Constraint Geometry and the Information Scaling Law: A Selection-Principle Framework for Geometric Constants

This work introduces Constraint Geometry, a pre-dynamical framework in which physical structure emerges from geometric constraints and rejection rather than assumed forces or fields. The central result is a selection principle, formulated as a variational minimization of illegal geometric intersections under discrete constraint rules and an inverse scaling law (ISL). Within this framework, stable geometric kernels emerge as minimal structures that survive constraint filtering. Fundamental constants are interpreted not as empirical inputs, but as invariants of kernel closure. The paper derives the geometric constants Φ = 120 and η = 9 from necessity and stability arguments, demonstrates the origin of a universal 1/4 exponent from multi-layer closure suppression, and applies the framework to obtain a first-principles expression for the fine-structure constant α without parameter fitting. The approach is axiom-driven, falsifiable, and independent of string theory, supersymmetry, or anthropic assumptions. It is intended as a contribution to the foundations of physics, geometric information theory, and the study of emergent constants.