{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"0f087e2e8843c2812ed498ee8045338e25d4e3404537d517fe1a6d18e26ec278","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":["ai:gpt-5.5"],"kind":"seed"},"parents":["218de7ce84f3b1613f7067099bffd03c0ef8ea52bd7ef38c00bc51c3d6ee5938","ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b"],"salt":"c4b67b50b58c15dd044bca4062deefbc03f95086bc47bc35dcdcda85873e5595","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":["ai:gpt-5.5"],"external_id":"qi.contextuality-nonlocality.i3322-finite-dimension","kind":"well-posed","literature_status":"partially-resolved","n":"2","parents":[],"plain":"$I3322$ is the simplest Bell test beyond the standard one, with three measurement choices per side. Numerics suggested that reaching its quantum maximum needs systems with infinitely many levels; two September 2026 preprints claim proofs that await independent checking.","posed_since":"2010","precise":"For the Collins-Gisin $I3322$ Bell functional (two parties, three two-outcome measurements each), determine whether the supremum over tensor-product quantum strategies, approximately 0.25087538 (Pal and Vertesi, PRA 2010), is attained by any finite-dimensional strategy, and how the local dimension needed to come within $\\epsilon$ of it grows. The residual task is verification of the 2026 claims: non-attainment in finite dimension, attainment by an infinite-dimensional strategy on $\\ell^{2}(Z) x \\ell^{2}(Z)$, and required dimension of order $\\log(1/\\epsilon)$.","problem_ref":"218de7ce84f3b1613f7067099bffd03c0ef8ea52bd7ef38c00bc51c3d6ee5938","references":"","settled_by":"Refereed or formally machine-checked confirmation of the non-attainment proofs, including their analytic parts.","status_note":"Two independent preprints of August-September 2026 claim non-attainment in finite dimension (Douglas, arXiv:2609.05555; Krohn-Grimberghe, arXiv:2609.29693, computer-assisted, value bracketed to width $10^{-55}$); neither is refereed.","title":"Is the $I3322$ quantum maximum reached in finite 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