{"paper":{"title":"Flavor in Ninths and a Discrete Gauge Origin of the QCD Axion","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-ex"],"primary_cat":"hep-ph","authors_text":"Vernon Barger","submitted_at":"2026-03-04T01:43:58Z","abstract_excerpt":"Quark and lepton hierarchies are organized by rational powers of a single parameter (the quark masses and mixings in ninths, the charged-lepton mass ratios in sixths). We argue that this structure points to a discrete $\\mathbb{Z}_{18}$ origin of Froggatt--Nielsen symmetry, fixed as the least common denominator $\\mathrm{lcm}(9,6)=18$, with its $\\mathbb{Z}_9$ subgroup governing the quark lattice and the full $\\mathbb{Z}_{18}\\cong\\mathbb{Z}_9\\times\\mathbb{Z}_2$ required to accommodate the half-integer lepton charges. The flavon is the unique $\\mathbb{Z}_{18}$-charged scalar with a large VEV, so i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.03631","kind":"arxiv","version":5},"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/2603.03631/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"}