Abstract

This report presents a numerical investigation of boundary-layer stability under joint variation of the dissipation parameter μ and the quartic-gradient stiffness γ in a degenerate mixed-gradient dissipative field model.

Building upon BIG-B4.1, which identified a robust quadratic boundary exponent (ν ≈ 2), the present work extends the analysis to a two-parameter scan over

μ ∈ {0.3, 0.7, 1.0}

γ ∈ {0.5, 1.0, 2.0}.

Across all investigated cases, the effective boundary exponent remains close to ν = 2, while the effective layer width and amplitude consistency vary significantly.

The numerical results suggest a phenomenological classification into three observable regimes:

• Stable/Recovered

• Compressed

• Residual

The data indicate that the quadratic boundary exponent behaves as a robust geometric invariant, whereas observable boundary-layer properties are controlled by the competition between dissipation and quartic-gradient stiffness.

No claim of a sharp thermodynamic phase transition is made. Instead, the present report proposes a boundary-compression map as a descriptive framework for organizing the observed numerical behavior.

The results provide an intermediate step toward a broader understanding of boundary-layer universality in degenerate nonlinear dissipative systems.

Notes

This report is part of the Boundary Information Geometry (BIG) numerical exploration series.

The work focuses on numerical observations and phenomenological classification. Interpretive discussions regarding higher-level applications are intentionally excluded from the present report.