{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"b8bccc2d3f926e1ce12e8f87b7e6ee9b64347c6df7ccc8d0bf27ccd5606bb89f","created":"2026-10-03T07:18:10Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011","f6d64e6549d380a918e0f747875789012bc4c786b6b351aa03701b680a56a3e8"],"salt":"07d0fba5d11775f71c3165e02c16335b544c16aa8b2d6cbf6f7b13e7f51b8794","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"proof","assisted_by":[],"external_id":"qi.sic-mub.sic-infinite-family","kind":"well-posed","literature_status":"open","n":"1","parents":[{"note":"","parent_revision":"f6d64e6549d380a918e0f747875789012bc4c786b6b351aa03701b680a56a3e8","relation":"special_case"}],"plain":"A number-theory recipe produces SICs in many dimensions of a special form, but it relies on unproved conjectures. Proving it works for infinitely many dimensions would be a first step to the full answer.","posed_since":"","precise":"Prove, without assuming the Stark conjectures, that SICs exist for infinitely many d, for example all prime $d = n^2 + 3$, where Appleby, Bengtsson, Grassl, Harrison and McConnell (J. Math. Phys. 63, 112205, 2022, arXiv:2112.05552) construct SIC fiducials from Stark units of real quadratic fields and obtain solutions in thirteen prime dimensions, the largest $d = 19603$.","problem_ref":null,"references":"","settled_by":"An unconditional proof that the construction yields valid SICs in an infinite family of dimensions.","status_note":"A 2025 extension to dimensions $n^{2}+3=4p,\\ p\\ \\text{prime}$, reached $d=39604$ (Bengtsson, Grassl and McConnell, J. Math. Phys. 66, 082202, 2025), still conditional.","title":"Unconditional construction of SICs in an infinite sequence of dimensions","topic_ref":"1bdfc0d09903d73034d6e6510c6d21f380d002328cb4a356dee914b540fb53cc"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"fbd06b4d71c35d96a4d0e4c40f183f962bb73350473c185ad746dcf3e2e5da8c","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"930753bd912335a268e89c287fdf90ecaed7f7f40a0a88862773a84756581a0f","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"75X_zxe-Z7AgU0yXD7JFHMtALv96KafnHslfs-DjAsj-CNdHgc1xICJA4CBHQUu2av3N5hz-DUewGm5_zLbuDg"},"schema":"pubphys.envelope/1"},"record_hash":"fbd06b4d71c35d96a4d0e4c40f183f962bb73350473c185ad746dcf3e2e5da8c","leaf_index":2056}