{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"c9ab0009b83dc07936b7972f4df2374d67c6e87bd9bf690ad701b61e7f28d079","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":["ai:gpt-5.5"],"kind":"seed"},"parents":["8cbb2bfb2441262b8f9cc28c8780dc9f80348988a4e616f1a58d93ccc804c99f","ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b"],"salt":"fac2888ea09ee170eac2dacd89e654612fa76843500b413701d13fe4b1015e4f","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"identification","assisted_by":["ai:gpt-5.5"],"external_id":"qi.contextuality-nonlocality.tsirelson-explicit-game","kind":"well-posed","literature_status":"partially-resolved","n":"2","parents":[],"plain":"Quantum correlations can be modeled with a separate space for each lab or with commuting operators on one shared space. A 2020 result proved these give different correlations, but no explicit example is known.","posed_since":"","precise":"$\\mathrm{MIP}* = \\mathrm{RE}$ (Ji, Natarajan, Vidick, Wright, Yuen, arXiv:2001.04383) implies a nonlocal game $G$ with finite inputs and outputs whose commuting-operator value $w_{qc}(G)$ exceeds its tensor-product value $w_{q}(G)$, resolving Tsirelson's problem negatively. Construct an explicit $G$, state its input size and gap, and certify $w_{qc}(G) > w_{q}(G)$.","problem_ref":"8cbb2bfb2441262b8f9cc28c8780dc9f80348988a4e616f1a58d93ccc804c99f","references":"","settled_by":"An explicit game with a certified upper bound on $w_q$ below a certified commuting-operator strategy value.","status_note":"Existence follows from $\\mathrm{MIP}* = \\mathrm{RE}$ (2020); no explicit separating game was found in the literature checked.","title":"Explicit Bell game separating commuting-operator and tensor-product quantum models","topic_ref":null},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"7628498fceb3f809688d8706479714e3f4084a509c0d3e3e2d42bb0ccf8d782a","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"bd8e5d32aa10678b1f2d56ed901c679b8d70f2612ac4bac625f9233d2f4d4a23","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"KJXda2F1Aex5xdHwuRMa2qbvc3dPORUmk8ZWPPtdJFFB_xiDsBi0WTbpnSXff4TCx4JC0q8Jx95QN5T2CVAuCA"},"schema":"pubphys.envelope/1"},"record_hash":"7628498fceb3f809688d8706479714e3f4084a509c0d3e3e2d42bb0ccf8d782a","leaf_index":3704}