Global Time Echoes: Distance-Structured Correlations in GNSS Clocks

Abstract

Phase-coherent spectral analysis of 62.7 million station-pair measurements from 364 GNSS stations (2023–2025; effective sample size N eff ≈ 25–28 independent distance bins after accounting for spatial correlation; see §Methods) reveals systematic distance-structured correlations in clock networks. These correlations follow an exponential decay with a Temporal Topology correlation length λ T = 3,330–4,549 km (exponential best fit; bootstrap 95% CIs: CODE 1,198–5,918 km; IGS 3,197–4,871 km; ESA 2,532–3,984 km) and show strong goodness-of-fit when evaluated on distance-binned means across three distinct analysis center solutions on largely shared raw inputs (CODE, IGS Combined, ESA Final; R² = 0.920–0.970; fits are to bin means, not raw pairs). Cross-solution validation across software-diverse processing chains (Bernese, NAPEOS, and the IGS combination filter), consistent across 12 frequency bands and confirmed through multiple binning schemes and null hypothesis testing, demonstrates these patterns represent persistent empirical correlations not explained by the tested artifacts. The patterns also show dependencies on station elevation and geomagnetic latitude, consistent with screened scalar fields via continuous Temporal Topology; these dependencies are also morphologically compatible with residual atmospheric and ionospheric organization, and the two readings are separated only by spatially resolved external controls identified as required follow-up. The primary inference rests on cross-centre distance-structured covariance and λ T ; the following planetary, Chandler, diurnal, and geomagnetic signatures are treated as secondary or exploratory consistency tests. The correlations show exploratory associations with Earth's orbital motion (r = -0.571 to -0.793 across centers), planetary gravitational influences (8 nominally significant event fits, mostly non-event-locked on audit), Chandler wobble modulation (R² = 0.377–0.471), and systematic diurnal temporal variations with synchronized early morning coherence peaks (Local Solar Time). Comprehensive validation demonstrates 24-61 × signal enhancement over randomized controls (z = 15.8-31.9 across 180 null test iterations), with FDR-BH: 203/388 tests (52.3%), Hierarchical EB: 154/388 (39.7%), and Bonferroni: 155/388 (40.0%) surviving multiple-comparison correction across 19 independent validation families. TID exclusion analysis shows 21–23 % signal improvement when excluding high-ionosphere periods—temporal ionospheric variability suppresses rather than creates the correlation, while the static geomagnetic-latitude dependence remains a separately quantified channel — bounded at ≲3% of the coherent signal by the local-night persistence test, with a spatially resolved GIM/ROTI morphology control identified as the required external closure. The investigation was structured to test predictions from the Temporal Equivalence Principle (TEP) framework, which suggested a Temporal Topology correlation length (λ T ) of 1,000–10,000 km. The discriminating content is structural rather than the decade-wide prior interval itself: the pooled-band estimate λ T = 3,330–4,549 km spans the geometric saturation radius R T (M ⊕ ) ≈ 4,150 km, which is calibrated on this scale; the correlation is band-localized (control-band R² ≈ 0.6 vs ≈ 0.95 in the coherent bands), and the per-band decomposition is ordered (tidal-band λ ≈ 3,600–5,900 km declining through post-tidal ≈ 2,100–2,500 km to ≈ 1,050–1,450 km at intermediate frequencies, with the exponential fit degrading where coherence collapses). Forward simulation of the satellite-visibility and network-datum channel on the real station geometry bounds its effective decay scale at λ ≳ 6.7 × 10 3 km; conditioned on the real product — true CODE ephemerides and the estimated satellite-clock content itself — the channel remains broader than every measured λ T (no realisation below λ = 5,075 km across 40 conditioned realisations) and produces a profile shape (near-unity correlation within 1 Mm, sign-definite anticorrelation beyond ~5 Mm) that the measured correlation does not contain (§4.6). The R T identification calibrates against the corpus's fitted ρ T convention (Paper 6); it is consistency with a corpus parameterization, not an independently derived prediction. Across products the fitted scale is conditioned by clock-product construction and estimator band floor: the multi-GNSS MGEX family returns λ = 1,862 ± 155 km, and a controlled decomposition on identical MGEX station-days bounds the spectral-resolution and common-mode contributions at ≲ ± 25% of the fitted scale while reproducing the same band-ordered profile (Paper 14, Step 3.5); the fitted amplitude is likewise a bounded phase-direction index whose cross-product values decompose into statistic saturation plus product and estimator conditioning rather than a coherence-amplitude conflict (Paper 14, Step 3.6). The R T comparison is therefore stated at the cross-product family level (~1.0–4.8 × 10 3 km). While cross-pipeline consistency across software-diverse solutions and extensive validation provide a strong basis for these findings, alternative explanations involving sophisticated systematics cannot be fully excluded. Raw-RINEX/SPP consistency and combined multi-GNSS product tests are now reported in Papers 3 and 14; raw carrier-phase analysis, separately processed per-constellation tests, and independent external replication remain critical next steps. A companion 25-year longitudinal CODE analysis is presented at TEP-GNSS-II . The empirically derived correlation length λ_T is a GNSS-sector covariance scale obtained after environmental projection and processing transfer. It is not the screening operator S_Σ(E) itself, and it is not the non-exact (disformal) covariance term, which this measurement does not access.