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

Abstract

A retained historical dark-sector cosmology record from an earlier phase of the programme (v2, May 2026, with supersession notes added June and July 2026), published here as its citable version of record. It derives five cosmological observables from the Z₃ ⊗ Q₃ discrete substrate on the 4.8.8 Archimedean tiling with zero free parameters once the substrate constants (Λ_QCD, α, a₀) and cosmological inputs are anchored: a cosmological-constant magnitude ρ_Λ = αΛ⁴_QCD·a₀/(4πL_H) that attacks the 120-orders problem at substrate level by taking Λ_QCD (not the Planck scale) as the natural UV cutoff — landing at 3.2×10⁻⁴⁷ GeV⁴ vs observed 2.5×10⁻⁴⁷, a 28% match; a present-day equation of state w₀ = −0.761 matching the DESI 2024 BAO+SN central value at 0.45σ; a dark-energy/dark-matter density ratio Ω_DE/Ω_DM = E/b₁ = 12/5 = 2.4 from pure graph combinatorics on the Q₃ cube (12 edges over first Betti number 5; observed 2.58); and a sterile right-handed neutrino mass m_νR = α²Λ_QCD ≈ 17.7 keV in the sterile-dark-matter window. Its headline cosmology is explicitly superseded: a prominent canon note marks the original fluid-coupled equation of state, the horizon-input dark-energy magnitude, the 12/5 ratio, and the fixed 80/20 composition as no longer current canon — replaced by the consolidated cosmology, dark-sector, defect-network, and falsification papers — and the 29 June rational dark-energy law w(a) = −1 + a/28 is likewise killed internally and kept only as a frozen reopen record. The current dark-sector frontier is instead the zero-mode/R4 reservoir with its CMB/halo/lensing readout, with K04 debris pinned as a fossil relic rather than the mobile cold halo; the 17.7 keV sterile-ν_R branch remains a named testable component but not a complete budget by itself.

Keywords

How to cite

Elliman, D. (2026). The Dark Sector from a Discrete Substrate: Cosmological Constant Resolution, Sterile Neutrino Mass, and the Coincidence Problem from Z3 ⊗Q3. Neuro-Symbolic Ltd technical report. https://doi.org/10.5281/zenodo.21251784

@techreport{elliman2026darksectorcosmology,
  author      = {Elliman, David},
  title       = {The Dark Sector from a Discrete Substrate: Cosmological Constant Resolution, Sterile Neutrino Mass, and the Coincidence Problem from Z3 ⊗Q3},
  institution = {Neuro-Symbolic Ltd},
  year        = {2026},
  doi         = {10.5281/zenodo.21251784},
  url         = {https://neusym.ai/papers/dark_sector_cosmology}
}