What happens when eight points collide? Their positions alone do not tell the whole story. Algebraic geometry uses a space called the Hilbert scheme to record both distinct points and the algebraic structures that can appear at collisions. This unrefereed proof candidate concerns eight points in four-dimensional affine space, over algebraically closed fields of characteristic zero. It claims that their Hilbert scheme is reduced: its defining algebra has no nonzero nilpotent elements, the hidden algebraic structure that an ordinary picture cannot show. Reduced does not mean smooth, and it does not mean that the space has only one component. The proposed argument compresses the global question to two local models. It then separates their components and combines explicit open charts with exact computations over two finite fields. A regular parameter is used to close the argument in every degree, rather than extrapolating from a finite list of checked degrees. The full evidence archive includes written proof modules, source code, large polynomial bases and comparison records. A short replay checks those saved records and their dependencies; it does not recompute all the large bases. Deeper reconstruction instructions are supplied. The main next step is scrutiny by unaffiliated specialists, together with independent reconstruction of the computational inputs. External mathematical validation remains absent. The review and software checks belong to the producer workflow. This is the Evidence Press release of 7 September 2026, an unrefereed candidate. The full paper, evidence and limitations are linked. This voice is AI-generated using an OpenAI synthetic voice. The audio is a communication aid, not additional research evidence.