A quartic Hessian problem in four variables is one of the first unresolved cases in a route toward the Jacobian conjecture. This Evidence Press release does not solve that problem. It makes one difficult boundary smaller and more explicit. First, exact characteristic-zero certificates exclude the case where the associated binary decimic has exactly five distinct roots. Second, on the tangent residual orbit, every one of the thirty-one equations defining the multiplicity-six target is proved to vanish on the clean normal layer. The remaining secant orbit is harder. There the release proves three successive rational colon identities, but not the full saturation. The closing experiment asks whether sixteen prospectively chosen sparse source directions survive exact lifting. They do: four characteristic-one-hundred-and-seventy-three solves lift the batch through the fourth p-adic digit, all five hundred and eighty-five thousand three hundred and ninety-two coordinates reconstruct uniquely, every matrix row replays, and a separate implementation expands all sixteen rational combinations to the zero polynomial. This is a positive structural signal, not fourth-target membership. The paper, full ZIP, exact receipts, failed routes, review record and replay scripts are public under DOI 10.5281/zenodo.22216400. This is the anonymous, AI-assisted, unrefereed version 0.1.0 candidate, published 1 September 2026. The voice is synthetic, and this briefing is a communication aid, not additional evidence.