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March 25, 20260 citationsOpen Access

BCT Letter 104: The Three-Body Problem from BCT Vacuum Topology — Topological Regularisation of Gravitational Chaos and Hopf Charge Conservation

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MCMichel Robert Cabrié

Key Points

  • To regularise the classical three-body problem using topological methods and explore implications for gravitational systems.
  • Applied BCT lattice incompressibility enforcing minimum separation between bodies.
  • Derived gravitational coupling using specific parameters.
  • Explored Hopf stability criterion for topological configurations.
  • Analyzed stability in the Sun-Earth-Moon system and generalized for hierarchical triple systems.
  • Established a topological lifetime for systems based on the Hopf criterion.
  • Found hierarchical systems under BCT criteria exhibit unusually long stability.
  • Predictions testable with upcoming observational data from Gaia DR3.

Abstract

The classical three-body problem is regularised by BCT lattice incompressibility imposing minimum separation rₘin = RBCT × lP = 1. 843 lP. Trilinear gravitational coupling g₃ = α₀² × rₜet/rₒct = 2. 98×10⁻⁵ derived with zero free parameters. Hopf stability criterion: Hₛystem ∈ ℤ gives topological lifetime τ = tU × exp (5329/n). Sun-Earth-Moon system explained as H=3 topologically locked configuration. Prediction #147: hierarchical triple stellar systems satisfying BCT Hopf criterion show anomalously long stability — testable with Gaia DR3. BCT SAR application to Machu Picchu subsurface mapping included. Zero free parameters.

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Cite This Study

Michel Robert Cabrié (2026) studied this question.

synapsesocial.com/papers/69c37bd4b34aaaeb1a67ea50https://doi.org/10.5281/zenodo.19172032
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