Claim FPRD-T23

Exact statement

For languages A and B with positive minimum word length m in A, the operator F(X)=AX union B is at most 2-to-the-minus-m contractive in the shortest-distinguishing-word ultrametric, has the unique fixed point A-star B, and its finite unfoldings become exact on bounded words; under the suffix-recognition lift the same fixed point solves the corresponding relational composition-and-union equation with exact remaining-suffix and complete-match readout.

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

Arden's rule, length-based contraction, and bounded convergence are classical or prior mechanisms. M15's obligation is their exact readout-aware suffix-relation realization.

Open work

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

Notes

Arden's rule, length-based contraction, and bounded convergence are classical or prior mechanisms. M15's obligation is their exact readout-aware suffix-relation realization.