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feat: add Ornstein–Weiss ℤᵈ Rokhlin lemma eval problem#309

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feat: add Ornstein–Weiss ℤᵈ Rokhlin lemma eval problem#309
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eval/ornstein-weiss

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@kim-em kim-em commented May 24, 2026

This PR adds an eval problem for the Ornstein–Weiss ℤᵈ Rokhlin
lemma (Ornstein–Weiss, 1987): the multidimensional generalization of
the classical Rokhlin lemma. For every free measure-preserving
ℤᵈ-action T on a standard Borel probability space (with d ≥ 1,
identity axiom T 0 = id, and the homomorphism axiom), every box size
N ≥ 1, and every ε > 0, there is a measurable base B such that
the translates T v '' B for v ∈ [0, N)ᵈ are pairwise disjoint
with measure ≥ 1 − ε. Additional statement of §109 of Knill's
Some Fundamental Theorems in Mathematics (the boxed main theorem
is the classical Rokhlin lemma).

Mathlib has MeasurePreserving, IsProbabilityMeasure,
Set.PairwiseDisjoint, Fintype.piFinset, Finset.Ico, and
StandardBorelSpace, but no Ornstein–Weiss lemma, no free
measure-preserving ℤᵈ-actions, no multidimensional Rokhlin towers.
The Challenge ships two small helper definitions (IsFreeAction and
boxShape).

No formalization found in any major prover.

🤖 Prepared with Claude Code

§109 of Knill's "Some Fundamental Theorems in Mathematics" (additional
statement; the boxed main theorem is the classical Rokhlin lemma).
The multidimensional generalization (Ornstein–Weiss, 1987): for every
free measure-preserving ℤᵈ-action T on a standard Borel probability
space, every box size N ≥ 1, and every ε > 0, there is a measurable
base B such that the translates T v '' B for v ∈ [0, N)ᵈ are pairwise
disjoint with measure ≥ 1 - ε. Mathlib has the supporting measure
theory and Finset / box machinery but no multidimensional Rokhlin
lemma and no free measure-preserving ℤᵈ-actions.

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
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