Temporal Information Dynamics in the Scalar Temporal Field Ontology: Part VIII — Global Information Geometry and the Unified τ –Flow Equation

This work constitutes Part VIII of Temporal Information Dynamics (TID) within the Scalar Temporal Field Ontology (STFO). Building on the geometric, thermodynamic, and quantum-informational foundations established in Parts I–VII, this installment develops the τ-adjoint formalism that governs non-Hermitian, dissipative, and information-nonconserving quantum evolution in the presence of temporal curvature and τ-noise. Where Part VII introduced τ-modified Schrödinger dynamics, decoherence kernels, τ-Lindblad evolution, and entanglement flow, Part VIII extends the framework by constructing: • the τ-adjoint operator associated with the effective disformal metric• a formally complete non-Hermitian τ-Hamiltonian governing open-system evolution• τ-dependent quantum continuity relations, including probability flux deformation• a temporal adjoint propagator and τ-corrected Green’s functions• the τ-antiunitary map connecting reversed temporal flow to geometric curvature• a unified treatment of τ-dissipation, decay channels, and information leakage• experimental predictions in interferometry, quantum optics, quantum hardware, and metrology This completes the quantum-dynamical layer of Temporal Information Dynamics. The τ-adjoint construction reveals how temporal geometry—through gradients, curvature, and fluctuations—induces non-Hermitian corrections, anisotropic decay rates, direction-dependent decoherence, and modified causal structure. As in Parts I–VII, all results are derived directly from the scalar temporal field τ(x), without phenomenological assumptions. Together with the previous installments, Part VIII advances TID into a complete, falsifiable, and fully geometric framework linking quantum evolution, information theory, decoherence, entanglement, channel capacities, Fisher information, and non-Hermitian dynamics, all unified by the scalar temporal field τ. Author: Cale Scott HoweProgram: Scalar Temporal Field Ontology (STFO)Contact: [email protected]