Learning Coherence: A Practical Introduction to Detectability and Scientific Thinking (Educational Layer) (v1.1)

This document defines a minimal structural framework ensuring mathematical coherence between observable quantities and decision variables within the COS45 framework. It belongs to the STRUCTURAL layer and acts as a bridge between observable proxies and admissibility conditions. No decision rule is defined.No inference claim is made. The framework formalizes consistency constraints linking observable quantities (e.g., spectral gap, curvature proxies) to δ (observable structure), while explicitly accounting for uncertainty τ. These relations are necessary but not sufficient for admissibility. They ensure that any transition from observable data to decision variables remains mathematically coherent and traceable. This document does not establish detectability, does not prove admissibility, and does not model system dynamics. Its role is strictly structural: to guarantee coherence before applying the DECISION layer of COS45. Version (v1.1) clarifies the minimal structural role of the framework and its separation from both observable definitions and decision rules. No change to underlying relations.