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Theorem with computational certificate

MMR-104

The shared Kronecker BCLR resource receipt

Exact statement

The declared separable square-BCLR DAG has exact base receipt (M,A,C,D,S,F)=(1000,4504,8128,19,2002,5)(M,A,C,D,S,F)=(1000,4504,8128,19,2002,5) and product-call frontier α=2000\alpha=2000.

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

Factor-fiber formulas prove A,CA,C; full DAG replay proves depth, liveness, and fan-out. The shared 322322 output circuit is coefficient-checked against the evaluated factor map.

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.