Concrete Floer realization of higher cyclic cap-layer strictness

Construct an equivariant marked-point Hamiltonian Floer persistence module for a closed symplectically aspherical manifold that realizes the formal strictness pattern in which the underlying cyclic persistence module and every single cap-operator image have vanishing multiplicity-sensitive spread, while a higher ideal-decorated cap layer yields a strictly positive obstruction, thereby producing a strictly stronger Hofer-geometric obstruction.

Background

The paper constructs an algebraic example on a graded subalgebra of the ordinary cohomology of the closed symplectically aspherical manifold M_0 = Σ_2 × Σ_3. In that example, the ordinary cyclic persistence module and all degreewise images of individual homogeneous cap operators have vanishing multiplicity-sensitive 2-spread, whereas a depth-two ideal-decorated cap layer has positive spread.

The authors explicitly state that this algebraic construction is not realized as a filtered Floer persistence module and therefore does not yet yield a strictly stronger Hofer-geometric obstruction. Achieving such a realization would require simultaneous control of the Floer differential, loop rotation, all single cap operators, and the higher image sum within an equivariant marked-point Floer calculation.