TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/HIGGS-MIXTURE-WICK-PROOF.txt
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000086 | 4. Exact whole-class discriminator
000087 | Let Cbar=int C_H dmu, and let omega_G be the quasifree state with that SAME
000088 | full two-point data, including zero anomalous pairs on this subalgebra.
000089 | Its left covariance is Abar tensor I3 and Tr Abar=int m_H dmu.
000090 | Equations(2)-(3), without any simultaneous diagonalization in H, imply
000091 |   omega(O)-omega_G(O)=24 Var_mu(m(u)).                      (4)
000092 | Thus if the actual positive H mixture has nonconstant u and a nonzero
000093 | quark Yukawa, this invariant four-field difference is STRICTLY positive.
000094 | The entire positive-weight class is decided by the proof, not by40 checks.
000095 | 
000096 | The covariance logarithm log((I-Cbar)Cbar^-1) remains an exact two-point
000097 | reader; its associated quasifree state fails(4). It cannot be the full
000098 | H-averaged source. In finite faithful restrictions, -log rho of the actual
000099 | mixed state contains terms beyond quadratic in the fermion operators.
000100 | This does NOT assert that its only missing term is quartic or determine a
000101 | physical coupling coefficient. Allowing arbitrary anomalous pairs in a
000102 | replacement changes other two-point data; it does not preserve this source.
000103 | 
000104 | 5. Limits and connection to the existing whole theory
000105 | At constant u, p=0, ell=0, or all quarkY=0 the strict witness can vanish;
000106 | vanishing is not a general proof of quasifreeness. A complex or signed
000107 | weight does not support the positive-variance conclusion. Additional
000108 | conditional interactions require their conditional four-point response,
000109 | which can contribute to or cancel the displayed defect. Arbitrary local
000110 | H(x), gauge fields and continuum measures are not derived by this theorem.
000111 | 
000112 | In particular a primitive quasifree C_Sigma BEFORE H integration remains
000113 | possible. The current original modular route must specify the order:
000114 | conditional source and carrier map first, whole H integration after, or
000115 | a genuine many-body reader preserving(4). Nothing here identifies the
000116 | given conditional H family with that primitive C_Sigma or derives mu/P_F.
000117 | 
000118 | R026's exact full-H cumulant functional is reused. R054 adds the explicit
000119 | invariant quark four-field witness and its strict all-positive-mixture
000120 | test against the covariance-only current reader, not another discovery