Scientific inquiry often supports disciplined Bayesian update only patchwise. Different instruments, evidential partitions, or reporting practices can each sustain a local public calculus without jointly yielding one global affine evidence space. The local/global problem for Bayesianism is therefore this: when do local canonical Bayes charts glue into one global canonical update law, and when does globalization fail by genuine obstruction rather than by mere local incoherence? The core result is a local/global duality. In one direction, global canonical Bayes exists exactly when local public quotients form effective descent data, that is, local quotient data that genuinely come from one common public object. In the other, a coherent but globally nonaffine update regime, not representable by one global affine public evidence space, can, under local canonicalizability conditions, be represented as a curved assemblage of locally Bayesian charts whose nonaffinity is measured by the associated descent obstruction. The obstruction therefore marks a limit on public epistemic integration, not a lapse into irrationality: inquiry can remain globally transport-coherent even when it admits no single global affine public evidence space. A standard-Borel Markov realization and several philosophical consequences place this geometry in the broader account of Bayesianness as affine evidence, now refined by the possibility of globally curved Bayesian order.
Lorand Bruhacs (Tue,) studied this question.