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Theorem, construction, or exact resource formula

MMR-016

Claim MMR-016

Exact statement

A coefficient matrix BB has row-wise compilation bounds A(B)≤nnz⁡(B)−z(B)A(B)\le\operatorname{nnz}(B)-z(B) and C(B)≤nnz⁡(B)C(B)\le\operatorname{nnz}(B).

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

Sum the dot-product cost over nonzero rows. These are upper bounds, consistent with Ju–Solomonik.

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.