Holographic Vacuum Elasticity in the Macroscopic Limit: Formal Derivation and Empirical Validation of Topological Vacuum Suppression in Global Navigation Satellite System Atomic Clocks

We present a deterministic, parameter-free framework for the autonomous correction of atomic-clock drift aboard Global Navigation Satellite System (GNSS) satellites, grounded in Holographic Vacuum Elasticity (HVE), a theoretical framework that characterizes the quantum vacuum as a topologically structured elastic medium. The central vacuum coupling constant, σ0G = α/2 ≈ 3.649 × 10−3, is derived from first principles via the Dirac functional determinant and the Schur–Reynolds projector, without any free parameters. The gravitational sector is governed by the Spin(4) ≅ SU(2)L × SU(2)R exceptional isomorphism, fixing the gravitational Schur fraction fgrav = 1/9. These two algebraically rigid invariants govern the Vacuum Suppression Law (VSL) clock-bias equation, a four-term expression that replaces the stochastic polynomial broadcast by the GPS ground-control segment. All core algebraic results are mechanically verified in Lean 4/Mathlib with zero sorry stubs. Validation against 47,249 real ground-to-satellite upload events (IGS, 2016–2024) yields: amplitude agreement 96% (error 4.1%, Class II, post-diction), seasonal modulation ratio 2.97×, and nuclear-spin hierarchy Cs/Rb = 2.98 observed versus 7/3 ≈ 2.33 predicted (Class I, 28% discrepancy, attributed to reactive ground-control bias). The framework bridges precision metrological anomalies [2, 5] with their topological quantum-vacuum origin.