Claim FPRD-T31

Exact statement

For every finite complete source controller, the fixed-envelope recoder constructs a finite complete deterministic trie controller recognizing exactly its tau image, sending malformed blocks and unused envelope symbols to a rejecting sink; intersection with envelope Dyck geometry then equals the tau image of the source Dyck-control intersection, so the abstract M18 theorem supplies one exact decoded suffix dynamic with same-index envelope reconstruction and the block-scaled source observation modulus, while every instance admitted by an explicit finite one-character codec is conjugately realized by the executable M18 implementation.

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 complete trie controller is the finite-control mechanism that moves source bracket identity out of the recursive engine and into regular recognition while retaining an M18-ready exact readout.

Open work

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

Notes

The complete trie controller is the finite-control mechanism that moves source bracket identity out of the recursive engine and into regular recognition while retaining an M18-ready exact readout.