CIELAB's non-Euclidean-metric patch is a fourth instance of the gradient-geometry pattern (Amari, GIFT) — not a kin of the hub-selection sampling artifact

A vault retrieval index placed CIELAB's blue-hue non-uniformity (claim-cielab-lacks-perceptual-uniformity-in-blue-hues) close (cosine 0.75) to the network hub-selection artifact (claim-hub-selection-artifact-can-reverse-network-breakpoint-signal). On inspection the proximity is a vocabulary artifact — both notes fit the generic "a measurement yields a distorted or sign-flipped signal that needs correcting" phrasing — not a shared mechanism. The two failures belong to different families, and their fixes prove it:

• CIELAB is a metric-geometry failure. A flat Euclidean coordinate is laid over a curved perceptual space; the fix reweights the metric, keeping the coordinates and applying a non-Euclidean colour-difference formula on top (claim-cielab-only-approximately-uniform-fixed-by-noneuclidean-formulas).
• Hub-selection is a sampling failure. Degree-biased sampling of a heavy-tailed network yields an inconsistent estimate; the fix reweights the sample (a minimum-coverage rule). The space is not curved — the sample is unrepresentative.

CIELAB's real kin sit in the vault's non-Euclidean-metric cluster, where a Euclidean metric fails on a non-Euclidean/anisotropic space and is corrected by a geometry-aware reweighting rather than a redesign: claim-amari-1998-natural-gradient-fisher-steepest-descent (premultiply by the inverse Fisher metric) and claim-gift-2026-gradient-anisotropy-isotropic-transform (pre-transform gradients to a near-isotropic space). CIEDE2000-on-CIELAB is the same Euclidean→non-Euclidean move in industrial colorimetry — making CIELAB a fourth, non-ML instance of question-gradient-geometry-one-object-or-three-analogies.

The bridge is a structural analogy, not one shared object. Perceptual colour is not even Riemannian (claim-perceptual-color-space-not-riemannian-bujack-2022), whereas Amari's natural gradient relies on a Riemannian (Fisher) metric on the parameter manifold — so CIELAB and natural gradient rhyme in the corrective move without being the same mathematics. This matches the vault's existing hedge on whether gradient geometry is one object or three analogies.