The System of Eternity (SOE) is a non-terminal civilizational governance framework designed to maintain long-term institutional stability while enabling continuous self-adjustment, upgrade, and peaceful replacement. SOE does not propose a final political system — it proposes a governance architecture in which civilization retains the permanent capacity to improve its institutions without collapse. This document presents SOE V4.2, comprising three layers: Civilizational Conditions (why new governance structures become necessary), System Architecture (the full SOE design including governance modules, decision systems, stability mechanisms, crisis response, and system evolution), and Civilizational Evolution (long-term survival, adaptation, and development). The Dynamic Architecture (Part IX) formalizes the mathematical core: a trust-based dynamic system expressed as dT/dt = −aD + bI − cC + R(T,t), with formal definitions of the stability mapping function g(T), recovery function R(T,t), and parameter operative ranges derived from simulation programs v12–v26. Five structural gaps identified in a multi-AI audit (April 2026) have been resolved in this version: the canonical recovery function R(T,t) is formally defined; parameter operative ranges are empirically bounded; a dual-failure recovery deadlock is resolved via a simulation-backed protected floor κ_min = 0.25; a verification paradox under high-disturbance conditions is addressed via cross-component consistency checks; and the stability mapping function g(T) is formally specified as a four-regime piecewise function. SOE is designed as a modular open framework. All components are independently functional and may be cited or recombined without reference to the full document.