{"id":"openai-math/A-nondegenerate-counterexample-to-the-Morse-number-Arnold-bound","pdf":"https://github.com/openai/math/blob/main/preprints/A-nondegenerate-counterexample-to-the-Morse-number-Arnold-bound-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/A-nondegenerate-counterexample-to-the-Morse-number-Arnold-bound-September-23-2026","tags":["symplectic-geometry","fixed-points","hamiltonian-dynamics"],"score":0,"title":"A nondegenerate counterexample to the Morse-number Arnold bound","domain":"Differential geometry","family":"347","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.DG","summary":"We construct a smooth one-periodic Hamiltonian on a closed symplectic twelve-manifold whose time-one map has fewer fixed points than the manifold's ordinary Morse number. Every fixed point is nondegenerate and has a contractible Hamiltonian trajectory. This disproves the Morse-number form of the Arnold conjecture. The deficit can be arbitrarily large among twelve-dimensional examples.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-23","reactions":{},"formalized":false,"family_title":"Counterexamples to stable-Morse and strong Arnold fixed-point bounds"}