FPRD LabShare an approach

← Claims

Theorem, construction, or exact resource formula

MMR-067

Claim MMR-067

Exact statement

An explicit length-rr polynomial degeneration with normalized error degree ee compiles over any field with e+1e+1 distinct nonzero points to an exact bilinear DAG with (e+1)r(e+1)r nonscalar products.

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; interpolate Q(ε)=ε−qP(ε)Q(\varepsilon)=\varepsilon^{-q}P(\varepsilon) at nonzero points and substitute the evaluated rank-rr decompositions. This is a literal construction, not a minimal-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.