Angular Relations as Informational Primitives: Relational Geometry, Phase-Induced Curvature, and Informational Closure

We propose a relational framework in which pairwise relations, endowed with amplitude and angular misalignment, constitute the fundamental representational substrate. Geometry, dynamics, and informational constraints emerge from structured configurations of relations rather than being assumed a priori. ​We introduce a discrete relational lattice (the fion lattice) and define an emergent geometric sector via diffusion maps. Angular misalignment modulates effective connectivity, leading to a measurable shift in an operational curvature proxy based on Ollivier–Ricci curvature. This establishes a falsifiable phase–curvature coupling without postulating new fields or particles. ​Independently, we derive an informational closure principle—the Self-Reference Bound (SR-Bound)—which constrains the algorithmic complexity of outputs generated by autonomous deterministic processes. Crucially, we extend the SR-Bound to phase fields: high-complexity phase structure implies non-autonomy unless externally supplied. ​All assumptions, algorithms, null models, proofs, and experimental protocols are stated explicitly. The framework is compatible with general relativity and quantum mechanics as effective theories while remaining empirically constrainable.