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Literature calibration

MMR-077

Claim MMR-077

Exact statement

Error degree and degeneration order are active quantitative debordering parameters; a current result states rank ≤(e+1)\le(e+1) times border rank and e≤2 orde\le2\,\mathrm{ord} in the general interpolation step.

StatusEstablished in cited literature and retained as calibration
External reviewThe cited result appears in external literature; that publication is not external review of the FPRD synthesis.

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

Ganesh–Koiran–Oliveira, arXiv:2608.10179v1, 10 August 2026, Lemmas 2.16 and 2.18. Their new contributions concern bounds on these parameters for special tensor classes, not Run 9's executable accounting.

Mathematical overview and evidence boundary →

Verification notes

The bibliography retains the primary-source attribution. The public record does not treat publication of the underlying theorem as review of this FPRD synthesis.

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

Confirm the primary citation, hypotheses, and exact scope through an independent source audit.