TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/native-octic-seam-origin-20261025/P1-SOURCE-EMBEDDING-AUDIT.txt
Original file SHA-256: daba8a2cc5ea350c1e2b3d9b005b8fe974a7b67590f3c0a32ec5b0d053ec8f6e
Inclusive original lines: 196-264
Line numbers below refer to the original source.
This bounded excerpt is source evidence; it is not a new proof/checker run.
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000196 | gap proof (3) cannot simply be copied to the enlarged net. A claim of failure
000197 | for the bounded enlarged net would still require bounded local functions or
000198 | spectral projections of a smeared root field with their domains controlled.
000199 | That additional test is irrelevant to the present CAR route.
000200 | 
000201 | 7. The smallest remaining P1 identification test
000202 | -------------------------------------------------
000203 | 
000204 | Let W be one proposed source to P1 unitary, with a compatible collar lift
000205 | W_coll. A complete positive identification must verify all three equations
000206 | with their domains and positive side localization:
000207 | 
000208 |   W Theta_CAR W^*=Theta_P1,                                  (5a)
000209 | 
000210 |   W_coll D_coll,CAR W_coll^*=D_coll,P1,
000211 |   W_coll Dom(D_coll,CAR)=Dom(D_coll,P1),                      (5b)
000212 | 
000213 |   W_coll D_ref,CAR W_coll^*=D_ref,P1,
000214 |   W_coll Dom(D_ref,CAR)=Dom(D_ref,P1).                        (5c)
000215 | 
000216 | The same W must already intertwine the bounded local net, Euclidean time,
000217 | Omega_d and Z. For a product collar one may test
000218 | 
000219 |   D_coll,CAR=J_n(partial_r+B_alpha),
000220 | 
000221 | but choosing this product geometry, its normal length and its reflection lift
000222 | is additional data until (5b) is proved for the original P1 collar. The exact
000223 | two face inverse theorem is conditional on those supplied data:
000224 | 
000225 |   experiments/theory-contracts/seam-full-collar-reconstruction-20261015/
000226 |   PROOF.txt:63--123.
000227 | 
000228 | Equation (5c) is essential. The available angular zeta determinant and the
000229 | alpha=3/4 conjugate ratio use a diagnostic reference which the source expressly
000230 | states is not the archived D_ref:
000231 | 
000232 |   experiments/theory-contracts/seam-collar-multifield-20261016/
000233 |   PROOF.txt:327--343.
000234 | 
000235 | Finite relative action follows only after the same reference, relative
000236 | operator, spectral profile, eta term and domains have been matched. Unitary
000237 | transport of the circle operator alone is insufficient; see
000238 | 
000239 |   experiments/theory-contracts/joint-native-algebra-selection-20261016/
000240 |   SCALAR-FIRST-ORDER-SOURCE-FIBER-AND-SEAM-WARD.txt:180--197.
000241 | 
000242 | 8. Final scope
000243 | --------------
000244 | 
000245 | Proved for the actual supplied source:
000246 | 
000247 |   * the normalized F8 response is an original neutral even CAR current
000248 |     composite with its exact point split prescription;
000249 |   * the same state and fixed Euclidean time provide a canonical RP history
000250 |     form and exponential Euclidean clustering on the bounded even algebra;
000251 |   * the original seam has winding and spectral flow one;
000252 |   * no E8 charge extension is needed for this mechanism.
000253 | 
000254 | Still open, and now isolated to a concrete comparison:
000255 | 
000256 |   * the simultaneous equations (5a)--(5c), including the original P1 collar,
000257 |     reference, domains and eta data;
000258 |   * the physical identification of the quotient localization with the P1
000259 |     local net.
000260 | 
000261 | If the three intertwiner equations hold, the existing operational collar
000262 | completion theorem applies to this actual CAR source. Until then the source is
000263 | an exact candidate supplying most Seedop entries, not a proved Seedop object.
000264 |