TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/original-local-source-variable-background-20261102/FUNCTOR.txt
Original file SHA-256: c1a42fe05bf60fcd4a80d4039bde520fede2e301f2e2f1515a48be8140c644e5
Inclusive original lines: 201-314
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.

000201 | the current paper's symbol P_F, whose separate physical identification
000202 | is conditional there. This scope is retained. It is not grounds to call
000203 | the reference operator in the E route missing: equations (1)-(8) construct
000204 | it through the actual full reader. No additional P_F is introduced.
000205 | 
000206 | 5. SPECTRAL FUNCTIONAL AND REFERENCE WEIGHT: WHAT IS NOW FORCED
000207 | 
000208 | For every justified common functional calculus and compatible trace,
000209 | 
000210 |  U*[f(D/chi)-f(D_ref/chi)]U
000211 |   =f(mathfrakD_h/chi)-f(mathfrakD_href/chi).                (9)
000212 | 
000213 | All complete spectra and eta invariants are unchanged, including zero
000214 | modes, the original boundary realization, regulator and spectral branch.
000215 | The boundary eta operator is itself transported with its boundary data.
000216 | An old-complex fixed unitary has not manufactured a compensating eta.
000217 | 
000218 | Accordingly, applying the SAME original reference functional to D_ref or
000219 | to mathfrakD_href gives the same reference weight. It is determined for
000220 | each already specified constructor. The same applies to its fermionic
000221 | Green/Berezin functional with all source legs transported. There is no
000222 | need to posit a second reference operator on the new chart.
000223 | 
000224 | Three original callers must remain typed: the primitive action literally
000225 | reads f(D_rel)-f(D_ref); the later geometric pair reads its actual full
000226 | anchored/fluctuated operator minus D_ref; and the fermion kinetic caller
000227 | reads its bilinear D (or original prescribed kinetic). Unitary transport
000228 | preserves EACH call exactly. It does not equate those three functionals,
000229 | identify a spectral trace with logdet of the kinetic operator, or silently
000230 | set the full S_adm to its spectral seed. The old full D_rel is transported
000231 | as U*(D-D_ref)U=[[0,delta_h],[delta_h,0]], where
000232 | delta_h=-i gamma(Phi-Phi_ref); the missing derivatives are not reinstated
000233 | by changing its name to h.
000234 | 
000235 | The remaining full-source comparison is therefore the actual supplied
000236 | caller identity on the same complete field tuple and integration basis.
000237 | Its spectral/fermionic reference input is now concretely transportable;
000238 | it is not an independent new reference choice. WEIGHT.txt gives the
000239 | same-functional spectral weights, and the original unnormalized denominator
000240 | and complete integration call remain those originals. This report neither
000241 | adds a free measure nor claims that a change of representation derives it.
000242 | 
000243 | More explicitly, for ANY actually supplied original full regulated source
000244 | call, perform this fixed coordinate change on its fermionic/source legs,
000245 | and carry every other original field, weight and reference factor unchanged.
000246 | Let scriptU denote that full coordinate map, including the dual source map.
000247 | Then, by change of integration coordinates with the above actual Jacobian,
000248 | 
000249 |  S_adm^U[phi',J']=S_adm[scriptU phi',J],
000250 |  Z_adm^U[J']=Z_adm[J], Z_ref^U[0]=Z_ref[0],
000251 |  Z_rel^U[J']=Z_rel[J].                                    (10)
000252 | 
000253 | This is equality of the WHOLE original source call, including its retained
000254 | bosonic/gauge/ghost factors, not just equality of two kinetic matrices.
000255 | It is conditional only on the same given original integral or functional
000256 | being used on both sides; it introduces no replacement integral. Where
000257 | the original source is defined by a compatible limit, equality is exact
000258 | at each regulator and hence passes to that SAME limit without a new
000259 | domination assumption. Differentiation with respect to the original H,
000260 | source legs and reference variables commutes with the fixed U, so all
000261 | existing source jets and normalized as well as unnormalized moments are
000262 | carried. The actual reference scalar is not reset to1.
