This paper states when horizon-localized boundary readouts license black-hole mass andentropy outputs, and which extra summary assumptions are needed before thermodynamiclanguage becomes valid. We locate black-hole mass and entropy as outputs of a representationprotocol acting on a fixed variational backbone. A horizon is defined as a representation-levelevent in which the readout map undergoes boundary-localized rank loss (or non-smooth/illconditioned behavior), enforcing admissible elimination on a thin layer around a codimensionone surface. Mass is defined as a spectral-gap readout of the induced effective operator, whileentropy is defined as fiber entropy with respect to a declared counting measure on protocolindistinguishable fibers (and, when admissible, by a spectral proxy such as a log-determinant).Within the class of boundary-localized horizon instances, the entropy output has leadingarea-type scaling, and the same Schur deformation yields a direct operator-level mass–entropycoupling. The absolute Bekenstein–Hawking coefficient is treated as a calibration statementrather than as a structural derivation. We then extend the output chart to (M, J, Q) andderive a first-law differential form as a conversion identity between outputs, with (T, Ω, Φ)interpreted as protocol conversion factors rather than structural inputs.