The A₂ Spectral Geometry of the 2026 Jacobian Counterexample

This research note studies the inverse cubic associated with the explicit three-dimensional counterexample to the Jacobian Conjecture announced in July 2026. The public verification manuscript proves that the generic inverse problem is governed by a binary cubic and that the map's nonproperness set is the cubic discriminant hypersurface. The note records three consequences. First, near the triple-root curve, an explicit coordinate change identifies the inverse family with the miniversal deformation u^3 + au + b of the A2 singularity, times one smooth parameter; the germ of the nonproperness locus is therefore the standard A2 cuspidal discriminant times a line. Second, the generic inverse cover has full S3 = W(A2) monodromy. Third, the pushforward algebra of the three-sheeted cover determines a canonical sl_3(C)-bundle with a Cartan subbundle, the six A2 root spaces, and Weyl monodromy. The deposit includes LaTeX source and an exact SymPy verification script. Research note; not peer reviewed. .