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Written-proof claim

FPRD-T03

Claim FPRD-T03

Exact statement

Every legal finite suffix-behavior table is denoted at its bound by a synthesized finite nonrecursive PEG expression; consequently the term- generated PEG algebra is dense in the ambient behavior algebra and its observational profinite completion for the bounded-input congruence chain is canonically isomorphic to that ambient algebra.

Statusinformal proof
External reviewNo documented external or specialist review of this FPRD result is recorded.

Context

This row is imported exactly from the governed FPRD claims ledger. The matrix assignment records normalized inventory coverage; it is not a new proof or a promotion of the ledger status.

Proof or evidence

The ledger points to OPEN_PROBLEMS.md. The matrix has not yet rewritten that source into a self-contained public proof summary.

OPEN_PROBLEMS.md →

Verification notes

Reviewed on 2026-08-25 for identifier, status, provenance, evidence-link presence, and dependency import only. Mathematical proof audit remains the next action unless separately documented.

Limitations

  • The proof constructs disjoint exact-input branches for arbitrary finite tables and then derives the inverse-limit comparison. It concerns the named bounded-observation chain, not all finite-index congruences. Density does not say that one finite PEG denotes every ambient behavior or recover presentation dynamics from an extensional completion point.

Open work

Audit the proof against its dependencies and publish a self-contained evidence summary before increasing maturity.

Notes

The proof constructs disjoint exact-input branches for arbitrary finite tables and then derives the inverse-limit comparison. It concerns the named bounded-observation chain, not all finite-index congruences. Density does not say that one finite PEG denotes every ambient behavior or recover presentation dynamics from an extensional completion point.