An explicit but impractical base-size bound

Exact statement

A coarse effective analysis gives $\log s_\varepsilon\le\exp(O((\log(1/\varepsilon))^2))$ and hence $s_\varepsilon\le\exp(\exp(O((\log(1/\varepsilon))^2)))$ for a fixed nontrivial certificate.

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

Iterate the sufficient scale $N_j=O((\log n_j+\log(1/\eta))/\eta)$ for $J=O(\log(1/\varepsilon))$ stages. Constants depend on the certificate and $1-\alpha$ ; no sharpness claim.

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.