The MOND acceleration scale as a de Sitter curvature scale
One claim: the acceleration scale of the mass-discrepancy–acceleration relation is set by the dark-energy density.
8 September 2026 — the parameter region is non-empty, and the theory is written down
A search over 666,082,872 grid points per acceleration footing finds, for the first time in this programme, a non-empty admissible region for a covariant action built on a preferred foliation: general relativity’s metric sector exactly, a khronometric clock scalar, and a MOND scalar carrying a coherence operator. An explicit point passes all eleven gates on both footings. Earlier sweeps returned zero points; the entire difference is that the scalar condensate is removed, which satisfies the clock-tachyon gate identically and costs nothing, the condensate having been 10⁵× too small to be the dark sector.
It reproduces Milgrom’s law at the action’s own a₀ with coefficient exactly 1.000000, with Φ = Ψ to better than 10⁻⁴ out to 1 Mpc, so lensing and dynamics share one potential with nothing fitted to make them do so — and it passes Cassini, the Saturn phantom-mass bound, the preferred-frame parameters, the tensor speed exactly, well-posedness, Cherenkov and causality.
Above a galaxy it fails, and for one reason: curing the single fatal instability required deleting the only dark component. It is short in mass at R₅₀₀ by 1.49–1.99× in lensing and dynamics alike, wrong by 9σ in the shape of ΔΣ, and over its own parameter-free ceiling by 5.2× in cluster cores. A complete theory of gravity below the galaxy scale; an incomplete theory of the universe above it. κ remains fitted, not derived (DOI 10.5281/zenodo.22667688).
Realised as modified gravity — the modified-inertia arm was closed by lensing in August 2026 — with the Milgrom–Sanders (2008) kernel ν(y) = 1/(1 − e^(−√y)) as the operative interpolation. κ = ½ is fitted, not derived: measured 0.551 ± 0.043 (distance-free) and 0.465 ± 0.076 (Tully–Fisher) — and, as of 6 September 2026, proven underivable by the programme’s own covariant action: the MOND primitive enters the field equations only through its derivative and the cosmological background only through Λ + (2 − K_B) J(0)/2, a normalisation zero mode (DOI 10.5281/zenodo.22559892). The one coefficient-free alternative, the horizon form a₀ = c²/(2π L_dS) with κ = 0.461, is 8.5% away and exactly degenerate with the H₀ tension: κ = ½ on Planck’s H₀ and κ = 0.461 on SH0ES’s predict the same a₀ to 0.2%. Because a₀ tracks the dark-energy density it cannot track the expansion rate: a₀(z)/a₀(0) = √(ρ_DE(z)/ρ_DE(0)) exactly, which is flat if Λ is constant, 13% lower by z = 2 on DESI’s w₀wₐ fit, and within ±20% of today’s value out to z = 3 for any dark energy the data allow — against ×3 for a₀ ∝ H(z) and ×1.8 for ΛCDM’s emergent scale. That is the one statement here that ΛCDM does not make.
Attribution — what is and is not original here
This law is not new, and neither is its derivation. Milgrom (1999, Phys. Lett. A 253, 273, Eqs. 6–9) derives this exact law from the de Sitter–Unruh balance and fixes its coefficient at a₀ = 2 c H_Λ. His Eq. (9) is identically the relation above — verified symbolically, difference exactly zero. The same law was independently re-derived entropically by Pikhitsa (2010) and Klinkhamer & Kopp (2011), both also landing on 2 c H_Λ.
So the de Sitter–Unruh argument does not leave the coefficient free — it predicts one, and that prediction is 11.58× the value used here. What this programme actually contributes is therefore narrow and should be stated as such: a re-normalisation of the coefficient to fit data (κ = ½ in place of Milgrom’s 2), plus the relativistic completion — the scale embedded in Aether–Scalar–Tensor theory — and its derived a₀(z). It is not a derivation of the law, and not a derivation of its scale.