FPRD LabShare an approach

← Claims

Theorem, construction, or exact resource formula

MMR-053

Claim MMR-053

Exact statement

Both Run 7 Strassen realizations have M(N)=Nlog⁡27M(N)=N^{\log_2 7} and A(N)=6Nlog⁡27−6N2A(N)=6N^{\log_2 7}-6N^2.

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

Run 2 recurrence with r=7r=7, a=18a=18, b=2b=2, C=0C=0. This is classical Strassen arithmetic recursion.

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.