Null-Structure Test of Orbital Dynamics: Why Earth Emerges as a Benchmark System Takayuki TakagiIndependent Researcher, Higashimatsuyama, Saitama, JapanORCID: 0009-0003-5188-2314 Abstract We introduce a partition-invariance test for orbital dynamics, applying identical methodology across Solar System bodies. The test partitions orbital element time series (eccentricity e, argument of perihelion ω) by temporal and phasic criteria, evaluating whether partition means differ beyond permutation-null expectations. Results reveal a taxonomy of breaking signals: DRIFT-type in Mercury, Mars, and Venus — rescued by linear detrending AUTOCORRELATION-type in Jupiter — rescued by circular-shift null DEGENERACY-type in Venus ω — from e → 0 instability Crucially, we introduce the observational completeness ratio η = Tₒbs / Tₒrb as a validity criterion; bodies with η < 3 (Saturn–Neptune) are excluded as window-limited. Among high-η systems, Earth alone exhibits no detectable partition asymmetry under any null model — the only body requiring no rescue. This reflects Earth's intermediate dynamical regime where drift, autocorrelation, and degeneracy are simultaneously minimized. Key Finding Earth's benchmark status is not anthropocentric selection but a constraint-satisfaction outcome. The key methodological advance is recognizing that: Null model selection is not a technical detail but a physical statement. Different null models diagnose different dynamical structures. Historical Parallel This finding parallels, in inverse form, Einstein's 1915 identification of Mercury as the unique system where relativistic precession becomes detectable: Where Einstein found the singular point of breaking, we find the singular point of silence. Contents Main manuscript (3 pages, MNRAS Letters format) Figure 1: Summary heatmap and breaking taxonomy Figure 5: Earth benchmark results (4 tests, all uninformative) Figure 9: Breaking strength vs. observational completeness η Data Source All orbital element data from JPL Horizons System (DE440/DE441): https: //ssd. jpl. nasa. gov/horizons/ Submission Status Submitted to Monthly Notices of the Royal Astronomical Society (Letters) License CC BY 4. 0 — Creative Commons Attribution 4. 0 International Citation Takagi, T. (2026). Null-Structure Test of Orbital Dynamics: Why Earth Emerges as a Benchmark System. Zenodo. https: //doi. org/10. 5281/zenodo. 18289126 Keywords orbital dynamics · partition-invariance · statistical methodology · Solar System · celestial mechanics · benchmark systems · null hypothesis testing
Takayuki Takagi (Sun,) studied this question.