The Dark Sector from a Discrete Substrate: Cosmological Constant Resolution, Sterile Neutrino Mass, and the Coincidence Problem from Z3 ⊗Q3

We derive five cosmological observables — the dark energy density ρΛ, the present-epoch equation-of-state parameter w0, the dark-energy / dark-matter density ratio ΩDE/ΩDM, the sterile neutrino mass scale mνR , and the exact w(z) trajectory — from a single discrete substrate Z3 ⊗Q3 on the 4.8.8 Archimedean tiling, with zero free parameters in the predic- tions themselves once the canonical substrate constants (ΛQCD,α,a0) and the cosmological inputs (LH,Ωm0) are anchored. The framework’s substrate-level identification of dark en- ergy as the macroscopic thermal exhaust of Lindbladian vacuum decoherence (ER=EPR on a discrete graph) yields a magnitude prediction ρΛ = αΛ4 QCDa0/(4πLH) that resolves the standard 120-orders-of-magnitude cosmological constant problem at substrate level: the framework’s natural UV cutoff is ΛQCD, not the Planck scale MP, dropping the discrep- ancy to∼45 orders immediately, with the remaining closure supplied by the holographic capacitance dilution a0/LH and the Bipartite Grassmann Trace rate α. The result lands at 3.2 ×10−47 GeV4 vs observed 2.5 ×10−47 GeV4 (28% match). The framework’s strictly linear scaling ρΛ ∝ 1/LH reduces the Friedmann equation to an algebraic quadratic in E(z) = H(z)/H0, giving an exact analytical expansion history with present-day equation- of-state w0 =−1 + Ωm0/(3(1 + Ωm0)) =−0.761, matching the DESI 2024 BAO+SN central value w0 =−0.73 ±0.07 at 0.45σ. The dark sector density ratio is derived from pure graph combinatorics on the Q3 cube as ΩDE/ΩDM = E/b1 = 12/5 = 2.4, where E = 12 counts the cube’s edges (active gauge-link excitations) and b1 = 5 is the first Betti number (independent topological cycle generators); the observed ratio is 2.58, a 7% match that closes the coinci- dence problem at substrate-combinatorial level. The sterile right-handed neutrino mass is derived as the double-bulk-hop Majorana scale mνR = α2ΛQCD ≈17.7 keV, sitting cleanly in the sterile neutrino dark matter window (Tremaine–Gunn lower bound 1 keV, Lyman-αup- per bound 50 keV) and directly testable by X-ray observations of putative sterile-neutrino decay lines. One falsifiable prediction remains open: the dynamical evolution parameter wa ≈+0.26 in the framework, in tension with DESI’s preliminary central value wa ≈−0.82. Euclid Year-2 results will resolve the sign question to ±0.10 precision within three years. Five substrate-derived predictions match observation; one is sharp falsifiable test. v2.0 (2026-06-12): an in-PDF dated status/erratum note has been added reflecting the June 2026 canon audit (DRIFT/ANCHOR ledger); see the paper's status note for the specific corrections, supersessions, or upgrades.