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Literature calibration

MMR-119

Claim MMR-119

Exact statement

Schönhage's classical R‾(⟨4,1,4⟩⊕⟨1,9,1⟩)≤17\underline R(\langle4,1,4\rangle\oplus\langle1,9,1\rangle)\le17 example yields ω≤2.547992912204408…\omega\le2.547992912204408\ldots.

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

ASI equation 16ω/3+9ω/3=1716^{\omega/3}+9^{\omega/3}=17; root independently bisected by `matrix_realization_run13_direct_sum_check.py`, SHA-256 `d4a2f1cff8f92ceecdbf3b0618d66dd4060bdace5118d69843d8d80d7ac91ea7`.

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.