TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/CLAUDE56-GROK57-FIRST-STEP-REVIEW.txt
Original file SHA-256: c24a7b1da0b3b6e6dcdaeeba534b6b81396f96df5714f4d52868dc8b3063eae8
Inclusive original lines: 1-47
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 | [OMITTED: non-scientific conversation or execution metadata]
000002 | [OMITTED: non-scientific conversation or execution metadata]
000003 | 
000004 | [OMITTED: non-scientific conversation or execution metadata]
000005 | [OMITTED: non-scientific conversation or execution metadata]
000006 | [OMITTED: non-scientific conversation or execution metadata]
000007 | [OMITTED: non-scientific conversation or execution metadata]
000008 | [OMITTED: non-scientific conversation or execution metadata]
000009 | [OMITTED: non-scientific conversation or execution metadata]
000010 | 
000011 | Smallest algebraic check: retain one supplied normalized Gaussian
000012 | fermionic factor Z_rel=sqrt((a+u k)/a_ref), a_ref fixed, u=|H|²,
000013 | and the already present logdet(a+u k+b). The whole coefficient of u is
000014 |   k[1/(a+b)-1/(2a)].
000015 | At a=b=1 it vanishes while the determinant-only coefficient is k/2.
000016 | This is a diagnostic counterexample to the claimed inference, NOT the
000017 | definition of original TFPT Z, its domain, Pfaffian, or regularization.
000018 | It shows why the missing relative-Z derivative cannot be silently dropped.
000019 | It does not establish actual TFPT cancellation or actual failure of it.
000020 | 
000021 | [OMITTED: non-scientific conversation or execution metadata]
000022 | [OMITTED: non-scientific conversation or execution metadata]
000023 | [OMITTED: non-scientific conversation or execution metadata]
000024 | 
000025 | For the isolated trace Tr(Ku² V Kd² V*) the unistochastic expression and
000026 | permutation extrema are correct. They do not imply that the ENTIRE master
000027 | has no nontrivial mixing extremum: its other terms and actual allowed
000028 | variations are not included in that linear functional. No new mixing
000029 | optimization is warranted; original rigid transports remain inputs.
000030 | 
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 | [OMITTED: non-scientific conversation or execution metadata]
000038 | [OMITTED: non-scientific conversation or execution metadata]
000039 | [OMITTED: non-scientific conversation or execution metadata]
000040 | [OMITTED: non-scientific conversation or execution metadata]
000041 | 
000042 | [OMITTED: non-scientific conversation or execution metadata]
000043 | [OMITTED: non-scientific conversation or execution metadata]
000044 | [OMITTED: non-scientific conversation or execution metadata]
000045 | [OMITTED: non-scientific conversation or execution metadata]
000046 | [OMITTED: non-scientific conversation or execution metadata]
000047 |