TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ROOT-COMMON-MARKED-FUCHS-HARDY-REVIEW.txt
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000001 | COMMON MARKED FUCHS FRAME AND THE ORIGINAL HARDY WORD
000002 | 30 October 2026. Root independent exact review.
000003 | 
000004 | The earlier single-loop intertwiner does not automatically transport the
000005 | quarter generator. The existing Gbase and its already proved metric supply
000006 | the stronger common frame directly, without fitting either generator.
000007 | 
000008 | Use the calibrated original rho and tau=i omega^2 from
000009 | ORIGINAL-FUCHS-ALGEBRAIC-FRAME.txt and the established identity
000010 |   Gbase Gbase^dagger=diag(27/10,9sqrt(3)/5,3sqrt(3)).
000011 | Let H0=(Gbase Gbase^dagger)^-1. Then
000012 |   H0^(1/2) Gbase=exp(7pi i/12) Bstar,
000013 |   Bstar=(1/sqrt(2)) [[0,0,-1+i],[1,i,0],[i,1,0]].
000014 | The common scalar phase cancels from endomorphism conjugation. It does
000015 | not repair a Yukawa phase by itself. Root directly evaluated the literal
000016 | Gbase and metric: residual5.47e-16. Bstar unitarity is exact.
000017 | 
000018 | With the actual based signed cycle Cs and signed quarter KQ from the
000019 | existing G frame, exact rational-complex matrix algebra gives
000020 |   Bstar Cs Bstar^dagger=M0,
000021 |   Bstar KQ^-1 Bstar^dagger=U, U=diag(1,i,-i).
000022 | Here M0 is the actual original v117 unitary monodromy, not a fitted matrix.
000023 | For every k=0,1,2,3 this yields, and root independently checked,
000024 |   Bstar KQ^-k Cs KQ^k Bstar^dagger=U^k M0 U^-k.
000025 | Thus the SAME source-normalized frame carries all four marked meridians
000026 | and their quarter generator. Matching one eigenvalue set was not used.
000027 | 
000028 | The certified Hardy contribution has a stronger original endpoint match:
000029 |   Bstar E02 Bstar^dagger=M0 P0,
000030 |   Bstar E22 Bstar^dagger=P0, P0=|e0><e0|.
000031 | Both identities were checked exactly. The already existing quarter-fixed
000032 | input line e0 is obtained by the fixed frame, not chosen to fit the Hardy
000033 | answer. Consequently the contribution kappa E02 is exactly kappa M0 P0
000034 | in the common originally marked monodromy/quarter frame. It is an explicit
000035 | open-word coefficient, compatible with the known primitive wedge consumer.
000036 | 
000037 | This is a positive common coefficient and endpoint identification. It does
000038 | not assert kappa P0=Kstr, that the whole Yukawa equals this rank-one term,
000039 | or that a specified Zadm derivative has already inserted the term. Entire
000040 | spine/Pstr/transport sums and their original source call must be retained.
000041 | For a lift to the full96 space, the real structure, Clifford operations
000042 | and endpoint marks must move with the complex Bstar. Holding J_F fixed
000043 | while changing only the family matrix would not be the same construction.
000044 | 
000045 | Root checks: workspace outputs/multi-model-source-search-20261029/
000046 | ROOT-COMMON-MARKED-FUCHS-HARDY-CHECK.json. All six exact identities pass.
000047 | Reuse actual path Cs and positive G-metric proof in
000048 | ROOT-ACTUAL-PATH-G-METRIC-REVIEW.txt and the existing algebraic frame/metric
000049 | records. No original sources, state, quantization, coupling weights,
000050 | physical time or ledger status were changed by this finite identification.