{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:G7WIHLZYA3SZ2JQXSBRZ3KFYLO","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":"fa7267ec2b47bded0ec459e737cee2455a74cbf5f6a536ce6319735c9f31177e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-05-03T12:43:05Z","title_canon_sha256":"89fd41b98ff546b9c7d9bb9de8d2640634c117f8cf96f49e5108fd5b6420b830"},"schema_version":"1.0","source":{"id":"1405.0578","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.0578","created_at":"2026-05-18T01:34:35Z"},{"alias_kind":"arxiv_version","alias_value":"1405.0578v4","created_at":"2026-05-18T01:34:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.0578","created_at":"2026-05-18T01:34:35Z"},{"alias_kind":"pith_short_12","alias_value":"G7WIHLZYA3SZ","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"G7WIHLZYA3SZ2JQX","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"G7WIHLZY","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:0a7a8858d1342310a27009d17cbe1d3bc5c56c6a87112ed82db4c3e664141472","target":"graph","created_at":"2026-05-18T01:34:35Z","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 show that any function in a Bergman space with exponential type weights admits a representation in terms of an infinite series of kernel functions.","authors_text":"Hicham Arroussi, Jordi Pau","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-05-03T12:43:05Z","title":"Atomic decomposition for Bergman spaces with exponential type weights"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0578","kind":"arxiv","version":4},"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":"sha256:3633eb6588f7639d4a60bf8f5c5c7882c4dd71be175f6add0a43717213c3083f","target":"record","created_at":"2026-05-18T01:34:35Z","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":"fa7267ec2b47bded0ec459e737cee2455a74cbf5f6a536ce6319735c9f31177e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-05-03T12:43:05Z","title_canon_sha256":"89fd41b98ff546b9c7d9bb9de8d2640634c117f8cf96f49e5108fd5b6420b830"},"schema_version":"1.0","source":{"id":"1405.0578","kind":"arxiv","version":4}},"canonical_sha256":"37ec83af3806e59d261790639da8b85b99ed36454efdfe0b9e8560621c59a53c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"37ec83af3806e59d261790639da8b85b99ed36454efdfe0b9e8560621c59a53c","first_computed_at":"2026-05-18T01:34:35.683577Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:35.683577Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zE/6HSvCyzOkdnhji6pOzgu+0q0TdR3xa+Tw2bVn8a9ewV+hh+dYyA9cE6Ibys6GC+3t9NN5hdK3mhLdKUpHBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:35.684033Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.0578","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3633eb6588f7639d4a60bf8f5c5c7882c4dd71be175f6add0a43717213c3083f","sha256:0a7a8858d1342310a27009d17cbe1d3bc5c56c6a87112ed82db4c3e664141472"],"state_sha256":"b4442be1fa2e263da71e9126b03a632a21a642acb1f9b067a19aefee868d8a12"}