Universal Application of the Intrinsic Gravitational Signature Metric and the Verification of the Signature Threshold

This research paper presents the extended quantitative validation of the Intrinsic Gravitational Signature (S = G .g = G^2.m^2 ) across diverse and complex astronomical configurations, cementing the universal consistency of the Universal Gravitational Signature Threshold, hereinafter referred to as the Signature Threshold (S_t = 2.0× 10^(-10) m^4/(kg .s^4)). While contemporary astronomy continues to rely on qualitative or empiric metrics for celestial classification, this study delivers a scale-invariant mathematical framework tested against three distinct cosmic architectures: the Pluto-Charon binary system, extra-solar systems (Kepler-22b and the giant exomoon Kepler-1625b I), invisible geometric Lagrangian points, and practical interplanetary trajectory bounds validated by historical Mars missions. The numerical outcomes establish that physical dimensions do not govern orbital independence; instead, the computed Intrinsic Gravitational Signature accurately characterizes spacetime stability fields, orbital insertion boundaries, and systemic captivity boundaries uniformly across the observable universe.