Dark Annihilation Remnant (DAR) Hypotesis.

This manuscript formalizes the definitive mathematical framework of the Dark Annihilation Remnant (DAR) hypothesis, resolving the critical problem of local energy-momentum conservation within Einstein's General Relativity spacetime. Originally formulated as a phenomenological accumulation law, the net injection of dark matter (DM) due to the metric "lag" of virtual particles required rigorous covariant support. In this extended edition, we demonstrate that dark matter is not generated ex nihilo, but rather through a dynamic covariant coupling with the dark energy sector (Λ). By treating quantum vacuum density as a dynamic field that decays as a function of the scale factor according to the law ρΛ(a) ∝ a-ζε , the covariant derivative of the universe's total energy-momentum tensor vanishes identically (∇μ Tμν total = 0). This deduction transforms the DAR model into a theoretical framework internally consistent with conservation principles and adopted hypotheses, while maintaining concordance with anomalous dark-matter-deficient galaxies observed at high redshifts (z > 10) by the James Webb Space Telescope (JWST).