Exceptional-set description in Manin's conjecture for Fano varieties

Let $X$ be a smooth projective geometrically integral Fano variety over a number field, and set $L=-K_X$. For a thin map $f:Y\to X$ from a smooth projective geometrically integral variety $Y$, let $a$ and $b$ be the corresponding invariants and let $\kappa$ denote Kodaira dimension. Manin's exceptional-set conjecture. Let $Z$ be the union of $f(Y(F))$ over all such thin maps satisfying

$$(a(X,L),b(F,X,L))\leq(a(Y,f^*L),b(F,Y,f^*L))$$

and one of: $\dim(Y)<\dim(X)$; $\dim(Y)=\dim(X)$ and $\kappa(K_Y+a(Y,f^*L)f^*L)>0$; or $\dim(Y)=\dim(X)$, $\kappa(K_Y+a(Y,f^*L)f^*L)=0$, and $f$ is face contracting. Then $Z$ coincides with the exceptional set in Manin's conjecture for $X$ with anticanonical polarization. This refines the expected exceptional set by including precisely the thin-map contributions that can obstruct the predicted asymptotic.