Characterization of the local P² generating series

Determine a substitute for the conifold gap property that, together with finite generation and the crepant transformation property, uniquely characterizes the all-degree generating series of Tot_{P²}(O(-1)^{⊕3}).

Background

The local P² geometry Tot_{P²}(O(-1)^{⊕3}) exhibits symmetry and polylogarithmic behavior analogous to the resolved conifold, but its Gromov–Witten series lacks a conifold gap when expanded around Q=1.

The authors therefore ask whether another structural condition can replace the conifold gap and yield a uniqueness characterization.