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Scoped exclusion

Direct Pfaffian closure fails local skew test in fixed scalar quarter chart

In the question: Automated construction of operator maps and sources

Only specified direct Pfaffian candidate at fixed scalar alpha with unchanged operators. No full P1 countermodel or general Pfaffian/TFPT no-go. Preserve given positive whole Clifford source,both faces,products,reflection and circle time. Actual J-odd charge connection or explicitly identified paired sectors are not excluded. Two faces are not automatically two quarter holonomy sectors. New conditional CAR insertion value repeats known target value rather than independently reading original source response.

Read the exact result, assumptions and evidence

Result

Actual old identity gives Jloc Dalpha Jloc^-1=−Dalpha+2alpha S. Thus beta_alpha(x,y)+beta_alpha(y,x)=2alpha<Jhat x,y>. A real compact radial profile in first normal slot with constant circle profile and J_F u=u gives beta_alpha(x,x)=alpha||x||²≠0 at both original quarters. The claimed unchanged beta_Dalpha Pfaffian source is excluded already on the interior smooth core. Old skew theorem at a^J=−a remains valid. Action comparison also requires a log profile with correctly counted full trace; eta alone determines neither magnitude nor source pairing. Later originals allow any declared f but do not thereby select a log profile; existing Frullani bridge explicitly treats scale-measure choice as input.

Required assumptions

  • Direct full Jloc Pfaffian at unchanged scalar quarter parameter

    Test new direct source closure beta_Dalpha=<Jloc.,Dalpha> in existing old-complex collar with N,Z,S=NZ,Jhat=I⊗J_F,Jloc=S Jhat,Dalpha=N(∂r+Z(-i∂theta+alpha I)−S Phi),alpha=1/4 or3/4. Phi retains existing selfadjoint,J_F and oddness identities; fields and scalar quarter parameter remain unchanged. Claim is same antisymmetric Pfaffian source directly equal to primitive spectral action. Do not presume a J-odd charge connection, additional paired holonomy sectors or a new relative log profile as original consequences.

  • Do not identify source types

    Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.

  • Geometric Clifford boundary with explicit changed complex structure

    Assume the existing free product class B=Gamma A or actual smooth tangential odd finite coefficient B_Phi=Z A-S Phi with total grading Z tensor gamma_F. Apply the standard Clifford boundary functor on the underlying real space with NEW complex structure Ical=i_old Gamma_tot and real structure C0=i_old gamma_n; the dual face has -C0. C0 is old-linear and new-antilinear,not identified with original charge J. This differs from full complex CAR quantization of both independent normal copies. State conclusions use the full graph as the actual quantum covariance in this functor. Its physical selection from P1/P2 is not presumed proved; Phi is a fixed classical background. Keep the fixed normal-independent product collar; a(theta) is smooth Hermitian and even,Phi(theta) smooth Hermitian and odd. No quantization of these bosonic backgrounds.

Original evidence

  • DECISION.txt lines 1–58

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/pfaff_source_review/DECISION.txt

    7fc10af4c8eef6a30cab621683fd0acb6e739ea4c017380388e6dcb99512f854

  • FIELD-AND-DOMAIN-REVIEW.txt lines 1–175

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/pfaff_source_review/FIELD-AND-DOMAIN-REVIEW.txt

    4c8ed227097cab138eb7868d973940b333a90ac612e3e4082ae15ae9179de35a

  • ROOT-QUARTER-PAIRING-CHECK.json lines 1–13

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/pfaff_source_review/ROOT-QUARTER-PAIRING-CHECK.json

    5c88b34c7ed5004529373da80b3f4280bf0e8fd3a7a00afd1b7ec154edf78de3

  • PFAFF-INDEPENDENT-REVIEW.txt lines 96–207

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/pfaff_source_review/PFAFF-INDEPENDENT-REVIEW.txt

    8a57d181fafc2b9f9bc0fe9df57cc8d1423bc03fa6606cbf158f0574b9b11283

  • DERIVED-PAIRING.txt lines 62–125

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/graded_boundary_functor/charge_transport/DERIVED-PAIRING.txt

    2b4de9e914669e368e5aa086e655b7a5ed2be5d4d268f58b6820fc3db8d7ae27

  • 001-section-primitive-core-and-carrier-interface-handoff.tex lines 302–350

    Source checked at this snapshot

    Original location and fingerprint

    documents/archive--tfpt-45--source_extracts--01_boundary_kernel_source/sections/001-section-primitive-core-and-carrier-interface-handoff.tex

    7d6e673d99c29d950dc601283cd51c1cc0b113567eeb79c8396fec9c82a02c79

  • 009-source.tex lines 125–146

    Source checked at this snapshot

    Original location and fingerprint

    documents/tfpt_research_contracts/sections/009-source.tex

    388f7e74c41945a9d59ed46bc24df463610397e8fd3bf1cd97ab69e86a1a3430

finding:fixed-quarter-jloc-pfaffian-closure-fails-local-skew-test