TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/collar-current-source-bridge-20261021/PROOF.md
Original file SHA-256: 2dae051bb6a3ee77cc96bc0d63470ac4875950b46057865d1177e4ed3322e5ac
Inclusive original lines: 11-32
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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000011 | positive normal length `ell`. The original product equation gives the closed
000012 | transfer `T=exp(-ell B)` and its orthogonal two-face graph projection
000013 | 
000014 | `G=[[A,C],[C,1-A]]`, `A=(1+exp(-2ell B))^-1`, `C=1/(2 cosh(ell B))`.
000015 | 
000016 | For two-sided unbounded B, T is not declared bounded. G is bounded and is
000017 | the projection onto its closed graph. The circle Fourier blocks `G_r` are
000018 | rank-one 2x2 projections with `tr_faces(G_r)=1`.
000019 | 
000020 | As in the original collar proof, ADD the charged CAR algebra on both faces
000021 | and the pure gauge-invariant quasifree state with covariance G. This field
000022 | and statistical premise is NOT derived from P1. Its second-face occupation
000023 | is `n_r=(1+exp(beta(r+alpha)))^-1`, `beta=2ell`.
000024 | The original one-face negative sea is `P_-=1_(B<0)`.
000025 | Do not identify a geometric graph projection, a mixed occupation, a finite
000026 | native code projector or the physical admissibility projector with each other.
000027 | 
000028 | Original sources reused:
000029 | * `seam-full-collar-reconstruction-20261015/PROOF.txt:63-143`, especially its
000030 |   explicit CAR premise and selected labeled second face at lines96-116.
000031 | * `joint-native-algebra-selection-20261016/ORIGINAL-ORDERED-CURRENT-KERNEL-AND-SEAM-GRADING.txt:33-161`.
000032 | * `joint-native-algebra-selection-20261016/ORIGINAL-DENSITY-GEOMETRY-AND-TIME-HISTORIES.txt:36-99`.