GPS Framework — HUB Nodes and Bridge Septenarii (A Geometric Interpretation of Prime Quintuplets)

This work presents a structural classification of HUB Nodes within the GPS (Geometric Prime System) framework. HUB Nodes correspond to prime quintuplets and are reinterpreted as geometric intersection points between GPS triplets. The paper documents their connection with GPS Septenarii through the node C = P + y + k and introduces the notion of Bridge Septenarii traversing two HUB Nodes. No new universal laws of primes are claimed; the contribution is a coherent geometric interpretation of known objects. Extended computational results, including residue-class–dependent distributions and high-order configurations (L ≥ 8), are provided as supplementary material in the associated Zenodo record. This supplementary document provides extended computational evidence supporting the structural persistence of GPS hub nodes and bridge septenaries across residue classes modulo 40. Computational scope and validity. All numerical experiments reported in this work were conducted within the following bounds:P≤5×105P \le 5 \times 10^5P≤5×105, y≤4×103y \le 4 \times 10^3y≤4×103, k≤1.1×103k \le 1.1 \times 10^3k≤1.1×103.Consequently, all tested integers satisfy n