44 Day–Night Differential Test of Path Redshift in Multi-Frequency Links to Near-Earth Spacecraft

Home ／ Appendix-Prediction and Falsification

This chapter follows the publication template for the falsification program. It uses plain language, avoids equations, and preserves the fixed structure. Under unified time and frequency standards and source-end calibration, we analyze one-way and two-way multi-frequency links between near-Earth spacecraft and ground stations. After removing multipath, ionosphere, troposphere, and device thermal terms, we test whether path-redshift residuals show a stable day–night difference that is predictable in sign and magnitude, non-dispersive across bands, and reproducible across stations and pipelines. If residuals scale with frequency dispersion, depend strongly on analysis choices, or fail in held-out repeats, the claim is disfavored.

I. One-Sentence Goal

Determine whether a non-dispersive day–night differential in path-redshift residuals exists in spacecraft links, co-occurs at zero lag across bands and stations, and follows predictable environmental geometry.

II. What to Measure

• Day–night consistency index (text grades):
  After common bandpass/timescale/alignment, extract constant and slow-slope terms from frequency-offset/group-delay/phase residuals for one-way and two-way links. Estimate day and night segments separately. Grade strong / medium / weak; uplift / depression; stable / unstable on a grid of spacecraft (orbit class × altitude) × band (S/X/Ka) × station/pipeline × solar-zenith windows and tag sign stability.
• Cross-band non-dispersion:
  Require the day–night difference to be insensitive to carrier and band edges. 1/f² or other dispersive scalings, or band-edge flips, indicate ionospheric/color/device residue.
• Zero-lag co-occurrence (cross-band/station/pipeline):
  Using a single external timescale, align residual time series and evaluate zero-lag peaks and side-lobe contrast near day–night transitions. Same-window, same-direction steps or plateaus across bands and stations support the claim.
• Geometry and environment profiles:
  Stratify by elevation, pierce-point local time, solar zenith angle, magnetic latitude/longitude, and pierce-point longitude. Profile the day–night differential as plateau / monotonic / threshold and test correlation with Total Electron Content (TEC), precipitable water vapor (PWV), geomagnetic activity (Kp/Dst), station altitude, and temperature gradients.
• Ratio robustness and “rigid shift, ratio unchanged”:
  After ionosphere and troposphere templates, verify inter-band amplitude/phase ratios are stable, while absolute residuals show smooth rigid shifts across day–night windows.
• One-/two-way separation and endpoint attribution:
  Use one-way (onboard clock) versus coherent two-way transponded links to isolate path-segment contributions. If a non-dispersive day–night differential persists in two-way, the path-term interpretation gains support.
• Environment-forward predictability:
  With geometry and environment layers only—solar zenith angle, pierce-point local time, season/latitude, Kp/Dst, TEC, PWV, station thermo-met fields, and logs of crustal-strain activity—issue prediction cards for sign/magnitude/thresholds, and score hit / wrong / null.

III. How to Do It

1. Observations and facilities:
   Select Low-Earth Orbit (LEO), Medium-Earth Orbit (MEO), and Geostationary Orbit (GEO) spacecraft with coherent two-way transponders and multi-frequency one-way downlinks (S/X/Ka; optical time/frequency if available). Operate a global station network spanning latitude/longitude/altitude, with ≥ 2 independent pipelines (time-domain / frequency-domain / wavelet–empirical-mode) in parallel. Acquire continuous cross-daynight arcs of 6–12 hours and repeat across seasons and geomagnetic levels.
2. Unified calibration and de-systematics:
   Publish hydrogen-maser stability, frequency-division chains, timestamp queues; standardize to a common time–frequency kernel with band-edge hold-outs.
   • Ionosphere: combine dual/tri-band differencing with conformal TEC templates fused from Global Navigation Satellite System (GNSS) meshes and occultation; run inject–recover to set caps.
   • Troposphere: use surface met, water-vapor radiometers, numerical weather fields to build wet-delay templates and mapping-function hold-outs.
   • Multipath/ground radiometry: model antenna surroundings; apply elevation masks, azimuth hold-outs, and reflection regressors.
   • Device thermals and phase centers: monitor up/down-conversion chains, cables, front-ends for temperature→phase/delay regressions with leave-out–refill controls.
3. Arc construction and windowing:
   Define day/night/twilight windows by pierce-point local time and solar zenith angle. Provide geometry controls for high vs low elevation, maritime vs inland, and summer vs winter. Publish day–night index tables and zero-lag indices per spacecraft × band × station/pipeline × window.
4. Stratification and stacking:
   Stack by orbit altitude and inclination, elevation, magnetic latitude of the pierce point, TEC, PWV, and Kp to identify plateau/monotonic/threshold shapes. Use method hold-outs (alternate bandpass/high-pass/windows/template families) to suppress overfitting.
5. Forward prediction, blinding, arbitration:
   The forward team uses only geometry and environment layers to issue day–night prediction cards. The measurement team independently reports non-dispersion/zero-lag/amplitude–profile summaries. The arbitration team scores hit / wrong / null by spacecraft/band/station/pipeline/window and publishes decisions.

