Variational Backbone and Regime Closures XVIII: The Dark Residual Source Mass and Dark Residual Sources from One Comparison-Representative Hessian

This Part of the VBRC series treats the dark residual source as a metric footprint of unread content under the Internal Invisibility Principle, rather than as a primitive dark fluid or bare dark-energy term. Starting from the inherited Part I comparison density and Part X metric gate, the closed/unread sector enters the retained metric law only through a licensed full summary. The central construction shows that the mass readout (open Schur complement SR=A−BC−1B∗S_R=A-BC^{-1}B^* SR=A−BC−1B∗) and the dark gravitational source (dual Schur complement SI=C−B∗A−1BS_I=C-B^*A^{-1}B SI=C−B∗A−1B) are opposite reductions of one comparison-representative Hessian, satisfying a determinant/index duality. A non-independence theorem follows: admissible DM-like and DE-like readouts must lift to one dual-Schur residual source and one hidden-summary closure load. The cosmological-constant term is identified with the metric-proportional infrared projection of the same reduced stress.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-05-18
DOI
https://doi.org/10.5281/zenodo.20264834
Primary Topic
Cosmology and Gravitation Theories
Type
preprint
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preprint

Variational Backbone and Regime Closures XVIII: The Dark Residual Source Mass and Dark Residual Sources from One Comparison-Representative Hessian

Yunbeom Yi
Zenodo (CERN European Organization for Nuclear Research)
Cosmology and Gravitation Theories
preprint

Variational Backbone and Regime Closures XVIII: The Dark Residual Source Mass and Dark Residual Sources from One Comparison-Representative Hessian

Yunbeom Yi
preprint en

Abstract

This Part of the VBRC series treats the dark residual source as a metric footprint of unread content under the Internal Invisibility Principle, rather than as a primitive dark fluid or bare dark-energy term. Starting from the inherited Part I comparison density and Part X metric gate, the closed/unread sector enters the retained metric law only through a licensed full summary. The central construction shows that the mass readout (open Schur complement SR=A−BC−1B∗S_R=A-BC^{-1}B^* SR=A−BC−1B∗) and the dark gravitational source (dual Schur complement SI=C−B∗A−1BS_I=C-B^*A^{-1}B SI=C−B∗A−1B) are opposite reductions of one comparison-representative Hessian, satisfying a determinant/index duality. A non-independence theorem follows: admissible DM-like and DE-like readouts must lift to one dual-Schur residual source and one hidden-summary closure load. The cosmological-constant term is identified with the metric-proportional infrared projection of the same reduced stress.

Zenodo (CERN European Organization for Nuclear Research)
Peace, Justice and strong institutions
Cosmology and Gravitation Theories
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