A Critical Orbital-Scale Transition in Temporal Phase Memory: Observational Constraints on a Time-Field Schrödinger Equation

We report evidence for a sharp orbital-scale transition in a time-series proxy for temporal 6 phase memory, extracted from multi-constellation GNSS satellite clock data. Using high-pass 7 filtered clock-bias time series sampled at 300 s, we quantify a target-band autocorrelation 8 feature near 25 min and interpret its amplitude as an effective “phase-memory strength” A(L) 9 at orbital radius L. Across geosynchronous-orbit (GEO) satellites (L ≈ 4.22×107 m) we find 10 consistently high target-band amplitudes (A ≃ 0.406), whereas a subset of medium-Earth- 11 orbit (MEO) satellites cluster at a much smaller amplitude (A ≃ 0.031) near L ≈ 2.66×107 m. 12 Model comparison favors a step-like logistic transition in A(L) over a power law or simple 13 group-mean model, yielding a critical radius Lc ≃ 2.658 × 107 m and asymptotic levels 14 Alow ≃ 0.0311, Ahigh ≃ 0.4063. We discuss how such an orbital-scale “phase transition” 15 can be incorporated as an empirical constraint on a Time-Field Schr¨odinger framework, in 16 which A(L) acts as an effective quantumness parameter controlling interference contrast 17 via a finite-memory phase kernel. The result motivates targeted tests with additional 18 constellations, processing centers, and independent observables to separate genuine physics 19 from constellation-specific systematics.