TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/CURRENT-CARRIER-ODD-READER-WHOLE-SOURCE.txt
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000001 | THE CURRENT CARRIER READER ON THE ACTUAL WHOLE COUPLED SOURCE
000002 | 30 October 2026. Exact source/operator continuation; no Atlas or original edit.
000003 | 
000004 | 1. What the current named P_F actually supplies
000005 | Current original: documents/tfpt_2_standard_model/sections/
000006 | 010-section-the-explicit-mass-gap-closes-dynamics-and-cluste.tex:306-309,
000007 | paper-source:2f8a823f065f3d3a1c82d4dc. The same call is printed at
000008 | documents/tfpt_research_contracts/sections/002-source.tex:228-236.
000009 | It is C_F=P_F C_Sigma P_F, then a logarithmic covariance reader. Neither
000010 | current paragraph gives a matrix/isometry formula defining this named P_F.
000011 | 
000012 | The graph-first code path is verification/v258_dirac_covariance_induction.py:
000013 | induce:65-69 receives ONLY C. Inbound calls are run:79-157 and the already
000014 | reviewed p1_insertion_tangent.covariance_checks:48-96. The former computes
000015 | its C from supplied Hermitian/Yukawa matrices; the latter differentiates
000016 | the reader and tests a moving comparison embedding. Neither call executes
000017 | a source-to-finite96 P_F constructor. The named P_F occurs in the docstring
000018 | and recorded physical-identification statement, not an operator argument
000019 | or a computed projection. This reuses finding:v258-forward-source-gap-is-
000020 | reused-not-solved-by-inversion; it is not a new absence theorem.
000021 | 
000022 | Crucially, the FULL ORIGINAL reader at v258:24-27 is
000023 |   D_ind=mu_geo Pi_odd^gamma log((I-C_F)C_F^-1),           (1)
000024 | where Pi_odd uses gamma_F, and mu_geo is the declared modular scale. The
000025 | short paper formula suppresses Pi_odd. Its presence changes what can be
000026 | obtained from the existing whole source; it must not be dropped.
000027 | 
000028 | 2. The already existing explicit carrier isometry and what it reduces
000029 | Reuse graded_boundary_functor/FINITE-COUPLED.txt:28-68. Its actual checker
000030 | check_finite_typing.py:28-42 imports v252.full_D and grading, then sets
000031 |   Pplus=(I+gamma)/2, Pminus=(I-gamma)/2,
000032 |   E v=(Pplus v,i Pminus v),
000033 |   Gamma_tot=Z tensor gamma,
000034 |   B_s=Z A-S Phi_s, h_s=A gamma-i gamma Phi_s.
000035 | The fixed identity E*E=I and exact BE=Eh are already tested at47-54.
000036 | This E retains the entire96 coefficient of the actual v252 builder.
000037 | Its projection is
000038 |   p_E=EE*=(I+Gamma_tot)/2, [p_E,B_s]=0.                 (2)
000039 | Thus E is an actual reducing isometry for the whole operator on its given
000040 | H1 domain, not a dimension match or an arbitrary frequency selection.
000041 | It is finite rank96 PER NORMAL FIBER. On the circle the projection has
000042 | infinite total rank, as the existing internal-carrier finding already states.
000043 | The C0 conjugate summand remains in the full T_faces field chart.
000044 | 
000045 | For the already labeled source faces, let j2(v)=(0,Ev). Then exactly
000046 |   j2* G(B_s) j2=(I+exp(2ell h_s))^-1=:C_s.             (3)
000047 | The face compression is NOT reducing for the full G: its crossing block
000048 | X_s is nonzero. Formula(3) is the actual known compression identity, not
000049 | a claim that compression commutes with an arbitrary spectral function.
000050 | Equivalently, take the given face2 KMS covariance first and then use E.
000051 | No new state, independent face species or bosonic background is selected.
000052 | 
000053 | 3. Execute ALL original reader factors, including the odd projection
000054 | Use exactly the real original inner-form family from the preceding report:
000055 |   Phi_s=(1+s)D_Y+D_MR, {gamma,Phi_s}=0.
000056 | For(3), spectral calculus on Dom(h_s)=H1 gives
000057 |   log((I-C_s)C_s^-1)=2ell h_s.
000058 | Now use the original Pi_odd^gamma(T)=(T-gamma T gamma)/2. Because A commutes
000059 | with gamma, A gamma is EVEN, while -i gamma Phi_s is ODD. Consequently
000060 |   mu_geo Pi_odd^gamma log((I-C_s)C_s^-1)
000061 |       =-2ell mu_geo i gamma Phi_s.                     (4)
000062 | All96 entries and the actual Majorana term are retained. Equation(4) is
000063 | independent of the Fourier momentum p. It is the bounded multiplication
000064 | operator I_circle tensor(-2ell mu_geo i gamma Phi_s), so its constant
000065 | finite coefficient is an actual96 matrix. It is not a finite rank operator
000066 | on the whole circle. No finite Fourier cutoff is needed to read that matrix.
000067 | 
000068 | For the fixed grading unitary U_gamma=exp(-i pi gamma/4),
000069 |   U_gamma Phi_s U_gamma*=-i gamma Phi_s.
000070 | Thus the EXACT output is 2ell mu_geo U_gamma Phi_s U_gamma*, and its jet is
000071 |   delta D_ind=2ell mu_geo U_gamma D_Y U_gamma*.
000072 | No value mu_geo=1/(2ell) has been selected or derived. The original modular
000073 | scale factor is explicit throughout. For the actual KO6 J_F,
000074 | J_F gamma J_F^-1=-gamma and antilinearity gives J_F U_gamma J_F^-1=U_gamma.
000075 | U_gamma also commutes with the represented even finite algebra and grading.
000076 | Hence this fixed comparison preserves the original charge/grade dictionary;
000077 | it is not an assertion that U_gamma is an inner physical gauge transformation.
000078 | 
000079 | E and Pi_odd are reused infrastructure. The new combined calculation is
000080 | their full current-reader chain on the actual coupled Phi_s, rather than
000081 | an inversion with its whole source and kinetic term suppressed.
000082 | 
000083 | 4. Precise result and source-name boundary
000084 | The existing typed source has a concrete reducing carrier chart E, followed
000085 | by a known nonreducing face compression. Applying the complete ORIGINAL
000086 | reader to that actual face recovers the whole finite coefficient by(4).
000087 | It does not recover the INITIAL COUPLING VALUES from data independent of
000088 | them: Phi_s was already the given coefficient of this source family.
000089 | 
000090 | In these current paragraphs and their v258 call graph the SYMBOL P_F is
000091 | not bound to j2, p_E, a finite Fourier projection or a distinct finite
000092 | Hilbert-space embedding. We do not
000093 | declare that binding proved. If the intended current reading is the usual
000094 | fiberwise internal carrier, equations(2)-(4) give a well-typed whole-source
000095 | implementation and remove any supposed need for an extra frequency cut.
000096 | If instead C_F is required to be a literal finite-rank compression from
000097 | the whole circle, that is a different operator call which(2) does not claim.
000098 | The original full joint-source routes remain available; this review imposes
000099 | neither choice as a new universal condition on P1.
000100 | 
000101 | No new test suite or unrelated covariance model was built. The old source,
000102 | both faces, conjugate slots, fixed domains and actual normalization factors
000103 | were retained. The bare pure projector G itself was never put into the
000104 | strict-contraction logarithm, and no nonlinear logarithm was commuted
000105 | through a newly selected projection.