Established in scope
Complete collar graph reconstructs the signed operator
In the question: Physical time and complete transfer
Exact spectral calculus for a supplied full product collar and known normal length. Without ell only ell B; no independent derivation of the original P1 kernel.
Read the exact result, assumptions and evidence
Result
The actual product equation gives T=exp(−ell B) and G=[[A,C],[C,1−A]], A=(1+exp(−2ell B))⁻¹. B=log(A/(1−A))/(2ell) reconstructs signs, magnitudes and operator frame. For unbounded T, T is the closure of C A⁻¹; the raw composition is defined only on D(T²). The executable reader needs no supplied B and rejects sign-only projections.
Required assumptions
- Complete data of both product-collar faces
A selfadjoint B occurs in an exact normal-independent product equation. The full orthogonal L2 Cauchy graph projection of both labeled faces, their actual fiber identification and independently known positive normal length ell are supplied. Selection of these data from P1/P2 is not presumed.
Original evidence
- PROOF.txt lines 63–94
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/seam-full-collar-reconstruction-20261015/PROOF.txt
9f4effed34316798c6a35e1ac0ec2832cd3720180f476cb8747bb32359b56e6a
- PROOF.txt lines 145–175
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/seam-full-collar-reconstruction-20261015/PROOF.txt
9f4effed34316798c6a35e1ac0ec2832cd3720180f476cb8747bb32359b56e6a
finding:full-two-face-collar-recovers-signed-operator