{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:7KCBCCED5HJ2S2KAOVOP5URRUH","short_pith_number":"pith:7KCBCCED","canonical_record":{"source":{"id":"0812.3422","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2008-12-17T22:24:17Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"bd5a265e20441fd7a45b59de8ee9d3aa626bb39c2647b3a9f17caf6e9e3a991b","abstract_canon_sha256":"90ee96cacd5183070e73b15441077a0878521639b91b59848433488f801ad140"},"schema_version":"1.0"},"canonical_sha256":"fa84110883e9d3a96940755cfed231a1eb736a26ce75fb39e1448f86830499a5","source":{"kind":"arxiv","id":"0812.3422","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.3422","created_at":"2026-05-18T04:13:46Z"},{"alias_kind":"arxiv_version","alias_value":"0812.3422v1","created_at":"2026-05-18T04:13:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.3422","created_at":"2026-05-18T04:13:46Z"},{"alias_kind":"pith_short_12","alias_value":"7KCBCCED5HJ2","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"7KCBCCED5HJ2S2KA","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"7KCBCCED","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:7KCBCCED5HJ2S2KAOVOP5URRUH","target":"record","payload":{"canonical_record":{"source":{"id":"0812.3422","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2008-12-17T22:24:17Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"bd5a265e20441fd7a45b59de8ee9d3aa626bb39c2647b3a9f17caf6e9e3a991b","abstract_canon_sha256":"90ee96cacd5183070e73b15441077a0878521639b91b59848433488f801ad140"},"schema_version":"1.0"},"canonical_sha256":"fa84110883e9d3a96940755cfed231a1eb736a26ce75fb39e1448f86830499a5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:13:46.021724Z","signature_b64":"4D7HVJH0MS7lsjHWXgbGiU+8p338bAS1QlISA6UL050tKz1/Jh3Nqu2UkO4Qh25sAPzV8yYTouRNdwB6CYauDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fa84110883e9d3a96940755cfed231a1eb736a26ce75fb39e1448f86830499a5","last_reissued_at":"2026-05-18T04:13:46.021360Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:13:46.021360Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0812.3422","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":"2026-05-18T04:13:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kd9hUT88hXH3jHthCvjrdQPE6eBRZF0eJ4wt98k8PW5yYiDOqnqhVkwl/BnWkTLcTuXLH+J3Ps6k0jV+ZYacDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T14:34:55.631378Z"},"content_sha256":"ee64d309ec153338f2f526830c8f969ffe3b0c4ac28d0a8179730d4fc3e0ffa5","schema_version":"1.0","event_id":"sha256:ee64d309ec153338f2f526830c8f969ffe3b0c4ac28d0a8179730d4fc3e0ffa5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:7KCBCCED5HJ2S2KAOVOP5URRUH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Function Spaces Related to the Dirichlet Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CV","authors_text":"Brett D. Wick, Eric Sawyer, Nicola Arcozzi, Richard Rochberg","submitted_at":"2008-12-17T22:24:17Z","abstract_excerpt":"We present results about spaces of holomorphic functions associated to the classical Dirichlet space. The spaces we consider have roles similar to the roles of $H^{1}$ and $BMO$ in the Hardy space theory and we emphasize those analogies."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.3422","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":"2026-05-18T04:13:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QUJDcLc+PhO+YBuCXLcJ17R/bGoYtGbJF7xLayi8Rzbgm2jSL7YKY504HFcAv/zdEu1leQ+B5DzMxu7+op8YDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T14:34:55.631736Z"},"content_sha256":"9612b6eaf0d555588187df777d665228f74865f3201a894b0395b2bb0b035dc6","schema_version":"1.0","event_id":"sha256:9612b6eaf0d555588187df777d665228f74865f3201a894b0395b2bb0b035dc6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7KCBCCED5HJ2S2KAOVOP5URRUH/bundle.json","state_url":"https://