{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:KKTSGHE33JWWWBQV3EF6W77EJA","short_pith_number":"pith:KKTSGHE3","canonical_record":{"source":{"id":"1408.4724","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-08-20T17:00:49Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"c00fa9409c4922c1dd150bfd4533f7161ea6bf82cf0de228bff1fadc4f4d66ae","abstract_canon_sha256":"741bbe0c9336f7ca50e8d6f2b36b9e5675154c12db60fa062efa3141a6b4105b"},"schema_version":"1.0"},"canonical_sha256":"52a7231c9bda6d6b0615d90beb7fe4482bb0154f14f2bc2a9556cda39887bbe0","source":{"kind":"arxiv","id":"1408.4724","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.4724","created_at":"2026-05-18T02:44:48Z"},{"alias_kind":"arxiv_version","alias_value":"1408.4724v1","created_at":"2026-05-18T02:44:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.4724","created_at":"2026-05-18T02:44:48Z"},{"alias_kind":"pith_short_12","alias_value":"KKTSGHE33JWW","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"KKTSGHE33JWWWBQV","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"KKTSGHE3","created_at":"2026-05-18T12:28:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:KKTSGHE33JWWWBQV3EF6W77EJA","target":"record","payload":{"canonical_record":{"source":{"id":"1408.4724","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-08-20T17:00:49Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"c00fa9409c4922c1dd150bfd4533f7161ea6bf82cf0de228bff1fadc4f4d66ae","abstract_canon_sha256":"741bbe0c9336f7ca50e8d6f2b36b9e5675154c12db60fa062efa3141a6b4105b"},"schema_version":"1.0"},"canonical_sha256":"52a7231c9bda6d6b0615d90beb7fe4482bb0154f14f2bc2a9556cda39887bbe0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:48.259425Z","signature_b64":"c4oPg9A4hfTewa3dslZV7vi+2AVk3gXP2K5bkbUZ3wbMZYOgaauUz0kpuJxtshIIGG3ywOOCj3aw0pn+Lt9QDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"52a7231c9bda6d6b0615d90beb7fe4482bb0154f14f2bc2a9556cda39887bbe0","last_reissued_at":"2026-05-18T02:44:48.259033Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:48.259033Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1408.4724","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":"2026-05-18T02:44:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"57+ORgPWvXXv/GIqO1de359E22LHfw3vsaHp8KcstY3SO1ucPG/aZRXDs8JgyZT0KoWf0Nmynts3UL4vBHdlCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T21:39:58.969470Z"},"content_sha256":"b89d3d5e591822c63a2b9348382984aa7c944d0e8adc9689a0445c6fe8f446c3","schema_version":"1.0","event_id":"sha256:b89d3d5e591822c63a2b9348382984aa7c944d0e8adc9689a0445c6fe8f446c3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:KKTSGHE33JWWWBQV3EF6W77EJA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Closure of Hardy spaces in the Bloch space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.CV","authors_text":"Jordi Pau, Nacho Monreal Gal\\'an, Petros Galanopoulos","submitted_at":"2014-08-20T17:00:49Z","abstract_excerpt":"A description of the Bloch functions that can be approximated in the Bloch norm by functions in the Hardy space $H^p$ of the unit ball of $\\Cn$ for $0<p<\\infty$ is given. When $0<p\\leq1$, the result is new even in the case of the unit disk."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.4724","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":"2026-05-18T02:44:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JZpl+os6MGQg9xgWU/BzqKrlUzEQV+WZ52IjQGiFVIIOMnA4kj9o7zuVIb0twbYlrMer3ZLKqJUMOFZKJM4XCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T21:39:58.969810Z"},"content_sha256":"d31f06c20593dee6398d70abdbe7421ef2be5705e82af8c3ef455c32e46a34fe","schema_version":"1.0","event_id":"sha256:d31f06c20593dee6398d70abdbe7421ef2be5705e82af8c3ef455c32e46a34fe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KKTSGHE33JWWWBQV3EF6W77EJA/bundle.json