{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"156c96ca6bcc0c27b492f2b8dd2135da425a56ef69afca4266ed365f2bbdba92","created":"2026-10-03T07:18:06Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"da55ef2e2e362d27db0ac5c63d7a222ce9b2a753a4a2c3b447e8d030eb54c8b4","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"proof","assisted_by":[],"external_id":"mathph.ising-rigorous.conformal-3d","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"At its critical point the 3D Ising model is believed to look the same under rotations and angle-preserving maps (conformal symmetry), which physicists use to compute exponents. In 2D this was proven; in 3D even rotation invariance is unproven.","posed_since":"","precise":"Show that the scaling limit of critical spin correlations on $Z^3$ exists, is rotation invariant, and transforms covariantly under conformal maps of $R^3$ with scaling dimension $\\Delta_{\\sigma}\\ \\text{approximately}\\ 0.51815$. Answer: a proof.","problem_ref":null,"references":"","settled_by":"A proof of rotation invariance of the 3D scaling limit, then of conformal covariance.","status_note":"Conformal invariance in 2D was proven by Smirnov (2010) and by Chelkak, Hongler and Izyurov (2015).","title":"Rotational and conformal invariance of the critical 3D Ising scaling limit","topic_ref":"0b88a0ded9bd47630f1a876bef355f9b17efdebced19bd55e73bb1cd79f5cae3"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"ee8893087010f079ca77ff5cb592af840a10e25be20d9512cde301eb26c2d192","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"371904059af23dc5e7cedb291a333f0fc797de15b71daf730c4c55ca3329ddf6","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"VSzvhhBDosCJuTochBpqtj87mjHA5ivxsjfjPvCDCgUtWPEBmDZoCMUlSt1dpighlrYSnrgtCbK1ww0lvNNABg"},"schema":"pubphys.envelope/1"},"record_hash":"ee8893087010f079ca77ff5cb592af840a10e25be20d9512cde301eb26c2d192","leaf_index":1628}