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

This paper states when horizon-localized boundary readouts license black-hole mass and
entropy outputs, and which extra summary assumptions are needed before thermodynamic
language becomes valid. We locate black-hole mass and entropy as outputs of a representation
protocol acting on a fixed variational backbone. A horizon is defined as a representation-level
event 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, while
entropy 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 leading
area-type scaling, and the same Schur deformation yields a direct operator-level mass–entropy
coupling. The absolute Bekenstein–Hawking coefficient is treated as a calibration statement
rather than as a structural derivation. We then extend the output chart to (M, J, Q) and
derive a first-law differential form as a conversion identity between outputs, with (T, Ω, Φ)
interpreted as protocol conversion factors rather than structural inputs.