Geometric Derivation of Gravitational Constant G as Rendering Latency – Validation of Universe OS V10-B: Proof Core v1.2 (Vol. 6) –

This paper presents a novel derivation of the gravitational constant ($G$) within the framework of Universe OS (UOS) V10-B, a digital physics paradigm that models the universe as a multi-layered computational system. Moving beyond the traditional view of gravity as a fundamental force, this study identifies $G$ as a "System Rendering Cost" (lattice impedance) occurring during coordinate updates in the system's middleware (Layer 456).

The derivation is based on the following architectural specifications:

\begin{itemize}

\item A 128-bit physical register width and a 512-division resource allocation.

\item Spatial compression via a projection window constant ($N_{\text{proj}}$).

\item A sampling-axis shift caused by a 7.17% synchronization lag ($\Delta_{\text{Res}}$) relative to 64 sampling arms.

\end{itemize}

Crucially, this revised audit redefines the previously identified 0.031% (310 ppm) residual not as an unresolved error, but as a systematic Observation Path Divergence. The analysis demonstrates that the CODATA 2018 value represents the System Rated Value ($G_{rated}$), while the derived value of $6.67637 \dots \times 10^{-11}$ represents the theoretical limit of the Static Rendering Path (torsion balance protocols).

By accounting for the $\pm 0.031\%$ divergence between static (rigidity-driven) and dynamic (latency-driven) measurement protocols, this paper provides a deterministic resolution to the long-standing "G-Tension" in experimental physics. This serves as a definitive foundation for subsequent validations (Proof Core series) regarding the Flyby Anomaly and the structural limits of the speed of light.