Variational Backbone and Regime Closures XIV: Horizon boundary readouts and black-hole outputs Validity conditions for mass/entropy readouts and thermodynamic summary assumptions

Part XIV treats a black-hole horizon as the clearest geometric instance of the Part Ivirtual-boundary principle. The exterior protocol cannot read the horizon complement asraw data; it may read only a licensed boundary summary. Thus black-hole mass, entropy,temperature, and first-law language are not introduced here as primitive horizon laws. Theyare horizon-side outputs of a declared boundary protocol acting on the Part I interfaceF = ΣH,P (II ),with the horizon representative written asFΣ = ΣHΣ,PΣ(II ) and, when declared, FΣ = DI,ΣII .After boundary-localized rank loss and admissible elimination, this licensed summary appearson the retained exterior channel through an effective operator LΣeff. The mass readout isthe calibrated spectral floor of this operator, while entropy is the logarithmic measure ofprotocol-indistinguishable completions in the horizon fiber. Area-type scaling follows undera boundary-layer counting representative; the absolute Bekenstein–Hawking coefficient, aHawking-type thermal spectrum, and Page-curve statements require additional calibration,KMS/thermalization, or typicality/unitarity gates. The aim of this Part is therefore not todetermine a unique horizon-complement ontology, but to state how exterior retained lawscan read horizon outputs from a licensed unread summary.