df2_dm_ratio
NGC 1052-DF2 receives the assigned dark-matter-to-stellar-mass ratio of 1.5. Researchers modeling ultra-diffuse galaxies under a substrate interpretation of dark matter cite this constant when contrasting DM-poor and DM-rich cases. The definition is a direct numerical assignment with no lemmas or reduction steps.
claimLet $r$ denote the dark-matter-to-stellar-mass ratio for NGC 1052-DF2. Then $r = 1.5$.
background
Recognition Science treats dark matter as a substrate whose distribution follows recognition coherence rather than particle dynamics. The module examines ultra-diffuse galaxies that show both high and low dark-matter content, with surface brightness below 24 mag/arcsec² and effective radii of 1-10 kpc. NGC 1052-DF2 is presented as the DM-poor example with ratio near 1-2, while Dragonfly 44 is the DM-rich counterpart.
proof idea
Direct definition that assigns the real number 1.5. No upstream lemmas are invoked and no tactics are executed.
why it matters in Recognition Science
The definition supplies the concrete input for theorems ngc1052df2_dm_poor, no_universal_ratio, standard_models_challenged, and udg_diversity_real. It anchors the EA-011 claim that spatially varying substrate coherence accounts for UDG diversity without requiring a universal mass ratio, thereby challenging ΛCDM uniformity predictions.
scope and limits
- Does not derive the numerical value from Recognition Science equations.
- Does not report measurement uncertainty or observational source.
- Does not apply the ratio to galaxies outside the UDG class.
- Does not claim the value is exact rather than representative.
Lean usage
theorem ngc1052df2_dm_poor : df2_dm_ratio < 3 := by unfold df2_dm_ratio; norm_numformal statement (Lean)
72noncomputable def df2_dm_ratio : ℝ := 1.5
proof body
Definition body.
73
74/-- Typical UDG surface brightness (mag/arcsec²).
75 Value: μ_V > 24 -/