Boundary-Layer Scaling in Degenerate Mixed-Gradient Dissative Fields: Numerical Dataset for Boundary Information Geometry (BIG)

Overview This dataset contains numerical measurements associated with the emergence of self-organized quadratic boundary layers in a degenerate mixed-gradient dissipative field model. The simulations were performed for ∂tφ = ∇·(φ²∇φ) − μφ − γ∇·(|∇φ|²∇φ) + S, where: μ controls dissipation, γ controls quartic-gradient stiffness, S is a localized source term. The dataset accompanies the exploratory Boundary Information Geometry (BIG) research program and focuses on numerical scaling properties of the field model. Contents The dataset includes: gamma parameter scans mu parameter scans quadratic boundary-layer measurements scaling-fit results publication-quality figures Included files: final_mu_scaling_table.csv final_gamma_scaling_table.csv final_scaling_fit_results.csv final_scaling_fit_results.json figure set (fig01–fig10) Main Numerical Observations The simulations provide evidence for: Persistent quadratic boundary layers with local exponent ν ≈ 2. Boundary-layer position scaling approximately as Rq ∝ √γ for fixed μ. Boundary-layer position scaling approximately as Rq ∝ 1/√μ for fixed γ. Progressive thinning of the quadratic boundary layer as μ increases. Transition from broad self-organized boundary layers to weak crossing-layer regimes at larger μ. These observations suggest that the effective boundary behaves as a finite self-organized boundary layer rather than a sharp support edge. Reproducibility All results were generated using finite-difference simulations and analyzed through local power-law fitting procedures. The dataset is intended to support independent verification, reproduction, and further investigation of boundary-layer scaling phenomena in nonlinear dissipative field systems. Relation to BIG This dataset originated from the broader Boundary Information Geometry (BIG) research program, which investigates the dynamical role of boundaries in nonlinear systems. The present dataset focuses exclusively on numerical observations and scaling relations.