The Architecture of Necessary Existence: Volume II — The Contained-Time Field

Volume II develops the temporal structure of The Architecture of Necessary Existence by introducing the Contained-Time Field — a formal extension of the proportional-delay constant δᴰ into geometric and dynamical time. Building on the stability architecture established in Volume I, this volume examines how bounded delay modifies curvature, collapse thresholds, and system trajectories. The work derives the contained-time integral t = ∫(1 − δᴰ) dτ and interprets δᴰ as a proportional correction to proper time in systems governed by recursive feedback. The analysis connects delay, curvature, and stability through Lyapunov methods, operator contraction, and bounded-curvature arguments. No empirical or numerical data are presented. The objective is theoretical: to formalise how δᴰ influences the structure of time and curvature across physical, computational, and abstract dynamical systems. Subsequent volumes extend this framework to cognition, intelligent systems, and global containment.