{"id":"openai-math/Hamiltonian-Fixed-Points-Below-the-Stable-Morse-Number","pdf":"https://github.com/openai/math/blob/main/preprints/Hamiltonian-Fixed-Points-Below-the-Stable-Morse-Number-October-5-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Hamiltonian-Fixed-Points-Below-the-Stable-Morse-Number-October-5-2026","tags":["symplectic-geometry","hamiltonian-dynamics","morse-theory","kahler-manifolds"],"score":0,"title":"Hamiltonian Fixed Points Below the Stable Morse Number","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 by constructing a simply connected closed Kähler manifold with sixteen fewer fixed points than its stable Morse number. All the corresponding periodic orbits are contractible. The construction combines a Hamiltonian involution with integral homology torsion at two different primes; its proof uses finite-dimensional Morse theory and complex blowups.","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"}