{"id":"openai-math/A-degenerate-counterexample-to-the-critical-number-Arnold-bound","pdf":"https://github.com/openai/math/blob/main/preprints/A-degenerate-counterexample-to-the-critical-number-Arnold-bound-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/A-degenerate-counterexample-to-the-critical-number-Arnold-bound-September-23-2026","tags":["symplectic-geometry","arnold-conjecture","fixed-points","hamiltonian-dynamics"],"score":0,"title":"Three fixed points on the symplectic quadric threefold","domain":"Differential geometry","family":"347","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.DG","summary":"We construct a smooth Hamiltonian diffeomorphism of the complex quadric threefold with exactly three fixed points, at least one of which is degenerate. The critical number and the unit-inclusive rational cup length of this manifold are both four. Thus the example disproves the unrestricted critical-number and rational cup-length forms of the Arnold conjecture.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-23","reactions":{},"formalized":true,"family_title":"Counterexamples to stable-Morse and strong Arnold fixed-point bounds"}