Universal N-Body Law from Metageometric Projection: A Regularised and Integrable Framework for Gravitational Dynamics

This paper develops a universal dynamical framework for gravitational systems based on metageometric projection, where gravitational interactions emerge from the coherent superposition of causal impulses (“khrons”) originating in an external causal space "Z_0". Within this structure, we derive a regularised and fully integrable N-body law that eliminates classical divergences and produces explicit quasi-periodic solutions for multi-body motion. The resulting dynamics recover the qualitative features of Poincaré’s analysis and modern KAM theory, while providing a new causal explanation for resonance patterns, stability transitions, and the onset of chaos in gravitational systems.The framework also reproduces two independent astrophysical consistencies: (1) the cosmic emergence threshold measured by JWST at z∼16;(2) the spectral morphology of the 20 GeV Fermi–LAT excess in the Milky Way halo. By embedding gravitational motion in a wider causal–geometric architecture, this work proposes a unified mechanism through which long-term stability, orbital families, and resonance structures arise naturally from the geometry of projection. The resulting universal N-body law offers a new route toward analytical tractability in celestial mechanics and a conceptual bridge between microscopic and cosmological scales - - - - - - - Keywords: Three-body problem • N-body problem • Celestial mechanics • Integrability • Stability • Analytical solutions • Quasi-periodic trajectories • Chaos • Emergent gravity • Orbital dynamics • Planetary ephemerides; Astrometry • Gravitational wave astronomy • Laboratory tests of gravity • Cymalogical framework • Khron-mediated dynamics • Universal law of motion • External causal space • Poincaré conjecture • Integrable systems - Phase space • Hamiltonian dynamics • Fundamental constants