DENS — the Density–ENergy of Space: the galactic acceleration scale a₀ = A√ρ, from SPARC rotation curves to the measured a₀(z)

The MOND acceleration scale a₀ is usually treated as a universal constant of nature, bolted onto Newtonian dynamics by hand. Here it is read instead as a direct observable of the local medium: a₀ = A√ρ, where ρ is the energy density of the vacuum at a given place. This is the central reading of DENS — the Density–ENergy of Space — the energy-first framework set out in full in a companion paper; its name carries its thesis, that space has an energy and that what gravitates is the density of that energy. Read this way, two facts that look unrelated become one. First, on the real sky the radial-acceleration relation (RAR) of 153 SPARC galaxies is reproduced by a derived, shape-parameter-free interpolation, g_obs = √(g_bar² + g_bar·a₀), at an intrinsic scatter (σ_int ≈ 0.053 dex) indistinguishable from the fitted MOND interpolation (0.052) and matching the published value (~0.057) — with one fewer free parameter. Second, the first measured redshift evolution of a₀ (MUSE-DARK III, a ~30σ rise) becomes, through a₀ = A√ρ, a direct reading of the vacuum energy density of each place: ρ(place)/ρ(here) = [a₀(place)/a₀(here)]², with no cosmic epoch assumed. The rise rules out a constant a₀ — and so rules out standard MOND — at ~30σ; the data's own authors note it climbs "faster than H(z)," which is exactly where a pure a₀ = cH(z)/2π reading is too shallow and a density reading is not. In this frame the dark sector is not two substances but two faces of one medium energy: dark energy the vacuum's own even level, dark matter the medium's gravitational gathering of energy on energy. One debt is stated openly rather than hidden: the exact steepness of the a₀(z) climb (observed ρ ∝ (1+z)^2.5) is set by how the medium's free energy and its trapped energy (matter) concentrate — a weight not yet derived from first principles. We hold the incumbent and this reading to one bar throughout: where they diverge is a prediction to be tested, not a result to be claimed.