{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:EWFD5OQP4XVUZGIV6IP3ZVCBNY","short_pith_number":"pith:EWFD5OQP","schema_version":"1.0","canonical_sha256":"258a3eba0fe5eb4c9915f21fbcd4416e00de27baf155e6686910cf50ae2ebfb4","source":{"kind":"arxiv","id":"2506.02042","version":1},"attestation_state":"computed","paper":{"title":"General Numerical Radius for Products of Sectorial Matrices","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Mohammad Alakhrass","submitted_at":"2025-05-31T12:32:45Z","abstract_excerpt":"In this paper, we investigate the generalized numerical radius $\\omega_N$, associated with a matrix norm $N$ defined by $\\omega_N(X) = \\sup_{\\theta \\in \\mathbb{R}} N(\\operatorname{Re}(e^{i\\theta}X))$. We focus on matrices whose numerical ranges are contained in sectors of the complex plane (sectorial matrices) and derive upper bounds for $\\omega_N(XY)$ and $\\omega_N(X \\circ Y)$ for such matrices $X$ and $Y$. Our results generalize and refine well known numerical radius inequalities. Several known inequalities for $\\omega(X)$ are recovered as special cases."},"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":"2506.02042","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.FA","submitted_at":"2025-05-31T12:32:45Z","cross_cats_sorted":[],"title_canon_sha256":"fa18004d9b8b27eea17d64dc556a27731d4a7e106fd59f831cd5c100db8c9237","abstract_canon_sha256":"ef9b31af17c2833b7fb02c12dada0e1b2e6b3e1f154c0d3f9b208042e9d4e721"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:14:31.308422Z","signature_b64":"+12B0Js9Sso1QYghEEt5TmbQfWFN7ZYLkIDqXLQ7T16US+P3I6xYNk0WJQcjZXj3tsHOhBD+fgI5ybBCu28DCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"258a3eba0fe5eb4c9915f21fbcd4416e00de27baf155e6686910cf50ae2ebfb4","last_reissued_at":"2026-07-05T11:14:31.308006Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:14:31.308006Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"General Numerical Radius for Products of Sectorial Matrices","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Mohammad Alakhrass","submitted_at":"2025-05-31T12:32:45Z","abstract_excerpt":"In this paper, we investigate the generalized numerical radius $\\omega_N$, associated with a matrix norm $N$ defined by $\\omega_N(X) = \\sup_{\\theta \\in \\mathbb{R}} N(\\operatorname{Re}(e^{i\\theta}X))$. We focus on matrices whose numerical ranges are contained in sectors of the complex plane (sectorial matrices) and derive upper bounds for $\\omega_N(XY)$ and $\\omega_N(X \\circ Y)$ for such matrices $X$ and $Y$. Our results generalize and refine well known numerical radius inequalities. Several known inequalities for $\\omega(X)$ are recovered as special cases."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.02042","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/2506.02042/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":"2506.02042","created_at":"2026-07-05T11:14:31.308058+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.02042v1","created_at":"2026-07-05T11:14:31.308058+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.02042","created_at":"2026-07-05T11:14:31.308058+00:00"},{"alias_kind":"pith_short_12","alias_value":"EWFD5OQP4XVU","created_at":"2026-07-05T11:14:31.308058+00:00"},{"alias_kind":"pith_short_16","alias_value":"EWFD5OQP4XVUZGIV","created_at":"2026-07-05T11:14:31.308058+00:00"},{"alias_kind":"pith_short_8","alias_value":"EWFD5OQP","created_at":"2026-07-05T11:14:31.308058+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/EWFD5OQP4XVUZGIV6IP3ZVCBNY","json":"https://pith.science/pith/EWFD5OQP4XVUZGIV6IP3ZVCBNY.json","graph_json":"https://pith.science/api/pith-number/EWFD5OQP4XVUZGIV6IP3ZVCBNY/graph.json","events_json":"https://pith.science/api/pith-number/EWFD5OQP4XVUZGIV6IP3ZVCBNY/events.json","paper":"https://pith.science/paper/EWFD5OQP"},"agent_actions":{"view_html":"https://pith.science/pith/EWFD5OQP4XVUZGIV6IP3ZVCBNY","download_json":"https://pith.science/pith/EWFD5OQP4XVUZGIV6IP3ZVCBNY.json","view_paper":"https://pith.science/paper/EWFD5OQP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.02042&json=true","fetch_graph":"https://pith.science/api/pith-number/EWFD5OQP4XVUZGIV6IP3ZVCBNY/graph.json","fetch_events":"https://pith.science/api/pith-number/EWFD5OQP4XVUZGIV6IP3ZVCBNY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EWFD5OQP4XVUZGIV6IP3ZVCBNY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EWFD5OQP4XVUZGIV6IP3ZVCBNY/action/storage_attestation","attest_author":"https://pith.science/pith/EWFD5OQP4XVUZGIV6IP3ZVCBNY/action/author_attestation","sign_citation":"https://pith.science/pith/EWFD5OQP4XVUZGIV6IP3ZVCBNY/action/citation_signature","submit_replication":"https://pith.science/pith/EWFD5OQP4XVUZGIV6IP3ZVCBNY/action/replication_record"}},"created_at":"2026-07-05T11:14:31.308058+00:00","updated_at":"2026-07-05T11:14:31.308058+00:00"}