{"paper":{"title":"A Constructive Approach to Zauner's Conjecture via the Stark Conjectures","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.CO","math.MG","quant-ph"],"primary_cat":"math.NT","authors_text":"Gene S Kopp, Marcus Appleby, Steven T Flammia","submitted_at":"2025-01-07T18:16:43Z","abstract_excerpt":"We propose a construction of $d^2$ complex equiangular lines in $\\mathbb{C}^d$, also known as SICPOVMs, conjectured by Zauner to exist for all d. The construction gives a putatively complete list of SICs with Weyl-Heisenberg symmetry in all dimensions d > 3. Specifically, we give an explicit expression for an object we call a ghost SIC, which is constructed from the real multiplication values of a special function and which is Galois conjugate to a SIC. The special function, the Shintani-Faddeev modular cocycle, is more precisely a tuple of meromorphic functions indexed by a congruence subgrou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.03970","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.03970/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}