Scoped exclusion
Complete Dirac vector phase pairs have no half Cartan Ward charges
In the question: Historical: common source, state and event selection
Only smooth vector-phase class and unchanged mixed Ward action in stated complete Dirac contract. No all-spinor/P1 no-go,arbitrary global-loop-holonomy theorem or infinite determinant theorem. C/1-C are grading components on one face. Chiral source, changed current representation and other original operations outside scope.
Read the exact result, assumptions and evidence
Result
Implementable commuting vector phases obey[J_i,vec(h),V_vec(f)]=0 because opposite grading cocycles cancel and noncentral term vanishes. At pi interval profile separate chiral components have opposite half endpoint residues; full vector sum0. Thus not a spinor pair withlambda_i=±1/2 under SAME8vector Cartan currents,including scalar renormalization and mixed-word limits. Finite exact control for any Hermitian C andunitaryg: chi_(1-C)(g)=detg conjchi_C(g),normal-order-corrected complete amplitude|chi_C|².
Required assumptions
- Complete vector phases with unchanged Cartan Ward action
Only original complete Dirac/CAR Lagrangian source with normal-commuting implementable smooth profiles H_i h and fI, common analytic domains and regular Weyl representation. Target comparison retains same8 vector Cartan currents and mixed Ward words. Two grading components C,1-C on ONE face are neither strip edges nor collar faces. Finite complementary determinants are algebraic controls only; no unregulated infinite determinant or automatic QWZ/Dirac source identification.
- 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.
- 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
- NEUTRAL-DEFECT-PAIRS-AND-VECTOR-WARDS.txt lines 76–157
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/mixed-current-origin-20261014/NEUTRAL-DEFECT-PAIRS-AND-VECTOR-WARDS.txt
e798405b02c979e0f9e77e223a097ea9ae269c3bd677a501f2becc8f00c0dda5
- check_neutral_pairs_and_vector_wards.py lines 1–194
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/mixed-current-origin-20261014/check_neutral_pairs_and_vector_wards.py
2f558542e6162dccdd123a2e68c2fd2a337e57adedb59a497779208c29a914c5
- neutral-pairs-and-vector-wards-results.json lines 1–97
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/mixed-current-origin-20261014/neutral-pairs-and-vector-wards-results.json
3181894c8896cbdbfa2d6041ecbe1c6f21f6d41938d9b97f1cffddb92b415dad
finding:complete-dirac-vector-phase-pair-has-zero-spinor-Ward-charge