Dual Attractor Basins at Fractal Phase Boundaries: A Universal Two-Population Structure in Nonlinear Coupled Systems

Description/Abstract: Paper 12 of Resonance Theory Series. Tests whether the two-population structure discovered in Paper 11 (Cascade Universe) is universal across nonlinear coupled systems. Six domains examined from first principles: Van der Waals liquid-gas coexistence, Onsager's exact 2D Ising solution, Bose-Einstein condensation, pipe flow turbulence, interior Schwarzschild spacetime metric, and astrophysical density distributions. Result: 4 PROVEN (established textbook physics reframed), 2 HYPOTHESES, 0 REFUTED. Central finding: at every critical transition, the topology permits exactly two stable configurations — possibilities, not probabilities. Keywords: dual attractor basins, phase transitions, bifurcation, Feigenbaum constant, fractal geometry, Landau theory, Van der Waals, Ising model, Bose-Einstein condensation, turbulence transition, Schwarzschild metric, universality, critical exponents, MESA Method, Resonance Theory