TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/seam-full-collar-reconstruction-20261015/PROOF.txt
Original file SHA-256: 9f4effed34316798c6a35e1ac0ec2832cd3720180f476cb8747bb32359b56e6a
Inclusive original lines: 145-175
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.

000145 | 6. What the automated calculation establishes
000146 | 
000147 | checker.py reconstruct --kernel accepts an exact rational two-face projection,
000148 | explicit face/mode labels and a positive known ell. It receives no B or target
000149 | spectrum. It checks symmetry, idempotence, graph rank/invertibility, positive
000150 | selfadjoint transfer and all graph blocks, then returns the unique spectral-log
000151 | operator expression. The generic non-diagonal fixture reconstructs [[2,1],[1,2]].
000152 | Sign-only limit projections, nonpositive transfers and nonprojections are rejected.
000153 | The diagnostic choice ell=4log(2) makes quarter-mode transfers rational and allows
000154 | exact recovery of the diagnostic B without numerical logarithms. That length and
000155 | these test modes are diagnostic inputs, not TFPT-derived physical constants.
000156 | 
000157 | The Lean certificate proves rational graph projection, graph range, injectivity,
000158 | and the anticommuting-involution identities. It does not formalize the unbounded
000159 | logarithm, Hilbert domains, CAR/KMS theory, locality or the microscopic P1 source.
000160 | The source-manifest replay detects changed inputs; it is not proof of source truth.
000161 | 
000162 | 7. Decisive continuation in the original source
000163 | 
000164 | Use the supplied product-collar structure before taking the infinite/sign limit.
000165 | Retain both endpoint fields, their actual comparison map, and the normal scale.
000166 | The scalar or matrix reconstruction then requires no separate search over B,
000167 | thermal occupations or compatible unitary time laws: these are consequences of G.
000168 | This reduces the remaining construction to the original full kernel/local algebra
000169 | and its marking action. It is not justified to generate G from a guessed B and
000170 | then call the inverse formula an independent derivation of that B from P1/P2.
000171 | 
000172 | The source definition permits cutting a finite collar from a GIVEN D_+; it does
000173 | not specify an independent numerical two-face kernel or select D_+ uniquely.
000174 | P2 carrier/interface data and the E8 extension are not supplied by the graph
000175 | inverse. A physical event law and all T1-T8 gates remain unproved by this contract.