Variational Backbone and Regime Closures XVI: The Mixed Gate as a Common Comparison-Representative Regime of Conservative and Dissipative Readout

Part XVI studies the mixed gate as the R2+R3 readout regime of a retained lawgenerated from the Part I summary-interface grammar and inherited through the Part XVreduced representative. The mixed gate is not a new primitive evolution law: it is thegate in which the dissipative reading R2 and the conservative (time-completed) reading R3remain simultaneously leading on the same retained branch of the fixed scalar comparisonrepresentative E ∈ EXV.By the Internal Invisibility Principle, unread content does not enter the retained equationas raw data. It enters only through the licensed summary-output channel F = ΣH,P (II ) =DI II . In the declared linearized representative of this Part, that summary-output footprintis encoded by a reduced response operatorKmixΣ := D RΣ D∗,so that the retained mixed equation takes the formMR∂2t u + ΓR∂tu + Leff u = 0, Leff = LR − η2 KmixΣ .In the quasistatic representative gate, Leff coincides with the common reduced Schur operatorSeff inherited from Part XV; memory-sensitive regimes correspond to a frequency-dependentrealization of the same reduction, not to a different primitive law.The principal retained readouts are the modewise dispersionMRω2 + iΓRω − Ω2eff(k) = 0, Ω2eff(k) = β|k|2 + m2eff − η2σΣ(k),and the mixed discriminant∆mix(k) = 4MR Ω2eff(k) − Γ2R,which classifies underdamped, critical, overdamped, and unstable windows within one retainedequation. The associated energy lawddtEmix(t) = −ΓR∥∂tu∥2shows that conservative storage and dissipative loss coexist inside the same licensed representative package. The unread side is not opened as a hidden physical sector: the auxiliaryvariable used in the linearized representative is a virtual-boundary device of the retaineddescription, and it appears in the retained law only through the licensed footprint KmixΣshifting Ω2eff(k). The principal contribution of this Part is therefore not a new formula butthe identification of ∆mix(k) as the licensed classifier of the simultaneous R2+R3 transitioncompletion of the inherited law-space; decoherence onset, Lindblad-type closure, and nearhorizon irreversible readout are treated only as downstream compatibility directions of thesame mixed branch, not as primitive starting points of this Part.