tight_threshold
plain-language theorem explainer
The tight threshold sets the refutation cutoff at 3.0 for median chi-squared per degree of freedom in SPARC galaxy rotation-curve fits under the phi-locked ILG model. Researchers comparing Recognition Science predictions to observational data would cite this constant to decide whether the expected median near 2.75 has been exceeded. The declaration is a direct real-number assignment with no further computation.
Claim. The tight threshold is the real number $3.0$ such that a median chi-squared per degree of freedom exceeding $3.0$ refutes the specific RS prediction for ILG rotation curves (while the broader framework may remain viable with adjusted parameters).
background
The SPARC Chi-Squared Falsifier module formalizes a test for the ILG rotation-curve model that uses zero per-galaxy free parameters. All constants are locked to phi-derived values: alpha_t = (1 - 1/phi)/2, C_lag = phi^{-5}, Upsilon_star = phi. For each of the ~175 SPARC galaxies the model produces a predicted curve, chi-squared per degree of freedom is evaluated, and the median across the sample is compared with the threshold. The upstream chi2 definition simply sums squared residuals over a list of species entries.
proof idea
One-line definition that directly assigns the constant 3.0.
why it matters
This constant supplies the cutoff used by RS_prediction_refuted to test the Recognition Science claim that the median chi2/dof should lie near 2.75. It implements the tight falsification criterion described in the module documentation and thereby connects the phi-derived parameters (alpha_t, C_lag, Upsilon_star) to an empirical decision rule. The definition closes one link in the falsification protocol that begins from the eight-tick octave and the Recognition Composition Law.
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