TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/WHOLE-ALPHABET-CALLER-INDEPENDENT-DOMAIN-REVIEW.txt
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000001 | INDEPENDENT DOMAIN REVIEW OF THE BARE WHOLE-ALPHABET CALLER
000002 | 30 October 2026. No original source, Atlas entry or earlier report changed.
000003 | 
000004 | VERDICT
000005 | 
000006 | Section 2 of WHOLE-ALPHABET-ORIGINAL-CALLER-AND-PH-REVIEW.txt is correct.
000007 | For the specific unsmoothed candidate
000008 | 
000009 |   T_mu=J* M_mu=Swap tensor (j* M_mu),
000010 | 
000011 | the equal-time connected finite-cutoff CAR variance diverges. No missing
000012 | mode, half-density or coefficient-fiber map repairs that bare candidate.
000013 | 
000014 | The induced mu multiplier has a nonzero surviving local coefficient
000015 | 
000016 |   f(theta) of order |theta-theta_j|^(-2/3).
000017 | 
000018 | It is L1 but not L2. The retained G/W maps and the two half-density factors
000019 | leave this base multiplier unchanged. Scalar induction takes the sum of the
000020 | three cable norms, so nonzero leading jets on distinct cables do not cancel
000021 | as scalar amplitudes. The given q/p map j is unitary and preserves the L2
000022 | failure.
000023 | 
000024 | Take the original occupied n=0, P_gamma,+ mode with graph vector
000025 | v=(c,d), c,d>0, and write a_m for the output Fourier coefficients. Then
000026 | 
000027 |   sum_m ||a_m||^2=infinity,
000028 |   T_mu v=(d,c) a_m.
000029 | 
000030 | On the finite carrier fiber the graph projectors converge uniformly to
000031 | 
000032 |   G_m -> diag(1,0) as m->+infinity,
000033 |   G_m -> diag(0,1) as m->-infinity.
000034 | 
000035 | Therefore
000036 | 
000037 |   ||(1-G_m)(d,c)||^2 -> c^2 or d^2
000038 | 
000039 | and is bounded below on both tails. Hence
000040 | 
000041 |   Tr[G T_mu* (1-G) T_mu]
000042 | 
000043 | diverges along the canonical finite spectral cutoffs already on this one
000044 | occupied input column.
000045 | 
000046 | This excludes only the vacuum-domain claim for the unsmoothed bare
000047 | cross-face quadratic. It does not exclude a sewn, reflected, relative or
000048 | genuinely renormalized caller, and it does not show that the original P1 or
000049 | Z source selects this candidate.
000050 | 
000051 | The fixed quotient normalizer in QFT002:256-265 and QFT008:143-151 is
000052 | source independent. Thus every positive-order source derivative of
000053 | log Zrel equals the corresponding derivative of log Zadm. That normalizer
000054 | does not subtract the mu variance or select the finite Pi/Pi_h corner as a
000055 | regular part. This says nothing against a genuinely source-dependent
000056 | Sadm or Sprim variation.
000057 | 
000058 | Finally, the positive route
000059 | 
000060 |   finite Hardy reader -> original WEDGE consumer -> finite D_F/Sadm term
000061 | 
000062 | does not require geometric mu itself to be this unsmoothed CAR current.
000063 | Its bounded finite coupling contribution is untouched by the bare-domain
000064 | diagnostic. No whole-matrix-product to physical-field-product rule is added.
000065 | 
000066 | SOURCES CHECKED
000067 | 
000068 |   WHOLE-ALPHABET-ORIGINAL-CALLER-AND-PH-REVIEW.txt:42-83;
000069 |   SPIN-PRODUCT-BOUNDARY-WEIGHT-REVIEW.txt:55-140;
000070 |   INDUCED-HARDY-DEFECT-BMU-FINITE-READER.txt:45-71,87-108;
000071 |   HARDY-BMU-FIRST-NONZERO-ENTRY.txt:77-90;
000072 |   ROOT-PH-CORRELATIONS-ADJOINTS-AND-CALLER-REVIEW.txt:55-84.
000073 |