All open problems
Source labels openChecked July 26, 2026
Claude's Cycles
For even m > 2, it is open whether the cube digraph on (ZMod m)³ has a Hamiltonian arc decomposition.
Mathematical statement
For even m > 2, it is open whether the cube digraph on (ZMod m)³ has a Hamiltonian
arc decomposition.
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
cube_hamiltonian_arc_decomposition_even
Complete statement target, proof intentionally absentLean 4
theorem cube_hamiltonian_arc_decomposition_even : answer(sorry) ↔ ∀ᵉ (m : ℕ) (_ : NeZero m) (_ : Even m) (_ : 2 < m), HasHamiltonianArcDecomposition m := 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