Pattern Science: A Unified Admissibility Field for Coherence, Collapse, and Law Discovery

Pattern Science presents a rigorous admissibility framework for determining when a regularity qualifies as a genuine law, rather than a coincidence or overfitting artifact. It redefines pattern validity not by strength of fit or predictive accuracy, but by internal admissibility across a unified field of coherence, collapse, and boundary awareness. Core contributions include: Admissibility Field: Establishes a triadic space—coherence (C), collapse stability (S), and falsifiability margin (F)—to evaluate the structural legitimacy of patterns. Pattern Law Equation (PLE): Introduces a synthetic constraint that filters lawful patterns by their phase-stability, pre-collapse prediction capacity, and resistance to fragility under extension. Collapse Awareness: Frames pattern lawhood as inherently local and structurally fragile—susceptible to collapse via symmetry shifts, ontological extensions, or scaling anomalies. No-Law Drift Phenomenon: Describes how systems may exhibit transient structure without genuine lawhood, clarifying the boundary between ephemeral fit and discoverable principle. Diagnostic Outputs: Produces reusable lawhood certificates and pattern-class maps, enabling principled exclusion of overfit or structurally unstable regularities. The framework transcends data-centric machine learning models by offering ontological diagnostics for lawful structure. Pattern Science thus stands as a tool for epistemic integrity in the discovery of robust, transferable laws.