Gamma-class overconvergence conjecture for quantum connections

Let $M$ be a monotone symplectic manifold, let $K$ be the coefficient field used for the rescaled quantum connection, and write $H^{\mathrm{even}}(M;K)$ for its even cohomology. For an invertible class $b\in H^{\mathrm{even}}(M;K)$, the Frobenius structure has constant term

$$\Phi_0(x)=p^{-\operatorname{deg}(x)/2}b\smile x.$$

Morita's $p$-adic Gamma function defines a multiplicative characteristic class $\Gamma_p(TM)$ of the tangent bundle $TM$.

Gamma-class overconvergence conjecture. For the quantum connection on any monotone symplectic manifold, the Frobenius structure with constant term above, where $b=\Gamma_p(TM)$, is overconvergent.

This is the concrete formulation of the paper's proposed Gamma-class correction to the Frobenius structure. The supplied text gives examples and motivation but no resolution.