TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/mixed-current-origin-20261014/REGISTER-GRADE-LIMITS-GAUSS-AND-DIRAC.txt
Original file SHA-256: 94dc3fe2f4b612b2a6f081db8339165f6b7beadfb764f4e3ae143b922d9aa8dd
Inclusive original lines: 301-344
Line numbers below refer to the original source.
This bounded excerpt is source evidence; it is not a new proof/checker run.
Conversation metadata and personal execution details are omitted where indicated.

000301 | No identification with the previously excluded internal Z8^f anomaly lift
000302 | is made: internal symmetry extension, spatial-cover descent, physical time
000303 | and geometric deck action are distinct objects. Equal group orders are
000304 | not an intertwiner. No new discrete Arf sign alone closes this problem.
000305 | 
000306 | The next original question is therefore more selective than 'smooth the
000307 | same half string': does P1 supply a localized transition of the relevant
000308 | DESCENT LIFT, with the correct unchanged-charge Ward action and chiral
000309 | measure/line, rather than a different global Wilson holonomy? Without that
000310 | map, the existing cover half-flux cannot be identified with the target
000311 | spinor by the fixed eightfold dictionary, even after fixing its locality.
000312 | 
000313 | 12. A physical projection inside the old carrier is not this Gauss map
000314 | 
000315 | There is also a complete finite-selector result under an explicit premise:
000316 | RETAIN the entire ORIGINAL even matter algebra and original time as
000317 | physical, and ask for an A/A*-admissible orthogonal projection P within
000318 | the old register-Fock Hilbert space. This is a tested comparison class,
000319 | not a new requirement imposed on all possible P1 physical subnets.
000320 | 
000321 | The even finite CAR algebra acts as full matrices on each parity block.
000322 | Schur's lemma therefore forces
000323 |   P=P_reg,+ tensor Pi_+ + P_reg,- tensor Pi_-.
000324 | For r!=s the time condition gives in each parity block
000325 |   (P_reg,eps)_(rs) Pi_eps(H_s-H_r)=0.
000326 | The actual QWZ seam hopping makes H_s-H_r nonzero on BOTH parity blocks:
000327 | a nonzero one-particle transfer gives an odd-sector witness, and adding
000328 | an untouched spectator gives an even-sector witness. Hence all register
000329 | offdiagonals vanish. P is diagonal in r and in particular [P,Z]=0.
000330 | If all F_A are also retained, selected r and r+2 blocks must agree; keeping
000331 | D_A requires all four r blocks agree. None makes Z inadmissible while
000332 | retaining those full original matter/time operations.
000333 | 
000334 | Thus merely relabeling the old Padm as a Gauss projector cannot implement
000335 | (3)-(5) under this premise. The actual completion changes the kinematic
000336 | local generators and their descent: the Wilson variable is global and
000337 | local electric links are present before restriction. If some old even
000338 | observables are instead removed, the premise is changed and the surviving
000339 | base currents/ALG-EXH require their actual derivation. This is not a demand
000340 | for code closure or an exclusion of all changed physical subnets.
000341 | 
000342 | check_register_words_and_fold.py verifies (1),(2),(6), the REAL quarter
000343 | countercontrol, actual width8 offdiagonal selector witnesses, and replays
000344 | every original Dirac assertion with explicit checks even under -OO.