{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"b96c51fed06704d93cba669ccfc1e3f09fee885ba2b68db0fc8984e3124ad48e","created":"2026-10-03T07:18:09Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"df65085d6817170868e16bdda0cfc690eaf5788dae40636cb5d92ff16999c6f2","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"identification","assisted_by":[],"external_id":"qi.contextuality-nonlocality.tsirelson-explicit-game","kind":"well-posed","literature_status":"partially-resolved","n":"1","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":"MIP* = 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":null,"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":"b07684c5fe91d012cf3f7701521f464b6170695b71db99db565aa3f747a6411c"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"8cbb2bfb2441262b8f9cc28c8780dc9f80348988a4e616f1a58d93ccc804c99f","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"7248955aee24dd0db9a4c5689fc289fb220dae2b324f72597a7f784e651968a9","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"7pvMImwjdNjWKz3AfE01pmKZAmuj0es4uqOE0VcHLcd8gYL98-4L4rx2I-RKVsmlibJJlnv6qHkZyt40qo4UCA"},"schema":"pubphys.envelope/1"},"record_hash":"8cbb2bfb2441262b8f9cc28c8780dc9f80348988a4e616f1a58d93ccc804c99f","leaf_index":1986}