Typed Epistemic Reconstruction: From Observational Collapse to Monadic Recovery

This work develops a formal framework for the reconstruction of structure from observable data using category-theoretic methods. The central problem is interpreted as a precise counterpart of a fundamental epistemic question: to what extent observations determine structure. Given a functor F: P → S, the paper distinguishes three levels of recovery: observational collapse, invariant reconstruction, and genuine object-level reconstruction. It is shown that the kernel-pair quotient associated with F classifies invariant functorial content but does not, in general, suffice for reconstructing objects. This leads to the notion of a reconstruction gap, measuring the discrepancy between observable invariants and full structure. The paper establishes that genuine reconstruction requires additional structure beyond quotient data and is governed by monadicity and descent conditions. To refine this analysis, typed epistemic registers are introduced, providing a stratified framework for observational regimes and their corresponding reconstruction limits. The framework provides a unified categorical account of the gap between observation and interpretation and clarifies its structural, rather than contingent, nature.