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Written-proof claim

FPRD-T99

Claim FPRD-T99

Exact statement

Let a deterministic visible-stack language have a complete family of a fixed positive finite number of lawful finalizable delayed resolvers, with finite input, visible-control, stack, resolver-control, and family carriers. Each branch has a deterministic PDA realization: a right endmarker may drain finish explicitly, and a finite augmented top-window construction eliminates that marker by predicting the same final readout. The projected language is therefore a finite union of DCFLs and belongs to PEL by Rubtsov--Chudinov Theorem 10, with complete-match semantics and no reversal.

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/notes/finalizable-delayed-resolver-cover-proof.md. The matrix has not yet rewritten that source into a self-contained public proof summary.

docs/notes/finalizable-delayed-resolver-cover-proof.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

  • Finiteness bounds both per-step output batches and finish length. The deterministic PDA alternates input and epsilon-drain phases, encodes empty-stack returns with a bottom record, and totalizes unused cases into a rejecting sink. Augmenting each physical stack symbol with a fixed logical top window makes finish acceptance a finite-control readout and removes dependence on the right-endmarker convention. This is an ordinary proof outside Lean. It uses the finite-union consequence of Rubtsov--Chudinov Theorem 10 directly, so unlike the LMR scaffold route its conclusion is X in PEL rather than X reversed in PEL.

Open work

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

Notes

Finiteness bounds both per-step output batches and finish length. The deterministic PDA alternates input and epsilon-drain phases, encodes empty-stack returns with a bottom record, and totalizes unused cases into a rejecting sink. Augmenting each physical stack symbol with a fixed logical top window makes finish acceptance a finite-control readout and removes dependence on the right-endmarker convention. This is an ordinary proof outside Lean. It uses the finite-union consequence of Rubtsov--Chudinov Theorem 10 directly, so unlike the LMR scaffold route its conclusion is X in PEL rather than X reversed in PEL.