","state_url":"https://pith.science/pith/KKTSGHE33JWWWBQV3EF6W77EJA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KKTSGHE33JWWWBQV3EF6W77EJA/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":"2026-06-22T21:39:58Z","links":{"resolver":"https://pith.science/pith/KKTSGHE33JWWWBQV3EF6W77EJA","bundle":"https://pith.science/pith/KKTSGHE33JWWWBQV3EF6W77EJA/bundle.json","state":"https://pith.science/pith/KKTSGHE33JWWWBQV3EF6W77EJA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KKTSGHE33JWWWBQV3EF6W77EJA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:KKTSGHE33JWWWBQV3EF6W77EJA","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":"741bbe0c9336f7ca50e8d6f2b36b9e5675154c12db60fa062efa3141a6b4105b","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-08-20T17:00:49Z","title_canon_sha256":"c00fa9409c4922c1dd150bfd4533f7161ea6bf82cf0de228bff1fadc4f4d66ae"},"schema_version":"1.0","source":{"id":"1408.4724","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.4724","created_at":"2026-05-18T02:44:48Z"},{"alias_kind":"arxiv_version","alias_value":"1408.4724v1","created_at":"2026-05-18T02:44:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.4724","created_at":"2026-05-18T02:44:48Z"},{"alias_kind":"pith_short_12","alias_value":"KKTSGHE33JWW","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"KKTSGHE33JWWWBQV","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"KKTSGHE3","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:d31f06c20593dee6398d70abdbe7421ef2be5705e82af8c3ef455c32e46a34fe","target":"graph","created_at":"2026-05-18T02:44:48Z","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":"A description of the Bloch functions that can be approximated in the Bloch norm by functions in the Hardy space $H^p$ of the unit ball of $\\Cn$ for $0<p<\\infty$ is given. When $0<p\\leq1$, the result is new even in the case of the unit disk.","authors_text":"Jordi Pau, Nacho Monreal Gal\\'an, Petros Galanopoulos","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-08-20T17:00:49Z","title":"Closure of Hardy spaces in the Bloch space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.4724","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:b89d3d5e591822c63a2b9348382984aa7c944d0e8adc9689a0445c6fe8f446c3","target":"record","created_at":"2026-05-18T02:44:48Z","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":"741bbe0c9336f7ca50e8d6f2b36b9e5675154c12db60fa062efa3141a6b4105b","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-08-20T17:00:49Z","title_canon_sha256":"c00fa9409c4922c1dd150bfd4533f7161ea6bf82cf0de228bff1fadc4f4d66ae"},"schema_version":"1.0","source":{"id":"1408.4724","kind":"arxiv","version":1}},"canonical_sha256":"52a7231c9bda6d6b0615d90beb7fe4482bb0154f14f2bc2a9556cda39887bbe0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"52a7231c9bda6d6b0615d90beb7fe4482bb0154f14f2bc2a9556cda39887bbe0","first_computed_at":"2026-05-18T02:44:48.259033Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:48.259033Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c4oPg9A4hfTewa3dslZV7vi+2AVk3gXP2K5bkbUZ3wbMZYOgaauUz0kpuJxtshIIGG3ywOOCj3aw0pn+Lt9QDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:48.259425Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.4724","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b89d3d5e591822c63a2b9348382984aa7c944d0e8adc9689a0445c6fe8f446c3","sha256:d31f06c20593dee6398d70abdbe7421ef2be5705e82af8c3ef455c32e46a34fe"],"state_sha256":"1ab603bfd330b846c78b25f83838295fea89bd8831a0a5004ab62717173ba61f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qVY68rfjlf2i8d7LG48NBjOd2JjBwNnw+A0paCBGTuU24JgY3GWdX5OObqfn5bqo7Jv8PFO22JX6oFpxuxYFCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T21:39:58.972156Z","bundle_sha256":"6a3f71c42124abddcb8e128850685c629ccaf2cebf602a3bf377ab0b81f53bdb"}}