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Computational finding

MMR-108

Claim MMR-108

Exact statement

Exact Laurent-majorant propagation through RPR-D12 gives Kr(s)≤768s−3K_r(s)\le768s^{-3} for every output and rounded-path increment ν=23\nu=23.

StatusVerified by retained finite computation; analytic proof is not implied
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

Every gate is propagated symbolically with nonnegative Laurent coefficients; output exponents lie in [−3,3][-3,3] and maximum coefficient sum is 768. Checker SHA-256 `9d01549aef3d1d3998e3cea414713870f5f812e9ddb5714a684045fd7cd16403`.

Mathematical overview and evidence boundary →

Verification notes

The exact checker and its recorded digest are preserved with the research record. This status remains computational until an analytic or formal proof is supplied.

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.