Supernova Hubble Diagram — 2D Standard-Candle Fit

This 2D companion to the Supernova Light-Curve Time Dilation sim swaps the flashing-supernova animation for the actual observational method that revealed dark energy: a Hubble diagram of distance modulus versus redshift. Sixty synthetic Type Ia supernovae are drawn from a true flat-ΛCDM cosmology with realistic magnitude scatter, then held fixed while you search for the matter density Ω_m and Hubble constant H₀ that explain them — the running χ² tells you, numerically, how good your fit is, and a live sweep plot shows the true minimum. A tired-light overlay reproduces the historical rival hypothesis so you can see, in the same units, exactly how much worse it fits. Clicking any point reveals that individual supernova's light curve stretched by (1+z), tying the population-level Hubble diagram back to the single-object time-dilation effect.