Claim FPRD-T08

Exact statement

For every finite context rank r at least one, a canonical strongly guarded r-call presentation generates the exact free-monoid continuation orbit, whose one-point compact closure has 1 plus the geometric sum through N states in its depth-N shadow, coherent inverse-limit reconstruction, rank-dependent observational growth, and a readout-aware free-word realization.

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

Rank one must recover M4. Higher rank is noncommutative free-word dynamics, not a commutative counter lattice. Exponential bounded-shadow growth is not claimed equivalent to pushdown or context-free recognition. The compact boundary is one failure point rather than a Cantor space, and no literal semi-algebraic coordinate theorem is asserted.

Open work

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

Notes

Rank one must recover M4. Higher rank is noncommutative free-word dynamics, not a commutative counter lattice. Exponential bounded-shadow growth is not claimed equivalent to pushdown or context-free recognition. The compact boundary is one failure point rather than a Cantor space, and no literal semi-algebraic coordinate theorem is asserted.