IV. Positive/Negative Controls and Artifact Removal

1. Positive controls (support a path-redshift day–night differential):
   • Within the same geometry window, multi-band–multi-station–multi-pipeline data show same-direction, similar-amplitude, non-dispersive day–night differences, robust to band edge/high-pass/window/template choices.
   • One-/two-way differencing attributes the differential to the path segment, nearly orthogonal to ground-end/space-end local-oscillator drift.
   • Profiles show monotonic/plateau/threshold behavior versus solar zenith, magnetic latitude, TEC, PWV, Kp, with twilight/high-Kp/high-PWV thresholds.
   • Prediction-card hit rates exceed chance and replicate in held-out seasons/stations/spacecraft.
2. Negative controls (argue against the claim):
   • Residuals scale as 1/f² or correlate with color/TEC/tropospheric models.
   • Significance appears only in one band/station/pipeline/orbit, or is fragile to bandpass/alignment/window/high-pass/template choices.
   • Label swaps, time reversals, method swaps, parameter shuffles still “detect” differences—selection/method bias.
   • With tighter ionosphere/troposphere constraints, low-elevation culls, and thermal regressions, the signal vanishes, or is reproduced by multipath/LO thermals/phase-center drift.

V. Systematics and Safeguards (Three Items)

• Rapid ionospheric disturbances and model extrapolation: bursty day-side or polar events leave dispersive residue. Safeguard: multi-band differencing + occultation–GNSS fusion, regional assimilation, and activity-threshold hold-outs.
• Tropospheric wet delay and ground multipath: low elevation biases mimic day–night steps. Safeguard: elevation cutoffs, azimuth hold-outs, radiometer constraints, and scene-aware multipath regressors.
• Thermal–LO coupling in the link chain: daytime warming causes slow phase/delay drifts. Safeguard: temperature–phase co-monitoring, thermal-model regression, one-/two-way orthogonal differencing, and endpoint-swap tests.

VI. Execution and Transparency

Pre-register spacecraft/orbit classes, bands and sampling, common time–frequency kernel, criteria for non-dispersion/zero-lag/profile shapes, geometry and environment variables, positive/negative controls, exclusions, and arbitration scores. Define held-out day/night/twilight windows and seasonal/station/activity bins. Enable cross-team replication by exchanging raw carrier/pseudorange/phase series, timestamp logs, calibration/color files, scripts, and running down-sampling/noise/kernel-variant/alignment-perturbation/template-family swaps. Publicly release prediction cards, day–night consistency tables, zero-lag/non-dispersion summaries, bandpass/color/ionosphere/troposphere/sampling/thermal logs, and key intermediates.

VII. Pass/Fail Criteria

1. Support (passes):
   • In ≥ 2 pipelines, ≥ 2 stations, ≥ 2 bands, and across multiple orbit classes and seasons, recover a non-dispersive, zero-lag day–night differential.
   • The differential is monotonic/plateau/threshold with geometry and environment and robust to bandpass/alignment/window/high-pass/template/elevation/thermal settings.
   • Arbitration significantly exceeds chance and held-out units replicate.
2. Refutation (fails):
   • Results are dominated by dispersion/wet delay/multipath/thermal coupling, or fail cross-band/station/pipeline/orbit/season replication.
   • High parameter fragility or disappearance/reversal in held-outs.
   • Arbitration near chance, indistinguishable from system/method artifacts.