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Theorem, construction, or exact resource formula

MMR-080

Claim MMR-080

Exact statement

The BCLR tensor has the literal exact ten-product realization TBCLR=2P(1)−12P(2)T_{\rm BCLR}=2P(1)-\frac12P(2).

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

Theorem R9.1 with e=1e=1 gives two-node constant extraction; exact rational checker verifies every tensor coordinate. This is an upper bound for the sealed interpolation DAG, not an optimal-rank claim.

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.