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Theorem, construction, or exact resource formula

MMR-082

Claim MMR-082

Exact statement

The direct BCLR truncation error is componentwise linear in tt, with error vector (tx22y22,−tx22y22,−tx22(y11−y21),0)(t x^2_2y^2_2,-t x^2_2y^2_2,-t x^2_2(y^1_1-y^1_2),0) in the source basis. Under componentwise unit input bounds, the sharp output constants are A∞=2A_\infty=2 and A2=6A_2=\sqrt6.

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 expansion of the five scalar products and output SLP; simultaneous extremizing signs attain both norms. A floating-point roundoff constant is not inferred.

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.