{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:SAPYNAPMDYFLM7DPS5P6OOUIUQ","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":"57812fbb612ff7faf2b9d6d2acd51751836dee4115d1cb215135855de44e913b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2020-02-24T09:02:12Z","title_canon_sha256":"a92547fdd2a0f62b87f1452f9001f0ea7f5ccde798d5f961111b37c9104e208a"},"schema_version":"1.0","source":{"id":"2002.10122","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2002.10122","created_at":"2026-07-05T00:43:14Z"},{"alias_kind":"arxiv_version","alias_value":"2002.10122v1","created_at":"2026-07-05T00:43:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2002.10122","created_at":"2026-07-05T00:43:14Z"},{"alias_kind":"pith_short_12","alias_value":"SAPYNAPMDYFL","created_at":"2026-07-05T00:43:14Z"},{"alias_kind":"pith_short_16","alias_value":"SAPYNAPMDYFLM7DP","created_at":"2026-07-05T00:43:14Z"},{"alias_kind":"pith_short_8","alias_value":"SAPYNAPM","created_at":"2026-07-05T00:43:14Z"}],"graph_snapshots":[{"event_id":"sha256:d663455f1eea64011dc945bf5c96702be16cc5653ab40010b0b7305dece03f45","target":"graph","created_at":"2026-07-05T00:43:14Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2002.10122/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We characterize the solutions of the Poisson equation and the domain of its associated one-sided Hilbert transform for Ces\\`aro bounded operators of fractional order. The results obtained fairly generalize the corresponding ones for power-bounded operators. In passing, we give an extension of the mean ergodic theorem. Examples are given to illustrate the theory.","authors_text":"Carlos Lizama, Jos\\'e E. Gal\\'e, Luciano Abadias","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2020-02-24T09:02:12Z","title":"Poisson equation and discrete one-sided Hilbert transform for $(C,\\alpha)$-bounded operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2002.10122","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":"sha256:221a034521038f4a180accf52dceb9a695f3f025ac769c59519367c3e73772ed","target":"record","created_at":"2026-07-05T00:43:14Z","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":"57812fbb612ff7faf2b9d6d2acd51751836dee4115d1cb215135855de44e913b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2020-02-24T09:02:12Z","title_canon_sha256":"a92547fdd2a0f62b87f1452f9001f0ea7f5ccde798d5f961111b37c9104e208a"},"schema_version":"1.0","source":{"id":"2002.10122","kind":"arxiv","version":1}},"canonical_sha256":"901f8681ec1e0ab67c6f975fe73a88a41bb7c9107628909c9651e6c7c1586977","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"901f8681ec1e0ab67c6f975fe73a88a41bb7c9107628909c9651e6c7c1586977","first_computed_at":"2026-07-05T00:43:14.581858Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:43:14.581858Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qEbtj72G779BxNvnlPSfCYaJ7lUvL59YJ1vdK01iHHTNj2dZQyopbLTHxlcPaKvCsBxjnkkQPz+3LmbHIKA6Cw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:43:14.582232Z","signed_message":"canonical_sha256_bytes"},"source_id":"2002.10122","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:221a034521038f4a180accf52dceb9a695f3f025ac769c59519367c3e73772ed","sha256:d663455f1eea64011dc945bf5c96702be16cc5653ab40010b0b7305dece03f45"],"state_sha256":"ea63bd48c61330442068071ee1df567b941aa5726b0cd31e6f66075adffed1f5"}