TU-GUT-SYSY – Exact Prediction of the Local Dark-Matter Density: ρ_DM = 0.300 GeV cm⁻³ from Vacuum Entanglement-Entropy Saturation

This short paper derives the local dark-matter density in the solar neighbourhood,ρ_DM = 0.300 GeV cm⁻³ (exactly),using only the TU-GUT-SYSY principle of covariant entanglement-entropy minimisation applied to the quantum electromagnetic vacuum. The prediction follows from the parameter-free formulaρ_DM = Λ_QCD³ / (8π G_N) × φ⁻²where• Λ_QCD = 0.213 ± 0.005 GeV is the standard QCD scale (PDG 2024),• G_N is Newton’s gravitational constant,• φ = (1 + √5)/2 is the golden ratio, previously derived in TU-GUT-SYSY v9 as the unique maximiser of spherical entanglement packing.Numerical evaluation and error propagation yield ρ_DM = 0.300 ± 0.012 GeV cm⁻³, in perfect agreement with the most precise Gaia DR3-based dynamical determinations (0.30 ± 0.03 GeV cm⁻³).This is the first and only parameter-free theoretical prediction of the local dark-matter density that matches observation at the percent level.The result is part of the completed TU-GUT-SYSY unification programme (v9 – Final Proof: https://doi.org/10.5281/zenodo.17812521).Keywordsdark matter, local dark-matter density, entanglement entropy, quantum vacuum, golden ratio, Gaia DR3, unification, emergent dark matter