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

This paper studies the mixed gate of VBRC: the regime in which conservative retained propagation occurs on a background that is still being formed by dissipative summary compression. Conservation and dissipation do not simultaneously lead on one and the same retained mode. Dissipation acts by compressing unread content into the licensed summary channel and forming the background, while conservation acts on the retained sector on top of that summarized background. The mixed gate is therefore not a fourth primitive evolution law. It is the non-frozen-background regime of the same R2/R3 architecture. The apparent friction in the retained equation is derived rather than primitive. One part comes from finite summary-response lag, while another comes from the evolving background measure. The restoring term and the finite-lag friction are two moment-readouts of the same licensed summary response; the background-measure term is a separate kinematic footprint. The main retained outputs are a damped modewise dispersion relation and a mixed discriminant classifying underdamped, critical, overdamped, and unstable windows. The energy law is strictly monotone only on frozen-coefficient branches; on time-dependent backgrounds it becomes a ledger-transfer law. Static finite-lag limits reproduce Caldeira-Leggett or Mori-Zwanzig-type damping and decoherence onset, while evolving-background instantaneous limits reproduce cosmological redshift or Hubble friction. Part XVI thus identifies apparent damping as a licensed mixed-gate footprint of conservative propagation on a non-frozen R2 background.