Simulated non-tip adjoint

With $f=\sigma =1$ and unit scalar $A$-factors, the displayed ${\mathcal{P}}_{5a}$ reduces to ${{\partial }_{s^0}}^2{{\partial }_{t^0}}^2\Psi$ for $\Psi =\exp (-((s^0-1.5{)}^2+(t^0{)}^2))$. Derivatives are taken before the chart evaluation. On $\gamma \in [-1.2,-0.4]$ and transverse radius at most $0.8$, with density $\beta /(8{\pi }^2|\gamma |)$ at $\beta =1.5$, dblquad returns $-0.004633651977461527$, error estimate $1.6\times 10^{-15}$. This is simulated scalar data, not the inherited component map.