Fuglede's conjecture in dimensions 1 and 2: Dim 2
Fuglede's conjecture* in two dimensions: A bounded subset of ℝ^2 with positive Lebesgue measure is spectral iff it tiles ℝ^2 by translation.
Mathematical statement
Fuglede's conjecture* in two dimensions: A bounded subset of ℝ^2 with positive Lebesgue measure is spectral iff it tiles ℝ^2 by translation.
Statement source: Wikipedia statement material
Statement terms: CC-BY-SA-4.0
Attributed source material. Reuse must follow the linked attribution and share-alike terms.
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
FugledeConjecture.variants.dim_2
theorem FugledeConjecture.variants.dim_2 : answer(sorry) ↔ FugledeConjectureFor 2 := 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