When Bayesianization Becomes Canonical: Reflective Collapse, Observation and the Geometry of Update

Reflective Bayesianization becomes the canonical update law of an observational regime exactly under specific structural conditions. The central result is an identification theorem: when the reflective quotient itself is observationally regular, unramified, and sufficiently separating, the update rule generated by disintegration is exactly reflective Bayesianization. In that setting, the Bayes report selected by equilibrium reasoning and the Bayes operator forced by strong observation are the same structure. Two consequence branches follow. First, equilibrium semantics that previously lived only at the quotient layer become semantics of the canonical operator itself, so Bayes/Nash commutation is internalized rather than merely transported. Second, once the resulting operator is strongly enough codable, the incompleteness ceiling proved for canonical observational update applies specifically to globally canonical Bayesianism. The philosophical payoff is that Bayesian update, equilibrium stabilization, and sufficiently strong observation are not rival foundations but convergent features of one public-score architecture. Bayes is neither a primitive law of rationality nor an arbitrary convention, but the coordinate calculus of a particular observational regime.