The Fourth K-ZFPD: The KnoWellian Cosmic Radius and the Rendering Deadlock of the Apeiron Leak

This paper presents the Fourth KnoWellian Zero-Free-Parameter Derivation (K-ZFPD 4), providing a rigorous geometric refutation of the infinite universe. Orthodox cosmology permits the logical absurdity of infinite mass spanning an infinite volume. The KnoWellian Universe Theory (KUT) demonstrates that reality operates as a closed metabolic loop bounded by a finite computational bandwidth: the Phase-Velocity of light (cKUT). We define the KnoWellian Cosmic Radius (RKW) as the absolute spatial edge of the universe. It is the exact radial distance where the aggregate hydrodynamic suction of all rendered mass (the Apeiron Leak) causes the spatial inflow velocity of the Chaos Field to reach cKUT, resulting in Global Rendering Deadlock. Furthermore, this paper proves the macroscopic boundary of the cosmos is topologically locked to microscopic geometry. The Absolute Cosmic Radius is derived holographically by scaling the base atomic dimension of the (3,2) Torus Knode through the structural recurrence of the Cosmic Octave (Ω = 10²⁴) and the bandwidth efficiency of the Fine-Structure Constant (α⁻¹). The universe is a finite, perfectly balanced, self-sizing metabolic cell.