OAI/Geometry/Arnold/Main.lean
1 declarations, 0 contain sorry, 0 declared as axioms
- theorem
OAI.ArnoldCounterexample.mainline 14Source documentation
The Hamiltonian counterexample, with the complete fixed set, the lower bound for all smooth functions, and a genuine nonzero quotient-tangent eigenvector.
Distinct definitions of this name: ComparatorChallenges/ArnoldCounterexample.lean:111 (same statement text; different proof or body). Qualify references as OAI.ArnoldCounterexample.main@path.
theorem main : ∃ φ : Q3 ≃ Q3, IsHamiltonian φ ∧ (fixedSet φ).encard = 3 ∧ (3 : ℕ∞) < 4 ∧ 4 ≤ criticalNumber ∧ HasDegenerateFixedPoint φ := by …Mentions: OAI.ArnoldCounterexample.Q3, OAI.ArnoldCounterexample.IsHamiltonian, OAI.ArnoldCounterexample.fixedSet, OAI.ArnoldCounterexample.criticalNumber, OAI.ArnoldCounterexample.HasDegenerateFixedPoint