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Conditional result

MMR-092

Claim MMR-092

Exact statement

Conditional on roundoff envelope Bku∣t∣−3kB_ku|t|^{-3k} with Bk/12kB_k/12^k at most exponential, choosing ∣t∣=Θ(1/k)|t|=\Theta(1/k) gives sufficient mantissa precision 3klog⁡2k+O(k+log⁡(1/τ))3k\log_2k+O(k+\log(1/\tau)).

StatusConditional on the stated hypothesis
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

Algebraic substitution in Run 10 for an unspecified/shared SLP. Run 11 derives BkB_k for the different row-wise DAG only. Not a lower bound.

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.