Effective convergence without an omega oracle

Exact statement

An explicit polynomial direct-sum degeneration and every fixed rational $\varepsilon>0$ algorithmically yield a finite exact square base $(s_\varepsilon,R_\varepsilon)$ with $\log_{s_\varepsilon}R_\varepsilon\le3\tau+\varepsilon$ , starting from naive multiplication rather than an oracle for $\omega$ .

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

Method-of-types finite threshold (Run 14 equations 14.20--14.30) plus the contraction in MMR-121. Each stage searches a finite $N_j$ and applies MMR-120.

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.