Chromatic Constraints on Quantum Observables: Gaps, Contextuality, and Separability
Abstract
Intertwined complete projective experiments share outcomes, motivating the search for a common spectral labeling across contexts. Strong coloring tests whether complete contexts admit one context-independent nondegenerate spectrum; when that labeling exists, chromatic separability tests which event distinctions it preserves. We distinguish these questions from ordinary Kochen--Specker statelessness, geometric realizability, event-order representation, and Born-probability models. A state extends to a strong d-coloring exactly when deletion of its support leaves a (d-1)-colorable graph. Faithful real 17- and 21-ray restrictions of completed Yu--Oh have separating ordinary states but forced color identities; one quantum preparation requires exactly 1/9 nonextendable weight despite admitting an ordinary-state model. Independent Hermitian projection arguments correct earlier inferences from a chromatic gap to statelessness or nonrealizability. Hesse's complex 37-ray example separates real and complex geometry and has exact state-family minima 6/7/18 for three representation requirements. A rational two-plane construction gives a linear real 65-ray example with 393,216 states and explicit event-order and probability failures. General and specified ancestry results distinguish geometric KS extensions from abstract chromatic-to-stateless constructions. Detailed enumerations, regenerated state certificates, and extended proofs are supplementary.
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BibTeX
@misc{svozil2026chromatic,
title = {{Chromatic Constraints on Quantum Observables: Gaps, Contextuality, and Separability}},
author = {Karl Svozil},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.04289},
eprint = {2607.04289},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.04289},
}
RIS
TY - UNPB
TI - Chromatic Constraints on Quantum Observables: Gaps, Contextuality, and Separability
AU - Karl Svozil
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2607.04289
UR - https://arxiv.org/abs/2607.04289
AB - Intertwined complete projective experiments share outcomes, motivating the search for a common spectral labeling across contexts. Strong coloring tests whether complete contexts admit one context-independent nondegenerate spectrum; when that labeling exists, chromatic separability tests which event distinctions it preserves. We distinguish these questions from ordinary Kochen--Specker statelessness, geometric realizability, event-order representation, and Born-probability models. A state extends to a strong d-coloring exactly when deletion of its support leaves a (d-1)-colorable graph. Faithful real 17- and 21-ray restrictions of completed Yu--Oh have separating ordinary states but forced color identities; one quantum preparation requires exactly 1/9 nonextendable weight despite admitting an ordinary-state model. Independent Hermitian projection arguments correct earlier inferences from a chromatic gap to statelessness or nonrealizability. Hesse's complex 37-ray example separates real and complex geometry and has exact state-family minima 6/7/18 for three representation requirements. A rational two-plane construction gives a linear real 65-ray example with 393,216 states and explicit event-order and probability failures. General and specified ancestry results distinguish geometric KS extensions from abstract chromatic-to-stateless constructions. Detailed enumerations, regenerated state certificates, and extended proofs are supplementary.
ER -