Seed-Invariant Metastable Stability (SIMS): Definition and Empirical Instantiation in a Toy Model

This record accompanies the paper “Seed-Invariant Metastable Stability (SIMS): Definition and Empirical Instantiation in a Toy Model.” We introduce Seed-Invariant Metastable Stability (SIMS) as a stability class for deterministic dynamical systems. SIMS is characterized by: a sharply localized, seed-invariant boundary in parameter space, and a strongly seed-dependent variability in coherence lifetime near that boundary. Unlike classical metastability, which is typically defined via asymptotic behavior or stochastic escape, SIMS is defined operationally using ensemble-based diagnostics that separate boundary localization from lifetime variability. The framework is empirically instantiated in a recursive geometric toy model used as a numerical laboratory. Dense parameter sweeps (up to 400 seeds per configuration) reveal a transition confined to a narrow band Δg ≈ 10⁻³, while the duration of coherent internal dynamics varies widely across seeds within that same band. Independent structural diagnostics confirm that coherence loss precedes numerical divergence, indicating a genuine internal stability transition rather than a numerical artifact. The model is intentionally abstract and is not claimed to describe any specific physical system. The contribution is methodological: SIMS provides a portable framework for classifying and detecting stability phenomena that are invisible to traditional asymptotic or linearized analyses. All simulations, diagnostics, and datasets used in the paper are reproducible and publicly available.plasticity_map.py has been updated slightly for these specific .csv file creation and belongs in the toy_model 3.8. The empirical behavior formalized here is based on extensive numerical studies reported in the companion Toy Model repository: TriOcta/SRG Toy Model — Patch 3.8: Metastable Plasticity and Slow Escape in Recursive Geometry (Zenodo DOI: 10.5281/zenodo.18031559).