000263 | 
000264 | Neither (9) nor (10) states S_adm=-log Z, S_adm=Gamma, or
000265 | S_adm=S_prim. An effective action, if originally defined by its Legendre
000266 | and regulator procedure, follows by transporting THAT procedure. Bare
000267 | and effective callers keep their original types. In particular (10)
000268 | does not prove a new equality of two different historical source callers;
000269 | it proves exact representation independence of each complete actual call.
000270 | 
000271 | 6. INDEPENDENT NATIVE CONTROL AND EXACT ORIGINAL REFERENCES
000272 | 
000273 | FUNCTOR-check.json reuses only the existing unchanged full96 constructor
000274 | prelude from graded_boundary_functor/check_finite_typing.py. It checks
000275 | the full U, its normal symbol, actual grading, both actual lifted references,
000276 | native J_F/Jloc, and both complete readers/inverses with symbolic tangential
000277 | and normal coefficients. It does not execute any canonical writer.
000278 | The coefficient check controls signs; (1)-(9) are the whole operator proof.
000279 | All20 checks passed with exact algebraic expansion. Reproduce with
000280 |  python3 work/reference_transport_G/check_functor.py
000281 | from the shared work root. The result records the actually executed source
000282 | hashes, including native v252 constructor SHA256
000283 | 820254440e178430422e50605067775656236602996307f67c9e69124ba5d163.
000284 | 
000285 | Source/hash verified originals read in this continuation:
000286 | 
000287 | * research-source:251a551b4d69f1b19f606881:1-103,
000288 |   graded_boundary_functor/FINITE-COUPLED.txt,
000289 |   SHA256 61d3d524801aff0147d393c518ad554e3ab550271165e2000d9efbf613b90234.
000290 | * research-source:039eb8d38b194a51c6147af4:1-108,
000291 |   aps_source_review/ORIGINAL-HIGGS-BOUND-REFERENCE-PROOF.txt,
000292 |   SHA256 13e79f2be052ca918fd2be8faf8cf6f1669fc3ad535ccf9a3fdff5b7c0b1b3c5.
000293 |   Full supplied base pullback and both reference formulas are50-74.
000294 | * research-source:59dc78be6ccd2e22cab708cc:1-105,
000295 |   aps_source_review/CURRENT-CARRIER-ODD-READER-WHOLE-SOURCE.txt,
000296 |   SHA256 d45db71f3a493d6699473be195bea821a402523c4cf1c2c4cb102dafc39e0d05.
000297 | * research-source:327a34bf933d5eceddd1a9b8:1-146,
000298 |   aps_source_review/LOSSLESS-CARRIER-ODD-READER-DICTIONARY-REVIEW.txt,
000299 |   SHA256 b6f457488f84a06f5d97288c36210fc06ee2d94eb709ed90118e0fb27e40b767.
000300 |   Full smooth class, inverse, retained A and complete graph are44-123.
000301 | * source:3547205653ff5459c8c2:1-80,
000302 |   verification/v258_dirac_covariance_induction.py,
000303 |   SHA256 16c60e831dceba773f3629466895f1009654827286e5b760ae01bd755fd5c0b1.
000304 |   Complete Pi_odd reader24-27; original conditional physical identification
000305 |   and declared status are46-59, so they are not upgraded here.
000306 | * graded_boundary_functor/charge_transport/DERIVED-PAIRING.txt:1-120,
000307 |   SHA256 2b4de9e914669e368e5aa086e655b7a5ed2be5d4d268f58b6820fc3db8d7ae27.
000308 |   Local read1-120; registered research-source:b9d504edd5f7f899d4274859
000309 |   independently hash-validates62-125. Actual Jloc/E and c are49-60;
000310 |   charge/quarter and full skew-domain qualifications are62-119.
000311 | 
000312 | See also sibling PAIR-TYPING.txt for the directly read old primitive versus
000313 | later geometric pair callers. No old bounded-relative-trace scan, new model,
000314 | new selfduality assumption or global CAR/clock hypothesis was introduced.