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Theorem, construction, or exact resource formula

MMR-060

Claim MMR-060

Exact statement

The count in MMR-059 is minimal among sealed copy-only fan-out-two compilations of the fixed literal expanded Strassen DAG.

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

The ownership compiler attains Lemma R8.1 independently on every original wire; a raw path of length ℓ\ell has 3ℓ+13\ell+1 consumers and uses exactly 3ℓ−13\ell-1 buffers. This is a graph-transformation lower bound, not an arithmetic lower bound.

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.