TECHNICAL MONOGRAPH Beyond the Hyperbola: The Torque‑Entrained Interstellar Object Taxonomy (TEIOT) and the Coherent Prototype 3I/ATLAS A Comprehensive Forensic Audit and Predictive Framework for Field‑Mediated Interstellar Kinematics. The detection of 3I/ATLAS signals a paradigm shift in celestial mechanics: the transition from the era of Passive Ballistics to the era of Field‑Mediated Kinematics. This work presents the Torque‑Entrained Interstellar Object Taxonomy (TEIOT), a unified framework that classifies hyperbolic trajectories into three deterministic regimes based on torque‑spin entrainment with the Solar Torque‑Spin Fieldscape (STSF). We establish 3I/ATLAS as the prototype Coherently Entrained object—a monolithic, nickel‑rich body whose motion is a phase‑locked helical traversal. Synthesizing Hubble multipole imaging and the JWST/MIRI geochemical audit, we resolve its core anomalies and forecast a deterministic, high‑jerk kinematic phase‑shift (the Sync‑In) during its Jovian encounter on March 16, 2026. This marks the first predicted re‑threading of an interstellar helix within a planetary magnetodisk, serving as the definitive discriminant for the TEIO model. Legacy volatile‑driven models fracture on its paradoxes, such as the 600% Hoogendam Torque-Transfer Signature, while the torque‑entrainment framework provides a singular, falsifiable mechanism. The encounter will test whether interstellar objects follow passive gravitational arcs or actively navigated helical paths within a structured galactic fieldscape. Keywords: 3I/ATLAS, Interstellar Objects (ISOs), Torque‑Entrained Interstellar Object Taxonomy (TEIOT), Torque‑Entrained Interstellar Object (TEIO), Torque‑Spin Entrainment (TSE), Inclination‑Interaction Relation, Non‑gravitational Acceleration, Helical Requisite (A₃), Solar Torque‑Spin Fieldscape (STSF), Sagittarius Dwarf Merger, Sgr‑inflow Cluster, Phase‑Shift Sync‑In, Field‑Mediated Kinematics.