The Constraint Problem: Toward an Axiomatic Primitive for Physical Ontology

Abstract This paper formulates the Constraint Problem: whether physical ontology can be reconstructed from an axiomatic primitive weaker than object, state, spacetime, field, measurement, or information. The paper does not propose a completed physical theory, nor does it derive existing theories. Its aim is methodological and foundational: to identify constraint as a candidate primitive and to define a research program in which closure, identity, stable distinguishability, boundary, and physical entity may be reconstructed rather than assumed. Constraint is not defined by reduction to objects or relations. It is treated as a candidate primitive to be characterized axiomatically. The central contribution is therefore not a new mathematical tool, but a disciplined problem formulation: what is the weakest primitive from which physical entity could, in principle, be reconstructed? The paper proposes a candidate axiom system for constraint structures, outlines the possible reconstruction chain from constraint to physical entity, clarifies the limited status of the proposal, and distinguishes it from existing work in closure theory, formal concept analysis, category theory, constraint satisfaction, and structural realism.