{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:OGSDBY7POO3PKY7ZT6E7ZR72QS","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":"6d5840c9ab66afd6fe3d21a6807fa63027e161a906fb459272e3133c5154f8fa","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-07T17:21:34Z","title_canon_sha256":"e98abe2e4a3ec990a49b319272f01e564be170e3e8b1a3f075d83fb6c7fb862a"},"schema_version":"1.0","source":{"id":"1711.02614","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.02614","created_at":"2026-05-18T00:31:07Z"},{"alias_kind":"arxiv_version","alias_value":"1711.02614v1","created_at":"2026-05-18T00:31:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.02614","created_at":"2026-05-18T00:31:07Z"},{"alias_kind":"pith_short_12","alias_value":"OGSDBY7POO3P","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"OGSDBY7POO3PKY7Z","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"OGSDBY7P","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:1ac69bebb8e8c511f0de012ec41c1521136ad1e353827f9c458713c086434277","target":"graph","created_at":"2026-05-18T00:31:07Z","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":"Our goal is to compare various results for Toeplitz $T$ and Hankel $H$ operators. We consider semibounded operators and find necessary and sufficient conditions for their quadratic forms to be closable. This property allows one to define $T$ and $H$ as self-adjoint operators under minimal assumptions on their matrix elements. We also describe domains of the closed Toeplitz and Hankel quadratic forms.","authors_text":"D. R. Yafaev","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-07T17:21:34Z","title":"Toeplitz versus Hankel: semibounded operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.02614","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":"sha256:751d57592ee615f2217b87d88bfb907fde91803f86c566995639b15dc5249e44","target":"record","created_at":"2026-05-18T00:31:07Z","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":"6d5840c9ab66afd6fe3d21a6807fa63027e161a906fb459272e3133c5154f8fa","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-07T17:21:34Z","title_canon_sha256":"e98abe2e4a3ec990a49b319272f01e564be170e3e8b1a3f075d83fb6c7fb862a"},"schema_version":"1.0","source":{"id":"1711.02614","kind":"arxiv","version":1}},"canonical_sha256":"71a430e3ef73b6f563f99f89fcc7fa848bd71ca90bb65d62013e1ae37c2ecf5a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"71a430e3ef73b6f563f99f89fcc7fa848bd71ca90bb65d62013e1ae37c2ecf5a","first_computed_at":"2026-05-18T00:31:07.435062Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:07.435062Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tfvBdnLAaJ2Nm9XnvFfcJRPMnR7WWBoqDRVhHK18s/dfA4Rw6aLYdgP2S0N2QI+odMHONIsT2qgq0HCNUUvsBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:07.435764Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.02614","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:751d57592ee615f2217b87d88bfb907fde91803f86c566995639b15dc5249e44","sha256:1ac69bebb8e8c511f0de012ec41c1521136ad1e353827f9c458713c086434277"],"state_sha256":"c5c12ebe467a8c00506264adc49e36e139c2422510e79f91297f0cabb1710dce"}