This article presents the Sieve Color Space (SCS), a color model derived from first principles through Persistence Theory and the arithmetic structure of the Sieve of Eratosthenes. From a single input, s = 1/2, and with zero adjustable parameters, the framework derives a luminance foundation (p = 2) and three active chromatic channels ({3, 5, 7}), together with a Fisher-information metric, a conservation law between saturation and luminance, chromatic complementarity, hue topology, and an optimal saturation near 70.7%. The paper compares SCS with CIE-based models on MacAdam ellipses, Berlin–Kay universals, and COMBVD. SCS improves on CIELAB in the dark region, while hybrid formulations outperform CIELAB globally, and ΔESCS00 surpasses CIEDE2000 itself. The article argues that SCS provides a principled geometric foundation for color science, with direct applications in color grading, gamut portability, skin-tone protection, and scientific visualization.A quick poc and pedagogic tools are available at https://igrekess.github.io/SieveColorSpace/demonstration/demo.html