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Variational Backbone and Regime Closures XVIII (Dark Sector): The Dark Residual Source Mass and Dark Residual Sources from One Comparison-Representative Hessian
VBRC treats the dark residual source as a metric footprint of unread content, not as an independently inserted dark-matter Lagrangian or bare dark-energy term. This Part is not a cosmological data-fitting rail and does not re-derive gravity: the Part X metric gate is inherited. Its task is the source-entry side of the theory, namely to show how licensed unread summaries can become mass-like, gravitational-source-like, DM-like, DE-like, and Λ-like readouts without inserting primitive dark fluids or a bare dark-energy term. Starting from the Part I comparison-density chain, the closed/unread sector is allowed to enter the retained metric law only through a licensed full summary Ffull = ΣXVIII(unread content), Ffull = DXVIII I II on the canonical first-order branch, and through the shifted displacement f = Ffull − F⋆ relative to a chosen background summary F⋆. For fixed metric g, the open variable is relaxed to u∗(g, f), giving a background-normalized residual energy Ered dark[g, f]. In the shifted representative, E red dark[g, 0] = 0, T dark µν [f] = − 2 p |g| δEred dark[g, f] δgµν . The central construction is that the mass readout is the open-Schur gap SR = A − BC−1B ∗ , whereas the dark gravitational source is generated by the opposite dual-Schur residual SI = C − B ∗A −1B. Thus mass and the dark source are not independent additions, but opposite reductions of one comparison-representative Hessian. A cosmological spectral gate then splits the shifted summary into infrared and inhomogeneous components. The inhomogeneous stress is DM-like only when its averaged density is positive, pressure-suppressed, and clustering on the readout cell; the infrared stress is DE-like only when it is approximately metric-proportional and slowly varying. The cosmological-constant term is identified with the metric-proportional infrared projection of the same reduced stress, not with a raw zero-point vacuum sum. The main structural output is a non-independence theorem: admissible DM-like and DE-like readouts must lift to one dual-Schur residual source and one hidden-summary closure 1 load. At the same quadratic level, SR and SI satisfy a determinant/index duality. In the scalar active-channel representative, their relative conversion has the normalized Lorentzian shape Kconv(k)/Kconv(0) = (1 + ℓ 2 dark|k| 2 ) −1 , ℓdark = p β/mA, which is independent of the coupling amplitude η in that representative, even though the dark response S −1 I , the source amplitude, and the critical scale retain η-dependence through κ 2 = η 2/(αβ). These are structural constraints, not a numerical fit of ΩDM, ΩDE, or w.
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