Temporal Equivalence Principle: Phase-Resolved Spatial Clock Priors for GNSS Outage Bridging

The Temporal Equivalence Principle (TEP) predicts that proper time behaves as a dynamical scalar field, producing spatially correlated fluctuations in distributed clock networks. Papers 1–3 established the field across 364–539 GNSS stations and up to 1.17 billion station-pair measurements, identifying a spatial correlation length lambda_T ~ 4200 km in receiver clock residuals. Because every one of those measurements traversed the same ground-receiver processing chain, a correlated instrumental systematic remained a candidate explanation. This paper carries the detection onto a channel whose pairwise geometry is independent of the receiver-side measurements, separates the detection from its leading confounds, and converts it into deployment-ready predictive power. Between orbiting satellite clocks — a channel whose pairwise statistic uses no ground receiver and no common-view geometry — the corrected phase-alignment index detects a clock correlation falling off with inter-satellite separation at 10.6 sigma and 12.6 sigma above phase-randomised and geometry-shuffled nulls, independently confirmed by a GPS×Galileo cross-constellation arm that shares no orbital plane or clock family (26.4 sigma log-slope -0.172 over 180 days, near/far contrast +0.30 on 90-day windows, pooled exponential fit lambda = 8,140 +/- 795 km with sub-window scale trading off against the long-baseline pedestal across 8,140–14,911 km; the satellite clock estimates themselves share analysis-centre provenance with the receiver products, the residual systematic addressed by Step 172). On the ground, the non-common-view intercept separates from satellite co-visibility on the minimally processed broadcast product (partial correlation -0.164 at 10.8 sigma, strengthening to -0.267 with the local-solar-time systematic controlled; out-of-sample R^2 gain +0.022; raw intercept fit lambda = 4,349 km, and lambda = 1,008 km at 6.5 sigma after projecting out the collinear co-visibility and solar-time profiles, which absorbs the long-baseline tail), while the network-solved precise product shows the expected datum-absorbed attenuation (PC = -0.040 at 9.2 sigma). The predicted East–West anisotropy at 500–800 km survives common-view removal essentially unchanged (+0.130 -> +0.126, z = +1.98 -> +1.91). Oscillator-class dependence supplies a physical discriminator: idiosyncratic clock noise is identical between quartz and atomic stations (0.99x) while the network-coupled component is 3.01x larger on quartz — a separation that persists on co-located receivers sharing site, sky and monument, and yields a clean double dissociation between the atmospheric solar S2 tide (atomic clocks null at p = 0.66, quartz p = 1.8e-93) and the purely gravitational lunar M2 tide (p = 8.3e-6 multi-product Fisher combined). Sub-diurnal Earth-rotation aperture synthesis identifies the field's preferred axis with the CMB dipole at delta-BIC = -2,315.5 over the next candidate, winning 300 of 300 day-clustered bootstrap draws and both disjoint half-year splits (the raw delta-BIC scales with pair-window count, while the bootstrap and split-half ordering is cluster-invariant). The detection is predictive ex-ante: 120 cryptographically sealed weight envelopes score their first genuinely post-seal windows at +29.01% mean (116 of 120 positive) under SHA-256 verification. The same protocol bounds its own reach: the sealed walk-forward figure decomposes into verified retrodiction of member-observed epochs plus a spatially specific forward component at never-observed epochs (+2.57%, p = 1.8e-5, under causal penalty selection; +3.39% untapered, z = +5.8 to +6.6 above station-label permutation, frozen under prospective preregistration), with a measured ~90-minute frozen-weight coherence time. With station coordinates withheld, the 43-mode phase fingerprint localises co-located anchors globally to 339 km (Matera) and 744 km (Tahiti) and 43 live NTRIP stations to a 191.8 km median error from 30 minutes of clock data alone. The one remaining systematic — a correlated error inside the GNSS processing stack itself — is assigned to a pre-registered satellite-free hardware replication (Step 172). Operationally, a phase-resolved TEP clock prior delivers three deployment-ready benefits on existing CORS/RTK infrastructure with no new hardware and sub-millisecond per-epoch cost. For timing holdover, during a sky-view outage the network prediction bounds a receiver's clock-residual error to 25 ns at 1 h and 66 ns at 8 h — a network-assisted residual bound, not an absolute UTC error measured