Urban, Rosen, Berns & Schleicher (2007) is reported to state that non-Euclidean CIELAB-based color-difference spaces have regions of nonzero Gaussian curvature obstructing isometric embedding — not yet quote-verified against the primary

Philipp Urban, Mitchell R. Rosen, Roy S. Berns, and Dierk Schleicher published "Embedding non-Euclidean color spaces into Euclidean color spaces with minimal isometric disagreement" in the Journal of the Optical Society of America A, volume 24, issue 6, pages 1516–1528 (2007). The paper examines three CIELAB-based color-difference formulas — CMC, CIE94, and CIEDE2000 — as non-Euclidean metric spaces. Multiple independent search-and-fetch passes on the publisher's own abstract page (opg.optica.org) consistently returned language to the effect that isometric embedding is investigated "owing to regions of nonzero Gaussian curvature within common non-Euclidean color spaces." Both attempts to reach the paper's actual PDF text (via extract_pdf, including a ResearchGate-hosted mirror) returned HTTP 403.

This paper is very likely the direct technical antecedent that Ahrens et al. 2024 implicitly measures itself against — Ahrens's own abstract claims improvement "over previous contributions" on the same CIEDE2000-anchored Euclidization task, seventeen years later. But that inference, and the Gaussian-curvature wording itself, rest only on a WebFetch summarization layer this session, never a raw document read. The vault's quote-provenance rule treats a summarizing layer's output as inadmissible for source_quote regardless of how consistent or well-formed it reads — a real prior failure mode (fabricated-but-plausible quotes from exactly this kind of tool) means consistency across passes is not the same as verification.