{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:O2F7UZ5HQUCLHJUEPTAKL3L745","short_pith_number":"pith:O2F7UZ5H","schema_version":"1.0","canonical_sha256":"768bfa67a78504b3a6847cc0a5ed7fe760cf49ff5e389fa195a0ae4d4e347c56","source":{"kind":"arxiv","id":"2507.14589","version":2},"attestation_state":"computed","paper":{"title":"Operators associated with a domain in $\\mathbb C^4$ and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.OA"],"primary_cat":"math.FA","authors_text":"Nitin Tomar, Sourav Pal","submitted_at":"2025-07-19T12:22:25Z","abstract_excerpt":"The hexablock is a domain arising from a special case of the $\\mu$-synthesis problem. We study the commuting operator tuples having the hexablock as a spectral set. Such a tuple is called a hexablock-contraction or simply $\\mathbb H$-contraction. We characterize the unitaries and isometries associated with $\\mathbb H$-contractions. Two different types of dilation results for $\\mathbb H$-contractions are obtained. We find connection of this theory with the operators associated with the symmetrized bidisc and tetrablock, two other domains related to the $\\mu$-synthesis problem."},"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":"2507.14589","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2025-07-19T12:22:25Z","cross_cats_sorted":["math.CV","math.OA"],"title_canon_sha256":"8ea0dfb976ebff9b5b42791c31b42ac7e99bad189c539273d269ca53fee881b1","abstract_canon_sha256":"4a2b774368b8ffc14fb423bb38715466560a67e8e5882d763d76fe28d6e8997c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-12T00:07:48.143366Z","signature_b64":"Gx0mif9jpAPlF/wUQCxglY4+2HPI/Fg4uFaT2i3XgQB2AYtcIUQ8AfRX8slcPPfvgEJXBw2XowJWiNr4gm6WBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"768bfa67a78504b3a6847cc0a5ed7fe760cf49ff5e389fa195a0ae4d4e347c56","last_reissued_at":"2026-06-12T00:07:48.142703Z","signature_status":"signed_v1","first_computed_at":"2026-06-12T00:07:48.142703Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Operators associated with a domain in $\\mathbb C^4$ and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.OA"],"primary_cat":"math.FA","authors_text":"Nitin Tomar, Sourav Pal","submitted_at":"2025-07-19T12:22:25Z","abstract_excerpt":"The hexablock is a domain arising from a special case of the $\\mu$-synthesis problem. We study the commuting operator tuples having the hexablock as a spectral set. Such a tuple is called a hexablock-contraction or simply $\\mathbb H$-contraction. We characterize the unitaries and isometries associated with $\\mathbb H$-contractions. Two different types of dilation results for $\\mathbb H$-contractions are obtained. We find connection of this theory with the operators associated with the symmetrized bidisc and tetrablock, two other domains related to the $\\mu$-synthesis problem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.14589","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/2507.14589/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":"2507.14589","created_at":"2026-06-12T00:07:48.142779+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.14589v2","created_at":"2026-06-12T00:07:48.142779+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.14589","created_at":"2026-06-12T00:07:48.142779+00:00"},{"alias_kind":"pith_short_12","alias_value":"O2F7UZ5HQUCL","created_at":"2026-06-12T00:07:48.142779+00:00"},{"alias_kind":"pith_short_16","alias_value":"O2F7UZ5HQUCLHJUE","created_at":"2026-06-12T00:07:48.142779+00:00"},{"alias_kind":"pith_short_8","alias_value":"O2F7UZ5H","created_at":"2026-06-12T00:07:48.142779+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":45,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/O2F7UZ5HQUCLHJUEPTAKL3L745","json":"https://pith.science/pith/O2F7UZ5HQUCLHJUEPTAKL3L745.json","graph_json":"https://pith.science/api/pith-number/O2F7UZ5HQUCLHJUEPTAKL3L745/graph.json","events_json":"https://pith.science/api/pith-number/O2F7UZ5HQUCLHJUEPTAKL3L745/events.json","paper":"https://pith.science/paper/O2F7UZ5H"},"agent_actions":{"view_html":"https://pith.science/pith/O2F7UZ5HQUCLHJUEPTAKL3L745","download_json":"https://pith.science/pith/O2F7UZ5HQUCLHJUEPTAKL3L745.json","view_paper":"https://pith.science/paper/O2F7UZ5H","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.14589&json=true","fetch_graph":"https://pith.science/api/pith-number/O2F7UZ5HQUCLHJUEPTAKL3L745/graph.json","fetch_events":"https://pith.science/api/pith-number/O2F7UZ5HQUCLHJUEPTAKL3L745/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/O2F7UZ5HQUCLHJUEPTAKL3L745/action/timestamp_anchor","attest_storage":"https://pith.science/pith/O2F7UZ5HQUCLHJUEPTAKL3L745/action/storage_attestation","attest_author":"https://pith.science/pith/O2F7UZ5HQUCLHJUEPTAKL3L745/action/author_attestation","sign_citation":"https://pith.science/pith/O2F7UZ5HQUCLHJUEPTAKL3L745/action/citation_signature","submit_replication":"https://pith.science/pith/O2F7UZ5HQUCLHJUEPTAKL3L745/action/replication_record"}},"created_at":"2026-06-12T00:07:48.142779+00:00","updated_at":"2026-06-12T00:07:48.142779+00:00"}