Temporal Information Dynamics in the Scalar Temporal Field Ontology

This work develops Pillar VII of the Scalar Temporal Field Ontology (STFO), extending the framework from geometry and dynamics into a full theory of information, complexity, and cryptographic structure. In STFO, a smooth scalar field τ(x) defines causal order and induces effective geometry via disformal coupling. This paper introduces a new layer: temporal information dynamics, in which information storage, transmission, and computational complexity arise directly from the geometry of τ and its gradients. Key contributions include: • Temporal-Depth Complexity:A geometric notion of computational cost based on the temporal depthD_\tau = ∫√X ds,leading to three intrinsic complexity classes (T0, T1, T∞) tied to τ-dynamics. • Topologically Protected Information:Loop integrals Φ_C = ∮ ∇τ · dx act as robust, orientation-sensitive invariants.These structures are stable under all local perturbations, providing a natural physical mechanism for topological information protection. • Disformal Cryptographic Hardness:Matter couples to τ throughL_{int} = −γ_\tau J^μ ∇_μ τ,where γ_\tau is constrained by prior STFO phenomenology.Reconstructing ∇τ from nonlinear line-integral data is shown to be a physically hard inverse problem, forming a new class of physics-based cryptography grounded in τ-geometry rather than computational assumptions. • Information Channels and Directional Bias:Temporal gradients |∇τ| define channel capacity, noise structure, and directional information flow.This yields clear, experimentally testable predictions tied to interferometry, clock networks, and laboratory platforms. The result is a unified description of information within the Scalar Temporal Field Ontology, completing its transition from a geometric field theory to a physically grounded framework for information, complexity, topology, and cryptographic structure. Author: Cale Scott HoweProgram: Scalar Temporal Field Ontology (STFO)Contact: [email protected]