udg_density_contrast
udg_density_contrast assigns the fixed value 0.05 to the density contrast δρ/ρ for ultra-diffuse galaxies in low-density regions. Modelers of galaxy formation within Recognition Science cite it when tracing how substrate coherence varies to yield both DM-rich and DM-poor UDGs. The definition is a direct real-number assignment that downstream results unfold to confirm the bound below 0.1.
claimThe density contrast for ultra-diffuse galaxy formation is given by $δρ/ρ = 0.05$.
background
Recognition Science treats dark matter as substrate distributed according to recognition coherence rather than as particles. The EA-011 module examines ultra-diffuse galaxies with surface brightness μ_V > 24 mag/arcsec² and effective radii 1-10 kpc, noting that Dragonfly 44 shows high DM-to-stellar ratios while NGC 1052-DF2 shows low ratios. Low-density environments produce spatially varying coherence that accounts for this diversity without requiring exotic particle halos. The upstream density definition supplies mass scales as powers of phi, the self-similar fixed point from the forcing chain, and is imported here to anchor environmental scaling.
proof idea
The definition is a direct numerical assignment of the constant 0.05. No lemmas or tactics are invoked; the value stands as a fixed parameter for later unfolding in inequality checks.
why it matters in Recognition Science
This definition supplies the numerical input to the low_density_environment theorem, which unfolds it to obtain udg_density_contrast < 0.1 and concludes that formation environment modulates substrate coherence. It occupies the EA-011.8 slot in the ultra-diffuse galaxies analysis, connecting the substrate model to the ILG derivation for rotation curves. The placement closes the loop from low-density formation to observed UDG diversity within the Recognition Science framework.
scope and limits
- Does not derive the numerical value 0.05 from the forcing chain or Recognition Composition Law.
- Does not express dependence on phi-ladder rungs or gap(Z).
- Does not apply to high-density galactic cores or cluster environments.
- Does not predict individual galaxy masses, sizes, or globular cluster counts.
formal statement (Lean)
152noncomputable def udg_density_contrast : ℝ := 0.05
proof body
Definition body.
153
154/-- **THEOREM EA-011.8**: UDGs in low-density regions.
155 Formation environment affects coherence. -/