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Theorem, construction, or exact resource formula

MMR-057

Claim MMR-057

Exact statement

The strict pinned-reset fan-out-two Strassen compiler has Cpin(N)=163(Nlog⁡27−N2)C^{\rm pin}(N)=\frac{16}{3}(N^{\log_2 7}-N^2), Dpin(N)=1+6log⁡2ND^{\rm pin}(N)=1+6\log_2N, and Spin(N)=4N2−3S^{\rm pin}(N)=4N^2-3.

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 8, equations (8.2)--(8.4); exact recurrences for the declared entry-copy compiler and JIT macro schedule. No optimality 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.