Chern–Segre positivity conjecture for tautological integrals

Let $X$ be a smooth complex variety, let $F$ be the bundle appearing in the tautological integral of Theorem, and write that integral as a polynomial in the Chern classes of $F$ and the Segre classes of $X$. Chern–Segre positivity conjecture. The tautological integral in Theorem has positive coefficients when written in Chern classes of $F$ and Segre classes of $X$. This is presented as a translation of Rimányi's positivity conjecture for Thom polynomials of Morin singularities; its formulation is described as surprising and mysterious, and no resolution is given in the supplied text.