{"id":"openai-math/Hamiltonian-Fixed-Points-Below-the-Stable-Morse-Number-in-Dimension-Twenty-Two","pdf":"https://github.com/openai/math/blob/main/preprints/Hamiltonian-Fixed-Points-Below-the-Stable-Morse-Number-in-Dimension-Twenty-Two-October-5-2026/hamiltonian-fixed-points-below-stable-morse-number.pdf","url":"https://github.com/openai/math/tree/main/preprints/Hamiltonian-Fixed-Points-Below-the-Stable-Morse-Number-in-Dimension-Twenty-Two-October-5-2026","tags":["symplectic-geometry","hamiltonian-dynamics","morse-theory","fixed-points"],"score":0,"title":"Hamiltonian Fixed Points Below the Stable Morse Number in Dimension Twenty-Two","domain":"Differential geometry","family":"347","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.DG","summary":"We disprove the stable Morse lower bound for nondegenerate Hamiltonian fixed points with examples in fixed real dimension twenty-two. For every integer m ≥ 1, we construct a simply connected closed Kähler manifold with stable Morse number $`80+1968m`$ and a Hamiltonian diffeomorphism with exactly $`80+1952m`$ fixed points, all nondegenerate and with contractible orbit loops. The deficit is therefore unbounded, and the fixed-point count is at most 127/128 of the stable Morse number.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-05","reactions":{},"formalized":false,"family_title":"Counterexamples to stable-Morse and strong Arnold fixed-point bounds"}