{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:FNLNAXKFFXS7ZVQVSGND37LGNV","short_pith_number":"pith:FNLNAXKF","canonical_record":{"source":{"id":"1412.6019","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-12-18T19:26:06Z","cross_cats_sorted":[],"title_canon_sha256":"ea73abff82147b80cf2128f146acbfc5ba147dc8bda78176e634d922539d267b","abstract_canon_sha256":"e9da1f297cdaff19113e98bb998f4c951a4af4a145c5f6359000617be9adf56c"},"schema_version":"1.0"},"canonical_sha256":"2b56d05d452de5fcd615919a3dfd666d715c7a12cd0ef015c0379be34e407f71","source":{"kind":"arxiv","id":"1412.6019","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.6019","created_at":"2026-05-18T02:30:55Z"},{"alias_kind":"arxiv_version","alias_value":"1412.6019v1","created_at":"2026-05-18T02:30:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.6019","created_at":"2026-05-18T02:30:55Z"},{"alias_kind":"pith_short_12","alias_value":"FNLNAXKFFXS7","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"FNLNAXKFFXS7ZVQV","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"FNLNAXKF","created_at":"2026-05-18T12:28:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:FNLNAXKFFXS7ZVQVSGND37LGNV","target":"record","payload":{"canonical_record":{"source":{"id":"1412.6019","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-12-18T19:26:06Z","cross_cats_sorted":[],"title_canon_sha256":"ea73abff82147b80cf2128f146acbfc5ba147dc8bda78176e634d922539d267b","abstract_canon_sha256":"e9da1f297cdaff19113e98bb998f4c951a4af4a145c5f6359000617be9adf56c"},"schema_version":"1.0"},"canonical_sha256":"2b56d05d452de5fcd615919a3dfd666d715c7a12cd0ef015c0379be34e407f71","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:55.671935Z","signature_b64":"yvRa3Y5F4QhMGdqSJB7dUl8U0fSFdvtrGPpMOlaEOMwiooXYOxIDORgZ/hZmEaA0JEaB4mLQQnCNlWKQ4VZzBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b56d05d452de5fcd615919a3dfd666d715c7a12cd0ef015c0379be34e407f71","last_reissued_at":"2026-05-18T02:30:55.671303Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:55.671303Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.6019","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":"2026-05-18T02:30:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u8G+ohRa0SMPql3kK7pYs2y8uh1LBwYIaww2Rqj59ScJfI9imtXiAHJPuVKTC3J425h99sIelhEqM3QGM5WOBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T07:21:56.565702Z"},"content_sha256":"6389c57d1209fca6b4852c95be13c0ce63bc55e9e6ce52a1064e1b75bca9af94","schema_version":"1.0","event_id":"sha256:6389c57d1209fca6b4852c95be13c0ce63bc55e9e6ce52a1064e1b75bca9af94"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:FNLNAXKFFXS7ZVQVSGND37LGNV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Hodge Theory of maps (Lectures 4 and 5)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Mark Andrea A. de Cataldo","submitted_at":"2014-12-18T19:26:06Z","abstract_excerpt":"Lecture notes of lectures delivered at the Hodge Theory Summer School in ICTP Trieste, June 2010."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.6019","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":"2026-05-18T02:30:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/82R41kJ9v0nLA1v4Dv8vrm3OflcruFJ5PkFi4WO8gvPSA/gcw73oJ6GIcDCq8N11xP7mOdKof5FmAf5B1bfBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T07:21:56.566039Z"},"content_sha256":"c8763af409da2a7ed2529ccb4b92165e3399b47cca6e675ac14fc36b6e768b2b","schema_version":"1.0","event_id":"sha256:c8763af409da2a7ed2529ccb4b92165e3399b47cca6e675ac14fc36b6e768b2b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FNLNAXKFFXS7ZVQVSGND37LGNV/bundle.json","state_url":"https://pith.science/pith/FNLNAXKFFXS7ZVQVSGND37LGNV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FNLNAXKFFXS7ZVQVSGND37LGNV/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":"2026-06-20T07:21:56Z","links":{"resolver":"https://pith.science/pith/FNLNAXKFFXS7ZVQVSGND37LGNV","bundle":"https://pith.science/pith/FNLNAXKFFXS7ZVQVSGND37LGNV/bundle.json","state":"https://pith.science/pith/FNLNAXKFFXS7ZVQVSGND37LGNV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FNLNAXKFFXS7ZVQVSGND37LGNV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:FNLNAXKFFXS7ZVQVSGND37LGNV","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":"e9da1f297cdaff19113e98bb998f4c951a4af4a145c5f6359000617be9adf56c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-12-18T19:26:06Z","title_canon_sha256":"ea73abff82147b80cf2128f146acbfc5ba147dc8bda78176e634d922539d267b"},"schema_version":"1.0","source":{"id":"1412.6019","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.6019","created_at":"2026-05-18T02:30:55Z"},{"alias_kind":"arxiv_version","alias_value":"1412.6019v1","created_at":"2026-05-18T02:30:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.6019","created_at":"2026-05-18T02:30:55Z"},{"alias_kind":"pith_short_12","alias_value":"FNLNAXKFFXS7","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"FNLNAXKFFXS7ZVQV","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"FNLNAXKF","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:c8763af409da2a7ed2529ccb4b92165e3399b47cca6e675ac14fc36b6e768b2b","target":"graph","created_at":"2026-05-18T02:30:55Z","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":"Lecture notes of lectures delivered at the Hodge Theory Summer School in ICTP Trieste, June 2010.","authors_text":"Mark Andrea A. de Cataldo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-12-18T19:26:06Z","title":"The Hodge Theory of maps (Lectures 4 and 5)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.6019","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":"sha256:6389c57d1209fca6b4852c95be13c0ce63bc55e9e6ce52a1064e1b75bca9af94","target":"record","created_at":"2026-05-18T02:30:55Z","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":"e9da1f297cdaff19113e98bb998f4c951a4af4a145c5f6359000617be9adf56c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-12-18T19:26:06Z","title_canon_sha256":"ea73abff82147b80cf2128f146acbfc5ba147dc8bda78176e634d922539d267b"},"schema_version":"1.0","source":{"id":"1412.6019","kind":"arxiv","version":1}},"canonical_sha256":"2b56d05d452de5fcd615919a3dfd666d715c7a12cd0ef015c0379be34e407f71","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b56d05d452de5fcd615919a3dfd666d715c7a12cd0ef015c0379be34e407f71","first_computed_at":"2026-05-18T02:30:55.671303Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:55.671303Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yvRa3Y5F4QhMGdqSJB7dUl8U0fSFdvtrGPpMOlaEOMwiooXYOxIDORgZ/hZmEaA0JEaB4mLQQnCNlWKQ4VZzBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:55.671935Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.6019","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6389c57d1209fca6b4852c95be13c0ce63bc55e9e6ce52a1064e1b75bca9af94","sha256:c8763af409da2a7ed2529ccb4b92165e3399b47cca6e675ac14fc36b6e768b2b"],"state_sha256":"f6592e9a443e2daff5ef51985a5acafe697dbfe56e1ae6c8ad23509347f12275"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"clXYarc4wYOdXwMwV7kPEZED+DsUx+Fe711UysjyiI8snoRnZg3vjBUJo5HULUaUqZUj5YOV0X4ni+rTIGfQCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T07:21:56.567979Z","bundle_sha256":"bec654a6adf5538c955d51c3eb306a3a75b21dcbabfcf1b7e8926305f82324ff"}}