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Theorem, construction, or exact resource formula

MMR-091

Claim MMR-091

Exact statement

The relative row-coefficient truncation of kk square BCLR tensor levels is at most [(1+∣t∣)2(1+2∣t∣)]k−1[(1+|t|)^2(1+2|t|)]^k-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

Corollary R10.3 from row-ℓ1\ell_1 tensor-product multiplicativity and a nonempty-subset expansion. ∣t∣=O(1/k)|t|=O(1/k) suffices; Θ(1/k)\Theta(1/k) is the largest constant-error scale for this envelope, not a necessity claim for the signed error.

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.