{"paper":{"title":"The Hexablock: a domain associated with the $\\mu$-synthesis in $M_2(\\mathbb C)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CV","authors_text":"Indranil Biswas, Nitin Tomar, Sourav Pal","submitted_at":"2025-06-18T05:13:32Z","abstract_excerpt":"We introduce a domain named \\textit{hexablock} in $\\mathbb C^4$ and show that its origin is a special case of $\\mu$-synthesis in $M_2(\\mathbb C)$, more precisely the $\\mu_E$-unit ball with respect to the linear subspace $E$ consisting of $2 \\times 2$ upper triangular matrices. The hexablock is denoted by $\\mathbb H$ and is defined by \\[ \\mathbb{H}=\\left\\{(a, x_1, x_2, x_3) \\,\\in\\, \\mathbb{C} \\times \\mathbb{E}\\,\\,\\big\\vert\\,\\, \\sup_{z_1,\\, z_2 \\,\\in\\, \\mathbb D}\\left|\\frac{a\\sqrt{(1-|z_1|^2)(1-|z_2|^2)}}{1-x_1z_1-x_2z_2+x_3z_1z_2}\\right| <1\\right\\}, \\] where $\\mathbb{E}$ is the \\textit{tetrablo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.15149","kind":"arxiv","version":2},"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/2506.15149/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"}