Evans' Law: A Predictive Threshold for Long-Context Accuracy Collapse in Large Language Models

Update – Version 2 (7 November 2025): This record now includes the complete dataset, regression notebook, and detailed methods note for replication. The work remains preliminary and exploratory. All data and code are provided for transparency, and independent validation is encouraged. Abstract Language models exhibit consistent performance decay as input and output lengths increase. This paper presents Evans’ Law, defining the relationship between context length and accuracy degradation. Evans’ Law: The likelihood of errors rises super-linearly with prompt and output length until accuracy falls below 50 percent, following a power-law relationship determined by model capacity and task complexity. Initial experimental validation confirms that the phenomenon exists and provides empirical data to refine the mathematical formulation. The updated dataset and regression analysis extend this validation, showing a sub-linear scaling curve consistent across multiple large-language-model families. Key materials in this version: • Full dataset of coherence-loss threshold measurements (evanslaw_dataset.csv) • Regression notebook (evanslaw_regression.ipynb) • Regression analysis export (evanslaw_regression.html) • Visualization of observed vs theoretical fits (evanslaw_plot.png) All data were collected under deterministic prompting conditions (temperature 0.2, top-p 1.0). Methods and limitations are documented in the accompanying methods_note.pdf.