Extended GRAVITAS: Semantic Spacetime and Emergent Temporal Dimension

Extended GRAVITAS: Semantic Spacetime and Emergent Temporal Dimension introduces a rigorous mathematical framework for modeling the evolution of concepts within a semantic manifold endowed with Lorentzian structure. In this paradigm, cognitive time is not external but emerges from causal dependencies among concepts, formalized through semantic causal sets and an adapted Benincasa–Dowker action. The work develops a coupled variational principle linking geometry and information, where entropy fields and Fisher information metrics act as sources of semantic curvature. This leads to modified Einstein-like field equations for informational dynamics. Extensions include a formulation of semantic special relativity, gauge theory analogues with spontaneous symmetry breaking, persistent homology for conceptual stability, and canonical quantization of semantic fields. Beyond theory, the framework proposes empirical validation protocols—ranging from prerequisite graph analysis to Fisher metric estimation from language models—bridging abstract mathematics with testable cognitive phenomena. By unifying causal structure, information geometry, and topological methods, Extended GRAVITAS positions itself as a novel paradigm at the intersection of physics, information theory, and cognitive science.