Five Worked Numerical Examples of Relativistic Phenomena Based on State-Update Mechanics and Vacuum Permittivity-Permeability Modulation in Space Phase-Locking Theory (SPLT)

This paper presents five concrete worked numerical examples applying the orthogonal allocation of finite state-update capacity and the modulation of vacuum permittivity and permeability of the Space Phase-Locking Theory (SPLT) to real astrophysical and precision metrological systems. Without evaluating 4-dimensional Riemannian metric derivatives or Christoffel symbols, we calculate step-by-step in 3-dimensional Euclidean space via the local state-update delay rate and the effective refractive index tensor: The daily clock offset correction for GPS satellites (+38.61 microseconds/day) The centennial perihelion precession angle of Mercury (42.98 arcseconds/century) The round-trip Shapiro time delay for deep-space laser communications grazing the Sun (247.2 microseconds) The frame-dragging Sagnac laser arrival time difference (0.173 femtoseconds) and annual Lense-Thirring gyroscope precession (40.87 milliarcseconds/year) around the rotating Earth The near-field strong-field birefringent light delay (0.150 milliseconds at r = 3rs) and far-field laser interferometer phase shift (1.323 x 10^-8 radians) during a binary black hole merger. All evaluated numerical results agree with empirical observations and standard relativistic predictions.