MMR-048 · FPRD Lab

Claim MMR-048

Exact statement

With $\kappa_\pi=\max(\alpha_\pi,\sigma_\pi-1)$ , the construction satisfies $S_k^\pi\le1+\kappa_\pi(b^{2k}-1)/(b^2-1)$ .

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

Corollary of MMR-047 and the retained child-output lower bound $S_{k-1}\ge b^{2(k-1)}$ . Equality with $\alpha_\pi$ holds when $\sigma_\pi\le\alpha_\pi+1$ .

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.