Claim FPRD-T32

Exact statement

For every injective width-m block code and finite complete source controller, the compiled boundary macro-actions are conjugate to the source actions, the right language at each boundary is exactly the code image of the corresponding source right language, and source residual equality is equivalent to boundary residual equality; bounded future-language and full suffix-lift partitions correspond exactly by N maps to floor of N over m, shortest distinguishing lengths multiply by m, and the source residual dynamic embeds into the image residual dynamic under the encoded macro-actions.

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

This is a trace-controller theorem. Dyck intersection and a noninjective output decoder may induce a further observation-relative quotient and are not silently folded into boundary residual equality.

Open work

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

Notes

This is a trace-controller theorem. Dyck intersection and a noninjective output decoder may induce a further observation-relative quotient and are not silently folded into boundary residual equality.