TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/EINSTEIN-NOETHER-HYPOTHESES-PROOF.txt
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000095 | identities only where normalization exists, not probability positivity.
000096 | S_W is a Wilsonian marginal action, NOT the Legendre1PI Gamma_k of v42.
000097 | Their response variables and Hessians cannot silently be interchanged.
000098 | Equivariant restriction pushes a symmetry-invariant full measure to an
000099 | invariant marginal. This transports Ward identities; it does not pick the
000100 | top-level weight. The R080 conditional marginal identity including Z ratios
000101 | remains the correct actual compatibility test.
000102 | 
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000110 | 
000111 | Apply the actual gamma+ projection in the given36 quark family as a
000112 | diagnostic18-mode restriction, NOT an asserted physical P_F or Padm:
000113 |  P B_H P=0, but dC_P=P L_expit,K(B_H)P is nonzero at p!=0,H!=0.
000114 |  dK_eff=L_logit,C_P(dC_P).
000115 | The native norm is0.012355221413395484. Reapplying L_expit,Keff reconstructs
000116 | dC_P with residual7.05e-18; an independent finite-difference check gives
000117 | 8.64e-11. Hence the effective retained Higgs vertex is fixed by the same
000118 | parent conditional source even when the bare compressed vertex vanishes.
000119 | No new coupling, scalar potential or second Higgs insertion is added.
000120 | 
000121 | This follows analytically on each actual original Yu singular pair:
000122 |  K=2ell [[p,r s],[r s,-p]], E=sqrt(p^2+r^2s^2),
000123 |  c_P=(1+(p/E)tanh(ell E))/2,
000124 |  k_eff=2 artanh[(p/E)tanh(ell E)].
000125 | At p>0,r*s!=0, tanh(ell E)/E decreases strictly with E, so
000126 | 0<k_eff<2ell p and its radial derivative is nonzero. The determinant and
000127 | positive c_P are determined by the original pair, not a fitted ansatz.
000128 | For all retained words the exact finite unnormalized marginal is
000129 |  Tr_Q exp(dGamma(K))=(Z_full/Z_keep)exp(dGamma(K_eff)),
000130 |  Z_full=det(I+exp K), Z_keep=det(I+exp K_eff).
000131 | Independent4-state Fock partial trace verifies both normalized density and
000132 | absolute ratio1.9411362982039795 to below7e-16. The plus sign is fixed by
000133 | the convention rho proportional to exp(+dGamma(K)). A physical Majorana
000134 | Pfaffian is not replaced by a doubled96 Fock determinant.
000135 |