{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:XPXXJ6ARGT6WMJRRVZB34Z2VMR","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":"8d788df1e19e645116b7c1ed0de0c370a7c6be463caf1607483da7e60cb6d864","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-03-26T07:55:48Z","title_canon_sha256":"abb4b1f599f66f1a461107c7e4b5425480e10b702ebee32f21d6e6b2d932941b"},"schema_version":"1.0","source":{"id":"1003.5059","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.5059","created_at":"2026-05-18T04:32:33Z"},{"alias_kind":"arxiv_version","alias_value":"1003.5059v1","created_at":"2026-05-18T04:32:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.5059","created_at":"2026-05-18T04:32:33Z"},{"alias_kind":"pith_short_12","alias_value":"XPXXJ6ARGT6W","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"XPXXJ6ARGT6WMJRR","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"XPXXJ6AR","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:b82ba8653cc13de79c0e32e2f9bee440d72587b1da2b1116fcfe7161fe5279ed","target":"graph","created_at":"2026-05-18T04:32:33Z","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":"We consider composition operators in the Dirichlet space of the unit disc in the plane. Various criteria on boundedness, compactness and Hilbert-Schmidt class membership are established. Some of these criteria are shown to be optimal.","authors_text":"H. Youssfi (LATP), K. Kellay (LATP), M. Shabankhah (LATP), O. El-Fallah","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-03-26T07:55:48Z","title":"Level sets and Composition operators on the Dirichlet space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.5059","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:a11ff705c661a120303076807ab56a52e40805bf92b48768ced98f7dbe2a3534","target":"record","created_at":"2026-05-18T04:32:33Z","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":"8d788df1e19e645116b7c1ed0de0c370a7c6be463caf1607483da7e60cb6d864","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-03-26T07:55:48Z","title_canon_sha256":"abb4b1f599f66f1a461107c7e4b5425480e10b702ebee32f21d6e6b2d932941b"},"schema_version":"1.0","source":{"id":"1003.5059","kind":"arxiv","version":1}},"canonical_sha256":"bbef74f81134fd662631ae43be67556463dc2d7c394dda15c197a1c22a59796b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bbef74f81134fd662631ae43be67556463dc2d7c394dda15c197a1c22a59796b","first_computed_at":"2026-05-18T04:32:33.963784Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:32:33.963784Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NQbDxbRavXwE/tFwszDbUsQn9v2BGbpOHouVRFCHMKkQMNnqY+FOocIPjS4a/9eN0DYM/GD57pp2hLC5c+85CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:32:33.964209Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.5059","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a11ff705c661a120303076807ab56a52e40805bf92b48768ced98f7dbe2a3534","sha256:b82ba8653cc13de79c0e32e2f9bee440d72587b1da2b1116fcfe7161fe5279ed"],"state_sha256":"04bf9e799cdb55eb95010d1aa01ddfdb938a778da0113d98cd9510d638e75d1a"}