of a Fourier component or derivation of the physical Yukawa/CP insertion. No independent q/p CAR species or joint state introduced.",
000030 |   "actual_endomorphism_channel": {
000031 |     "action": "Ad(Pc)Y=Pc Y Pc^T",
000032 |     "omega_squared_eigenspace_dimension": 3,
000033 |     "basis": [
000034 |       "Q",
000035 |       "Q Pc",
000036 |       "Q Pc^2"
000037 |     ],
000038 |     "Q": "diag(1,omega,omega^2)",
000039 |     "counterexample_to_unique_clock_from_Pc_alone": "Q and Q Pc are unitary eigenoperators with the same character and are not scalar multiples. Uniqueness needs extra marked-basis conditions.",
000040 |     "physical_cp_claim_checked": false
000041 |   }
000042 | }