Established in scope
Full memory reconstruction preserves every ordered word under nesting
In the question: Automated construction of operator maps and sources
Coefficientwise theorem on supplied domain; familiar Schur/Feshbach mathematics. No physical source selection, general analytic UV closure or noncommutative determinant. Whole original Z and unobservable factors are not inferred from a single boundary response; reuse completed F1.M1-M3.
Read the exact result, assumptions and evidence
Result
For M=I-sum x_a A_a in formal free variables, F_P(F_R(M))=F_P(M) exactly for P<=R with identical variables and order. All block inverses have identity constant term. Full exterior feedback and input/output legs preserve every word coefficient. Gram positivity follows from actual word-vector norms. Minimal representation can be structurally fixed while responses change; stationarity or physical time does not follow.
Required assumptions
- Given original invariant word domain and nested readouts
Actual operators and adjoints preserve common word domain D; original orthogonal P<=R preserve D. Formal free variables retain order. Analytic evaluation requires common inverses and domains separately. No new physical source, operation selector or time assumed.
Original evidence
- RECURSIVE-WORD-SOURCE-PROOF.txt lines 1–110
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/RECURSIVE-WORD-SOURCE-PROOF.txt
06d651e747e392a5a9c021c071fea3865687203aa58d75cee26fceb7035f5af5
finding:full-memory-schur-reconstruction-preserves-every-ordered-word-under-nesting