The Three-Body Phase Structure and Transition Classification paper presents a falsifiable computational methodology for improving finite-horizon prediction of transitions and orbital outcomes in gravitational three-body systems.
The Newtonian equations governing three point masses are already known, but arbitrary three-body trajectories can exhibit periodic, quasi-periodic, hierarchical, scattering, collisional, and chaotic behavior, with strong sensitivity to initial conditions across substantial regions of phase space. This work does not propose a new gravitational force, does not claim a universal closed-form solution, and does not replace direct N-body integration. Instead, it tests whether a dimensionless structural representation of evolving three-body dynamics can add predictive information beyond strong conventional baselines.
The framework begins by nondimensionalizing the Newtonian equations using a characteristic length , total mass , and characteristic timescale
A time-dependent structural state vector is then constructed from explicitly normalized quantities describing close-encounter compression, pairwise binding-energy redistribution, hierarchy formation, finite-time dynamical instability, recurrence in reduced phase space, and preregistered phase coherence.
The paper also corrects an earlier formulation in which a weighted “structural pressure” variable combined heterogeneous orbital quantities. That interpretation is removed. The revised framework treats the structural representation strictly as a classifier input, not as a new physical pressure or conserved quantity. Total energy and total angular momentum drift are reserved for numerical quality assurance, while redistribution among pairwise or orbital components is treated separately.
A deterministic routing scheme defines six primary finite-horizon outcomes:
Collision → Ejection → Persistent Hierarchy → Coherent Periodic/Quasi-Periodic Motion → Bounded Chaotic Persistence → Unresolved/Censored.
This routing prevents overlapping orbital descriptions from producing ambiguous benchmark labels.
The principal hypothesis is prospective: a frozen structural-temporal model should improve prediction of transition probability and eventual outcome class relative to initial-condition baselines, conventional stability and chaos diagnostics, and flexibility-matched temporal controls. Generalization is tested using group-aware, leave-one-family-out evaluation across six trajectory classes: equal-mass nonhierarchical systems, hierarchical triples, restricted three-body systems, near-resonant systems, known periodic-orbit families, and random scattering configurations.
A secondary phase-locking hypothesis uses preregistered integer phase relations and circular statistics to test whether emergence or rupture of coherence predicts resonance capture, resonance escape, or transition into coherent motion. These tests must survive multiplicity correction and structure-preserving surrogate controls.
The manuscript includes explicit lead-time requirements to prevent terminal-event leakage, strong conventional comparators, deterministic outcome definitions, a 10-part falsification matrix, numerical conservation gates, preregistration rules, and a protocol-level reproducibility package.
The reproducibility package contains frozen computational definitions, benchmark and result templates, executable software-level demonstrations, phase-surrogate code, unit tests, citation metadata, and SHA-256 integrity checksums. The included synthetic demonstrations verify only that the analysis pipeline operates as specified; they are not empirical evidence for the proposed three-body hypotheses.
The current work is therefore intended as a theoretical/computational methodology and preregistration protocol. Empirical validation requires execution of the full six-family benchmark corpus and reporting of held-out predictive scores, calibration, confidence intervals, lead-time performance, surrogate tests, and cross-family transfer.