Asymmetric Coupling and the Basin Architecture of Flat Regions

Fixed-point enumeration (Δγ=0.01, 150 starts per γ, n=21 values) and basin volume estimation (n=1000 uniform ICs per γ) in an n=4 gradient-flow simulator with asymmetric cumulative coupling parameter γ. Reveals a stable two-class landscape architecture across γ=0.20–0.40: peripheral high-escape fixed points (‖z‖≈1.27) and outer-manifold low-escape fixed points (‖z‖≈2.71) coexist at all γ values. Basin volumes are stable across the tested range (peripheral 87–93%, outer manifold 6–13%) with no universal critical threshold. Flat-region dynamics emerge when initialization lands in outer-manifold basins — not as a global landscape property. γ modulates basin geometry but does not produce topological bifurcation. The governing variable is initialization: which basin does the system enter from its actual starting conditions? Extends Paper 1 from structural topology (add factor) to structural parameterization (modify coupling geometry). Fourth paper in a four-paper sequence on substrate-agnostic coupling dynamics. Companion to Dunn (2026a, Zenodo) and arXiv:2602.12176.