The galactic acceleration scale and the cosmological constant: the coefficient on SPARC, and what it takes to measure its redshift evolution

Preprint (Author's Original Version): submitted to Monthly Notices of the Royal Astronomical Society; not peer reviewed. This is the version as submitted, posted under the publisher's self-archiving policy for the author's original version. If the paper is accepted, this record will be updated with the journal DOI. The galactic acceleration scale a0 is close to c sqrt(G rho_Lambda), built from c, G and the density of the cosmological constant. We write a0 = kappa c sqrt(G rho_Lambda), measure kappa and ask what testing its evolution requires. On SPARC, with distances and rho_Lambda on one H0, three estimators give kappa = 0.45 +- 0.07, 0.58 +- 0.18 and 0.43 +- 0.08. The value 1/2 is consistent with all three, as are Milgrom's c H_Lambda / 2pi and c H0 / 2pi; on the critical density it lies 2.1-2.2 sigma from two, and a published joint inference puts it at 2.6 sigma. The coefficient is fitted, degenerate with H0 and set by the stellar mass-to-light zero point. A Lambda-anchored scale is constant; one tied to the critical density grows as H(z) (+0.58 dex at z = 2.5); LCDM haloes of low-acceleration discs give +0.22 dex. Existing samples decide nothing. With stellar-population masses plus scaling-relation gas, the baryons exceed the dynamics in 41 of 100 discs at 0.6 < z < 2.5 (half of those at z > 2), so this route measures the baryon calibration, not a0. The MUSE-DARK rise at z ~ 1 is not recovered with these masses, though which masses are biased is unknown; a lean towards a0 proportional to H(z) at z ~ 1.5 turns on unmeasured gas and pressure support. Inferring a0 amplifies errors unless g_bar < 0.3 a0. Expected odds of 20:1 need about eight lensed discs at z ~ 2.5 measured to 0.20 dex if the baryonic-mass calibration is exact, 20 or 34 if it is shared to 0.05 or 0.06 dex; no gas tracer yet provides that. Every quantitative statement is produced by a public script whose checks can fail (paper_numbers.py and reproduce_all.sh in the linked repository, at the tag of the submitted version). Generative AI tools assisted with code, literature checks, table transcription and drafting (Anthropic's Claude, and models from OpenAI, DeepSeek, Zhipu AI, Alibaba, Google, Tencent, Moonshot AI and xAI); the author checked every result and takes sole responsibility for the content.