Scoped exclusion
Automatic full Dirac identification of the chiral current phase fails
In the question: Historical: common source, state and event selection
Original complete two-component Dirac collar and explicit CAR/Lagrangian/implementability class; no novelty claimed for standard current/Dirac theory. No exclusion of all P1 sources or chiral-measure/inflow realizations. Cauchy projection, APS sign subspace and OS Padm stay distinct. No computed fixed-domain spectral response, physical event execution or 4D no-go. Higher-dimensional trace formulas need separate control. All original native4/5/20/carry/E8/eight-preimage structure retained; no new finite-code closure requirement. Prior measure/log-profile boundary and open chiral/determinant-line contracts reused, not closed.
Read the exact result, assumptions and evidence
Result
Excluded is the automatic identification of the complete normal-commuting Dirac-CAR vector current with the original nonzero chiral current phase, only under the stated premises. UR.COLLAR.FACE_CURRENT.01, DIRAC-LIFT continuation: For a complete Lagrangian Dirac Cauchy projection C with N C N*=1-C, c_(1-C)=-c_C. For implementable X,Y commuting with N, unitary covariance also gives c_(1-C)=c_C, hence c_C=0. In the existing product collar B=diag(A,-A), occupations n(A) and1-n(A) on ONE boundary face give -2i,+2i and total0 for the original four-mark-fixed profiles. This differs from the earlier two-face cancellation of one scalar block. Fixed Clifford symbols force g I2 on this two-component module; diag(g,I) changes the normal/tangential symbol. The complete lift D_phi=D-i chi_prime phi Jn-chi phi_prime Jn Gamma is a bounded Hermitian perturbation. Transported domain/reference/Padm give frame covariance; a fixed original selfadjoint domain remains analytically valid but specifies a relative boundary attachment not physically selected here. Explicit extra Dref/Drel commutator terms are retained at fixed geometric R; fixing R alone does not break covariance when U commutes with R. Nonconstant four-mark-fixed profiles do not preserve the old APS sign subspace, which is not a selfadjointness no-go. Original Gamma already identifies D_plus, but not its physical measure/line connection. The prior scalar result remains conditionally valid.
Required assumptions
- 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.
- Fixed scalar Hardy model with quarter time
H=L²(S¹), C projects onto n≥0, B_alpha=−i∂theta+alpha with alpha=1/4 or 3/4. C and B remain fixed for every candidate. Consider scalar unimodular multiplication operators: continuous symbols for isometry classification and H1 symbols for finite excitation energy. This source class is not derived from P1/P2.
- 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 Dirac Cauchy source with Lagrangian normal action
Complete orthogonal Dirac Cauchy projection C on the entire boundary module, with actual normal unitary Clifford action N satisfying N C N*=I-C. Explicitly assume charged CAR quantization with pure quasifree covariance C. Bounded current generators X,Y commute with N and have Hilbert-Schmidt commutators with C. The existing compact product collar B=diag(A_alpha,-A_alpha) on both components and both faces is the concrete control; its smooth scalar boundary multipliers are implementable. Statistics and physical measure selection are not derived from P1; no automatic extension of the unrenormalized trace to higher boundary dimensions.
Original evidence
- DIRAC-LIFT-ADMISSIBILITY.md lines 1–124
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/collar-current-source-bridge-20261021/DIRAC-LIFT-ADMISSIBILITY.md
dc50b3805ba93a1a4e19890ea0accb04e66cebe192ce526e405cb362a6cdda6a
- DIRAC-LIFT-ADMISSIBILITY.md lines 125–248
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Original location and fingerprint
experiments/theory-contracts/collar-current-source-bridge-20261021/DIRAC-LIFT-ADMISSIBILITY.md
dc50b3805ba93a1a4e19890ea0accb04e66cebe192ce526e405cb362a6cdda6a
- check_dirac_lift.py lines 1–117
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Original location and fingerprint
experiments/theory-contracts/collar-current-source-bridge-20261021/check_dirac_lift.py
1e0047ba99ab68b3d1bc71d10a8ef7d894cd86bab6b7e401bdd4cbff1dee7c02
- dirac_lift_results.json lines 1–54
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Original location and fingerprint
experiments/theory-contracts/collar-current-source-bridge-20261021/dirac_lift_results.json
f6afbd6af36efd7ffdea93bebd1bbcea296c91efc841ff54725fbe69055e1f4a
- contract_index.json lines 1–61
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Original location and fingerprint
experiments/theory-contracts/collar-current-source-bridge-20261021/contract_index.json
80de96c729cf3e744da3fdc8ae5da56f3588692de12a8f62dd7602036d92e108
- PROOF.txt lines 21–61
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Original location and fingerprint
experiments/theory-contracts/seam-full-collar-reconstruction-20261015/PROOF.txt
9f4effed34316798c6a35e1ac0ec2832cd3720180f476cb8747bb32359b56e6a
- 001-section-primitive-core-and-carrier-interface-handoff.tex lines 65–80
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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
- 001-section-primitive-core-and-carrier-interface-handoff.tex lines 302–343
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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
- 002-section-closure-theorems-from-the-admissibility-complex.tex lines 12–123
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Original location and fingerprint
documents/archive--tfpt-45--source_extracts--04_qft_source/sections/002-section-closure-theorems-from-the-admissibility-complex.tex
61ecee7727bdec47936bbffc028d3dbac5260a025b6dbcce30124a60d635fc9c
- P1-COVARIANT-INSERTION.txt lines 26–146
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Original location and fingerprint
experiments/theory-contracts/seam-collar-multifield-20261016/P1-COVARIANT-INSERTION.txt
ebb9e0cb15cdc017914d8567131c8d8b75855f20e05551b6f7b350989061e152
- PROOF.txt lines 271–326
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Original location and fingerprint
experiments/theory-contracts/seam-collar-multifield-20261016/PROOF.txt
3537a2b080df0bb8b5d30c73da7dd83dc8e1ae5a6cfea4bb48a8b99f0080dfce
- 015-source.tex lines 235–266
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Original location and fingerprint
documents/tfpt_research_contracts/sections/015-source.tex
2ec9c3ab6903e9d29823ee5a52ef588cf8504848df6c51c21f0412f31f9eb886
- 017-source.tex lines 239–285
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Original location and fingerprint
documents/tfpt_research_contracts/sections/017-source.tex
492599a0d20043a5589ca610ce7e1ebceffb8de043eae8eb406e4469d3e4be83
- status_ledger.csv lines 746–746
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Original location and fingerprint
verification/status_ledger.csv
8723b921bdc50a6157acc6bee4342b40586eb89bec6d7dcc0abc3309562c78b4
- status_ledger.csv lines 758–758
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Original location and fingerprint
verification/status_ledger.csv
8723b921bdc50a6157acc6bee4342b40586eb89bec6d7dcc0abc3309562c78b4
finding:full-dirac-cauchy-vector-cocycle-cancels-and-endpoint-domain-distinction