TID_Part_V_Temporal_Complexity_and_Information_Geometry

This manuscript constitutes Part V of Temporal Information Dynamics (TID) within the Scalar Temporal Field Ontology (STFO), extending the information-theoretic framework introduced in Parts I–IV. While the scalar temporal field τ(x) defines causal structure, geometry, and dynamical flow, this work develops a full theory of temporal information geometry, complexity structure, and curvature-driven information behavior. We introduce a geometric Fisher metric induced by τ-gradients, define temporal curvature functionals that govern information distortion, and show how τ(x) generates intrinsic information-geometric manifolds. A scalar-temporal complexity tensor is derived, linking algorithmic cost, temporal depth, and field geometry into a unified structure. Key contributions include: • Geometry of τ-induced information manifolds• Temporal Fisher metric and curvature invariants• Scalar-temporal complexity tensor and runtime geometry• Distortion, geodesics, and curvature-driven information flow• Integration with thermodynamics (Part IV) and channels (Part III)• Experimental access via interferometry, clock networks, and noise spectroscopy Together with Parts I–IV, this manuscript completes the transition of STFO from a geometric field theory into a full information-theoretic, thermodynamic, and complexity-analytic framework. The result is a unified picture of how information, computation, entropy, and geometry arise from a single ontological structure: the scalar temporal field τ(x). Author: Cale Scott HoweProgram: Scalar Temporal Field Ontology (STFO)Contact: [email protected]