Associated forms in classical invariant theory and their applications to hypersurface singularities

It was conjectured in the recent article by Eastwood and Isaev that all absolute classical invariants of forms of degree (Formula Presented) on (Formula Presented) can be extracted, in a canonical way, from those of forms of degree (Formula Presented) by means of assigning every form with non-vanishing discriminant the so-called associated form. This surprising conjecture was confirmed for binary forms of degree (Formula Presented) and ternary cubics. In the present paper, we settle the conjecture in full generality. In addition, we propose a stronger version of this statement and obtain evidence supporting it.