A Five-Dimensional Diagnostic Scalar for Solar System Dynamics: Dual-Source Validation and Ranking Freeze

We introduce a dimensionless diagnostic scalar κ that compresses five classical orbital invariants——Hill-sphere mass factor, vis-viva deviation, semi-latus rectum, position-velocity synergy angle, and gravitational binding depth——into a single cross-planetary comparable quantity through symmetric normalization and multiplicative coupling. On the standard orbital-dynamics benchmark of the circular restricted three-body problem, the resulting maps recover the co-orbital tadpole and horseshoe regions and trace the analytic resonance web (median offset 0.043 Jupiter radii from the nearest mean-motion resonance), computed without the variational-equation machinery of standard chaos indicators; a direct calibration against the Fast Lyapunov Indicator (FLI) delimits the diagnostic as a coherence and resonance tool orthogonal to chaos detection. Applied to the nine planets over 26 years of NASA JPL Horizons data (2000–2026, N=9649 days) through two physically independent ephemeris paths——direct orbital elements versus state-vector retro-propagation——the two versions agree to better than 0.06% in mean value, with temporal Pearson correlations r>0.998 for all planets. Remarkably, the κ ranking among the nine planets remains frozen at 100% consistency across the entire observation window, exhibiting a clear mass–distance stratification. Three distinct reference-system strategies (virtual, fixed, and sliding ideal-body) all confirm this rigid immunity to data format and algorithmic path, with Neptune showing the largest——yet still insignificant——discrepancy due to Direction-dimension boundary artifacts at the 0°/360° true-anomaly crossing. The results demonstrate that κ is not a fitting artifact but an intrinsic projection of gravitational structure, providing a continuous, cross-planetary diagnostic tool complementary to traditional orbital elements and Lyapunov-based stability indicators.