Established in scope
The same collar supplies its canonical selfdual kinetic pairing
In the question: Automated construction of operator maps and sources
Exact kinetic dictionary inside the already given geometric Clifford source,with existing smooth normal-independent classical Phi and both total grades. No new source,field copy or J choice. This differs from <Jloc,D>_old;its quarter counterexample remains valid. A closed skew realization requires the actual isotropic boundary domain or C0DomL=DomL*. Cauchy projector is not an inverse Green operator and does not fix the unnormalized determinant scalar. Physical functor use,original reference/phases/profile and OS time still require comparison with the actual original source. A supplied operational Seed requires no additional free state choice.
Read the exact result, assumptions and evidence
Result
The unchanged normal symbol gives new-complex-linear L=−ND=partial_r+B. On the common interior core,C0LC0=−L* and L*L=D². Hence <C0x,Ly>_new is skew,including scalar quarter holonomy. Endpoint defect is exactly [<C0x,y>]_0^ell. In the complete charged chart,L=diag(L+,−bar(L+*)),L+=partial_r+h,and its skew matrix [[0,−L+^t],[L+,0]] has Pf=(−1)^{n(n+1)/2}detL+ on a compatible finite regulator. D and L have the same whole Cauchy graph,transported by T_faces to G(h)⊕(1−barG(h)).
Required assumptions
- 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.
- Complete data of both product-collar faces
A selfadjoint B occurs in an exact normal-independent product equation. The full orthogonal L2 Cauchy graph projection of both labeled faces, their actual fiber identification and independently known positive normal length ell are supplied. Selection of these data from P1/P2 is not presumed.
- 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.
Original evidence
- SELFDUAL-KINETIC-PAIRING.txt lines 1–117
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/pfaff_source_review/SELFDUAL-KINETIC-PAIRING.txt
5543c7cf0360985377e388cbd80c8e2eb3faa554f5c6e7e1f50bb1fae88bb065
- NORMAL-KINETIC-PAIRING.txt lines 1–143
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/pfaff_source_review/NORMAL-KINETIC-PAIRING.txt
28061f015df5c5bb2a07a12ffd1d45f84cab49fb84939606201a1efe77b49f62
- CLIFFORD-KINETIC-INDEPENDENT.txt lines 1–100
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/pfaff_source_review/CLIFFORD-KINETIC-INDEPENDENT.txt
59d098be379a8a21003e1d703862abceb137308566f68c66bb97ffb0b4f0ed1a
- ROOT-SELFDUAL-KINETIC-CHECK.json lines 1–12
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/pfaff_source_review/ROOT-SELFDUAL-KINETIC-CHECK.json
e25327117946bcbe95eb3d0dee08556a0d743ffc88ca4281fc4d1f0a1d66c38e
- PROOF.txt lines 20–140
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/graded_boundary_functor/PROOF.txt
708dad21942cc00dd56d3348eacee3f0d90ccfc53e3f4987e39ded00ddc70841
- FINITE-COUPLED.txt lines 14–100
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/graded_boundary_functor/FINITE-COUPLED.txt
61d3d524801aff0147d393c518ad554e3ab550271165e2000d9efbf613b90234
- DERIVED-PAIRING.txt lines 83–125
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
finding:same-collar-has-canonical-selfdual-kinetic-pairing-and-charged-determinant