TFPT scientific source excerpt Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/pfaff_source_review/DECISION.txt Original file SHA-256: 7fc10af4c8eef6a30cab621683fd0acb6e739ea4c017380388e6dcb99512f854 Inclusive original lines: 1-58 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 | FIXED QUARTER PFAFFIAN CANDIDATE: REVIEWED DECISION 000002 | 29 October 2026 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 | 000009 | Use the actual earlier D_a,N,Z,S,Jhat,Jloc definitions. The established 000010 | identity is Jloc D_a Jloc^-1=-D_(-a^J). The actual old skew theorem requires 000011 | a^J=-a and a selfadjoint invariant domain. For scalar a=alpha I this is 000012 | instead -D_alpha+2alpha S. Thus on the inner smooth core, 000013 | beta_alpha(x,y)+beta_alpha(y,x)=2alpha. 000014 | Choose x=f(r)e_R tensor u, real compactly supported f, constant periodic 000015 | circle profile and J_F u=u. The normal derivative integral is zero and 000016 | the Phi pairing has orthogonal normal components, giving 000017 | beta_alpha(x,x)=alpha||x||^2. 000018 | It is nonzero at BOTH original quarters1/4 and3/4. This particular beta 000019 | cannot be the proposed same-parameter antisymmetric Grassmann kinetic form. 000020 | The exact independent finite matrix check retains the normal/KO6 algebra; 000021 | it is a check of this defect, not a complete physical P1 countermodel. 000022 | 000023 | Taking its skew part removes this scalar holonomy. The existing winding 000024 | changes alpha to1-alpha; it does not fix either quarter. A J-odd charge 000025 | connection or an explicitly identified paired-holonomy source is not ruled 000026 | out. Neither may be silently substituted for the stated scalar chart or 000027 | identified with its two geometric boundary faces. C0 and Jloc are distinct. 000028 | All existing positive whole Clifford/R/state/time maps remain valid. 000029 | 000030 | The proposed determinant-magnitude test is also already a logarithmic 000031 | classification. On a full signed Dirac pair the correct necessary condition 000032 | is2 x f'(x)+1=0. On an undoubled complex kinetic block it is x f'(x)+1=0. 000033 | Pf([[0,K],[-K^t,0]])=sign detK, so formal doubling gives no extra physical 000034 | half. A phase-only eta comparison cannot repair a real-profile mismatch. 000035 | 000036 | The older regular positive Bernstein class cannot equal this logarithm on 000037 | an open variable spectral interval. The newer source001 allows ANY declared 000038 | profile and calls Bernstein an analytic choice. Hence this is NOT a global 000039 | P1 exclusion of logarithmic relative profiles. A relative heat integral 000040 | with dt/(4t), compatible kinetic reference, UV and zero-mode treatment is a 000041 | valid conditional construction. Its scale-flow idea was already present in 000042 | v477 and the original text explicitly leaves the scale measure an input. 000043 | The primitive deck-even D_ref is not automatically that fermion reference. 000044 | 000045 | A pure normalized graph G determines its CAR state. It is not a bulk inverse 000046 | Green operator or the unnormalized Pfaffian amplitude. These require the 000047 | actual common integration/source pairing and reference. The direct defect 000048 | above settles only the proposed fixed-quarter beta_D identification; it 000049 | is not a no-go for TFPT, Pfaffians, complex Dirac fields or the positive 000050 | coupled source already constructed. 000051 | 000052 | [OMITTED: non-scientific conversation or execution metadata] 000053 | [OMITTED: non-scientific conversation or execution metadata] 000054 | [OMITTED: non-scientific conversation or execution metadata] 000055 | [OMITTED: non-scientific conversation or execution metadata] 000056 | [OMITTED: non-scientific conversation or execution metadata] 000057 | [OMITTED: non-scientific conversation or execution metadata] 000058 | [OMITTED: non-scientific conversation or execution metadata]