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Ayala Core is an exploratory framework for identifying which distinctions in a system's state are relevant to a specified task contrast. The framework formalizes task-relevant equivalence through quotient representations, distinguishes transformation-order effects from more general task contrasts, and separates latent reproducible effects from noisy observed differences. It connects task relevance with experimental identifiability and task-preserving observation compression, and introduces an empirical stability requirement for recovering task-relevant structure from repeated measurements. Four empirical regimes are distinguished: negligible effects, broadly shared effects, stable heterogeneous effects, and apparent heterogeneity dominated by instability or noise. The framework is intended as a structural synthesis and research program rather than a replacement for established statistical, causal-inference, information-theoretic, or experimental-design methods.