A Curvature-Boundedness Fixed-Point Generator for a Universal Stability Constant

This paper introduces a proof-oriented mechanism for generating a universal stability constant χ∈(0,1) using curvature boundedness in a recursive shell framework. A two-sided stability functional is constructed to penalize both curvature blow-up and collapse, inducing a stability selection rule for shell-to-shell coupling ratios. In a one-dimensional Dirichlet reduction, the curvature functional admits a closed spectral form, yielding a closed-form minimizer for the stability-selected ratio. Under an asymptotic curvature-budget normalization convention, the coupling ratio converges to a universal constant χ\chiχ, which is proven to be irrational under rational normalization parameters. The framework provides a mathematically explicit pathway from curvature regulation to a uniquely selected dimensionless constant.