TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/paper-source-reconstruction-20261025/PAPER-COLLAR-REFERENCE.txt
Original file SHA-256: de7f343439701bc7b86c46802387f0a69f835fceb93f6aa79c6a1375cf2508bc
Inclusive original lines: 201-271
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 | 
000202 | the fold audit proves that F is unitary on the one-particle space, preserves
000203 | the CAR and transports the state and excitation Hamiltonian by second
000204 | quantization. See
000205 | 
000206 |   experiments/theory-contracts/v16-operator-pullback-20261014/
000207 |   FOLD-AUDIT.md:10--86.
000208 | 
000209 | Thus Gamma(F) identifies the original cover CAR presentation with its
000210 | eight-component quotient presentation, including the fixed transported state
000211 | and Euclidean time. The octic field is already an affiliated even current
000212 | composite of that bounded CAR net, with the fixed point-split prescription.
000213 | 
000214 | What is not supplied is the second arrow
000215 | 
000216 |   quotient even CAR net --iota--> original P1 A_adm net. (6)
000217 | 
000218 | The paper names A_E, A_M and P_adm abstractly, but none of the cited source
000219 | theorems defines (6) on the actual fold generators or checks its state,
000220 | reflection and collar domains. C_seed cannot construct (6), because its input
000221 | already contains A_loc, tau, Theta, omega, the seam and D_coll.
000222 | 
000223 | The smallest decisive next test is therefore not a search for a global W.
000224 | It is one explicit bounded generator test for (6): choose an original even
000225 | CAR Weyl operator or bounded function of a smeared current and verify
000226 | 
000227 |   iota(A*)=iota(A)*,
000228 |   omega_P(iota(A*)iota(A))=omega_CAR(A*A),
000229 |   iota(tau_t A)=tau_t iota(A),
000230 |   iota(Theta A)=Theta iota(A),                              (7)
000231 | 
000232 | together with invariance of its cyclic image under A, A*, P_adm and the seam.
000233 | If (7) fails, the proposed source identification fails before any collar
000234 | analysis. If it passes on a generating bounded net, the next and only stronger
000235 | test is the elliptic collar/domain and finite-relative-action condition above.
000236 | 
000237 | 5. Corrected hierarchy of claims
000238 | --------------------------------
000239 | 
000240 | Field mechanism:
000241 |   (1)--(5) on the bounded even local net are sufficient. A global unitary onto
000242 |   the whole P1 Hilbert space is unnecessary.
000243 | 
000244 | Complete operational seed:
000245 |   The same local image must carry a reflection-regular elliptic collar and
000246 |   finite relative action. This remains open for the supplied fold.
000247 | 
000248 | Equality with the canonical defect-minimal P1 seed:
000249 |   Only this final claim requires unitary equivalence of complete displayed
000250 |   structures plus the applicable minimality/classification theorem. Neither
000251 |   the local CAR map nor C_seed alone proves it.
000252 | 
000253 | Accordingly, the previous three global equations for Theta, D_coll and D_ref
000254 | are valid as a test of full presentation equivalence. They are not the first
000255 | necessary test of the CAR boundary mechanism and must not be used as the
000256 | definition of Seedop membership.
000257 | 
000258 | 6. Scope and excluded shortcuts
000259 | --------------------------------
000260 | 
000261 | This audit does not claim that the actual quotient CAR fold is already the
000262 | P1 admissible net, or that its collar is already the archived P1 collar. It
000263 | does not choose a new product collar or a diagnostic zeta reference. It does
000264 | not use the disputed identification of Calderon polarization with geometric
000265 | reflection, and it does not use the false general claim that every bounded
000266 | coefficient first-order perturbation is infinitesimally operator bounded.
000267 | 
000268 | The exact advance is the categorical reduction from a global equivalence
000269 | problem to the local map (6), followed by one explicit collar admissibility
000270 | test. This is the strongest source-backed reconstruction statement present in
000271 | the current papers.