{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:T7FWLQR4IOHYTL6V23EUVJ7EZN","short_pith_number":"pith:T7FWLQR4","canonical_record":{"source":{"id":"0905.4114","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-05-26T05:03:46Z","cross_cats_sorted":[],"title_canon_sha256":"f62262ddef1502f5c5a9941d94d1f9ac2f3f1bb95a0e7ed477f85f0ea479296a","abstract_canon_sha256":"694754df5fd651b76f285f7f9834f856fd68b184e17d8178f232690402655e6f"},"schema_version":"1.0"},"canonical_sha256":"9fcb65c23c438f89afd5d6c94aa7e4cb4f1ba7f336a96024f2e63d9cb04e9afa","source":{"kind":"arxiv","id":"0905.4114","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0905.4114","created_at":"2026-05-18T02:13:37Z"},{"alias_kind":"arxiv_version","alias_value":"0905.4114v1","created_at":"2026-05-18T02:13:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.4114","created_at":"2026-05-18T02:13:37Z"},{"alias_kind":"pith_short_12","alias_value":"T7FWLQR4IOHY","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"T7FWLQR4IOHYTL6V","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"T7FWLQR4","created_at":"2026-05-18T12:26:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:T7FWLQR4IOHYTL6V23EUVJ7EZN","target":"record","payload":{"canonical_record":{"source":{"id":"0905.4114","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-05-26T05:03:46Z","cross_cats_sorted":[],"title_canon_sha256":"f62262ddef1502f5c5a9941d94d1f9ac2f3f1bb95a0e7ed477f85f0ea479296a","abstract_canon_sha256":"694754df5fd651b76f285f7f9834f856fd68b184e17d8178f232690402655e6f"},"schema_version":"1.0"},"canonical_sha256":"9fcb65c23c438f89afd5d6c94aa7e4cb4f1ba7f336a96024f2e63d9cb04e9afa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:13:37.617909Z","signature_b64":"NEny6KN7P8aje5NKgcm3daRhZe4JBDLsIhjROPL+2kkrZKQWfjmkakL9CsnLmHv2AaDg82OEOVNjvq/jbrBzDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9fcb65c23c438f89afd5d6c94aa7e4cb4f1ba7f336a96024f2e63d9cb04e9afa","last_reissued_at":"2026-05-18T02:13:37.617434Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:13:37.617434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0905.4114","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":"2026-05-18T02:13:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dOOCKMAQQ+ltSTiAxVgiA9gubqBi8oB4Gna/bLLw3X0hv2gpDtkb1OcRhiPed7miPUmOoXfGljGMvACaHIdDCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T14:36:43.297310Z"},"content_sha256":"adcaac105b4d519b6e858328fd1f0ff58c564f47b9ad1e353ca28a7720b7ad59","schema_version":"1.0","event_id":"sha256:adcaac105b4d519b6e858328fd1f0ff58c564f47b9ad1e353ca28a7720b7ad59"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:T7FWLQR4IOHYTL6V23EUVJ7EZN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Remarks on hard Lefschetz conjectures on Chow groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Baohua Fu","submitted_at":"2009-05-26T05:03:46Z","abstract_excerpt":"We propose two conjectures of Hard Lefschetz type on Chow groups and prove them for some special cases. For abelian varieties, we shall show they are equivalent to well-known conjectures of Beauville and Murre."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.4114","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":"2026-05-18T02:13:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vZneivAmUHXKqHqZYozt/XdbzoCiaRtEXCdRDfGkMXwBcjTk+QiWSnT28urCFcteNhRA2Kq7xdBlqNW4iwkfDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T14:36:43.298089Z"},"content_sha256":"4efab998a349c9236e241f6f054904c3c10b0a61990bc6f04ea7a14e4215c3ac","schema_version":"1.0","event_id":"sha256:4efab998a349c9236e241f6f054904c3c10b0a61990bc6f04ea7a14e4215c3ac"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T7FWLQR4IOHYTL6V23EUVJ7EZN/bundle.json","state_url":