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Computational finding

MMR-079

Claim MMR-079

Exact statement

The proof-consistent five-term BCLR curve for the partial 2×22\times2 matrix-multiplication tensor has (r,q,D,e)=(5,1,2,1)(r,q,D,e)=(5,1,2,1).

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

Exact polynomial expansion in the Run 9 checker recovers the six target monomials as the coefficient of tt and finds total degree two. Formula reconstructed from Landsberg--Ryder, arXiv:1509.08323, Eq. (2) and its derivative proof.

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.