The Sieve Color Transform: A First-Principles Color Space from the Sieve of Eratosthenes

The Sieve Color Space (SCS) is an information-geometric substrate for color derived from a single input (s = 1/2) on a prime-gap dynamical system — the Persistence Theory framework. It yields a luminance channel (p = 2), three active chromatic channels ({3, 5, 7}), a Fisher-information metric on the chromatic simplex, an S + L sum rule, and a candidate equilibrium saturation at 1/√2 ≈ 70.7%. The channel ordering γ₃ > γ₅ > γ₇ is computed, not fitted, and matches the L>M>S cone-bandwidth ordering.

Performance on COMBVD (3813 pairs). Pure SCS with zero fitted parameters sits below CIELAB globally (r = 0.500 vs 0.755), but wins in the dark region (L* < 25) and on MacAdam ellipse orientation (18/25, RMS Δθ = 37.8° vs 52.0°). As an additive channel on top of a cortical model, SCS improves hybrid formulations: SCS + CIECAM02 reaches r = 0.824 (6 Ridge-regressed weights), and ΔE_SCS00 surpasses CIEDE2000 itself (r = 0.893 vs 0.878, p < 0.0001, 5 regressed weights).

SCS is proposed as a principled geometric layer alongside iCAM, CAM02-UCS, and JzAzBz — not a replacement for the CIE toolkit. Chromatic adaptation, viewing conditions, and observer variability are explicitly outside scope. The paper is self-contained and states three falsifiable predictions (Koide JND null at 1/√2, 105-state discrimination ceiling, tetrachromat p=11 signature), each tractable in a three-month experiment.

Code, datasets, regression weights, and a public benchmark leaderboard:
https://github.com/Igrekess/SieveColorSpace

Quick grading application demo:
https://igrekess.github.io/SieveColorSpace/demonstration/demo.html