This work presents a nonlinear Threshold-Limited Mode Modulation (TLMM) framework for bounded-optimum structural suppression under constrained observability conditions. Unlike linear response models, the proposed nonlinear TLMM predicts that excessive envelope averaging or coupling does not monotonically enhance suppression, but instead reduces structural efficiency beyond an optimal regime. The framework derives: - a bounded-optimum effective stiffness function,- a non-monotonic suppression functional,- an optimal entrainment window,- a proxy-constrained viable interval for the cross-scale coupling coefficient α,- a characteristic-timescale-dependent observability function,- and a joint detectability landscape governed by phase-lock stability and coupling strength. The manuscript develops a closed-form minimal theoretical model linking stiffness saturation, detectability thresholds, phase-lock constraints, and timescale-gated observability. Figures 1–5 visualize the emergence of constrained detectability regimes and bounded-optimum suppression behavior. This repository includes:- the full manuscript PDF,- LaTeX source,- Python figure-generation code,- and all generated figures used in the study. The framework is intentionally minimal and exploratory, aimed at providing a compact mathematical basis for studying nonlinear suppression dynamics under realistic observational constraints.
Koji Okino (Thu,) studied this question.