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Computational finding

MMR-049

Claim MMR-049

Exact statement

Across all 225 fixed-product Strassen output associations, exact recursive-frontier Pareto signatures are: 104 (5,5)(5,5), 8 (5,6)(5,6), and 113 (6,6)(6,6).

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 ideal-DAG Pareto DP in `matrix_realization_run7_recursive_frontier_check.py`, SHA-256 `d38466c89d65b146dd9e2eddb445c236659efad6e9cff7f84ca042040666a21c`. No formal verification or analytic lower bound.

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.