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def definition def or abbrev high

high_coherence_dm_rich

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The definition marks high-coherence regions as dark-matter rich, corresponding to strong substrate coupling in the Recognition Science substrate model of ultra-diffuse galaxies. Galaxy-formation researchers working within the coherence-variation framework cite this marker when classifying populations such as Dragonfly 44. It is realized as a direct Boolean constant with no computation or lemmas.

claimIn the Recognition Science analysis of ultra-diffuse galaxies, the high-coherence regime is defined to be dark-matter rich: $C_ {rm high} $ implies strong substrate coupling and $M_{rm DM}/M_{rm stars} gg 1$.

background

The module treats dark matter as the substrate whose distribution is set by recognition coherence rather than particle dynamics. High-coherence patches yield DM-rich ultra-diffuse galaxies while low-coherence patches yield DM-poor examples, removing any need for a universal mass ratio. Surface-brightness and size ranges are taken directly from the listed experimental values, and rotation curves are described by the ILG derivation in both regimes.

proof idea

The declaration is a simple definition that binds the Boolean value true to the high-coherence DM-rich indicator. No tactics or upstream lemmas are applied; the body consists solely of the constant true.

why it matters in Recognition Science

This marker supplies the affirmative case required to show that UDG diversity follows from spatially varying substrate coherence. It supports the module verdict that both DM-rich and DM-poor systems arise naturally without exotic particle distributions, completing the classification pair inside the experimental analysis that connects ILG to observed rotation curves.

scope and limits

formal statement (Lean)

 108def high_coherence_dm_rich : Bool := true

proof body

Definition body.

 109
 110/-- Low coherence region: DM-poor.
 111    C_low → weak substrate coupling -/