Leading-term conjecture for stable orbital integrals in unitary and symplectic Lie algebras

Let $F$ be a non-Archimedean local field, let $\boldsymbol{o}$ be its ring of integers, and use the notation $B(\gamma)^{\mathrm{irred}}$, $B(\gamma)^{\mathrm{split}}$, $d_i$, $\bar d_{g_i}$, and $l$ from the paper. Assume $\operatorname{char}(F)=0$ or $\operatorname{char}(F)>n$, and let $\gamma$ be regular semisimple with $B(\gamma)^{\mathrm{irred}}$ a singleton. Leading-term conjecture. If $\gamma\in\mathfrak{u}_{n,\boldsymbol{o}}(\boldsymbol{o})$, then

$$\mathcal{SO}_{\gamma}=\frac{\#\operatorname{U}_n(\kappa)}{q^{n^2}(1+q^{-l})}(1+O(q^{-l}))\prod_{i\in B(\gamma)^{\mathrm{split}}}\frac{q^{2d_i}}{q^{2d_i-2}}\left(1+\alpha(\bar d_{g_i})q^{-2d_i}+O(q^{-4d_i})\right),$$

while if $\gamma\in\mathfrak{sp}_{2n,\boldsymbol{o}}(\boldsymbol{o})$ and $\overline{\chi}_\gamma(x)=x^{2n}$, then

$$\mathcal{SO}_{\gamma}=\frac{\#\operatorname{Sp}_{2n}(\kappa)}{q^{2n^2+n}}(1+O(q^{-1}))\prod_{i\in B(\gamma)^{\mathrm{split}}}\frac{q^{d_i}}{q^{d_i}-1}\left(1+\alpha(\bar d_{g_i})q^{-d_i}+O(q^{-2d_i})\right).$$

This extends the proposed optimal leading-term behavior from the general linear case to the unitary and restricted symplectic cases. The supplied text gives no resolution status.