Level-two (1,1)-profile has dimension 25

Proved

mme_entropy_regional_profile_11_exists

by Tamas Fulop · Sep 15, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

matrix-multiplicationmore-asymmetryregional-entropy

The level-two boundary profile on the word $(1,1)$ exists and has dimension $25$ . At level $\ell = 2$ with a single position, the profile counting the word $(1,1)$ once has multinomial coefficient $1$ and $5$ -power $5^2$ , giving

\dim = 25.

This is the boundary profile feeding the More Asymmetry regional construction: its dimensions $(5,5,1)$ multiply to $25$ . Formalization Note Lean states existence of a Boundary.Profile 2 1 of dimension $25$ .

Preamble

import Definitions.Def_mme_recursive_yz_boundary_data

set_option autoImplicit false

Formal statement

theorem mme_entropy_regional_profile_11_exists :
    exists (prof : MME.RecursiveYZ.Boundary.Profile 2 1), prof.dim = 25 := by sorry

Source

Alman et al., More Asymmetry Yields Faster Matrix Multiplication, https://arxiv.org/html/2404.16349v2#S6, Section 6 regional construction; the level-two profile on the word (1,1) contributes 5^2=25 dimensions

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