Established in scope
The same collar graph connects restricted state and time
In the question: Physical time and complete transfer
Conditional on charged CAR/Wick identification and the same graph covariance. No P1/P2 selection of physical statistics, normal length, marking or events. Existing quarter holonomy is retained; Clifford quarter-turn algebra is not a holonomy derivation.
Read the exact result, assumptions and evidence
Result
The second face of the supplied pure quasifree graph state has n=1−A=(1+exp(2ell B))⁻¹. Thus log((1−n)n⁻¹)=2ell B, without separately inserted occupations or a second time generator. This realizes the already known faithful KMS inverse through the full collar boundary relation.
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.
- Charged quasifree state for the complete graph covariance
Additionally identify the actual field algebra with charged CAR(H direct_sum H) and the state with the gauge-invariant quasifree state whose occupation covariance is G_ell. This is an extra physical premise, not a consequence of the geometric projection calculation.
Original evidence
- PROOF.txt lines 96–143
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/seam-full-collar-reconstruction-20261015/PROOF.txt
9f4effed34316798c6a35e1ac0ec2832cd3720180f476cb8747bb32359b56e6a
finding:two-face-graph-state-time-same-datum