The inhomogeneous arithmetic transfer conjecture

Let $F/F_0$ be ramified and let $n\geq3$ be odd. Let $S(F_0)$ be the inhomogeneous symmetric space, let $U_0$ and $U_1$ be the relevant unitary groups, let $K_0\subset U_0(F_0)$ be the chosen compact subgroup, and let $\operatorname{Int}(g)$ denote the intersection number for $g\in U_1(F_0)_{\mathrm{rs}}$. Inhomogeneous arithmetic transfer conjecture. (a) There exists $f'\in C_c^\infty(S(F_0))$ transferring to $(\mathbf{1}_{K_0},0)$ such that

$$2\omega(\gamma)\operatorname{\partial Orb}(\gamma,f')=-\operatorname{Int}(g)\cdot\log q$$

for every matching pair $\gamma\in S(F_0)_{\mathrm{rs}}$ and $g\in U_1(F_0)_{\mathrm{rs}}$. (b) For every such $f'$ there exists $f'_{\mathrm{corr}}\in C_c^\infty(S(F_0))$ such that

$$2\omega(\gamma)\operatorname{\partial Orb}(\gamma,f')=-\operatorname{Int}(g)\cdot\log q+\omega(\gamma)\operatorname{Orb}(\gamma,f'_{\mathrm{corr}})$$

for every such matching pair. This is the ramified arithmetic-transfer prediction, with part (b) allowing a correction by an ordinary orbital integral.