Global Time Echoes: 25-Year Analysis of CODE Precise Clock Products

Analysis of 25.3 years of global GNSS timing data (165.2 million station-pair observations) documents persistent velocity-dependent correlations in atomic clock networks. Critically, this work proposes that standard GNSS processing algorithms, designed to remove energetic (common-mode) errors via datum constraints, inadvertently preserve the subtle, geometry-dependent (differential) correlations that are the focus of this work. Building on the multi-centre study's validation (R²=0.92-0.97 between CODE, IGS, ESA), the extended temporal baseline confirms long-baseline recovery and enables investigation of long-period geophysical phenomena inaccessible in shorter baselines. Seven convergent signatures are identified: (1) Spatial anisotropy persists with EW>NS (global EW/NS ratio=2.16, strength=1.981 ± 0.23 resampling SE, integrated 25.3-year aggregate), (2) anisotropy ratio correlates with orbital velocity (r=-0.888; surrogate p < 2×10⁻⁷, 0/5M exceeded; t-test p≈2.6×10⁻⁴ with N_eff≈11) across a 25.3-year baseline with ≈19% annual geometric ratio modulation, (3) a multi-resolution full-sky directional search down to 1° resolution recovers a stable preferred direction at RA=6°, Dec=+4° (r=0.746; exploratory directional-rank p < 10⁻⁵; global sky-search significance not yet evaluated) coincident with Earth's orbital velocity tangent at aphelion (~6°) and ~162° from the CMB dipole — a heliocentric-orbital-phase signature that excludes the Solar Apex template at ~16,000× variance ratio (R²=55.7% vs 0.003%), (4) planetary alignment coupling validated in the 40-event outer-planet opposition subset at 5.5× over matched random dates (p < 10⁻¹⁷) alongside a continuous planetary-potential correlation (r = +0.116, p = 0.012), whereas the broader 156-event free-centre pulse scan (56/156 ≥2σ) reflects repeatable estimator behaviour on the seasonal curve, (5) preliminary coupling to 18.6-year lunar nutation (R²=0.641±0.10 over 1.36 cycles; permutation p=0.0016, single-cycle-dominated) and a semiannual coherence component (R²=0.904, p=2.7×10⁻⁵; permutation p=0.00027, peaked near the orbital apsides), (6) collective network covariance score (0.582) replicating the multi-centre range, and (7) null results for solar rotation (27-day) and lunar standstill consistent with selectivity for orbital-gravitational phenomena over surface features. The 19% modulation describes changes in the geometric shape of the correlation field (ratio of spatial correlation lengths), not clock frequency variations; individual clock-rate effects remain at standard GR-modelled fractional-frequency levels. On the held-out MGEX product the distance-structured coherence replicates (λ ≈ 1,862 km), while the anisotropy and primary orbital-velocity metrics do not replicate robustly. In-sample, a free-phase annual sinusoid is preferred over the velocity template (ΔAIC = 11.2); the signature is therefore reported as an annual modulation phased near the apsides. Observed patterns are compatible with key TEP expectations: the recovered spatial correlation length (azimuth-averaged isotropic exponential λ = 3,210 ± 389 km, with cross-sector directional dispersion λ̄_T = 4,201 ± 1,967 km across eight azimuthal sectors) lies within the pre-specified 1,000–10,000 km search window (Paper 0 §10.E); across products the fitted scale is conditioned by clock-product construction and estimator settings (reported product-level values ~1.0–4.8×10³ km; MGEX λ = 1,862 ± 155 km, Paper 14), with the same band-ordered profile recovered in each product and consistent with the geometric saturation radius R_T(M_⊕) ≈ 4,150 km calibrated on this scale (Paper 6). Model discrimination is primarily established through kernel-form selection (Gaussian and squared-exponential kernels preferred by AIC/BIC with R² = 0.965, exponential ΔAIC = 12.8 and R² = 0.945, strongly ruling out scale-free power-law forms with ΔAIC > 30), velocity-dependent anisotropy (r = -0.888), and geometric alignment (EW/NS = 2.16). The absence of GM/r² scaling is physically consistent with the datum-projection mechanism in which common-mode components are absorbed by GNSS estimation while differential geometric structure is transmitted (validated via synthetic signal injection and product-conditioned forward kernels in Paper 1, raw-RINEX pseudorange controls in Paper 3, and multi-GNSS MGEX product-error kernels in Paper 14). Raw carrier-phase analysis, separately processed per-constellation solutions, and independent external replication represent the critical next steps. The empirically derived spatial correlation length λ_T (the Temporal Topology covariance scale) is a GNSS-sector covariance scale obtained after environmental projection and processing transfer. It is not the screening operator 𝒮_Σ(ℰ) itself and should not be identified numerically with response coefficients from other TEP channels. In the near-Earth environment, this correlation length acts as the macroscopic geometric proxy for the continuous saturation of Temporal Topology, anchoring the differential clock correlations without committing to specific subatomic microphysics. The primary result is 25.3-year aggregate consistency of distance-structured covariance and EW/NS anisotropy. The in-ecliptic orbital-phase direction, planetary event response, and nutation couplings are secondary covariance-structure signatures requiring held-out replication. †Smawfield, M. L. (2025). Global Time Echoes: Distance-Structured Correlations in GNSS Clocks. Zenodo. https://doi.org/10.5281/zenodo.17127229