  The Green-Griffiths-Lang conjecture says that for every complex projective
algebraic variety $X$ of general type there exists a proper algebraic
subvariety of $X$ containing all nonconstant entire holomorphic curves
$f:\mathbb{C} \to X$. We construct a compactification of the invariant jet
differentials bundle over complex manifolds motivated by an algebraic model of
Morin singularities and we develop an iterated residue formula using
equivariant localisation for tautological integrals over it. We show that the
polynomial GGL conjecture for a generic projective hypersurface of degree
$\mathrm{deg}(X)>2n^{10}$ follows from a positivity conjecture for Thom
polynomials of Morin singularities.
