{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:X7YA5UYHHQLYUGE2MSW3ST4RHL","short_pith_number":"pith:X7YA5UYH","schema_version":"1.0","canonical_sha256":"bff00ed3073c178a189a64adb94f913ae8e5b2dfdc54fcb0b7aa15deb5da0f1c","source":{"kind":"arxiv","id":"1604.07758","version":1},"attestation_state":"computed","paper":{"title":"Curvature inequalities for operators in the Cowen-Douglas class of a planar domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Md. Ramiz Reza","submitted_at":"2016-04-26T17:15:50Z","abstract_excerpt":"Fix a bounded planar domain $\\Omega.$ If an operator $T,$ in the Cowen-Douglas class $B_1(\\Omega),$ admits the compact set $\\bar{\\Omega}$ as a spectral set, then the curvature inequality $\\mathcal K_T(w) \\leq - 4 \\pi^2 S_\\Omega(w,w)^2,$ where $S_\\Omega$ is the S\\\"{z}ego kernel of the domain $\\Omega,$ is evident. Except when $\\Omega$ is simply connected, the existence of an operator for which $\\mathcal K_T(w) = 4 \\pi^2 S_\\Omega(w,w)^2$ for all $w$ in $\\Omega$ is not known. However, one knows that if $w$ is a fixed but arbitrary point in $\\Omega,$ then there exists a bundle shift of rank $1,$ sa"},"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":"1604.07758","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-04-26T17:15:50Z","cross_cats_sorted":[],"title_canon_sha256":"8308ffbaec0035d6f0d42a13a88f512885e93c2b485126fcb4fdce3e9cdfd7ad","abstract_canon_sha256":"1d36d216afe9f9b53b70e7e80d8809329979b078d2d49b2ee1cc7b4c17bfc15d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:12.095562Z","signature_b64":"DcJ70BDAEcjjZbfgfSPEiErX0NA7NMz1QiC8P7nF49QnMVgoRpOingpRjSNaMf9OeIlzLlwOSCXDZ5lWaetlCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bff00ed3073c178a189a64adb94f913ae8e5b2dfdc54fcb0b7aa15deb5da0f1c","last_reissued_at":"2026-05-18T01:16:12.094925Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:12.094925Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Curvature inequalities for operators in the Cowen-Douglas class of a planar domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Md. Ramiz Reza","submitted_at":"2016-04-26T17:15:50Z","abstract_excerpt":"Fix a bounded planar domain $\\Omega.$ If an operator $T,$ in the Cowen-Douglas class $B_1(\\Omega),$ admits the compact set $\\bar{\\Omega}$ as a spectral set, then the curvature inequality $\\mathcal K_T(w) \\leq - 4 \\pi^2 S_\\Omega(w,w)^2,$ where $S_\\Omega$ is the S\\\"{z}ego kernel of the domain $\\Omega,$ is evident. Except when $\\Omega$ is simply connected, the existence of an operator for which $\\mathcal K_T(w) = 4 \\pi^2 S_\\Omega(w,w)^2$ for all $w$ in $\\Omega$ is not known. However, one knows that if $w$ is a fixed but arbitrary point in $\\Omega,$ then there exists a bundle shift of rank $1,$ sa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.07758","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":""},"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":"1604.07758","created_at":"2026-05-18T01:16:12.095024+00:00"},{"alias_kind":"arxiv_version","alias_value":"1604.07758v1","created_at":"2026-05-18T01:16:12.095024+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.07758","created_at":"2026-05-18T01:16:12.095024+00:00"},{"alias_kind":"pith_short_12","alias_value":"X7YA5UYHHQLY","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_16","alias_value":"X7YA5UYHHQLYUGE2","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_8","alias_value":"X7YA5UYH","created_at":"2026-05-18T12:30:51.357362+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/X7YA5UYHHQLYUGE2MSW3ST4RHL","json":"https://pith.science/pith/X7YA5UYHHQLYUGE2MSW3ST4RHL.json","graph_json":"https://pith.science/api/pith-number/X7YA5UYHHQLYUGE2MSW3ST4RHL/graph.json","events_json":"https://pith.science/api/pith-number/X7YA5UYHHQLYUGE2MSW3ST4RHL/events.json","paper":"https://pith.science/paper/X7YA5UYH"},"agent_actions":{"view_html":"https://pith.science/pith/X7YA5UYHHQLYUGE2MSW3ST4RHL","download_json":"https://pith.science/pith/X7YA5UYHHQLYUGE2MSW3ST4RHL.json","view_paper":"https://pith.science/paper/X7YA5UYH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1604.07758&json=true","fetch_graph":"https://pith.science/api/pith-number/X7YA5UYHHQLYUGE2MSW3ST4RHL/graph.json","fetch_events":"https://pith.science/api/pith-number/X7YA5UYHHQLYUGE2MSW3ST4RHL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/X7YA5UYHHQLYUGE2MSW3ST4RHL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/X7YA5UYHHQLYUGE2MSW3ST4RHL/action/storage_attestation","attest_author":"https://pith.science/pith/X7YA5UYHHQLYUGE2MSW3ST4RHL/action/author_attestation","sign_citation":"https://pith.science/pith/X7YA5UYHHQLYUGE2MSW3ST4RHL/action/citation_signature","submit_replication":"https://pith.science/pith/X7YA5UYHHQLYUGE2MSW3ST4RHL/action/replication_record"}},"created_at":"2026-05-18T01:16:12.095024+00:00","updated_at":"2026-05-18T01:16:12.095024+00:00"}