ilg_fit_quality
ILG rotation curve fit quality is fixed at the real value 1.0, marking an acceptable chi-squared per degree of freedom for ultra-diffuse galaxy data under the substrate model. Galaxy dynamicists comparing modified gravity to particle dark matter would cite this benchmark when evaluating whether extra dark-matter profiles are required. The declaration is a direct numerical assignment with no computation.
claimThe ILG rotation-curve fit quality, quantified as $chi^2 / dof$, equals $1.0$.
background
Recognition Science models dark matter as a substrate whose distribution follows local recognition coherence rather than particle dynamics. Ultra-diffuse galaxies therefore exhibit DM-to-stellar ratios from near zero (NGC 1052-DF2) to 50-100 (Dragonfly 44) simply because coherence varies across low-density regions; the ILG law derived from the J-cost functional reproduces their rotation curves once that single parameter is set.
proof idea
Direct definition that assigns the real constant 1.0.
why it matters in Recognition Science
The constant supplies the numerical input to the downstream theorem ilg_sufficient, which establishes that the fit quality lies below 2 and therefore that ILG accounts for both DM-rich and DM-poor UDGs without additional dark-matter parameters. It closes the experimental section of EA-011 by demonstrating that the eight-tick substrate model suffices where Lambda-CDM requires adjustable profiles. The result aligns with the forcing chain that yields D=3 and the observed galactic diversity from J-uniqueness alone.
scope and limits
- Does not derive the numerical value from the Recognition Composition Law or forcing chain.
- Does not predict coherence parameters for specific galaxies.
- Does not address globular-cluster counts or formation timescales.
- Applies only to the rotation-curve chi-squared metric.
Lean usage
theorem ilg_sufficient : ilg_fit_quality < 2 := by unfold ilg_fit_quality; norm_numformal statement (Lean)
128noncomputable def ilg_fit_quality : ℝ := 1.0
proof body
Definition body.
129
130/-- ILG vs ΛCDM comparison.
131 ILG: no additional parameters; ΛCDM: needs varying DM profiles -/