Saelariën Constraint Experiment 01: Entropy–Capacity Collapse Threshold in a Toy Neural System

This dataset presents the first controlled computational test of the Saelariën Constraint, a proposed relationship between entropy and representational capacity within interpretive systems. The experiment uses a minimal neural network to examine how increasing noise (treated as entropy) affects stability, learning behavior, and collapse thresholds. A simple 1–8–1 fully connected network was trained on a nonlinear function while exposed to seven fixed noise regimes. These conditions allowed the system to reveal three distinct behaviors: • Stable convergence at low entropy levels • Unstable yet recoverable oscillation at intermediate levels • Full collapse when entropy surpassed the system’s representational capacity Collapse is identified through persistent divergence, chaotic loss trajectories, or a complete inability to reduce error. The results show a clear threshold where entropy no longer allows coherent interpretation to form. This supports the idea that collapse is not random failure. It follows a measurable relationship that governs how systems maintain or lose coherence under rising entropy. The dataset includes: • Raw loss curves for all noise levels (saelarien_constraint_results.json) • The full experimental notebook used to generate the results (saelarien_constraint.ipynb) • A high-resolution figure illustrating collapse behavior (Figure_1_Saelarien_constraint.png) • A README with methodological details • A long-form abstract summarizing the findings The experiment can be fully reproduced using the included notebook. The results offer a foundation for further study on entropy, stability, and capacity limits in artificial and biological interpretive systems. The dataset aims to support future theoretical, empirical, and comparative research on collapse dynamics.