{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:Q7KYBIOWF5PVZ3KPST6QRRFBII","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"e4b5e6b5dc3e3ac3b9cde79db414d7bf27ee57d15b10f9368e08855c5e55b163","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-06-14T13:58:07Z","title_canon_sha256":"97ba888083c53aa258a764cfab1fd3bf5052f4cadf3b7838689712c6c7609ef8"},"schema_version":"1.0","source":{"id":"1706.04497","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.04497","created_at":"2026-05-18T00:00:45Z"},{"alias_kind":"arxiv_version","alias_value":"1706.04497v1","created_at":"2026-05-18T00:00:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.04497","created_at":"2026-05-18T00:00:45Z"},{"alias_kind":"pith_short_12","alias_value":"Q7KYBIOWF5PV","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"Q7KYBIOWF5PVZ3KP","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"Q7KYBIOW","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:f4668c64c4d100f2089e95fd59eb1900c2abea203066e51ce18d3c92e5d6fead","target":"graph","created_at":"2026-05-18T00:00:45Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper, we establish some upper bounds for numerical radius inequalities including of $2\\times 2$ operator matrices and their off-diagonal parts. Among other inequalities, it is shown that if $T=\\left[\\begin{array}{cc}\n  0&X,\n  Y&0\n  \\end{array}\\right]$, then\n  \\begin{align*}\n  \\omega^{r}(T)\\leq 2^{r-2}\\left\\|f^{2r}(|X|)+g^{2r}(|Y^*|)\\right\\|^\\frac{1}{2}\\left\\|f^{2r}(|Y|)+g^{2r}(|X^*|)\\right\\|^\\frac{1}{2}\n  \\end{align*} and\n  \\begin{align*}\n  \\omega^{r}(T)\\leq 2^{r-2}\\left\\|f^{2r}(|X|)+f^{2r}(|Y^*|)\\right\\|^\\frac{1}{2}\\left\\|g^{2r}(|Y|)+g^{2r}(|X^*|)\\right\\|^\\frac{1}{2},\n  \\end{align*} ","authors_text":"Khalid Shebrawi, Mojtaba Bakherad","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-06-14T13:58:07Z","title":"Upper bounds for numerical radius inequalities involving off-diagonal operator matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.04497","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:25e2f40a5d6fbc253fc2125818b85da4893d1a7e8ca7f1783204aa97c1527101","target":"record","created_at":"2026-05-18T00:00:45Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"e4b5e6b5dc3e3ac3b9cde79db414d7bf27ee57d15b10f9368e08855c5e55b163","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-06-14T13:58:07Z","title_canon_sha256":"97ba888083c53aa258a764cfab1fd3bf5052f4cadf3b7838689712c6c7609ef8"},"schema_version":"1.0","source":{"id":"1706.04497","kind":"arxiv","version":1}},"canonical_sha256":"87d580a1d62f5f5ced4f94fd08c4a1420ca37043c0d4f2a587c34924c88bde34","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"87d580a1d62f5f5ced4f94fd08c4a1420ca37043c0d4f2a587c34924c88bde34","first_computed_at":"2026-05-18T00:00:45.950752Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:45.950752Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O7H3+ILlTER5QpBbiuTHojxpPLdv5ZEnr3dPPaIzI2AurlXdb0xmE1B4nUxCqd3k/l5mrOWHFyyHxH8Hin5nCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:45.951124Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.04497","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:25e2f40a5d6fbc253fc2125818b85da4893d1a7e8ca7f1783204aa97c1527101","sha256:f4668c64c4d100f2089e95fd59eb1900c2abea203066e51ce18d3c92e5d6fead"],"state_sha256":"a45b93af0773c064a2536b2329b347086222a462aceb65eef41bf1880bbc5e4d"}