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Literature calibration

MMR-021

Claim MMR-021

Exact statement

A current fixed-rank algorithm can improve addition count solely by changing the explicit linear SLP.

StatusEstablished in cited literature and retained as calibration
External reviewThe cited result appears in external literature; that publication is not external review of the FPRD synthesis.

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

Karunaratne–Idamekorala, arXiv:2607.28676, gives a rank-23 3×33\times3 scheme with an explicit 55-addition SLP.

Mathematical overview and evidence boundary →

Verification notes

The bibliography retains the primary-source attribution. The public record does not treat publication of the underlying theorem as review of this FPRD synthesis.

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

Confirm the primary citation, hypotheses, and exact scope through an independent source audit.