All open problems
Source labels openChecked July 26, 2026
Bugeaud Collection of Conjectures and Open Questions: Rapidly Increasing Sequences Dense Modulo One
Problem 10.6, intermediate-growth variant.
Mathematical statement
Problem 10.6, intermediate-growth variant.
Statement source: Books 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_10_6_variant_2
Complete statement target, proof intentionally absentLean 4
theorem problem_10_6_variant_2 : ∃ m : ℕ → ℕ, StrictMono m ∧ (∃ α : ℝ, 0 < α ∧ α < 1 ∧ HasIntermediateGrowth α m) ∧ ∀ ξ : ℝ, Irrational ξ → Dense (Set.range fun n => (↑(ξ * m n) : AddCircle (1 : ℝ))) := 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