TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/JOINT-HIGGS-TWOFACE-SOURCE-CONSTRAINT-20261102.txt
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Inclusive original lines: 64-93
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000064 | cross block X_H=(2 cosh(ell h_H))^-1 at fixed constant H, h_H^2=p^2+Phi_H^2.
000065 | With a shared real face frame, define
000066 | 
000067 |  B_Q = (1/2) sum_{a in Q}(a^dagger_{left,a} a_{right,a}+h.c.).
000068 | 
000069 | The two face labels are not the internal L/R chiralities. Put u=H^dagger H,
000070 | and y_j the six given quark Yukawa singular values. Then
000071 | 
000072 |  g(u)=<B_Q>_H=Tr_Q X_H
000073 |      =6 sum_{j=1}^6 [2 cosh(ell sqrt(p^2+y_j^2 u))]^-1. (4)
000074 | 
000075 | Each of six singular values has multiplicity 3 colors times 2 chiralities.
000076 | For ell>0, p>0 and at least one y_j nonzero, g is strictly decreasing on
000077 | u>=0. For f(u)=u/(1+u), any positive normalized mu with nonconstant u gives
000078 | 
000079 |  Cov_mu(f,B_Q) = (1/2) integral integral (f(u)-f(v))
000080 |                             (g(u)-g(v)) dmu(u)dmu(v) < 0.  (5)
000081 | 
000082 | If mu assigns masses m_A,m_B to [0,a] and [b,infinity), 0<=a<b, then
000083 | Cov_mu(f,B_Q) <= -m_A m_B [f(b)-f(a)][g(a)-g(b)]. Both f and B_Q are
000084 | bounded for this finite carrier. A common unitary frame transformation on
000085 | both faces leaves B_Q invariant. Independent face gauge transformations
000086 | require the actual transported identification; no Wilson bridge is assumed.
000087 | 
000088 | The real face chart, inclusion of the conditional H fibers in the same
000089 | original source, all further vertices, reference/eta/Z0, H-dependent weights,
000090 | and comparison with the primitive P1 source remain to be established. In
000091 | particular no actual Higgs probability or nonzero H fluctuation follows here.
000092 | The finite constant-H slice alone says nothing about generic H(x) measures.
000093 |