upsilon_locked
Upsilon_locked assigns the stellar mass-to-light ratio the value of the golden ratio phi. Modelers fitting ILG rotation curves to the SPARC sample cite it to enforce zero per-galaxy free parameters. The definition is a direct noncomputable assignment drawn from the imported phi constant.
claimThe stellar mass-to-light ratio satisfies $U_∗ = ϕ$.
background
The SPARC Chi-Squared Falsifier module formalizes a zero-parameter test of the ILG rotation-curve model against the SPARC galaxy sample. All constants are required to be locked to phi: alpha_t = (1 − 1/phi)/2, C_lag = phi^(−5), and Upsilon_star = phi. This definition supplies the locked value for the mass-to-light ratio Upsilon_star.
proof idea
One-line definition that directly assigns the imported constant phi.
why it matters in Recognition Science
The definition supplies the Upsilon_star entry required by GlobalOnlyPolicy and SPARCFalsifierCert. Those structures certify that the ILG model uses only catalog-level phi-derived constants and zero per-galaxy parameters when computing median chi-squared per degree of freedom. It therefore implements the RS-native locking of constants to phi for the falsification protocol described in the module documentation.
scope and limits
- Does not compute any chi-squared values or median statistics.
- Does not reference observed rotation velocities or photometric profiles.
- Does not introduce or depend on per-galaxy free parameters.
- Does not evaluate falsification thresholds or pass/fail criteria.
formal statement (Lean)
76noncomputable def upsilon_locked : ℝ := phi
proof body
Definition body.
77
78/-- The lag coupling is locked to phi^(-5) ≈ 0.090. -/