The Q-Network as a Universal Border Atlas: Scientific Formulas as Local Instantiations of Limit Positions

Scientific formulas are traditionally organised by domain. This paper shows that formulas from distinct and independent domains do not cluster by discipline, but by recurrent border configurations in the finite Q-network of Constrained Generative Systems (CGS). Using the master reduction Ω (E1, E2|L) →S, 1, Ø and a five-step structural entry protocol (SDL-PROC-001), seventy-four formulas from twenty-six scientific domains are mapped onto the operative Q-network established in Q2. Cross-domain coincidences on the same Q-nodes, Q5 across ten physical domains, Q23 across arithmetic, semantics, music and biochemistry, Q20 across music, relativity and molecular biology, demonstrate that formulas are local instantiations of limit positions rather than domain-specific descriptions. The atlas distinguishes universally compatible nodes (the 11-node triple intersection C∩P∩I from Q2) from locally operative nodes reachable only under specific regime conditions. A closure law (H) is derived: as the number of mapped domains increases, the number of active Q-nodes stabilises. The framework produces genuine exclusions, the entry protocol yields Ω→1 and Ω→Ø verdicts, and Q-node assignment is a falsifiable structural prediction, not a post-hoc label.