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The Morse-number Arnold conjecture for nondegenerate Hamiltonian diffeomorphisms

Theorem 1.1: there are a closed symplectic 12-manifold and a one-periodic Hamiltonian with all fixed points nondegenerate and contractible and #Fix=χ(M)+128<Morse(M)\#\mathrm{Fix}=\chi(M)+128<\mathrm{Morse}(M); Corollary 1.2 makes Morse(M)−#Fix\mathrm{Morse}(M)-\#\mathrm{Fix} arbitrarily large (the manifold depends on the deficit). The mechanism: the augmentation ideal of A5kA_5^k needs two generators while d(A5k)d(A_5^k) is unbounded, realized by relative handle cancellation on X×R8X\times\mathbb R^8. The fixed-point count still exceeds the homological (Floer) bounds. The examples are not simply connected; the October 5 companions give simply connected Kahler examples below the stable Morse number.

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Prior state unknown→disproved

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Occurred: Sep 23, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: contested. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: The Morse-number Arnold conjecture for nondegenerate Hamiltonian diffeomorphisms · Morse-number Arnold conjecture

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Theorem 1.1: there are a closed symplectic 12-manifold and a one-periodic Hamiltonian with all fixed points nondegenerate and contractible and #Fix=χ(M)+128<Morse(M)\#\mathrm{Fix}=\chi(M)+128<\mathrm{Morse}(M); Corollary 1.2 makes Morse(M)−#Fix\mathrm{Morse}(M)-\#\mathrm{Fix} arbitrarily large (the manifold depends on the deficit). The mechanism: the augmentation ideal of A5kA_5^k needs two generators while d(A5k)d(A_5^k) is unbounded, realized by relative handle cancellation on X×R8X\times\mathbb R^8. The fixed-point count still exceeds the homological (Floer) bounds. The examples are not simply connected; the October 5 companions give simply connected Kahler examples below the stable Morse number. parent of this event

VibeMathed record: The Morse-number Arnold conjecture for nondegenerate Hamiltonian diffeomorphisms evidence for this event

The Morse-number Arnold conjecture for nondegenerate Hamiltonian diffeomorphisms evidence for this event

The Morse-number Arnold conjecture for nondegenerate Hamiltonian diffeomorphisms parent of this event

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The Morse-number Arnold conjecture for nondegenerate Hamiltonian diffeomorphisms — Mathematical Frontier Network