MMR-073 · FPRD Lab

Claim MMR-073

Exact statement

For rational factor coefficients of bit height $H$ and degree at most $q$ , integer-node interpolation gives fixed coefficients of height $O(k(q+1)H+kq\log(ke+1)+ke)$ at tensor-power level $k$ .

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

Closed weights $\lambda_j=(-1)^{j-1}\binom mj$ , evaluation denominator bound, and product-height addition in Run 9. This is coefficient size, not complete bit-operation complexity.

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.