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← Claims

Theorem, construction, or exact resource formula

MMR-002

Claim MMR-002

Exact statement

Naive 2×22\times2 multiplication has (M,A,D,S)=(8,4,2,5)(M,A,D,S)=(8,4,2,5) in RPR-S1.

StatusProved in the FPRD research record
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

Explicit output-at-a-time schedule; last-product lower bound for S≥5S\ge5. Fixed naive DAG only.

Mathematical overview and evidence boundary →

Verification notes

The analytic argument is preserved in the research record. Independent external review is not recorded.

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

Independently re-audit the complete derivation before any further promotion.