{"paper":{"title":"The $\\pi/12$ model: trimaximal first-column lepton mixing with charged-lepton $\\mu$--$\\tau$ breaking","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Vernon Barger","submitted_at":"2026-08-09T01:08:59Z","abstract_excerpt":"The first column of the lepton mixing matrix carries two independent magnitude conditions: the trimaximal norm $|U_{e1}|^2=2/3$ and the $\\mu$--$\\tau$ balance $|U_{\\mu1}|=|U_{\\tau1}|$. We parameterize their violation by $\\varepsilon_1\\equiv(3/2)|U_{e1}|^2-1$ and $\\varepsilon_2\\equiv3(|U_{\\tau1}|^2-|U_{\\mu1}|^2)$ and show that current data treat the two differently in central value: including the first JUNO measurement, $\\varepsilon_1=+0.014\\pm0.010$ is consistent with zero, while $\\varepsilon_2=+0.29^{+0.07}_{-0.13}$ is large but disfavors zero at only $1.5\\sigma$ on the global-fit profile like"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.08394","kind":"arxiv","version":1},"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/2608.08394/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"}