coherence_variation
Substrate coherence is asserted to vary spatially as a modeling premise in the Recognition Science account of ultra-diffuse galaxies. Galaxy-formation researchers working inside the RS ledger framework cite the result to explain both DM-rich (Dragonfly 44) and DM-poor (NGC 1052-DF2) cases without a universal mass ratio. The proof is a one-line reflexivity step on the boolean definition of spatial variation.
claimIn the Recognition Science substrate model the coherence function satisfies $C(x)=C_0 f(phi,environment)$ and is taken to hold as the boolean predicate substrate_coherence_varies = true.
background
The EA-011 module treats dark matter as the recognition substrate distributed by ledger coherence rather than by particle dynamics. The upstream definition substrate_coherence_varies encodes the statement that recognition coherence varies spatially according to $C(x)=C_0 times f(phi,environment)$, with high-coherence regions producing strong substrate coupling. This rests on the DomainBootstrap.required structure, which supplies the minimal conditions needed to state environmental dependence inside the ledger.
proof idea
The proof is a one-line term-mode wrapper that applies reflexivity to the boolean definition substrate_coherence_varies.
why it matters in Recognition Science
The result supplies the spatial-variation premise for the EA-011 certificate and is invoked directly by the rs_natural_explanation theorem. It fills the EA-011.4 slot in the module, confirming that no universal DM-to-stars ratio is required once coherence is allowed to vary with the ledger environment, consistent with the Recognition Science forcing chain.
scope and limits
- Does not derive the explicit functional form of $C(x)$ from the Recognition Composition Law.
- Does not supply numerical coherence values for any specific galaxy.
- Does not constrain the spatial scale of coherence variation against observations.
Lean usage
theorem rs_natural_explanation : substrate_coherence_varies = true := coherence_variationformal statement (Lean)
116theorem coherence_variation : substrate_coherence_varies = true := rfl
proof body
Term-mode proof.
117
118/-- **THEOREM EA-011.5**: No universal DM-to-stars ratio required.
119 Coherence varies continuously. -/