Source labels openChecked July 26, 2026

Weak tiling problems

Problem 4.2.* Let $\Omega \subset \mathbb{R}$ be a finite union of three or more intervals. If $\Omega$ weakly tiles its complement, must it also tile its complement properly?

Harmonic analysis AMS 42 AMS 46

Mathematical statement

Problem 4.2.* Let $\Omega \subset \mathbb{R}$ be a finite union of three or more intervals. If $\Omega$ weakly tiles its complement, must it also tile its complement properly?

Statement source: Papers statement material

Statement terms: Source-specific

Source-specific terms. Therefore does not assert reuse rights beyond attributed display.

Statement artifacts, not proofs

These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.

Pinned Lean formulation 1

problem_4_2

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem problem_4_2 :    answer(sorry) ↔ ∀ (n : ℕ) (_ : 3 ≤ n) (Ω : Set ℝ)      (_ : IsUnionOfNIntervals n Ω) (ν : Measure ℝ) (_ : IsWeakTilingMeasure Ω ν),      ∃ T : Set ℝ, IsProperTiling Ω T := by  sorry

Statement source: Formal Conjectures
Lean version: v4.27.0
Placeholder: Present; no proof artifact
Source evidence: Pinned source index
Fidelity review: Community formulation

References

Pinned Formal Conjectures sourceformalization arxiv/2506.23631background