The physicists' Euler number conjecture for stringy Euler characteristics

Let a finite group $G$ act on a manifold $M$, and let $M/G$ be stratified by stabilizer subgroups. The stringy Euler number $e_{\text{string}}(M,G)$ is the invariant obtained by summing the ordinary Euler numbers of the strata, weighted by the numbers of conjugacy classes of their stabilizers.

Physicists' Euler number conjecture. In appropriate circumstances,

$$e_{\text{string}}(M,G)=\text{the Euler number of a minimal resolution of }M/G.$$

This conjecture relates orbifold or string-theoretic data to the topology of resolutions of quotient singularities. The phrase “appropriate circumstances” is not made precise in the statement, and the source does not establish a general resolution of the conjecture.