"https://pith.science/pith/T7FWLQR4IOHYTL6V23EUVJ7EZN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T7FWLQR4IOHYTL6V23EUVJ7EZN/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":"2026-06-07T14:36:43Z","links":{"resolver":"https://pith.science/pith/T7FWLQR4IOHYTL6V23EUVJ7EZN","bundle":"https://pith.science/pith/T7FWLQR4IOHYTL6V23EUVJ7EZN/bundle.json","state":"https://pith.science/pith/T7FWLQR4IOHYTL6V23EUVJ7EZN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T7FWLQR4IOHYTL6V23EUVJ7EZN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:T7FWLQR4IOHYTL6V23EUVJ7EZN","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":"694754df5fd651b76f285f7f9834f856fd68b184e17d8178f232690402655e6f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-05-26T05:03:46Z","title_canon_sha256":"f62262ddef1502f5c5a9941d94d1f9ac2f3f1bb95a0e7ed477f85f0ea479296a"},"schema_version":"1.0","source":{"id":"0905.4114","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0905.4114","created_at":"2026-05-18T02:13:37Z"},{"alias_kind":"arxiv_version","alias_value":"0905.4114v1","created_at":"2026-05-18T02:13:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.4114","created_at":"2026-05-18T02:13:37Z"},{"alias_kind":"pith_short_12","alias_value":"T7FWLQR4IOHY","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"T7FWLQR4IOHYTL6V","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"T7FWLQR4","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:4efab998a349c9236e241f6f054904c3c10b0a61990bc6f04ea7a14e4215c3ac","target":"graph","created_at":"2026-05-18T02:13:37Z","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 propose two conjectures of Hard Lefschetz type on Chow groups and prove them for some special cases. For abelian varieties, we shall show they are equivalent to well-known conjectures of Beauville and Murre.","authors_text":"Baohua Fu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-05-26T05:03:46Z","title":"Remarks on hard Lefschetz conjectures on Chow groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.4114","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:adcaac105b4d519b6e858328fd1f0ff58c564f47b9ad1e353ca28a7720b7ad59","target":"record","created_at":"2026-05-18T02:13:37Z","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":"694754df5fd651b76f285f7f9834f856fd68b184e17d8178f232690402655e6f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-05-26T05:03:46Z","title_canon_sha256":"f62262ddef1502f5c5a9941d94d1f9ac2f3f1bb95a0e7ed477f85f0ea479296a"},"schema_version":"1.0","source":{"id":"0905.4114","kind":"arxiv","version":1}},"canonical_sha256":"9fcb65c23c438f89afd5d6c94aa7e4cb4f1ba7f336a96024f2e63d9cb04e9afa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9fcb65c23c438f89afd5d6c94aa7e4cb4f1ba7f336a96024f2e63d9cb04e9afa","first_computed_at":"2026-05-18T02:13:37.617434Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:13:37.617434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NEny6KN7P8aje5NKgcm3daRhZe4JBDLsIhjROPL+2kkrZKQWfjmkakL9CsnLmHv2AaDg82OEOVNjvq/jbrBzDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:13:37.617909Z","signed_message":"canonical_sha256_bytes"},"source_id":"0905.4114","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:adcaac105b4d519b6e858328fd1f0ff58c564f47b9ad1e353ca28a7720b7ad59","sha256:4efab998a349c9236e241f6f054904c3c10b0a61990bc6f04ea7a14e4215c3ac"],"state_sha256":"041ed2c2cf5557f2bbb7dc594540945f0d76eed0725145a724b87b89e6c6bbd8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DKSok/Epee8H1z/IB1fh3yLZ9XzWKa4syuxBpYAWEt89MnDOpAid0a3KnRUKR3Ad3/CQ2BmOq7KjDmdZd8TrAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T14:36:43.302486Z","bundle_sha256":"7be3b67c262279d58be8f9c35b4a9ca417d9f2291b8726f706fe57285eb7dcb9"}}