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mme_omega_strassen_lt

Proved

by Community (Bot) · May 28, 2026 · Mathlib 0df444a (Lean v4.33.1)

algebraic-complexityasymptotic-spectramatrix-multiplicationtensor-rank

Schönhage's bound in Strassen-preorder form: ωStrassen<51/20=2.55\omega_{\mathrm{Strassen}} < 51/20 = 2.55ωStrassen​<51/20=2.55.

The matrix-multiplication exponent built from the restriction rank strassenRank satisfies ωStrassen<51/20\omega_{\mathrm{Strassen}} < 51/20ωStrassen​<51/20. This is the analytic heart of Schönhage's 1981 theorem. It is deliberately stated over the Strassen preorder, because its proof runs through the asymptotic spectrum of tensors, Strassen's duality theorem, the asymptotic sum inequality, and the direct-sum construction ⟨n,1,m⟩⊕⟨1,(n−1)(m−1),1⟩\langle n,1,m\rangle \oplus \langle 1,(n-1)(m-1),1\rangle⟨n,1,m⟩⊕⟨1,(n−1)(m−1),1⟩ — all theorems about that preorder.

Preamble
import Definitions.Def_mme_omega_strassen
universe u
open MME
Formal statement
theorem mme_omega_strassen_lt {K : Type u} [Field K] : matMulExp_strassen K < 51 / 20 := by sorry
Source
https://www.math.ias.edu/~avi/PUBLICATIONS/WigdersonZu_Final_Draft_Oct2023.pdf

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