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May 20, 20260 citationsOpen Access

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

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YYYunbeom YiOldham Council

Key Points

  • The research reevaluates dark residual sources under the Internal Invisibility Principle as metric footings, not as typical dark energy.
  • Utilized comparison density and metric gates from previous parts of the VBRC series to establish a theoretical framework.
  • Developed formulations of the mass readout and dark gravitational source through dual Schur complements and Hessians.
  • Demonstrated a determinant/index duality between mass readouts and dark gravitational sources, confirming their conceptual relations.
  • Identified the cosmological constant with a reduced stress projection, aligning it with metric considerations.

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∗SR=A-BC^-1B^* SR=A−BC−1B∗) and the dark gravitational source (dual Schur complement SI=C−B∗A−1BSI=C-B^*A^-1B 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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Cite This Study

Yunbeom Yi (2026) studied this question.

synapsesocial.com/papers/6a0d50bdf03e14405aa9cce7https://doi.org/10.5281/zenodo.20264834
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