TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/FINITE-PH-QUADRATURE-INDEPENDENT-REVIEW.txt
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000001 | INDEPENDENT REVIEW OF THE FOUR FINITE PARTICLE-HOLE QUADRATURES
000002 | 30 October 2026. No original source, Atlas entry or earlier report changed.
000003 | 
000004 | VERDICT
000005 | 
000006 | The four-dimensional real covariance in
000007 | ROOT-PH-CORRELATIONS-ADJOINTS-AND-CALLER-REVIEW.txt is algebraically correct
000008 | and agrees with ROOT-ACTUAL-PH-CAR-AND-ADJOINT-REPLAY.json.
000009 | 
000010 | Let
000011 | 
000012 |   h=|I02|^2+|I21|^2,
000013 |   z=-2i I02 I21,
000014 |   g=16(2/pi)^2 tanh^2(ell_NS/2).
000015 | 
000016 | The finite canonical Pi/Pi_h corner has
000017 | 
000018 |   C(F*,F)=C(N*,N)=g h,
000019 |   C(F*,N)=C(F,N*)=0,
000020 |   C(F,N)=g z,
000021 |   C(F*,N*)=g conjugate(z).
000022 | 
000023 | For the selfadjoint quadratures, each normalized by 1/sqrt(2),
000024 | 
000025 |   ReF=(F+F*)/sqrt(2),      ImF=(F-F*)/(i sqrt(2)),
000026 |   ReN=(N+N*)/sqrt(2),      ImN=(N-N*)/(i sqrt(2)),
000027 | 
000028 | direct expansion gives the real symmetric covariance
000029 | 
000030 |   g [[h,0,Re z,Im z],
000031 |      [0,h,Im z,-Re z],
000032 |      [Re z,Im z,h,0],
000033 |      [Im z,-Re z,0,h]].
000034 | 
000035 | Its characteristic polynomial is
000036 | 
000037 |   [lambda-g(h+|z|)]^2 [lambda-g(h-|z|)]^2.
000038 | 
000039 | Since |z|=2|I02||I21|, the eigenvalues are
000040 | 
000041 |   g(|I02|+|I21|)^2, multiplicity 2,
000042 |   g(|I02|-|I21|)^2, multiplicity 2.
000043 | 
000044 | They are strictly positive because |I21|/|I02|=3.347597664... is not one.
000045 | This also confirms why C(F,F)=C(N,N)=0 does not imply absence of ordinary
000046 | selfadjoint fluctuations.
000047 | 
000048 | The 64-dimensional CAR replay reports all eleven relevant identities,
000049 | including the Pauli compression, the directed pairings, both positive
000050 | adjoint norms, the zero adjoint cross term, the quadrature matrix and its
000051 | positive spectrum. Its symbolic sech/tanh parameters match the analytic
000052 | face calculation before any physical value of ell_NS is chosen.
000053 | 
000054 | SCOPE
000055 | 
000056 | This is the covariance of the canonical finite E/Eh particle-hole corner,
000057 | including the actual rank-16 P_gamma,+ carrier trace per family. It is not
000058 | the full unsmoothed source response, the complete J_F/KO-real field, a CP or
000059 | CKM observable, or a proof that the original Z caller selects this corner.
000060 | 
000061 | SOURCES CHECKED
000062 | 
000063 | [OMITTED: non-scientific conversation or execution metadata]
000064 | [OMITTED: non-scientific conversation or execution metadata]
000065 | [OMITTED: non-scientific conversation or execution metadata]
000066 | [OMITTED: non-scientific conversation or execution metadata]
000067 | [OMITTED: non-scientific conversation or execution metadata]