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Theorem with computational certificate

MMR-097

Claim MMR-097

Exact statement

The declared eager row-wise depth-first schedule has exact peak storage Sk=1+2000(144k−1)/143<14N2S_k=1+2000(144^k-1)/143<14N^2 for N=12kN=12^k.

StatusSupported by an analytic argument and retained computation
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

Base replay gives (σ,α)=(2001,2000)(\sigma,\alpha)=(2001,2000); analytic recurrence Sk=max⁡{2001 144k−1,2000 144k−1+Sk−1}S_k=\max\{2001\,144^{k-1},2000\,144^{k-1}+S_{k-1}\} then solves exactly. Not a global lower bound.

Mathematical overview and evidence boundary →

Verification notes

The analytic derivation and executable corroboration are retained together. Neither is treated as external review.

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

Obtain an independent implementation or analytic proof before any further promotion.