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Theorem, construction, or exact resource formula

MMR-081

Claim MMR-081

Exact statement

The displayed one-level BCLR evaluation admits a shared-output SLP with five nonscalar products, eleven additions/subtractions total, three or four input fixed-scalar products depending on sharing, and two output scalings by t−1t^{-1}.

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

Direct gate count of equations (9.26) and (9.33). Counts describe this SLP and are not minima.

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.