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← Claims

Theorem, construction, or exact resource formula

MMR-110

Two BCLR realizations are Pareto-incomparable

Exact statement

RPR-D11 and RPR-D12 are Pareto-incomparable: RPR-D12 improves A,C,F,RA,C,F,R and keeps amplification base 768, while worsening raw depth, declared storage by one scalar, and rounded-path increment.

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

Exact same-certificate comparison in Run 12. This distinguishes the two fixed DAGs; it is not a lower bound over all SLPs realizing the coefficient matrices.

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.