Established in scope
Mixed vector axial current is a subalgebra of the existing full CAR source
In the question: Common clock sectors, quartic geometry and operational reconstruction
Applies known two-dimensional current algebra to the statistically supplied full source, with no general novelty claim. Does not prove physical P1 intervention admissibility, original full source map, OS time/reflection or a free current subtheory in every coupled P1 source. The old vector exclusion remains valid in its original scope.
Read the exact result, assumptions and evidence
Result
In the supplied complete Dirac CAR collar, J_R=(J_V+J_A)/2=:Psi* fP_R Psi: is an explicit local subcurrent. The old opposite component cocycles c,-c give c_VV=c_AA=0,c_VA=c_AV=2c,c_RR=c; at the original profiles mixed=-4i and right=-2i. The old normal-commuting vector exclusion explicitly did not cover this generator. Existing free B0 time satisfies [B0,P_R X_n]=-nP_R X_n on the actual one-particle path, with n->8n after folding. Restricting this existing subalgebra needs no separate chiral determinant. The second face remains thermal, so no positive vacuum generator has been derived.
Required assumptions
- 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.
- 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.
- Given charged CAR quantization of the full two-face Cauchy graph
As in section4 of the original collar proof, additionally assume charged CAR(H direct_sum H) and the pure gauge-invariant quasifree state with occupation G_ell. The second labeled face has n=(1+exp(2ell B))^-1. This is a field/statistics premise, not a consequence of P1; reduction does not select or physically execute a one-face operation. The long-collar limit is used only within this declared operator/CAR class.
- Constant Dirac product with mixed current generators
Assume the existing normal-independent two-component collar A=-i partial_theta+alpha, alpha=1/4 or3/4, Gamma=diag(1,-1), Jn=[[0,-1],[1,0]], S=Jn Gamma. In the supplied complete complex CAR system consider smooth one-face quadratic generators fI,fGamma,fP_R under actual HS/implementability conditions. For the product test Phi is a constant finite self-adjoint coefficient with B_Phi=Gamma A-S tensorPhi on the same H1 domain. A is internally scalar. Reducing projections are constant and reduce every Fourier momentum. For v252 also retain actual gamma_F and {Phi,gamma_F}=0. No physical P1 selection, separate chiral determinant, new vacuum or identification of tangential time with original OS Hamiltonian is presumed.
Original evidence
- PROOF.txt lines 1–200
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/original_insertions/PROOF.txt
637007e39986ac8f2ec07a6c2ce96f0d5686171583b226699ea9dfe9ca3bb4fc
- PROOF.txt lines 201–255
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Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/original_insertions/PROOF.txt
637007e39986ac8f2ec07a6c2ce96f0d5686171583b226699ea9dfe9ca3bb4fc
- check_original_insertions.py lines 1–191
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/original_insertions/check_original_insertions.py
ed2a7cd49a68528ea68f92c2cbf039d1e6980b563d1d8915aea7acdc76123cde
- results.json lines 1–75
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Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/original_insertions/results.json
aa268cad36cde7493cfb6c658ecdaa2dd5eebaa1220fabd3ea58f46fa4c625b8
- REVIEW.txt lines 1–40
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Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/original_insertions/REVIEW.txt
f0b4691202ac083431414734a7caef5c7892a7d6744951a1bcb9ee4b1220384e
- ERGEBNIS-EINFACH.txt lines 1–58
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Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/original_insertions/ERGEBNIS-EINFACH.txt
b4d0482b9d5347f58b1a5479f9aea86cb52a8bf8bac9477fc9fa043feb1bcd3e
- DIRAC-LIFT-ADMISSIBILITY.md lines 1–82
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Original location and fingerprint
experiments/theory-contracts/collar-current-source-bridge-20261021/DIRAC-LIFT-ADMISSIBILITY.md
dc50b3805ba93a1a4e19890ea0accb04e66cebe192ce526e405cb362a6cdda6a
- HIGGS_VARIATION_PROOF.txt lines 135–182
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Original location and fingerprint
experiments/theory-contracts/seam-joint-source-origin-audit-20261016/HIGGS_VARIATION_PROOF.txt
84004fc583641a52096c8571844aaed825d16d8165635eafd1a6b2562708e6be
- NORMAL-INDEX-TRANSPORT.txt lines 1–129
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Original location and fingerprint
experiments/theory-contracts/original-admissible-source-closure-20261025/NORMAL-INDEX-TRANSPORT.txt
f66b65fb9e23a2fe97c95ad924bd6ee39ea9c182111031392010cf4507620099
- NORMAL-CONNECTION-MARKS-COVER.txt lines 18–69
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Original location and fingerprint
experiments/theory-contracts/original-admissible-source-closure-20261025/NORMAL-CONNECTION-MARKS-COVER.txt
33448654daa781525df039173b862274036f8ef2c267865afec6555c12b4c9de
- v252_full_finite_triple.py lines 86–168
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Original location and fingerprint
verification/v252_full_finite_triple.py
820254440e178430422e50605067775656236602996307f67c9e69124ba5d163
finding:mixed-vector-axial-current-is-existing-full-car-subalgebra