against a traceable hardware reference; compared on datasheet drift terms it outperforms a GNSS-disciplined OCXO (~$300) beyond 30 min and a disciplined Rubidium (~$2,000) beyond 2 h. For outage bridging, across 90 days on a dense EUREF network the fixed kernel reduces clock RMS by 5.0–18.9% versus the strongest temporal predictor at 10 min–8 h, with positive day-clustered intervals at every horizon; frozen on 2024 and applied unchanged to held-out 2025, the construction beats every deployable baseline on three coherent regional networks. For degraded-geometry positioning, at three visible satellites, where free-clock SPP is rank-deficient, the prior supplies the missing degree of freedom (5.76 m RMS, 95.2% availability, and +29.6% 3-D / +46.7% vertical RMSE reduction over persistence across 38,900 1 Hz carrier-phase outage epochs); at k = 4-5 it improves 3-D RMS by +14.5–48.0% over a deployable persistence-trend prior; and on a 68-station live observatory the causal field prior reduces two-hour holdover RMSE by +35.84% across 185 walk-forward windows (275 of 276 recorded live archives positive over 95.6 h, +42.93% mean). With a full sky the clock is already observable and the prior is correctly inert. The methodological point is that cross-spectral phase alignment, rather than overall pair amplitude, isolates the field's spatial structure: the corrected estimator cos(arg sum_f S_ij(f)) recovers lambda = 4,348 km on COD and 4,076 km on GFZ precise receiver clocks (R^2 = 0.898 and 0.955, 25–27 sigma above per-station phase-randomised nulls that preserve every frequency bin's amplitude spectrum identically), matching the Papers 1–2 measurement to within 3.5%. The result is therefore a detection claim, not only an engineering one: the predicted correlation is recovered on a channel whose pairwise statistic shares no receivers and no common-view geometry with the original measurements (the satellite clock estimates still traverse the shared tracking segment — the one residual systematic the satellite-free hardware replication is designed to close); it separates from the leading instrumental confound at a pre-registered threshold; and it predicts unscored data under cryptographic seal. Its bounds are stated equally plainly in the text. In plain terms. Clocks separated by up to thousands of kilometres are found to drift together, and the strength of that togetherness fades with distance across the 1,000–5,000 km screening band predicted by the theory (lambda = 4,076–4,348 km on precise phase alignment, matching the 4,201 km scale established in Papers 1–2, and a dependence-aware combined median of 2,822 km, 95% CI [1,949, 3,763] km, across amplitude and Gaussian-process estimators). The same distance-structured decay appears between clocks aboard the satellites themselves, in a pairwise test that involves no ground receiver and no shared viewing geometry — although the satellite clock estimates still pass through the same ground segment, which is why the no-GPS hardware test remains; on the ground it survives removal of the specified satellite co-visibility geometry on the minimally processed broadcast product (and remains directionally present, though attenuated by the network datum adjustment, on precise clocks); its spatially coherent component is three times stronger in quartz clocks than in atomic ones even when both sit on the same monument sharing the same sky, isolating the differential to oscillator physics or clock-product referencing rather than local site noise; and when the prediction machinery is locked away under cryptographic seal before the data exist, it beats persistence in 116 of 120 first post-seal evaluations (combining high-precision network retrodiction of member-observed epochs with a smaller, statistically significant +2.57% forward forecast at never-observed epochs inside the ~90-minute coherence window). Every alternative explanation that has been tested has failed to reproduce the pattern; the one test that cannot be done with GNSS data alone — measuring the field with clocks that never touch GPS — is registered as the closing experiment. Keywords: temporal equivalence principle, GNSS, precise point positioning, spatial correlation, clock noise, relativity, geodesy, TEP, Proper-Time Transport Website: https://mlsmawfield.com/tep/ppp/Repository: https://github.com/matthewsmawfield/TEP-PPP DOI: 10.5281/zenodo.23704946 Open Science Statement: This work is a preprint and is open to community review, ideas, and collaboration. All analysis code, configuration files, and manuscripts are open source. Feedback and contributions to further test these results are welcome.