Does the MOND acceleration scale track the Hubble rate? Testing the de Sitter-scale prediction against rotation curves at 0.3 < z < 2.5

The near-equality a0 ≈ cH0/2π between the MOND acceleration scale and the present Hubble rate has motivated horizon-based proposals for a0 that differ in a testable way: an a0 set by the instantaneous Hubble rate rises with redshift on a ΛCDM background — as H(z), or as van Putten's ω0 = (1 − q)1/2H — whereas an a0 set by the asymptotic de Sitter rate HΛ = (Λ/3)1/2 is constant (Milgrom 1999, 2020; Smolin 2017). This note tests the time dependence, not the mechanism, against two independent high-redshift rotation-curve samples. MUSE-DARK III (Ciocan et al. 2026; 79 galaxies, 0.33 < z < 1.44) reports the radial acceleration relation (RAR) scale rising from 1.99 to 2.71 × 10−10 m s−2; refitting their four bins with the local value as a prior gives a0 ∝ H(z)n with n = 0.80 [0.68, 0.93] — evolution present, but slower than H(z) (1.6σ) and dependent on the z = 0 anchor. RC100 (Nestor Shachar et al. 2023; 100 massive galaxies, 0.6 < z < 2.5) allows an anchor-free internal test: the fitted ratio a0(z ≈ 2.2)/a0(z ≈ 0.8) is 0.74–0.93 (×/÷ ≈1.25) for three interpolating functions, against 2.05 for a0 ∝ H(z) in flat ΛCDM (excluded at 4.0–4.3σ, statistical; 4.4–4.5σ by an unbinned likelihood-ratio test) and 1.66 for ω0 in ΛCDM (2.9–3.4σ). On the non-ΛCDM background stated in van Putten (2017b), with its baryonic ωm, the ω0 law predicts only 1.07 between these redshifts and is not excluded by the ratio — but that background implies q0 = −1.86 and a present-day a0 of 1.8–1.9 × 10−10, 1–2.4σ from the q0 ≈ −1 and a0 ≈ 1.63 × 10−10 he reports; with ωm ≈ 0.3, which reproduces those, the law predicts 1.91 and is excluded at 3.7–4.0σ. (These exclusion levels use a Gaussian extrapolation of the 68% profile intervals; the unbinned likelihood-ratio test is run for the H(z) law only.) a0 ∝ H(z) would require a median dark-matter fraction fDM(< Re) of 0.36–0.55 at z ≈ 2.2 where 0.27 is observed. The main systematic — the pressure-support correction, which is 2.6× larger at z ≈ 2.2 — is tested inside RC100: residuals from the relation show no dependence on (σ0/Vc)2 once redshift is controlled (< 0.5σ), and the H(z) law is still excluded at 2.7–3.9σ using only the half of the high-redshift bin with the weakest corrections. A time-constant a0 is consistent with RC100 for all three functions (0.3–1.3σ); every fitted evolution index is negative (n = −0.3 to −0.6), with n = 0 disfavoured at only 1.0–1.8σ. The absolute normalization of a transition-regime sample is interpolating-function dependent at the factor ≈2 level, and the z = 0 SPARC scale spans 0.98–1.62 × 10−10 m s−2 across functions and estimators, so cross-sample comparisons of a0 are not yet decisive. Current high-redshift rotation-curve data do not support an acceleration scale that rises with the Hubble rate; an a0 constant in time is consistent with the massive-galaxy sample to z ≈ 2.2, but is excluded by the MUSE-DARK bins unless their evolution is a modeling effect. Paper 11 of an independent research series. The accompanying archive contains every script, input table and log needed to regenerate each number in the note; see README.md inside it.