{"paper":{"title":"On a conjecture concerning totally extremal ideal Perron similarities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.RT"],"primary_cat":"math.SP","authors_text":"Erica J. Artemis, Pietro Paparella","submitted_at":"2026-06-01T20:29:13Z","abstract_excerpt":"Identifying ideal Perron similarities is a problem of central interest in the longstanding nonnegative inverse eigenvalue problem (NIEP). A normalized ideal Perron similarity is called totally extremal if every entry has modulus one. Recently, Gershnik et al. [J. Algebra 694 (2026), 782--800] proved that the character table of a finite Abelian group is totally extremal and conjectured the converse.\n  In this paper, we settle this conjecture in the affirmative by first showing that the rows of a totally extremal normalized ideal Perron similarity form a group under the Hadamard product. Then, i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.02865","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/2606.02865/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"}