Chaos Onset as Spectral Regime Transition: Hypergraph Laplacian Analysis of N-Body Gravitational Systems via PMIR

This is the sixth preprint in the Phase-Modulated Information Rivalry (PMIR) series. It extends the PMIR spectral framework to N-body gravitational dynamics using hypergraph Laplacian analysis, establishing a new connection between information-theoretic trajectory analysis and orbital chaos onset. The central finding is that chaos onset in multi-body systems corresponds to a spectral regime transition — but only when the system is represented in an observation-induced frame sensitive to multi-body information content, not in the classical configuration-space (force-based) frame. Key results: Configuration-space hypergraph Laplacians place the Sun–Jupiter–Saturn (SJS) system 12 orders of magnitude below the PMIR spectral regime boundary — a correct description of the Newtonian regime, but structurally blind to chaos onset. Observation-induced Laplacians (trajectory cross-correlation and total-correlation weights) place SJS at α = 3.09 ± 0.27, or 54.4% of the critical threshold α_crit = 5.67. Adding Uranus (SJSU) compresses the spectral gap by 4.3× (p < 10⁻¹⁰, Mann–Whitney), converting the system from regime-oscillating to permanently transitional — consistent with known weak chaos of the outer solar system. The four-body total-correlation hyperedge weight reaches α₄ = 4.97 ± 0.45 (87.7% of α_crit), within Δα = 0.70 of the regime boundary. The Fiedler eigenvector recovers the Great Inequality slow mode (Jupiter–Saturn anti-phase) from spectral structure alone, without computing secular precession. In the SJSU system it transforms to a collective four-body mode — a spectral signature of genuine multi-body chaos. PMIR rivalry dynamics produce power-law exponents p ∈ [1.47, 2.19] that co-vary with spectral regime occupancy across epochs. Relation to prior work: This preprint builds directly on five prior PMIR preprints (Zenodo: 10.5281/zenodo.18210474, 18226938, 18275923, 18282356, 18293869) and a companion solar-system manuscript (10.5281/zenodo.18509187). It is targeted for submission to Physical Review E. Code: https://github.com/richardschorriii/PMIR_verification