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    "title": "Kochen and Specker: finite obstruction to noncontextual quantum valuations",
    "summary": "Kochen and Specker constructed a finite three-dimensional quantum-observable structure that cannot receive noncontextual values preserving functional relations for compatible measurements, while exhibiting a contrasting two-dimensional classical model.\n\nCan every quantum observable carry a predetermined value that remains the same whichever compatible measurements surround it? The paper makes that question algebraically precise. Only operations on compatible observables must be preserved, avoiding an unrestricted additivity assumption imposed on incompatible measurements. A finite configuration in three dimensions forces contradictory value assignments. The source distinguishes a117-point construction with no allowed valuation from a smaller17-point illustration of failure to embed without identifying distinct elements. It also constructs a classical model for a restricted two-dimensional system, showing why the dimension matters. Its physical illustration is a proposed spin-one measurement arrangement, not a completed experimental test reported in this article. Context-dependent models, finite-precision tests and later smaller constructions require separate statements and credit.",
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        "description": "The obstruction concerns assigning noncontextual values to the specified quantum observables while preserving their functional relations, in the relevant dimension. It is not a ban on every hidden-variable theory or a proof about arbitrary classical information. Contextual models, lower-dimensional cases and later finite constructions retain separate treatment.",
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      "statement": "# Kochen and Specker: finite obstruction to noncontextual quantum valuations\n\nKochen and Specker constructed a finite three-dimensional quantum-observable structure that cannot receive noncontextual values preserving functional relations for compatible measurements, while exhibiting a contrasting two-dimensional classical model.\n\nCan every quantum observable carry a predetermined value that remains the same whichever compatible measurements surround it? The paper makes that question algebraically precise. Only operations on compatible observables must be preserved, avoiding an unrestricted additivity assumption imposed on incompatible measurements. A finite configuration in three dimensions forces contradictory value assignments. The source distinguishes a117-point construction with no allowed valuation from a smaller17-point illustration of failure to embed without identifying distinct elements. It also constructs a classical model for a restricted two-dimensional system, showing why the dimension matters. Its physical illustration is a proposed spin-one measurement arrangement, not a completed experimental test reported in this article. Context-dependent models, finite-precision tests and later smaller constructions require separate statements and credit.\n\n## Scientific scope\n\nThe obstruction concerns assigning noncontextual values to the specified quantum observables while preserving their functional relations, in the relevant dimension. It is not a ban on every hidden-variable theory or a proof about arbitrary classical information. Contextual models, lower-dimensional cases and later finite constructions retain separate treatment.\n\n## People and systems\n\nSimon Kochen; E. P. Specker\n\n\n\n## Original sources\n\n- [Kochen and Specker: finite obstruction to noncontextual quantum valuations — original scientific article](https://www.iumj.indiana.edu/IUMJ/FTDLOAD/1968/17/17004/pdf)\n- [Kochen and Specker: finite obstruction to noncontextual quantum valuations — publisher deposit](https://api.crossref.org/works/10.1512%2Fiumj.1968.17.17004)\n",
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      "title": "Kochen and Specker: finite obstruction to noncontextual quantum valuations"
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