CPrefix: A Combinatorial Tensor Framework for Structured Discrete Color Mappings

Yvan Richard

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arXiv · 2608.03863

CPrefix: A Combinatorial Tensor Framework for Structured Discrete Color Mappings

Yvan Richard

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Abstract

Discrete multi-channel mappings are typically represented through sampled values, providing accurate evaluations but limited insight into their underlying structure. We introduce CPrefix, a combinatorial observable representation for discrete mappings, realized within a unified tensor framework that enables representation, reconstruction, and structural analysis. The framework is based on a counting tensor induced by multinomial counting observables. Its support forms a discrete Pascal simplex, not as a constraint on the observable space, but as a latent combinatorial representation from which mappings are reconstructed. This formulation separates the combinatorial organization of a mapping from its measured values, exposing the observable structure underlying the mapping. The framework is validated on ICC display and printer profiles through latent reconstruction and perceptual gamut transport. Accurate reconstruction demonstrates that color mappings admit faithful observable representations, while reconstruction residuals provide insight into the compatibility of the underlying mapping with the proposed representation. Although demonstrated on color transformations, the framework is independent of the physical interpretation of the observables, making it applicable to structured multi-channel mappings arising from color imaging, spectral measurements and other discrete systems.

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Yvan Richard. 2026-08-08. CPrefix: A Combinatorial Tensor Framework for Structured Discrete Color Mappings. https://arxiv.org/abs/2608.03863

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