{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"e56ff558383a15894d07106ef602175a0a46b4dc4a5bb4d208b8f2ff79603367","created":"2026-10-03T07:18:09Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"7d142ce8f0363f05018230f40108bb165cdf29b4af6651af1724c5b474749eac","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"qi.contextuality-nonlocality.i3322-finite-dimension","kind":"well-posed","literature_status":"partially-resolved","n":"1","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 l^2(Z) x l^2(Z), and required dimension of order $\\operatorname{log}(1/\\epsilon)$.","problem_ref":null,"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 1e-55); neither is refereed.","title":"Is the $I3322$ quantum maximum reached in finite dimension?","topic_ref":"b07684c5fe91d012cf3f7701521f464b6170695b71db99db565aa3f747a6411c"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"218de7ce84f3b1613f7067099bffd03c0ef8ea52bd7ef38c00bc51c3d6ee5938","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"a80471f90796e1a6d0d3928af5f881548bff0612dcf422f7eb15edf41b7c75c0","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"plKmhgSckm8BygQ-ObfRIwJZ2Xk6AFstR3aLgmcjUOqUxVgTT5xcn6ivDHtj48FzKNfHj5q_ZPV0rSisyrKFCQ"},"schema":"pubphys.envelope/1"},"record_hash":"218de7ce84f3b1613f7067099bffd03c0ef8ea52bd7ef38c00bc51c3d6ee5938","leaf_index":1983}