Conditional result
Exact conditional parity-Gauss representation localizes half flux without new physical dimension
In the question: Historical: common source, state and event selection
Redundant kinematic generators and local Gauss/observable rule are ADDED premise, not P1-derived. No new physical dimension relative to EVEN original carrier, but different local net. No QWZ/Dirac-source identification, spinor-field limit, FE-GEN/ALG-EXH/E8, chiral measure selection or mirror absorption. f(Z) references can become nonlocal.
Read the exact result, assumptions and evidence
Result
Explicit gauge-orbit isometry E is onto full Gauss space for all sizes, E*E=1,GxE=E,HnewE=EHold,WE=EZ,tau_a^x E=E F_[0,a]. Full even register-matter dimension, all transported state words, positivity, adjunction and common original time preserved; old local register Z becomes GLOBAL Wilson loop. Exact whole128dim control and48 actual width8 one-body gauge cases check signs; all-size theorem rests on orbit proof. Mere word-preserving gauge representation cannot give complete Dirac vector-current response a new central phase.
Required assumptions
- Conditional local parity-Gauss completion with common original time
ADDED comparison contract, NOT P1-derived: old four-state register with total-even matter; redundant Z2 link qubits and local Gx=(-1)^nx tau_(x-1)^x tau_x^x=1; gauge-invariant local observable net. Original QWZ hopping coefficients, common microscopic Hamiltonian and energy reference; no new electric energy. Sector-specific f(Z) subtractions must map to f(W) and can be nonlocal. No identification of Gauss space with original Padm.
- 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
- REGISTER-GRADE-LIMITS-GAUSS-AND-DIRAC.txt lines 112–235
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/mixed-current-origin-20261014/REGISTER-GRADE-LIMITS-GAUSS-AND-DIRAC.txt
94dc3fe2f4b612b2a6f081db8339165f6b7beadfb764f4e3ae143b922d9aa8dd
- check_gauge_locality_completion.py lines 1–197
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/mixed-current-origin-20261014/check_gauge_locality_completion.py
00a825e406e510e445034e7b7b6aee68196bef709932c5a39beae47abbbeb69c
- gauge-locality-completion-results.json lines 1–19
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/mixed-current-origin-20261014/gauge-locality-completion-results.json
47bf102ccffb109dc061c89fd9985819560f8ba9928c389f3135d3e5966e1f93
finding:exact-parity-gauss-locality-completion-of-register-source