TERM™ RW–0: Relational Closure Geometry — A Relational Foundation for Persistent Physical Structure

RW–0 proposes that structural persistence, rather than matter or background geometry, should be regarded as the primary phenomenon requiring explanation in foundational physics. We introduce a purely relational, pre-geometric framework based on category-theoretic groupoids, in which no primitive notions of particles, fields, spacetime, coordinates, or dynamics are assumed. Closed relational compositions generally fail to return exactly to the identity morphism, generating algebraic deviations termed closure defects. These defects define a global variational principle whose stable minima correspond to self-sustaining relational organizations. Within this framework, triadic organization appears naturally as the minimal simplicial topology capable of breaking the fluid dyadic degeneracy of one-dimensional networks, providing a natural conceptual bridge to background-independent quantum gravity approaches like Causal Set Theory and Loop Quantum Gravity. This work serves as the definitive foundational relational layer for the broader TERM™ research programme.