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Definition

FPRD-D26

Claim FPRD-D26

Exact statement

For a controlled-Dyck trace L and a nonnegative access budget b, the state-budget function nu_D(L;b) is the minimum number of states in a finite regular controller whose intersection with the fixed Dyck envelope is L and whose legal-entry balanced diameter is at most b, with value infinity when no such finite controller exists.

Statusdefinition
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/m31-entry-atlas-sewing-tradeoffs.md. The matrix has not yet rewritten that source into a self-contained public proof summary.

docs/specs/m31-entry-atlas-sewing-tradeoffs.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

  • Unreachable padding does not change the minimum. This function records one presentation-size/access tradeoff relative to a fixed Dyck envelope; it is not claimed invariant under recoding the envelope.

Open work

Add a self-contained definition page with examples, nonexamples, and dependency boundaries.

Notes

Unreachable padding does not change the minimum. This function records one presentation-size/access tradeoff relative to a fixed Dyck envelope; it is not claimed invariant under recoding the envelope.