Where general relativity computes time dilation from a known gravitational source, the chronodynamic program inverts the question and recovers the source from the observed time dilation. The inversion is performed under the weak-field limit, where the first post-Newtonian approximation is exact to the precision of modern atomic clocks.
The first concrete result
The first concrete result of this inversion is the recovery of the geocentric gravitational constant GM directly from Galileo satellite atomic-clock data, to a median precision of 4 × 10−7 across more than one million measurements, and cross-validated on a second satellite. The recovery uses no external mass input.
Method
The experiment uses high-eccentricity Galileo satellites (E14 and E18, which entered eccentric orbits as a result of the Fregat upper-stage anomaly) to provide the altitude variation necessary for a single-satellite inversion. Sequential clock-drift pairs are computed at half-orbital-period intervals, and the relativistic 1PN time-dilation equation is inverted analytically using Float106 quad-precision arithmetic to control numerical cancellation in the subtraction of nearly equal quantities.
Open data and reproducibility
The complete experiment is available with its source code on GitHub; the full reference data set is published openly on Zenodo with a persistent DOI. The data set includes the GNSS clock and ephemeris files needed to reproduce the recovery end-to-end.
Context within the Center
Chronodynamics is the second of the Center's three research areas and the first to produce a concrete empirical result. The use of DeepCausality as the computational substrate for the inversion is itself a demonstration that the dynamic-causality foundation is productive in a quantitative physical setting.
Resources
- chronodynamics on GitHub — source, methodology, and results
- Reference dataset on Zenodo — canonical chronometric data set with DOI
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