EduCEQ-Toolkit: A Python Framework for Co-Enrichment Structure Diagnosis with Runtime Decidability Contracts

Ratio-type measures of structural association compare observed co-occurrence with what the marginal distribution would produce, and they return a number whether or not that number can be read. EduCEQ-Toolkit is a Python framework that declines to do so: on a public panel of 4,785 U.S. higher-education institutions, its runtime contract reports that no bandwidth between 50 and 500 km is decidable, and the call returns a structured non-decidability object instead of a coefficient. The framework generalizes the co-location quotient to an arbitrary non-negative pairwise weight, so distance, attribute similarity and network proximity are handled by one estimator. It implements three composable kernel families, an exact first- and second-order decomposition, conditional permutation inference with false discovery rate control, and a three-step contract binding the population count, the neighbourhood count and the coverage proportion. We present the contract as a reusable design pattern for research software: where a condition on a method's validity can be computed, it belongs in the execution path rather than in the manual. Evaluation covers threshold calibration, a decidable case, a refusal case on public data, and computational cost.