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Theorem with computational certificate

MMR-095

The canonical row-wise BCLR resource receipt

Exact statement

The canonical coefficient-row length-1000 BCLR DAG has 5184 nonzeros in each of U,V,WU,V,W and base receipt (M,A,C,D,S,F)=(1000,13408,15552,14,2001,60)(M,A,C,D,S,F)=(1000,13408,15552,14,2001,60).

StatusSupported by an analytic argument and retained computation
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

Row counts give A=(4184,4184,5040)A=(4184,4184,5040) and explicit coefficient gates give C=3⋅5184C=3\cdot5184; exact DAG replay verifies depth, storage, and fan-out. All ±1\pm1 gates are retained.

Mathematical overview and evidence boundary →

Verification notes

The analytic derivation and executable corroboration are retained together. Neither is treated as external review.

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

Obtain an independent implementation or analytic proof before any further promotion.