TFPT scientific source excerpt Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/CLAUDE31-CP-INFERENCE-AND-OPEN-PATH-REVIEW.txt Original file SHA-256: 97d973edd656fcfb57129315cffe12b0cfc863163bfbd8cc3cb92910975dc33d Inclusive original lines: 191-293 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. 000191 | local analytic factor, the exponent, a tangent/log branch and the associated 000192 | connection matrix. Changing a local Frobenius frame acts exactly as an 000193 | endpoint change in (9). If those factors are carried on all three legs, they 000194 | cancel in the closed trace. Dropping one of them can manufacture a complex 000195 | coordinate phase, but not a frame-independent observable. 000196 | 000197 | This does not say that all open path matrix elements are real. A scalar 000198 | 000199 | (10) 000200 | 000201 | can be complex and can participate in a nonzero Jarlskog invariant when the 000202 | source fixes the endpoint vectors/covectors and correlates several such 000203 | elements between Y_u and Y_d. Under (9), ell_i and r_j must transform too. 000204 | Keeping coordinate basis vectors fixed while changing the endpoint frames is 000205 | not an invariant definition of (10). 000206 | 000207 | The existing exact Fuchs construction supplies Psi, its signed deck and 000208 | quarter actions, the flat metric and a transported closed operator domain. 000209 | It explicitly does not choose the physical insertion, endpoint evaluation, 000210 | charge or normal trace. Therefore it makes (7) computable after paths and 000211 | endpoints are specified, but it does not specify the consumer (10). 000212 | 000213 | Sources: 000214 | 000215 | [OMITTED: non-scientific conversation or execution metadata] 000216 | [OMITTED: non-scientific conversation or execution metadata] 000217 | [OMITTED: non-scientific conversation or execution metadata] 000218 | [OMITTED: non-scientific conversation or execution metadata] 000219 | [OMITTED: non-scientific conversation or execution metadata] 000220 | [OMITTED: non-scientific conversation or execution metadata] 000221 | [OMITTED: non-scientific conversation or execution metadata] 000222 | [OMITTED: non-scientific conversation or execution metadata] 000223 | [OMITTED: non-scientific conversation or execution metadata] 000224 | [OMITTED: non-scientific conversation or execution metadata] 000225 | [OMITTED: non-scientific conversation or execution metadata] 000226 | [OMITTED: non-scientific conversation or execution metadata] 000227 | [OMITTED: non-scientific conversation or execution metadata] 000228 | [OMITTED: non-scientific conversation or execution metadata] 000229 | 000230 | 5. Exact missing source data, without adding a free state 000231 | 000232 | The finite CP diagnostic is already defined once Y_u and Y_d are defined. 000233 | The fixed whole-source state and time do not select the missing matrices, and 000234 | an additional freely chosen state is not the remedy. To turn the proposed 000235 | open path calculation into an original-source answer, the source must fix: 000236 | 000237 | 1. the actual regular or tangential endpoints representing each left and 000238 | right family label in the up and down sectors; 000239 | 2. the homotopy classes and orientations of every Gamma_ij^min; 000240 | 3. the endpoint evaluation vectors/covectors, including their correlated 000241 | Frobenius frames and branch conventions; 000242 | 4. the typed contraction that combines the rho Hodge character with real 000243 | Kummer/deck/path channels inside the same Y entry, or proves that it 000244 | factorizes as one global sector phase; 000245 | 5. the embedding of the resulting Y matrices into the already fixed F5/96 000246 | operator, rather than replacement by newly selected control matrices. 000247 | 000248 | The original hard-holonomy formula names e_i, Gamma_ij^min and the canonical 000249 | family holonomy, but the reviewed source does not identify these data with 000250 | the explicit v117 Frobenius endpoints and does not display item 4. Its proof 000251 | sketch inserts the Z6 base phase verbally into the closed triangle although 000252 | the bare v117 closed character is real. 000253 | 000254 | The next decisive calculation is therefore not a free scan of open triangles. 000255 | It is a source readback locating one explicit endpoint/evaluation dictionary 000256 | for the existing e_i and Gamma_ij^min. If it exists, (7), (9) and (10) give a 000257 | finite exact test with no new state or fitted phase. If it does not exist, 000258 | the open-path proposal remains a computable family of gauge-fixed matrices, 000259 | not an original prediction of rho or CKM CP violation. 000260 | 000261 | [OMITTED: non-scientific conversation or execution metadata] 000262 | 000263 | Accepted here: 000264 | 000265 | * a global scalar phase on a complete Yukawa sector is invisible in H_f; 000266 | * a real-structure-invariant full configuration has zero odd CP observable 000267 | when the actual evaluation intertwines that real structure; 000268 | * bare closed v117 holonomy traces are real; 000269 | * a consistently closed product of bare open Fuchs transports cannot create 000270 | the missing pi/3 phase. 000271 | 000272 | Rejected as unproved: 000273 | 000274 | * the universal claim that every factor assembled from T_rho and its listed 000275 | original lifts is CP inert; 000276 | * the inference from a nonreal scalar character before evaluation to a common 000277 | removable phase after every allowed evaluation; 000278 | * the claim that unspecified open transports between marked points already 000279 | define physical Yukawa entries or a phase observable. 000280 | 000281 | Still viable and precisely bounded: 000282 | 000283 | * an original relative coherent evaluation of real and rho-character legs 000284 | could generate CP, as (1)-(5) demonstrate algebraically; 000285 | * the exact v117 frame makes that hypothesis testable once the original 000286 | endpoint and contraction dictionary is supplied; 000287 | * none of this derives that dictionary, the value pi/3, or a physical source 000288 | execution. 000289 | 000290 | [OMITTED: non-scientific conversation or execution metadata] 000291 | [OMITTED: non-scientific conversation or execution metadata] 000292 | [OMITTED: non-scientific conversation or execution metadata] 000293 | [OMITTED: non-scientific conversation or execution metadata]