The Two Jobs of the Conditioning Bar

Bayesian notation commonly writes a posterior as p(theta| X). The expression is always relative to a declared model. Writing that declaration explicitly gives p(theta| X,M), or, more carefully when M serves as an index of the probability construction, p_M(theta| X). That restoration is familiar. The consequence examined here appears only when the two inputs are also typed by how they entered the analysis. X enters through an evidence event. M enters through a declaration. Formal epistemology already distinguishes evidence update from expansion or revision of the hypothesis space. The additional problem arises in statistical practice: ordinary posterior notation places the realized evidence and the declared model inside one conditional presentation while the analysis record usually omits the transition type by which either changed. This paper develops a record-level consequence. Bayes' theorem supplies lawful conditionalization inside a fixed declared model. A workflow can also criticize and replace that model. If the transcript records posterior states while suppressing model identity and transition type, two different histories can have the same transcript: one in which every transition is conditionalization under a fixed model and another containing a model-constitution event. The applicability of Bayes' theorem to a displayed transition is then record-undecidable: no decision rule using that transcript alone can recover the transition's type in every compatible history. The term names observational underdetermination of the record. Turing decidability lies outside the claim. The constructive repair is a typed inference lineage. A conditioning edge adds evidence within one declared model version. A constitution edge establishes a new declared model version and starts a new inferential episode. Retained evidence may then be recomputed under the new declaration; any compressed transfer from the old episode requires its own explicit transport contract. This typing clarifies sequential Bayes, model checking, probabilistic programming, provenance, distributed inference, and approximate streaming updates. It also explains why modern Bayesian workflow necessarily contains tools outside posterior conditionalization itself: model criticism supplies evidence about declarations, computational diagnostics examine implementation fidelity, and software provenance records changes across model versions. The mathematical content of Bayes' theorem remains unchanged. The object added here is its missing paperwork: a record rich enough to show where the theorem applies.