Scalar Temporal Field Ontology v26.1: Unified UV-Complete Framework for Time, Geometry, and Energy

This work presents Scalar Temporal Field Ontology v26: Unified UV-Complete Framework for Time, Geometry, and Energy, the definitive edition of the scalar-temporal theory developed by Cale Scott Howe. Time is modeled as a smooth scalar field τ(x^μ) whose gradient ∇μτ defines local causal directionality. Matter couples to an observable disformal metricg^eff{μν}=A(τ)g_{μν}+B(τ)∇_μτ∇_ντ,so that spacetime curvature, inertia, and energy emerge as resonant structures of temporal flow. At low gradients (X≪1) the dynamics follow a variational Lagrangian P(τ,X)=½A X – V(τ)+½β X²/Λ⁴, recovering General Relativity to O(ε²) with c_T = 1 and full compliance with GW170817. At high gradients the theory closes under a nonlinear feedback couplingΩ(τ,X)=λ X / (1+κ X),which drives stress–energy and curvature to finite asymptotic values, producing intrinsic ultraviolet saturation (“asymptotic silence”) without external regulators. The field equations, matching conditions, and renormalization behavior establish a single continuous ontology from infrared to ultraviolet scales. The unified formulation reproduces all results of v25 (effective IR ontology) and the UV Extension while integrating them into a continuous, radiatively stable framework. It remains falsifiable and observationally consistent with Planck 2023 and DESI Y1 data, with predicted corrections testable through atomic interferometry, gravitational-wave phase analyses, and optical-clock comparisons. This document supersedes previous versions and constitutes the final, UV-complete statement of the Scalar Temporal Field Ontology. Correction Note (Oct 2025)Equation (2.3) contains a sign typo.For X=−gμν∇μτ∇ντX=-g^{\mu\nu}\nabla_\mu\tau\nabla_\nu\tauX=−gμν∇μτ∇ντ, the correct scalar equation is ∇μ(PX∇μτ)=−12Pτ.\nabla_\mu(P_X\nabla^\mu\tau) = -\tfrac12 P_\tau .∇μ(PX∇μτ)=−21Pτ. All other derivations, results, and conclusions remain unchanged.This version supersedes v26.0.