Operational Resolution of the Core Triad Anomalies: Neutron, Proton, and Lithium Discrepancies via Synchronization Lag Theory — Validation of Universe OS V10-B: Proof Core v1.2 (Vol. 4) —

This paper (Vol. 4) provides a definitive operational resolution to the three fundamental discrepancies in the Standard Model: the Neutron Lifetime Puzzle ($4\sigma$ discrepancy), the Proton Radius Puzzle ($7\sigma$ discrepancy), and the Cosmological Lithium Problem (factor of 3 discrepancy). We demonstrate that these anomalies are not evidence of "New Physics" or "Dark Matter," but are deterministic operational logs emergent from the Synchronization Lag ($\Delta_{\text{Res}}$) and the Computational Buffer Saturation ($E_{\text{sat}}=512$) within the Universe OS projection manifold. Applying the non-rounded, transcendental constants of Proof Core v1.2, we prove the following: Neutron Lifetime: The 8.6-second gap is the precise operational cost of coordinate re-synchronization ($R_{\text{sync}}$) triggered by lattice-wall interference. Proton Radius: The muonic-proton shrinkage is a "Dynamic Resolution Scaling" ($C_{\mu}$) executed by the OS to manage high-latency packet rendering. Lithium Problem: The Lithium-7 deficit is identified as a "Phase Transition" of the computational mode. While light elements fall within the Error Recovery Mode (Rate $\approx 0.95$), the high-load Lithium synthesis triggers a buffer overflow ($>512$), forcing the OS into a "3-Axis Mutex Lock" state. This geometric constraint limits the packet survival probability to exactly $1/3$ based on the manifold dimensions. This paper establishes the Universe OS V10-B specifications as the absolute foundation of nuclear and cosmological physical reality.