{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:JBE6KHQT5SRUDKJQQYIC2PXBSL","short_pith_number":"pith:JBE6KHQT","canonical_record":{"source":{"id":"1304.5958","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-04-22T14:18:38Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"3851d578bf4e585eb5b8992b647dd2e0e4808e65aaa1762ff6637cf6b615b860","abstract_canon_sha256":"970c0ae6e71fec80b700bb861a6d96815228c6294037a8e5d39491911dc911dc"},"schema_version":"1.0"},"canonical_sha256":"4849e51e13eca341a93086102d3ee192e7f0b2bcc99bc08f0e4ef2cb00b5f731","source":{"kind":"arxiv","id":"1304.5958","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.5958","created_at":"2026-05-18T03:27:23Z"},{"alias_kind":"arxiv_version","alias_value":"1304.5958v1","created_at":"2026-05-18T03:27:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.5958","created_at":"2026-05-18T03:27:23Z"},{"alias_kind":"pith_short_12","alias_value":"JBE6KHQT5SRU","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JBE6KHQT5SRUDKJQ","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JBE6KHQT","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:JBE6KHQT5SRUDKJQQYIC2PXBSL","target":"record","payload":{"canonical_record":{"source":{"id":"1304.5958","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-04-22T14:18:38Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"3851d578bf4e585eb5b8992b647dd2e0e4808e65aaa1762ff6637cf6b615b860","abstract_canon_sha256":"970c0ae6e71fec80b700bb861a6d96815228c6294037a8e5d39491911dc911dc"},"schema_version":"1.0"},"canonical_sha256":"4849e51e13eca341a93086102d3ee192e7f0b2bcc99bc08f0e4ef2cb00b5f731","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:27:23.679061Z","signature_b64":"XbpLo1mc39cvADJUQ5oQKEVbszDAVRohHI2grMPKt6oHFscH0qx/RggmefjvbPM6i1Lryf/ZBPwhIkGEkH7yCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4849e51e13eca341a93086102d3ee192e7f0b2bcc99bc08f0e4ef2cb00b5f731","last_reissued_at":"2026-05-18T03:27:23.678416Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:27:23.678416Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.5958","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:27:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CA6qoPE1BrYFfg7r5CBD6c6VuwwcQbDAV8TwNuTUWIWEDo5RNe0uOQliBAE8bjGzKJZQ7JOE6SjrWNCe+e9XCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T10:31:46.173968Z"},"content_sha256":"2179b3a53ad6c0f193db7203f0c138516e729d3dd27a32fc7ce2e5f9b02d953e","schema_version":"1.0","event_id":"sha256:2179b3a53ad6c0f193db7203f0c138516e729d3dd27a32fc7ce2e5f9b02d953e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:JBE6KHQT5SRUDKJQQYIC2PXBSL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Characterizations of Dirichlet-type Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CV","authors_text":"Gerardo R. Chac\\'on, Xiaosong Liu, Zengjian Lou","submitted_at":"2013-04-22T14:18:38Z","abstract_excerpt":"We give three characterizations of the Dirichlet-type spaces $D(\\mu)$. First we characterize $D(\\mu)$ in terms of a double integral and in terms of the mean oscillation in the Bergman metric, none of them involve the use of derivatives. Next, we obtain another characterization for $D(\\mu)$ in terms of higher order derivatives. Also, a decomposition theorem for $D(\\mu)$ is established."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5958","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:27:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZIkAlqjnGfUKz9h0LGlgMw+rs+PROWsr5V4hl9EIsHQiduEtFXrzm0fht3X2lbqQevVJg9jWkWsduHTZxgM9DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T10:31:46.174633Z"},"content_sha256":"e87b441e4be31ec3361e1cb3b49b30c6d62a054e182aa68ae8f62256b7ee1165","schema_version":"1.0","event_id":"sha256:e87b441e4be31ec3361e1cb3b49b30c6d62a054e182aa68ae8f62256b7ee1165"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JBE6KHQT5SRUDKJQQYIC2PXBSL/bundle.json","state_url":"https://pith.science