{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:O543UHPXGT5MKS2H7QNOW6IK7F","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":"e35cdf432761e6bada5c6d8dba5d7370cf42f66fcfc0a79def07e83895d497c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-05-31T10:44:24Z","title_canon_sha256":"3cd10ef619bdfc2eb2aa84e6fe2662ba5a2e4d45996b957e7f08d9c1db41ff7b"},"schema_version":"1.0","source":{"id":"1305.7350","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.7350","created_at":"2026-05-18T01:09:32Z"},{"alias_kind":"arxiv_version","alias_value":"1305.7350v1","created_at":"2026-05-18T01:09:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.7350","created_at":"2026-05-18T01:09:32Z"},{"alias_kind":"pith_short_12","alias_value":"O543UHPXGT5M","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"O543UHPXGT5MKS2H","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"O543UHPX","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:5a78cca9beaec91cac3ab0ccb61a04bc949eca2d32532daf47cc55f493dbe449","target":"graph","created_at":"2026-05-18T01:09:32Z","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 study the action of some generalized integral operators of Bergman type on pointwise multipliers of holomorphic Triebel-Lizorkin spaces. We construct nontrivial examples of pointwise multipliers in Hardy-Sobolev spaces and give applications of all these results.","authors_text":"Carme Cascante, Joan F\\`abrega, Joaqu\\'in M. Ortega","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-05-31T10:44:24Z","title":"On multipliers for Hardy-Sobolev spaces and holomorphic potentials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.7350","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":"sha256:8ae60f48bce0475eff8913745001584f88c716597d5526e692ed626c2b655b78","target":"record","created_at":"2026-05-18T01:09:32Z","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":"e35cdf432761e6bada5c6d8dba5d7370cf42f66fcfc0a79def07e83895d497c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-05-31T10:44:24Z","title_canon_sha256":"3cd10ef619bdfc2eb2aa84e6fe2662ba5a2e4d45996b957e7f08d9c1db41ff7b"},"schema_version":"1.0","source":{"id":"1305.7350","kind":"arxiv","version":1}},"canonical_sha256":"7779ba1df734fac54b47fc1aeb790af943c265317d662df60d8fb73e6451a8cf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7779ba1df734fac54b47fc1aeb790af943c265317d662df60d8fb73e6451a8cf","first_computed_at":"2026-05-18T01:09:32.691784Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:32.691784Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Qvd2AYZYmqq5S38MkkdyZ0H2Nm9X670STQdqfpJCnWTXN5oiimqAI4+txqfXBK+rulVIZn4VkoeMXlT/ikTtCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:32.692202Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.7350","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8ae60f48bce0475eff8913745001584f88c716597d5526e692ed626c2b655b78","sha256:5a78cca9beaec91cac3ab0ccb61a04bc949eca2d32532daf47cc55f493dbe449"],"state_sha256":"a001583e7847cffc07e6bccf64d51d20ee980365fd6c39ff2e73527b4fe01d71"}