{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:XGYUYE4OPUPVUI2LTQHWG6BXKD","short_pith_number":"pith:XGYUYE4O","schema_version":"1.0","canonical_sha256":"b9b14c138e7d1f5a234b9c0f63783750cbd9a630ac10cb4d579162386267c05c","source":{"kind":"arxiv","id":"2506.15149","version":2},"attestation_state":"computed","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2506.15149","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2025-06-18T05:13:32Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"35438c7e79efa7cdda0981740f42667293159567d02cb778902fa9e35607922e","abstract_canon_sha256":"cc0da9d07d3d0e3d7256d6db3f2e0ab171686ebe98e6e64f491019a0a1fc22da"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-26T01:15:44.581865Z","signature_b64":"kfLhBnMkHMeb/b//w7PQS7qoRAnG+tYFyWcxLKlOgS0xakDI7zKVl5J+jtmY6QCbwN7tUJ0kB4qN2EeamG2YBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b9b14c138e7d1f5a234b9c0f63783750cbd9a630ac10cb4d579162386267c05c","last_reissued_at":"2026-06-26T01:15:44.581399Z","signature_status":"signed_v1","first_computed_at":"2026-06-26T01:15:44.581399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2506.15149","created_at":"2026-06-26T01:15:44.581462+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.15149v2","created_at":"2026-06-26T01:15:44.581462+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.15149","created_at":"2026-06-26T01:15:44.581462+00:00"},{"alias_kind":"pith_short_12","alias_value":"XGYUYE4OPUPV","created_at":"2026-06-26T01:15:44.581462+00:00"},{"alias_kind":"pith_short_16","alias_value":"XGYUYE4OPUPVUI2L","created_at":"2026-06-26T01:15:44.581462+00:00"},{"alias_kind":"pith_short_8","alias_value":"XGYUYE4O","created_at":"2026-06-26T01:15:44.581462+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2608.00819","citing_title":"Function theory of the hexablock and applications to the tetrablock and Euclidean biball","ref_index":26,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XGYUYE4OPUPVUI2LTQHWG6BXKD","json":"https://pith.science/pith/XGYUYE4OPUPVUI2LTQHWG6BXKD.json","graph_json":"https://pith.science/api/pith-number/XGYUYE4OPUPVUI2LTQHWG6BXKD/graph.json","events_json":"https://pith.science/api/pith-number/XGYUYE4OPUPVUI2LTQHWG6BXKD/events.json","paper":"https://pith.science/paper/XGYUYE4O"},"agent_actions":{"view_html":"https://pith.science/pith/XGYUYE4OPUPVUI2LTQHWG6BXKD","download_json":"https://pith.science/pith/XGYUYE4OPUPVUI2LTQHWG6BXKD.json","view_paper":"https://pith.science/paper/XGYUYE4O","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.15149&json=true","fetch_graph":"https://pith.science/api/pith-number/XGYUYE4OPUPVUI2LTQHWG6BXKD/graph.json","fetch_events":"https://pith.science/api/pith-number/XGYUYE4OPUPVUI2LTQHWG6BXKD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XGYUYE4OPUPVUI2LTQHWG6BXKD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XGYUYE4OPUPVUI2LTQHWG6BXKD/action/storage_attestation","attest_author":"https://pith.science/pith/XGYUYE4OPUPVUI2LTQHWG6BXKD/action/author_attestation","sign_citation":"https://pith.science/pith/XGYUYE4OPUPVUI2LTQHWG6BXKD/action/citation_signature","submit_replication":"https://pith.science/pith/XGYUYE4OPUPVUI2LTQHWG6BXKD/action/replication_record"}},"created_at":"2026-06-26T01:15:44.581462+00:00","updated_at":"2026-06-26T01:15:44.581462+00:00"}