Nonreduced orthogonal nine-frames in dimension eight

An open-ended autonomous run of Recursive Reasoning Exploration (RRE) generated a counterexample to the conjecture that the ideal of pairwise orthogonality relations is radical for every number of vectors and every ambient dimension. For nine vectors in dimension eight, this ideal is nonradical over every field of characteristic different from two, for every nondegenerate symmetric bilinear form. An explicit open chart reduces the claim to ten cubic equations in twenty-four variables. A 36-term polynomial represents a nonzero square-zero class. An integral ideal-membership identity and an integral linear functional certify the two assertions, so the arithmetic verification works over every field, including characteristic two, without a Gröbner-basis computation. This all-characteristic conclusion concerns the auxiliary diagonal-parameter scheme; its identification with an open frame chart requires characteristic different from two. We provide the certificate and a short checker using only Python's standard library. Stabilization gives nonreducedness whenever d >= 8 and n >= d + 1. An accompanying three-view visualization guides the reader through the discovery route, proof dependencies, and provenance of the mathematical inputs.