TFPT scientific source excerpt Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ROOT-C6-KO-CANDIDATE-REVIEW.txt Original file SHA-256: f691ed00544966a616cebfa260517a6a464ef7d68bc805f4e1ca6a0122e84a03 Inclusive original lines: 1-70 Line numbers below refer to the original source. This bounded excerpt is source evidence; it is not a new proof/checker run. Conversation metadata and personal execution details are omitted where indicated. 000001 | Root review, 30 October 2026 000002 | 000003 | [OMITTED: non-scientific conversation or execution metadata] 000004 | [OMITTED: non-scientific conversation or execution metadata] 000005 | 000006 | 1. Original EM3:80-125, EM4:353-389 and EM5:118-242 were read through 000007 | tfpt-knowledge with registered paths and source hashes. They confirm the 000008 | structural inverse square root, the finite six-word resolvent and the four 000009 | cosine eigenvalues. With A=D_f P_str, A^dagger A=H on Ran P_str, the given 000010 | gap makes K=H^(-1/2) unique. V=A K is isometric because V^dagger V=K H K=I. 000011 | The original Yukawa consumer uses Hol K. Substituting Hol V would change 000012 | the original coefficient formula. K is a coupling coefficient and is not 000013 | required to be a CAR field map. Its failure to be an isometry excludes only 000014 | that proposed identification, not its legitimate original use in Y. 000015 | 000016 | 2. The cubic inverse-square-root interpolation in the C6 Gram report was 000017 | checked symbolically at c=1,-1,1/2,-1/2: all four residuals are exactly zero. 000018 | It requires no additional physical integration measure. The resolvent 000019 | integral for delta K is a functional-calculus identity, not a newly derived 000020 | P1 scale measure. Delta Y=(delta Hol)K+Hol delta K is the actual next 000021 | coefficient comparison, including frame variation if the frame varies. 000022 | 000023 | [OMITTED: non-scientific conversation or execution metadata] 000024 | [OMITTED: non-scientific conversation or execution metadata] 000025 | [OMITTED: non-scientific conversation or execution metadata] 000026 | [OMITTED: non-scientific conversation or execution metadata] 000027 | [OMITTED: non-scientific conversation or execution metadata] 000028 | [OMITTED: non-scientific conversation or execution metadata] 000029 | [OMITTED: non-scientific conversation or execution metadata] 000030 | [OMITTED: non-scientific conversation or execution metadata] 000031 | [OMITTED: non-scientific conversation or execution metadata] 000032 | [OMITTED: non-scientific conversation or execution metadata] 000033 | [OMITTED: non-scientific conversation or execution metadata] 000034 | [OMITTED: non-scientific conversation or execution metadata] 000035 | [OMITTED: non-scientific conversation or execution metadata] 000036 | 000037 | 4. The existing exact whole96 checker was independently replayed by root: 000038 | PASS, rank64, repeated nonzero family singular value1.699157120653 for 000039 | the printed rounded inputs. Its generic test matrix has binary-exact 000040 | dyadic real and imaginary coefficients; the symbolic identities above 000041 | provide the general proof. No physical mass prediction follows from this 000042 | unscaled conditional matrix. The actual raising identity 000043 | [T_plus,X_w2]=X_w1 forbids unrelated bare family coefficients on those two 000044 | components of this fixed doublet. Original sector-specific intertwiners 000045 | and HolK consumers remain allowed and must not be excluded by this test. 000046 | 000047 | 5. Root independently integrated the proposed second ray with continuous 000048 | factorized zeta(w)=-omega sqrt(1-w)sqrt(1+omega w), zeta(0)=-omega: 000049 | I'=0.4213752856971043792014444689166786680972 000050 | -1.572593975275444788048708055806669722451 i, 000051 | I'/I=3.347597664025180155360831848819267811936, 000052 | numerical imaginary residual <1.9e-66 at65digits. 000053 | This confirms the proposed RAY INTEGRAL magnitude. It does not calibrate 000054 | the actual G q1/p0 reader or establish a complete original M21 entry. 000055 | The general KO exclusion above does not depend on such a calibration. 000056 | 000057 | 6. The original primitive wedge consumer remains positively established. 000058 | It reads the actual directed nonzero Hardy coefficient as+kappa and the 000059 | fixed signed KO pairing as-kappa. No missing weak-operation gate is 000060 | introduced. The source question is the actual original representation or 000061 | variation of the Hol K coefficient, not a requirement that this one moment 000062 | replace every original Yukawa matrix. 000063 | 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] 000068 | [OMITTED: non-scientific conversation or execution metadata] 000069 | [OMITTED: non-scientific conversation or execution metadata] 000070 | [OMITTED: non-scientific conversation or execution metadata]