TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ORIGINAL-HIGGS-BOUND-REFERENCE-PROOF.txt
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000001 | ORIGINAL VARIABLE HIGGS, BOUND REFERENCE AND CONFORMAL SOURCE MAP
000002 | 31 October2026. R032/R033. Conditional original-source calculations.
000003 | No new Y, lift, spacetime, action, reference prescription or ledger promotion.
000004 | 
000005 | 1. Reused originals and the genuinely new question
000006 | Keep R026-R031, actual full96 v252 finite coefficients and entire source.
000007 | The old reviewed DECK-REFERENCE-AND-ACTION.txt already proves the two full
000008 | lift identities below, including the BASE pullback. Do not repeat their
000009 | constant-field classification or the old bounded-Drel trace obstruction.
000010 | The new step is the whole VARIABLE Higgs/derivative/reference response,
000011 | and the original Dsigma sandwich with the same metric and field map.
000012 | The geometric source uses Dgeo=Dref+Drel=D, and a separate displayed
000013 | Ksigma=Dsigma,geo+Brel. Its local anchor is Dgeo, NOT Padm Drel Padm.
000014 | Primitive f(Drel)-f(Dref) and geometric f(Dfull)-f(Dref) are different
000015 | operator contracts. No claim here replaces one by the other.
000016 | 
000017 | 2. A fixed Clifford connection forces the Higgs Clifford factor
000018 | On the given local complex spin4 module S tensorF, Clifford acts by
000019 | gamma^mu tensorI. Assume D(H)=Dconn+V0+W(H), with fixed Clifford connection,
000020 | H only in order zero, and no change of first-order coefficients in D(H)^2.
000021 | The first-order change is -i{gamma^mu,W(H)}nabla_mu. It vanishes iff
000022 |  {gamma^mu,W}=0 for every mu.                         (1)
000023 | Since gamma5 anticommutes with every gamma, gamma5 W then COMMUTES with
000024 | the irreducible complex Clifford action. Its commutant is Ispin tensorEndF.
000025 | Thus W=gamma5 tensorL(H), uniquely. An H-independent V0 is not constrained
000026 | by this derivative statement; use the already given V0=gamma5 tensorDM
000027 | only when that is the actual original baseline. An H-dependent Bochner
000028 | connection, different Clifford action, or different anchor changes (1).
000029 | 
000030 | This removes an independent gamma-factor choice WITHIN this fixed-connection
000031 | contract; it does not derive the original4D manifold, module or connection.
000032 | In the supplied collar choose gamma^r=PauliY tensorI2 and the three tangent
000033 | gammas=PauliX tensorPauli_i. Their volume is PauliZ tensorI2. Hence the
000034 | existing normal Z is precisely gamma5 in that chart, not a newly fitted
000035 | mass matrix. S=PauliX tensorI preserves the tangent gammas and reverses