/pith/JBE6KHQT5SRUDKJQQYIC2PXBSL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JBE6KHQT5SRUDKJQQYIC2PXBSL/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-10T10:31:46Z","links":{"resolver":"https://pith.science/pith/JBE6KHQT5SRUDKJQQYIC2PXBSL","bundle":"https://pith.science/pith/JBE6KHQT5SRUDKJQQYIC2PXBSL/bundle.json","state":"https://pith.science/pith/JBE6KHQT5SRUDKJQQYIC2PXBSL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JBE6KHQT5SRUDKJQQYIC2PXBSL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:JBE6KHQT5SRUDKJQQYIC2PXBSL","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":"970c0ae6e71fec80b700bb861a6d96815228c6294037a8e5d39491911dc911dc","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-04-22T14:18:38Z","title_canon_sha256":"3851d578bf4e585eb5b8992b647dd2e0e4808e65aaa1762ff6637cf6b615b860"},"schema_version":"1.0","source":{"id":"1304.5958","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.5958","created_at":"2026-05-18T03:27:23Z"},{"alias_kind":"arxiv_version","alias_value":"1304.5958v1","created_at":"2026-05-18T03:27:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.5958","created_at":"2026-05-18T03:27:23Z"},{"alias_kind":"pith_short_12","alias_value":"JBE6KHQT5SRU","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JBE6KHQT5SRUDKJQ","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JBE6KHQT","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:e87b441e4be31ec3361e1cb3b49b30c6d62a054e182aa68ae8f62256b7ee1165","target":"graph","created_at":"2026-05-18T03:27:23Z","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 give three characterizations of the Dirichlet-type spaces $D(\\mu)$. First we characterize $D(\\mu)$ in terms of a double integral and in terms of the mean oscillation in the Bergman metric, none of them involve the use of derivatives. Next, we obtain another characterization for $D(\\mu)$ in terms of higher order derivatives. Also, a decomposition theorem for $D(\\mu)$ is established.","authors_text":"Gerardo R. Chac\\'on, Xiaosong Liu, Zengjian Lou","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-04-22T14:18:38Z","title":"Characterizations of Dirichlet-type Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5958","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":"sha256:2179b3a53ad6c0f193db7203f0c138516e729d3dd27a32fc7ce2e5f9b02d953e","target":"record","created_at":"2026-05-18T03:27:23Z","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":"970c0ae6e71fec80b700bb861a6d96815228c6294037a8e5d39491911dc911dc","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-04-22T14:18:38Z","title_canon_sha256":"3851d578bf4e585eb5b8992b647dd2e0e4808e65aaa1762ff6637cf6b615b860"},"schema_version":"1.0","source":{"id":"1304.5958","kind":"arxiv","version":1}},"canonical_sha256":"4849e51e13eca341a93086102d3ee192e7f0b2bcc99bc08f0e4ef2cb00b5f731","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4849e51e13eca341a93086102d3ee192e7f0b2bcc99bc08f0e4ef2cb00b5f731","first_computed_at":"2026-05-18T03:27:23.678416Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:27:23.678416Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XbpLo1mc39cvADJUQ5oQKEVbszDAVRohHI2grMPKt6oHFscH0qx/RggmefjvbPM6i1Lryf/ZBPwhIkGEkH7yCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:27:23.679061Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.5958","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2179b3a53ad6c0f193db7203f0c138516e729d3dd27a32fc7ce2e5f9b02d953e","sha256:e87b441e4be31ec3361e1cb3b49b30c6d62a054e182aa68ae8f62256b7ee1165"],"state_sha256":"50c9f8cd1df7cae1f3d8037ad31a38b2c3641bd5d295372cc46b0ecdaf90fc59"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wNa+0nQiNWX9Fe2aFTqLAYAn136uqgRgM63I87u7ZmxXbk9dI6kXBdwzWOtT/YNmKa7srWaBJdZNYkC45cM6CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T10:31:46.178682Z","bundle_sha256":"7e86af6b14dbb6aa18c8abdff7934ead3c39064d2e344fac718d2d5dade746d7"}}