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Level-one N=2 steps exist

Proved
mme_N2_step_inhabited_L1

by Tamas Fulop · Sep 18, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

matrix-multiplicationmore-asymmetryregional-entropy

There exists an integer regional step at level 111 with two elementary positions.

The skeleton is forced (R=1R=1R=1, n=[1]n=[1]n=[1], L=2L=2L=2, half=2half=2half=2, parent 1+1+2=41+1+2=41+1+2=4) and completed with a delta mass at one split, grade-matching delta profiles, and a large tolerance. This is the base point every copy-bound argument at N=2N=2N=2 must start from.

Formalization Note Explicit instance; the predicate is trivial so the source obligation is immediate.

Preamble
import Definitions.Def_mme_integer_regional_CW_recipe
set_option autoImplicit false
Formal statement
theorem mme_N2_step_inhabited_L1 : exists (S : MME.RegionRealization.IntegerStep 1 2 (fun _ _ => True)), True := by sorry
Source
Explicit instance for Alman et al., More Asymmetry, https://arxiv.org/html/2404.16349v2#S6, Section 6 skeleton at N=2.

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