Auditing coherence through the principle of a single functional mapping

The reliability of scientific conclusions is increasingly challenged by combining diverse datasets and evaluating predictive models. Apparent consensus can hide structural breaks or hidden disorder, leading to miscalibration and incorrect inferences. We introduce the Agreement–Entropy Map (AEM), a rigorously developed classifier that combines overlap-gated structural tests with entropy-based disorder detection. The framework supports the principle of a single functional mapping: only subsets or models that are consistent in both structure and disorder are considered reliable. Formal derivations show that entropy predictably rises with variance imbalance, slope offsets, or multimodality, complementing the Chow test, which does not detect such disorder. When applied to predictive models, the AEM measures coherence with physical laws and offers a systematic way to audit physics-informed machine learning. In doing so, it adds a missing axis of reliability for modern science—one that differentiates genuine coherence from apparent agreement amid vast, diverse data.