{"paper":{"title":"Fermion mass relations in one-parameter modular models","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"hep-ph","authors_text":"J. T. Penedo, Omar Medina, Salvador Centelles Chuli\\'a, Xiang-Gan Liu, Xueqi Li","submitted_at":"2026-06-23T18:00:02Z","abstract_excerpt":"Modular flavour symmetries provide a possible organizing principle for the Standard Model Yukawa sector, by replacing generic couplings with a potentially small number of modular forms controlled by a single complex modulus. We study the extreme limit of this idea: \\acp{OPM}, in which each charged-fermion mass matrix is fixed by a single modular invariant contraction. We develop a systematic method to construct such models, showing that the \\ac{OPM} requirement is already highly constraining at the level of possible fermion hierarchies. In a concrete realization, the charged-lepton and down-qu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.25027","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/2606.25027/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"}