Title: Gravitational Phase Fraction on an Elastic Torus: Cosmological Doppler Effect and the Emergence of G and ΛDescription:This dataset accompanies the paper "Gravitational Phase Fraction on an Elastic Torus: Cosmological Doppler

Title: Gravitational Phase Fraction on an Elastic Torus: Cosmological Doppler Effect and the Emergence of G and ΛDescription:This dataset accompanies the paper "Gravitational Phase Fraction on an Elastic Torus: Cosmological Doppler Effect and the Emergence of G and Λ." Within the Phase Emergence Dynamics (PED) framework, gravity and dark energy are interpreted as alternating phases of a single complex scalar field evolving on a toroidal topology. We present numerical simulations of the Gross-Pitaevskii equation (GPE) on both static and expanding one-dimensional tori.Key results: (1) On a static torus, the gravitational phase fraction α_G saturates to ~28% in the weak-nonlinearity limit, establishing it as an intrinsic geometric property. (2) On an elastic (expanding) torus, the cosmological Doppler effect stretches the attractive phase, increasing α_G toward the observed cosmological value of ~58%. (3) The function α_G(H₀) exhibits a non-monotonic maximum, suggesting the observed universe occupies a dynamically stable configuration—the cosmological analogue of Feynman's principle of stationary phase.The package includes the compiled paper (PDF), LaTeX source, all simulation code (Python), numerical results in HDF5 and JSON formats, and publication-quality figures. All simulations are fully reproducible.Keywords: cosmological constant problem, dark energy, gravitational phase transition, elastic torus, Doppler effect, Gross-Pitaevskii equation, phase emergence dynamics, Hubble tension, quantum vacuumCopiá y pegá directo.