Conditional result
The same B,u pair conditionally reconstructs the entire channel and canonical seam line
In the question: Common clock sectors, quartic geometry and operational reconstruction
Complete infinite-dimensional theorem within the explicit operator hypotheses, independently reviewed. Original B_Sigma/u_Sigma time and index identification remains open; coordinate arcs are not spacetime localization. Additional phase, CAR quantization and the original source functional do not follow from index one.
Read the exact result, assumptions and evidence
Result
Strong covariance and actual index -1 make S=P_BuP_B isometric and Pi=P_B-uP_Bu*=1_(0,1](B) rank one. Spectral bands u^n Pi u^-n sum strongly to I; on all H one gets basis u^n psi and B=-i partial_theta+epsilon with H1 domain and 0<epsilon<1. Actual monodromy i fixes epsilon=1/4. No external Hardy space or new source is chosen.
Required assumptions
- Conditional strong seam covariance, gap and index of the same operator pair
Conditional operator contract only: on the same original complex H, B is selfadjoint and u unitary; exp(itB)u exp(-itB)=exp(it)u for every real t, zero is outside sigma(B), and ind(P_B u P_B)=-1 with P_B=1_(0,infinity)(B). Actual exp(2 pi i B)=i I is an additional condition only for epsilon=1/4. These conditions are not derived from the reviewed original TFPT passages; P_C is not identified with P_B or a CAR covariance.
Original evidence
- SPECTRAL-SEAM-RECONSTRUCTION.txt lines 1–200
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/primitive-seam-operator-reconstruction-20261025/SPECTRAL-SEAM-RECONSTRUCTION.txt
45c472819667e7a981f7da4246d74d31e15104335e941cde0e0893808d674654
- SPECTRAL-SEAM-RECONSTRUCTION.txt lines 201–278
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/primitive-seam-operator-reconstruction-20261025/SPECTRAL-SEAM-RECONSTRUCTION.txt
45c472819667e7a981f7da4246d74d31e15104335e941cde0e0893808d674654
- REVIEW.txt lines 1–200
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/primitive-seam-operator-reconstruction-20261025/REVIEW.txt
3e103349852b57a7e53af3148986ab0d9418a073b89b9d94d9168877d377bc88
- REVIEW.txt lines 201–217
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/primitive-seam-operator-reconstruction-20261025/REVIEW.txt
3e103349852b57a7e53af3148986ab0d9418a073b89b9d94d9168877d377bc88
finding:original-b-u-pair-conditionally-reconstructs-whole-circle-channel