Sharpness of the Cyclic Integral Floer Bound Below the Stable Morse Number
We construct a simply connected closed Kähler manifold of real dimension 3332 and minimal Chern number one whose Hamiltonian fixed-point count attains the cyclic integral Floer bound while falling below the stable Morse number. The Hamiltonian diffeomorphism has exactly $1\,872\,232$ fixed points, all nondegenerate and with contractible orbit loops, whereas the stable Morse number is $1\,872\,264$. Thus the stronger stable Morse bound fails by exactly 32, even when the cyclic integral bound is sharp.
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