LG Time Flow Theory: Planetary and Quantum Validation of the Redefined LG Operator

This component presents the empirical and cross-domain validation of the redefined LG operator introduced in the companion theoretical component. Using only the universal spiral law b = J / (M c R) And the LG kinematic consequence derived from the operator □_LG The theory is applied to planetary flyby missions and quantum systems without phenomenology, parameter fitting, or external corrections. In the planetary domain, the LG framework reproduces the observed millimeter-per-second velocity residuals reported during Earth and Mars flyby missions (NEAR Shoemaker, Rosetta, Dawn). The predicted residuals arise purely from rotational geometry and directional alignment, matching observed magnitudes within measurement uncertainty. In the quantum domain, the LG spiral strength naturally resolves to the fine-structure constant α through the relation b = vₑ / c for the hydrogen atom, identifying α as the minimum stable spiral pitch of time rather than an independent fundamental constant. Together, these results demonstrate that the same geometric operator governs time-flow behavior from atomic scales to planetary systems. This component establishes LG Time–Flow Theory as a scale-independent geometric framework, with direct implications for precision timing, orbital dynamics, and future experimental tests.