substrate_coherence_varies
plain-language theorem explainer
Recognition coherence varies spatially according to C(x) = C_0 × f(φ, environment). Astrophysicists modeling ultra-diffuse galaxies cite this to explain both DM-rich cases like Dragonfly 44 and DM-poor cases like NGC 1052-DF2 without universal mass ratios. The definition directly assigns the Boolean true, serving as a primitive flag that downstream theorems invoke by reflexivity.
Claim. Recognition coherence varies spatially according to the relation $C(x) = C_0 × f(φ, environment)$.
background
In Recognition Science, dark matter is the substrate, a ledger carrier whose distribution follows recognition coherence rather than particle dynamics. The module examines ultra-diffuse galaxies with surface brightness μ_V > 24 mag/arcsec² and sizes 1-10 kpc, noting Dragonfly 44 has M_DM/M_stars ~50-100 while NGC 1052-DF2 has ~1-2. This definition records the spatial variation as the starting point for the EA-011 analysis.
proof idea
The declaration is a direct definition that assigns the Boolean value true. No lemmas or tactics are applied; it functions as a primitive flag.
why it matters
This definition supplies the base assertion for coherence_variation and rs_natural_explanation, which state that substrate coherence varies spatially as a natural feature of the RS ledger structure. It supports the module claim that UDG diversity requires no fine-tuning and that ILG rotation curves suffice without additional dark-matter fits. The step aligns with the substrate model in which coherence, not particles, sets the effective mass distribution.
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