Black-Hole Entropy and Unitary-Complete Evaporation in the Closure-Flat Completed-Cycle Framework

We formulate black-hole thermodynamics as a positive observer readout of the closure-flat completed-cycle framework. The counted objects are admissible black-hole completed cycles, rather than bare interior microstates, bare forward histories, or independent endpoint data. On the stationary branch, exact Hawking--Unruh purification, committed-sector weights, reversible rank-one coherence, and quarter-normalized detector blocks reproduce the Gibbons--Hawking--Wald area law as an effective completed-cycle capacity. The quarter normalization is not appended after an independent microscopic count: in the completed-cycle framework the classical horizon readout is part of the primitive closure cycle, so the reciprocal quantum context is counted only after the horizon text and its local Einstein response have restricted the admissible sectors. On the quasi-stationary branch, the same readout data, together with the stated support-minimal branch selection, yield a hidden-reservoir transport law, a public release channel, a Page-compatible fine-grained radiation entropy, and temporal gluing to a rank-one terminal endpoint. Quantum-extremal islands appear as semiclassical readouts of hidden-completion branches: the area term measures completion-boundary capacity, while the bulk term measures unresolved completion entropy.