paper2_mean_chi2
plain-language theorem explainer
paper2_mean_chi2 supplies the constant 4.23 as the mean chi-squared per degree of freedom for the ILG model on the SPARC Q=1 galaxy sample from Paper II. Galaxy dynamics researchers comparing Recognition Science predictions to MOND would reference this value when assessing model performance under zero free parameters. The definition is a direct numerical assignment with no computation.
Claim. The reported mean value of chi-squared per degree of freedom for the ILG rotation-curve model on the SPARC Q=1 sample equals 4.23.
background
The SPARC Chi-Squared Falsifier module formalizes the test for the ILG rotation curve model. Parameters are locked from the golden ratio: alpha_t = (1 - 1/phi)/2 approx 0.191, C_lag = phi^(-5) approx 0.090, Upsilon_star = phi approx 1.618. The protocol applies these to approximately 175 SPARC galaxies with zero per-galaxy free parameters, computes chi-squared per degree of freedom for each, and checks the median against thresholds of 5.0 (generous) or 3.0 (tight). This definition provides the mean chi-squared value reported in Paper II for the Q=1 subset.
proof idea
The declaration is a direct definition that assigns the numerical constant 4.23. No tactics or lemmas are invoked beyond the assignment itself.
why it matters
This value anchors the falsification certificate in SPARCFalsifierCert, which demands that control tests inflate chi-squared above the ILG result. It appears in the theorem ilg_better_mean_than_mond demonstrating that ILG achieves a lower mean chi-squared than MOND under the global-only policy. Within the Recognition Science framework, it supplies the empirical input for testing the phi-locked gravity predictions against SPARC data.
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