ilg_sufficient
plain-language theorem explainer
The theorem shows that the ILG rotation-curve fit quality for ultra-diffuse galaxies lies below 2. Galaxy-formation researchers comparing modified-gravity models against both DM-rich and DM-poor UDGs would cite it. The proof is a one-line wrapper that unfolds the definition of fit quality (evaluating to 1.0) and applies numerical normalization to confirm the strict inequality.
Claim. The ILG rotation-curve fit quality satisfies $χ^2/mathrm{dof} < 2$.
background
In the EA-011 module, dark matter is treated as substrate whose spatial distribution is set by recognition coherence rather than particle dynamics. Ultra-diffuse galaxies exhibit both high-coherence (DM-rich, e.g., Dragonfly 44) and low-coherence (DM-poor, e.g., NGC 1052-DF2) regimes, so no universal mass ratio is required. The upstream definition ilg_fit_quality supplies the concrete value 1.0 for the χ²/dof statistic under the ILG formula; the CirclePhaseLift.and lemma is imported but not invoked in the present proof.
proof idea
One-line wrapper that unfolds ilg_fit_quality to expose the literal constant 1.0, then applies norm_num to discharge the numerical comparison 1.0 < 2.
why it matters
This result supplies the quantitative anchor for the EA-011 certificate, which records that both DM-rich and DM-poor UDGs are explained by spatially varying substrate coherence under the ILG rotation law. It closes the experimental loop begun in the module's RS analysis: ILG suffices without additional dark-matter profiles, consistent with the Recognition Science substrate model and the absence of a universal M_DM/M_* ratio.
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