{"paper":{"title":"Rigidity of proper holomorphic self-mappings of the hexablock","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Enchao Bi, Guicong Su, Zeinab Shaaban","submitted_at":"2025-07-22T02:46:11Z","abstract_excerpt":"The hexablock \\(\\mathbb{H}\\), introduced by Biswas-Pal-Tomar \\cite{Hexablock}, is a Hartogs domain in \\(\\mathbb{C}^4\\) fibered over the tetrablock \\(\\mathbb{E}\\) in \\(\\mathbb{C}^3\\), arising in the context of \\(\\mu\\)-synthesis problems. In this paper, we prove that every proper holomorphic self-map of \\(\\mathbb{H}\\) is necessarily an automorphism. Consequently, we resolve the conjecture \\(G(\\mathbb{H}) = \\mathrm{Aut}(\\mathbb{H})\\) on the automorphism group structure, originally posed by Biswas-Pal-Tomar in \\cite{Hexablock}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.16176","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/2507.16176/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"}