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Theorem, construction, or exact resource formula

MMR-101

Claim MMR-101

Exact statement

Relative to the 12k12^k natural output scale, combining MMR-100 with Run 10 truncation gives a sufficient mantissa law p=3klog⁡2k+O(k+log⁡k+log⁡(1/τ))p=3k\log_2k+O(k+\log k+\log(1/\tau)).

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

Choose ∣t∣=O(1/k)|t|=O(1/k) from MMR-091 and solve the finite-uu inequality. A power-of-two parameter handles exact representation. This is not a precision 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.