BIG-B7: Persistence of the Free-Boundary Exponent Across a Runaway Transition in Degenerate Mixed-Gradient Dissipative Fields

This package contains the BIG-B7 numerical investigation of free-boundary behavior in degenerate mixed-gradient dissipative fields. The governing equation is ∂tφ = ∇·(φ^m∇φ) − μφ − γ∇·(|∇φ|²∇φ) with fixed mobility exponent m = 1. The study focuses on the existence of a runaway transition driven by the quartic-gradient coefficient γ and on the behavior of the free-boundary exponent near the critical region. Main results: • Identification of a runaway threshold γc ≈ 0.8735 ± 0.0005 • Persistence of the free-boundary exponent ν ≈ 1.91 across the transition. • Smooth evolution of boundary curvature through the critical interval. • Evidence that the runaway transition originates from a global dynamical instability rather than a breakdown of local free-boundary geometry. The package includes: - PDF manuscript - Numerical summary tables - Critical-scaling datasets - Boundary-fit datasets - Figures used in the manuscript - Original numerical scan outputs The results support a separation between local free-boundary universality and global stability transitions in degenerate mixed-gradient dissipative systems.