G's parameter-free a₀, against real galaxies

Pick a galaxy from the SPARC survey. The dark curve is what was measured. The red curve is what Newtonian gravity predicts from the visible matter alone — it falls short. The green curve adds no dark matter and fits nothing: it applies the MOND relation built on G's derived a₀ = C_S²·cH₀/(2π) ≈ 1.19×10⁻¹⁰ m/s², a number that never saw a galaxy. The picker is a curated 24-galaxy subset of the survey — dwarfs to giants, gas- to bulge-dominated, noisy curves deliberately included — kept small so the page stays light; the self-verifying proof runs all 175. Everything here runs on your machine; the physics is the same code.

Galaxy (curated 24 of 175 SPARC)

H₀ (km/s/Mpc) — moves a₀

Interpolating function

observed Newtonian (baryons) MOND · G's a₀

Rotation curve — velocity vs radius

this galaxy RAR · G's a₀ 1:1 (Newtonian)

Radial acceleration relation — g_obs vs g_bar (log g)

What you're looking at

The mass-to-light ratios are fixed (Υ_disk=0.5, Υ_bulge=0.7, the standard SPARC values) — nothing is tuned per galaxy. Drag H₀ and watch a₀ move with it: that coupling is the framework's sharpest falsifiable claim — if a₀ were shown independent of H₀, the derivation dies.

Honest limits

This is consistency, not proof — it shows G's a₀ is the same floor MOND already fits; it doesn't prove the derivation is right physics.
The picker holds 24 of the 175 galaxies — a curated spread from dwarfs to giants, ordered by measured V_max, noisy curves deliberately included — so the page stays light. The proof runs all 175: raw scatter 0.199 dex over 3,389 points with no quality cuts at all; 0.144 dex under the survey's own published velocity-error cut (robust σ ≈ 0.12 — the published ~0.11–0.13 band).
The RAR interpolating function is an empirical fit; swapping it (try the μ selector) shifts the green curve slightly. a₀ is what's under test, not the fitting form.

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