Claim FPRD-T09

Exact statement

For every finite context rank r at least one, the polynomial actions F_i(p) = End / (terminal-c_i ; p), generated from End, have the exact finite prefix-tree orbit and a compact closure indexed by finite and infinite context words, with longest-common-prefix metric, Cantor boundary at rank at least two, explicit finite node/cylinder shadows, inverse-limit reconstruction, and a uniform prefix 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

The theorem must keep finite parser inputs separate from infinite boundary coordinates. It compares equal free action monoids with different recognition compactifications and makes no grammar-extraction, CFG, pushdown, or semi-algebraic claim.

Open work

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

Notes

The theorem must keep finite parser inputs separate from infinite boundary coordinates. It compares equal free action monoids with different recognition compactifications and makes no grammar-extraction, CFG, pushdown, or semi-algebraic claim.