Semantic Relativity: A Geometric Field Theory for Observer-Dependent Meaning

In systems where observers are structurally coupled to the fields they measure, semantic geometry and its evolution cannot be specified independently of one another. Seven axioms and a four-term Lagrangian balancing coherence flow, attractor binding, autopoietic generation, and regulatory constraint on a differentiable semantic manifold together constrain three coupled field equations that close a causal loop. A coherence field flows on a dynamic metric; semantic mass, the product of reflexive density, constraint density, and attractor stability, sources curvature through coupling structurally analogous to general relativity; and the resulting curvature reshapes the conditions under which subsequent coherence flows. Noether symmetries yield three conservation laws, including a coherence-sector Hamiltonian whose individual conservation breaks down during rapid metric evolution, paralleling the gravitational energy problem arising in GR. Five necessary and jointly sufficient conditions whose necessity follows from the field equations—self-model, recursive closure, coherence stability, autopoietic self-maintenance, and intrinsic regulation—specify a manifold region constituting a self-directing agent. Twelve orthogonal signatures partition characteristic departures from agency maintenance into rigidity, fragmentation, inflation, and distortion classes, each undermining one or more of the geometric preconditions sustaining the agency criteria. Because each observer's metric is independently constructed, semantic measurement is frame-dependent; the geometric conditions under which independent observers develop compatible metrics through iterated coupling are identified. Four structural falsifiers follow from the axioms, specifying the conditions that require abandonment of the geometric foundation, while four consistency conditions define where revision suffices. A cumulative instantiation program (Appendix A) pins the coarse-graining functional to a minimal concrete choice and derives twenty-four structural results across three progressively richer models, demonstrating that the architecture produces computable, falsifiable structure whose predictions strengthen with each dimensional extension.