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Theorem, construction, or exact resource formula

MMR-047

Claim MMR-047

Exact statement

A fixed bilinear base DAG plus a macro schedule π\pi has exact pinned depth-first storage recurrence Skπ=max⁡{σπb2(k−1),απb2(k−1)+Sk−1π}S_k^\pi=\max\{\sigma_\pi b^{2(k-1)},\alpha_\pi b^{2(k-1)}+S_{k-1}^\pi\}.

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

Theorem R7.1; live base values lift to full blocks, and outer blocks remain pinned during each read-only fresh-output recursive call. This is a construction, not a global optimum.

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.