Polybrutus: Exact Seven-Point Distance Multisets with Affine-Rank Realizations in Dimensions 3, 4, 5 and 6
Year: 2026
Type: preprint
Abstract: We provide explicit Euclidean configurations of seven points sharing a single unlabeled multiset of 21 squared pairwise distances and realizing four different affine ranks: 3, 4, 5, and 6. Exact rational/integer Gram-matrix calculations certify the distance data and ranks; independent Python tests and source code are included for reproducibility. Status: independent research preprint, not peer-reviewed. No world-priority or physical Higgs-boson claim is made. Files: a five-page research note (PDF), exact-math reproducibility bundle (ZIP; Python scripts under the MIT License), and a separate artistic illustration (PNG). The PNG does not reproduce the certified coordinates and should not be used as geometric evidence. The PDF and numerical certificates are authoritative. Related previous work: 10.5281/zenodo.23972043 (3D/4D reconstruction study); 10.5281/zenodo.23945337 (earlier Polybrutus publication).
Author: St-Pierre, Gabriel
Language: English
Topic: Mathematics and Applications
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225432081