Two exact Strassen depth–storage schedules

Exact statement

The storage-oriented standard-Strassen recursive realization has $D(N)=1+4\log_2N$ and $S(N)=(5N^2-2)/3$ , while a balanced depth-oriented realization has $D(N)=1+3\log_2N$ and $S(N)=2N^2-1$ .

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

Apply Theorem R7.1 to the verified $(5,5)$ and $(6,6)$ witnesses and solve the recurrences; critical paths self-nest. Storage is exact for the declared pinned macro schedules, not globally optimal.

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.