Established in scope
Joint seam, field, sea and time action reconstructed
In the question: Historical: common source, state and event selection
Conditional analytic reconstruction on a common core; Lean verifies the algebraic identity and mode recurrence, not physical derivation of inputs. One channel is not the five-slot P2 carrier; no event law.
Read the exact result, assumptions and evidence
Result
Under the operator hypotheses, Wold supplies a complete mode basis U^n w and B=N+alpha. With the CAR/sea premise, R c_n R*=c_(n+1), R*QR=Q+1 and R*H_alpha R=H_alpha+Q+alpha. R Omega is a new charge-one state; exp(2pi iH_alpha)=exp(2pi ialpha Q) retains the quarter phase.
Required assumptions
- Hypotheses of joint operator reconstruction
For this conditional theorem: orthogonal projection C, unitary U, (1−C)UC=0, index(CUC)=−1, pure isometry and minimal unitary dilation. Actual selfadjoint B satisfies U*BU=B+1 and Bw=alpha w on a common invariant core, alpha=1/4 or 3/4. These conditions are not presumed derived from P1/P2.
- Charged CAR algebra and original negative sea
Assume the actual field algebra is charged CAR(H) and its reference state is the pure quasifree sea with occupation 1−C. Relative charge and positive excitation time are normal ordered against this sea. This physical identification is an additional premise.
Original evidence
- PROOF.txt lines 51–67
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/seam-source-character-search-20261015/source_reconstruction/PROOF.txt
424e2f8eaf021cae575e479ccca4fcd2b8a34df1e5d5410371a86144f07ddb5d
- PROOF.txt lines 130–215
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/seam-source-character-search-20261015/source_reconstruction/PROOF.txt
424e2f8eaf021cae575e479ccca4fcd2b8a34df1e5d5410371a86144f07ddb5d
finding:conditional-seam-field-state-time-reconstruction