Variational Backbone and Regime Closures VI (Source): Open Schur Elimination and Closed-Summary Source/Background Readouts A dual-Schur response operator under downstream source/background gates

This paper computes the closed-summary response operator generated by the VBRC variational core. It is the dual calculation to Part V. Instead of reading a retained spectral gap after eliminating the summary variation, Part VI eliminates the retained, open variation and studies the resulting response on the licensed summary channel. Under the Internal Invisibility Principle, the active closed-side variable is not a raw unread coordinate. It is a licensed summary variation around a declared background summary. Linearizing the retained-summary pair and applying Schur reduction gives a closed-summary effective operator with a resolvent-shaped response. This response is determined by the same variational core, rather than by inserting an independent dark component. Source-like, background-like, dark-matter-like, and dark-energy-like interpretations arise only after additional downstream readout gates are declared. Before such gates, the generic output is one mixed closed-summary response operator. The source/background split is therefore a readout decomposition, not an ontological division into independent fluids. Part VI does not claim a completed dark-sector phenomenology, a unique halo profile, or a unique equation of state.