Coherence as a Natural Transformation: A Categorical Unification of Physical, Thermodynamic, and Evaluative Coherence

Resolves the open question from the Universal Coherence Invariant paper: are the correspondences between quantum, thermodynamic, information-geometric, and evaluative coherence analogies or isomorphisms? Answer: isomorphisms. Specifically, they are components of a natural transformation η: FQ ⇒ FE between functors from the category of physical systems to the category of coherent systems. This means coherence is not a property that appears at multiple scales by coincidence — it is a morphism in the categorical structure of reality. Additionally derives Kcrit = ℏω₀ / (kBTₑff ln2) from fundamental constants without empirical calibration, recovering 0. 127 at institutional timescales. Collapse is identified as categorical failure: the system exits the category Coh. E=R is the condition for remaining an object in the category of coherent systems. Part of the Spektre corpus (github. com/spektre-labs/corpus).