Variational Backbone and Regime Closures XI: Quantum Probability as a Retained Readout in R3 Hilbert/Born compatibility, measurement update, and Bell audit

Part XI places the standard quantum probability and measurement package inside theVBRC representation layer. The paper does not claim that quantum mechanics is the uniquemicroscopic law of the unread side, nor does it identify the unread coordinate with a hiddenphysical sector. In accordance with Part I, unread content reaches retained physics onlythrough a licensed summaryFXI = ΣXI(IXII), ΣXI := ΣHXI,PXI ,with any first-order formulaFXI = DXIIIXIItreated as a representative realization rather than as a universal primitive.The starting point is an already generated R3 retained channel, inherited from the lawgeneration papers. Part XI asks how this retained channel becomes a quantum observationinstance. The core result is that, once a normalized retained protocol weight, possiblyrepresented by a Hilbert state or by a configuration density/current under an additional localconfiguration gate, and a readout channel are declared, outcome probabilities are obtainedas pushforwards and conditional laws of the declared observation protocol:νt = (Πδobs)#µt.Thus probability is not inserted as a new structural force; it is the protocol-level readout ofpartial observation under IIP.The usual Born, PVM/POVM, and measurement-update formulas are then recorded asthe standard Hilbert-compatible branch:pk = Tr(ρEk), ρ 7→ ρk,under the declared positivity, normalization, event-additivity, and update gates. Theseformulas are not presented as a derivation of a unique microscopic ontology, but as thecompatibility readout by which the retained R3 channel agrees with ordinary quantummechanics where the Hilbert/Born gates are valid.Finally, Part XI records the EPR/Bell compatibility condition. VBRC does not posita local hidden-variable factorization behind the retained readout. Bell-violating quantumcorrelations are therefore not excluded by the framework; they are handled by the standardbipartite Hilbert/Born readout, while local factorizing hidden-variable representations areclassified as incompatible gates for the quantum branch.