Residue-formula q-polynomial for general local algebras

Identify and explicitly compute, for an arbitrary finite-dimensional local algebra Q, the q-polynomial appearing in the iterated-residue representation of the Thom series Ts(η_Q). Concretely, determine the equivariant fundamental class q of the locus of associative algebras isomorphic to Q inside the space of (not necessarily associative) algebras with prescribed numerical characteristics, for a suitable choice of filtration.

Background

In the test-curve/space-of-non-associative-algebras approach, the entire Thom series is encoded by a finite datum: a rational expression whose only non-obvious ingredient is the polynomial q in the numerator.

This q-polynomial has a geometric meaning (an equivariant fundamental class), but in general its explicit form is unknown, even for seemingly simple algebras beyond small cases (e.g., A_10).