Laws as Constraint Residues: Toward a Structural Ontology of Law

Article accepted by Erkenntnis. This paper proposes a structural account of scientific laws as stabilized residues of constraint regimes, rather than as metaphysical primitives or regularities. Drawing on recent developments in the philosophy of science and structural ontology, we argue that lawhood arises from the persistence of invariant patterns across admissible variations within a regime of constraint. Our framework reconceives laws as functional invariants extracted from the internal architecture of scientific models, formalized via projection operators and local neighborhoods in constraint space. This structural residue approach captures the operational role of laws in guiding prediction, explanation, and theoretical unification, while remaining neutral on ontological commitments to universals or modal realism. We compare our proposal with alternative accounts of lawhood, including counterfactual stability (Lange) and interventionist invariance (Woodward), and conclude by outlining the implications of our framework for the natural and social sciences.