Dark Energy as Vacuum-Energy Continuity Across a Planck-Boundary Black Hole

See https://doi.org/10.5281/zenodo.19117903 for updated equations, narrowed ranges ... This paper extends the information–geometry cosmology developed in earlier work by providing a natural, falsifiable explanation for dark energy and the ∼9% early–late Hubble discrepancy. In this framework, a collapsing black hole that reaches the Planck–limit surface (Ξ = 1) nucleates a child FRW universe. A fraction of the parent black hole’s information appears as warm dark matter (WDM), while a residual fraction manifests as an inherited vacuum–energy term. We show that this inherited vacuum energy relaxes slowly over cosmic time, producing a small epoch‑dependent deviation from a constant Λ and naturally generating the observed Hubble tension without modifying general relativity. Two mechanisms are proposed: One‑off relaxation: a fixed vacuum‑energy offset inherited at nucleation that decays with timescale τ ≈ 8–12 Gyr. Accretion‑driven leakage: ongoing information inflow into the parent black hole drives a steady, tap‑like leakage of vacuum energy into the child universe through the Planck‑boundary rupture. Using the warm‑dark‑matter mass scale (m_WDM ≈ 2–4 keV) and the local halo density of Andromeda, we obtain a local number density of ~1.1×10¹¹ WDM particles per cubic metre, providing a direct observational anchor for the inherited information density. Combining this with the inherited‑information budget (I_child ≈ 10⁸⁷ bits) and the parent black hole capacity (I_BH ≈ 10⁹³ bits for M_BH ≈ 10⁸ M_⊙), we show that only a minute fraction of the parent manifold’s information is required to generate both warm dark matter and the observed dark‑energy behaviour. The model is fully falsifiable, requires no exotic fields, and offers a unified information‑geometric origin for warm dark matter, dark energy, and the Hubble tension.