paper2_median_chi2
The definition records the median chi-squared per degree of freedom value of 2.75 reported for the ILG rotation curve model on the SPARC Q=1 subset. Galaxy dynamics researchers comparing zero-parameter predictions against observational data would reference this benchmark when evaluating control tests such as velocity permutations. The entry is supplied as a constant definition drawn from the cited paper.
claimThe median value of $chi^2 / N$ for the ILG model fitted to the SPARC galaxy sample with zero free parameters is $2.75$.
background
SPARC denotes the sample of spiral galaxies with high-quality rotation curve data. ILG is the Indisputable Logic Gravity model whose parameters (alpha_t, C_lag, Upsilon_star) are locked to the golden ratio phi with no per-galaxy adjustments. The chi-squared statistic sums squared residuals between observed and predicted velocities, normalized per degree of freedom, as defined upstream by the sum-of-squares function on a list of species entries.
proof idea
The definition is a direct numerical assignment of the constant 2.75 taken from the external paper report. No lemmas are applied; it serves as a reference value for subsequent control comparisons.
why it matters in Recognition Science
This constant anchors the falsification tests in the SPARC module. It is used by the gas-stars swap, rotation 180, and velocity permutation controls to verify that any deviation inflates the chi-squared above the reported ILG median. The entry implements the specific RS prediction of median chi2/dof ~2.75 under phi-locked parameters, closing the loop from the forcing chain to observable galaxy dynamics.
scope and limits
- Does not compute the chi-squared from raw velocity data.
- Does not vary with galaxy selection or Q-value cuts.
- Does not incorporate systematic error estimates beyond the reported median.
- Does not claim to be the exact theoretical prediction, only the paper-reported value.
Lean usage
def velocity_permutation_control (chi2_perm : ℝ) : Prop := paper2_median_chi2 < chi2_permformal statement (Lean)
110def paper2_median_chi2 : ℝ := 2.75
proof body
Definition body.
111
112/-- Paper II reports ILG mean chi2/N = 4.23 on SPARC Q=1 subset. -/