Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 347-04. A nondegenerate counterexample to the Morse-number Arnold bound
Manuscript map · lines 9075–9084
OpenAI@2026-10-07#rem:oai-p-347-04
Authors: OpenAI. Family 347.
Title: A nondegenerate counterexample to the Morse-number Arnold bound.
Abstract: 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.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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