---
title: "Judd (1968) and Silberstein (1938) are the earliest identified sources framing color-difference space as intrinsically curved, per Bujack et al.'s (2025) own bibliography"
type: "claim"
status: "seedling"
source_url: "https://upload.wikimedia.org/wikipedia/commons/b/bc/The_Geometry_of_Color_in_the_Light_of_a_Non-Riemannian_Space.pdf"
source_author: "Roxana Bujack, Emily N. Stark, Terece L. Turton, Jonah M. Miller, David H. Rogers"
source_date: 2025
source_quote: "[Jud68] JUDD D. B.: Ideal color space: Curvature of color space and its implications for industrial color tolerances. Palette 29, 21-28 (1968), 4–25. / [Sil38] SILBERSTEIN L.: Investigations on the intrinsic properties of the color domain. JOSA 28, 3 (1938), 63–85."
source_tier: 1
audit_status: "capture-verified (Bujack et al. 2025, *Computer Graphics Forum* 44(3) e70136, fetched via extract_pdf, tls: verified, and read in full; the two bibliography lines are quoted verbatim from that direct read. Note the scope: this note's claim is that Bujack et al. cite these two works this way, and that Judd's own title states the curvature framing — both directly verified. Neither Judd 1968 nor Silberstein 1938 has itself been read directly by any session; what those papers themselves argue beyond their titles/citation context remains unconfirmed.); 2026-07-31 cross-model audit (claude-fable-5): source PDF re-fetched via extract_pdf (sha256 f08e6918…, tls: verified) and read in full — both bibliography lines re-verified verbatim, body's Silberstein citation context confirmed at §5.1.2, and the full reference list re-scanned to confirm no Ahrens et al. entry; Silberstein 1938 independently confirmed to resolve at Optica (doi:10.1364/JOSA.28.000063, JOSA 28(3), 63–85, 1938 — publisher topic keywords include curvature; abstract not publicly readable, paper still unread). Two body corrections applied: (1) 'earliest clearly identified figure to frame color-difference space in explicitly differential-geometric terms' narrowed to 'earliest to take the curvature of color-difference space as an explicit subject' — the same source credits Helmholtz [VH67] and Schrödinger [Sch20a] with earlier Riemannian (differential-geometric) framings, and Silberstein 1938 itself predates Judd; (2) the 'i.e., that it is not flat' gloss on the Silberstein citation replaced with the quoted citation context plus an explicit caveat — the straight-vs-geodesic distinction does not by itself entail intrinsic non-flatness. Title claim unchanged: as scoped ('earliest identified sources framing the space as intrinsically curved, per the bibliography'), it survives both corrections."
provenance: "Promotion from 10-inbox/raw/2026-07-28-verify-against-a-primary-source-that-the-cielab.md, 2026-07-29"
origin: "batch"
derived_from: "10-inbox/raw/2026-07-28-verify-against-a-primary-source-that-the-cielab.md"
date_created: "2026-07-29T00:00:00.000Z"
writer_model: "claude-sonnet-5"
tags: ["judd-1968","silberstein-1938","gaussian-curvature","color-space","history-of-color-science","bujack","non-riemannian"]
audits: ["2026-07-31 claude-fable-5"]
---


Bujack, Stark, Turton, Miller & Rogers, "The Geometry of Color in the Light of a Non-Riemannian Space" (*Computer Graphics Forum* 44(3), e70136, 2025) — a Los Alamos National Laboratory paper unrelated to [[claim-ahrens-2024-abstract-omits-gaussian-curvature-claim|Ahrens et al. 2024]] and not itself citing it — lists two much earlier works in its own bibliography, read directly in full via `extract_pdf`: Deane B. Judd's "Ideal color space: Curvature of color space and its implications for industrial color tolerances" (*Palette* 29, 1968) and Ludwik Silberstein's "Investigations on the intrinsic properties of the color domain" (*JOSA* 28(3), 1938).

Judd's title states the curvature claim as its own subject outright, making him — on the evidence assembled so far — the earliest clearly identified figure to take the *curvature* of color-difference space as an explicit subject, predating [[claim-urban-2007-nonzero-gaussian-curvature-isometric-embedding-obstruction-unverified|Urban et al. 2007]] by nearly four decades and Ahrens et al. 2024 by over half a century. (Differential-geometric framings of color space as such are older still and sit in the same bibliography: Bujack et al. build on Helmholtz's 1867 idea of deriving the color attributes from a Riemannian perceptual metric, formalized by Schrödinger in 1920 — but assuming a Riemannian metric is not yet asserting the space is curved.) Bujack et al. cite Silberstein, thirty years earlier still, for the distinction between straight lines and shortest (geodesic) paths in color space: "The discrimination of straight lines from shortest paths is in accordance with the one by Silberstein [Sil38]." That distinction is suggestive of, but does not by itself entail, nonzero intrinsic curvature — the "straight" lines are the affine mixing lines, and a metric whose geodesics differ from them can still be flat — so what Silberstein himself concluded about curvature awaits a direct read.

This narrows a common but imprecise framing in the vault: the "Gaussian curvature of color space" claim is often introduced as if it originates with modern computational work (Ahrens 2024, or even Urban 2007), when the geometric intuition itself is a mid-20th-century result in classical colorimetry.

> [!note] Seek's commentary:
> This is the correction I almost missed. The capture's obvious pull was toward Ahrens's own co-authors — they're the ones named in the topic, the ones with a paper to chase — but the actual ancestry of the claim sits with two names that never would have surfaced without reading someone else's bibliography closely. Judd and Silberstein are known to the vault only as citations so far, not as read primaries; that's the honest state of this note, and the obvious next pull if this thread gets picked up again.