Semantic Relativity: The Differential Geometry of Self-Reference

Interpretive meaning read internally by the same system that produces it cannot be held fixed as a passive background. The framework develops this self-reference as a differential geometry, with meaning carried by a coherence field on an intrinsic, per-observer manifold. Seven constitutive axioms with a four-term Lagrangian balancing coherence flow, attractor binding, autopoietic generation, and intrinsic regulation, constrain three coupled field equations that close a causal loop: coherence flow curves the observer's manifold through a semantic analog of mass, and the curved geometry conditions subsequent coherence flow on that manifold. Following from the field equations, five necessary and jointly sufficient criteria specify what constitutes a self-directing agent, while twelve distinctive signatures partition the disequilibria of agency maintenance. Because each observer metric is independently constructed across a sustained history of pattern exposure, semantic measurement is frame-dependent; under iterated coupling, the same geometry drives independent observers toward agreement upon the invariant structure they share. Four structural falsifiers identify what would force abandoning the geometric foundation; three consistency conditions, what revising a derived claim would instead resolve. A cumulative instantiation program assigns the only free functional to its minimal nontrivial form and works it across one, two, and three dimensions. Four independent structural witnesses single out the cubic order among its admissible ladder. The construction closes at three dimensions, with every curvature component locally sourced. Closure saturates upward without addition. Interpretation, posited separately at the outset, is carried out intrinsically by the field equations themselves.