A finite cyclic type-class compiler

Exact statement

Given an exact square base $(n,R)$ , a type- $\mathbf c$ of an $N$ th direct-sum power, and explicit normalized error degree $e$ , the three-cyclic common-curve compiler produces $s=n^{3\lfloor\log_R\binom N{\mathbf c}\rfloor}\prod_i v_i^{c_i}$ with exact rank at most $(3Ne+1)r^{3N}$ .

StatusProved in the FPRD research record

External reviewNo documented external or specialist review of the FPRD synthesis is recorded.

Context

This result belongs to the reconstruction from algebraic matrix-multiplication certificates to explicit arithmetic dependency DAGs and their resource receipts.

Hypotheses and scope

All resource conclusions are restricted to the arithmetic, storage, fan-out, coefficient, and precision models named in the source record.

Proof or evidence

Theorem R14.1 one-step lemma: type restriction, injection of the old algorithm's rank terms, three cyclic tensor orientations, then one coefficient extraction. Infinite field or explicit extension compiler required.

Mathematical overview and evidence boundary →

Verification notes

The analytic argument is preserved in the research record. Independent external review is not recorded.

Limitations

The record does not improve the known matrix-multiplication exponent and does not imply that omega equals two.
Construction bounds are not optimality, communication, I/O, or hardware claims unless the exact statement says so.

Open work

Independently re-audit the complete derivation before any further promotion.