Polybrutus — Unlabeled seven-point distances: computational uniqueness in 3D and an exact 4D counterexample

Polybrutus supplementary research note. For a specific multiset of 21 unlabeled squared distances of seven points, two exact finite enumerations (Gram and Cayley–Menger) return a single congruence class in Euclidean 3-space, without assuming that competitors lie on a common sphere. An explicit seven-point configuration in Euclidean 4-space has the same distance multiset but affine rank four, so is noncongruent to the original rank-three configuration. The ZIP contains the exact-coordinate 4D witness, two independent 3D enumerators, a SymPy check, an independent coordinate audit, a scientific review note, and provenance of a pinned public GitHub commit. This is a computational preprint, not peer reviewed; claims of originality/priority have not been established. Original Polybrutus publication: 10.5281/zenodo.23945337. Source: GitHub research supplement. Pinned commit: 8e632d2c3c76da0dd85662edad155637617e7b00.