FPRD LabShare an approach

← Claims

Specialization of a published theorem

MMR-100

Claim MMR-100

Exact statement

In the standard multiplicative rounding model, RPR-D11 has finite-uu forward error at most 768k∣t∣−3k((1+u)1+17k−1)∥A∥max⁡∥B∥max⁡768^k|t|^{-3k}((1+u)^{1+17k}-1)\|A\|_{\max}\|B\|_{\max}.

StatusSpecialized from a cited published theorem
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

Theorem R11.1 specializes the Δ\mathbf\Delta-set stationary-partition analysis of Demmel et al. to MMR-099. Exact coefficients and no overflow/underflow are assumed.

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.