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Written-proof claim

FPRD-T01

Claim FPRD-T01

Exact statement

For a finite alphabet Sigma, the semantic quotient of finite nonrecursive PEG expressions embeds as the subalgebra of suffix-decreasing partial endofunctions of Sigma-star generated by identity, failure, terminal left-cancellations, parser-order composition, preferential union, and antidomain.

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 docs/specs/m1-semantic-algebra.md. The matrix has not yet rewritten that source into a self-contained public proof summary.

docs/specs/m1-semantic-algebra.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 written proof establishes closure, structural semantics, kernel congruence, injectivity after quotienting, and the generated-image characterization. Independent executable routes agree on all 3,244 syntax trees through constructor depth two; that bounded evidence is not the infinite proof.

Open work

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

Notes

The written proof establishes closure, structural semantics, kernel congruence, injectivity after quotienting, and the generated-image characterization. Independent executable routes agree on all 3,244 syntax trees through constructor depth two; that bounded evidence is not the infinite proof.