pith.science/pith/7KCBCCED5HJ2S2KAOVOP5URRUH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7KCBCCED5HJ2S2KAOVOP5URRUH/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":"2026-06-01T14:34:55Z","links":{"resolver":"https://pith.science/pith/7KCBCCED5HJ2S2KAOVOP5URRUH","bundle":"https://pith.science/pith/7KCBCCED5HJ2S2KAOVOP5URRUH/bundle.json","state":"https://pith.science/pith/7KCBCCED5HJ2S2KAOVOP5URRUH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7KCBCCED5HJ2S2KAOVOP5URRUH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:7KCBCCED5HJ2S2KAOVOP5URRUH","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":"90ee96cacd5183070e73b15441077a0878521639b91b59848433488f801ad140","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2008-12-17T22:24:17Z","title_canon_sha256":"bd5a265e20441fd7a45b59de8ee9d3aa626bb39c2647b3a9f17caf6e9e3a991b"},"schema_version":"1.0","source":{"id":"0812.3422","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.3422","created_at":"2026-05-18T04:13:46Z"},{"alias_kind":"arxiv_version","alias_value":"0812.3422v1","created_at":"2026-05-18T04:13:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.3422","created_at":"2026-05-18T04:13:46Z"},{"alias_kind":"pith_short_12","alias_value":"7KCBCCED5HJ2","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"7KCBCCED5HJ2S2KA","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"7KCBCCED","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:9612b6eaf0d555588187df777d665228f74865f3201a894b0395b2bb0b035dc6","target":"graph","created_at":"2026-05-18T04:13:46Z","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 present results about spaces of holomorphic functions associated to the classical Dirichlet space. The spaces we consider have roles similar to the roles of $H^{1}$ and $BMO$ in the Hardy space theory and we emphasize those analogies.","authors_text":"Brett D. Wick, Eric Sawyer, Nicola Arcozzi, Richard Rochberg","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2008-12-17T22:24:17Z","title":"Function Spaces Related to the Dirichlet Space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.3422","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:ee64d309ec153338f2f526830c8f969ffe3b0c4ac28d0a8179730d4fc3e0ffa5","target":"record","created_at":"2026-05-18T04:13:46Z","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":"90ee96cacd5183070e73b15441077a0878521639b91b59848433488f801ad140","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2008-12-17T22:24:17Z","title_canon_sha256":"bd5a265e20441fd7a45b59de8ee9d3aa626bb39c2647b3a9f17caf6e9e3a991b"},"schema_version":"1.0","source":{"id":"0812.3422","kind":"arxiv","version":1}},"canonical_sha256":"fa84110883e9d3a96940755cfed231a1eb736a26ce75fb39e1448f86830499a5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fa84110883e9d3a96940755cfed231a1eb736a26ce75fb39e1448f86830499a5","first_computed_at":"2026-05-18T04:13:46.021360Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:13:46.021360Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4D7HVJH0MS7lsjHWXgbGiU+8p338bAS1QlISA6UL050tKz1/Jh3Nqu2UkO4Qh25sAPzV8yYTouRNdwB6CYauDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:13:46.021724Z","signed_message":"canonical_sha256_bytes"},"source_id":"0812.3422","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee64d309ec153338f2f526830c8f969ffe3b0c4ac28d0a8179730d4fc3e0ffa5","sha256:9612b6eaf0d555588187df777d665228f74865f3201a894b0395b2bb0b035dc6"],"state_sha256":"263b49e392ea588f1bd7e9f7d28533453a07fc042da2eaff25db96a66cb0595f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DkFrN0S8ItKggflg8v5Zh2B3fv0ki9ontrtvUhUi4eqeXUVbuaQ6DXu72mIbJ73/tMF4KlmaAOvdMIk3dXkhCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T14:34:55.634475Z","bundle_sha256":"8ef5a6017594fdcf52f43ad3bd970a845759a196258f2bcd9d5bd9971d54a1f2"}}