{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:JLSIYK6LD5NJL3IXQ7GUQPZQOJ","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":"67f410708df08bbc7056a862fe9847a861761da43b80d1ec5bc9ebdb4fd0a6d4","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2014-04-03T20:29:02Z","title_canon_sha256":"73bad7aa4db90262e0c6bebfe40649d850782e6e82c593f5f9fb47bbc5a296c7"},"schema_version":"1.0","source":{"id":"1404.1092","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.1092","created_at":"2026-05-18T02:54:54Z"},{"alias_kind":"arxiv_version","alias_value":"1404.1092v1","created_at":"2026-05-18T02:54:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.1092","created_at":"2026-05-18T02:54:54Z"},{"alias_kind":"pith_short_12","alias_value":"JLSIYK6LD5NJ","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"JLSIYK6LD5NJL3IX","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"JLSIYK6L","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:a4f81417d9aef6fe6b18858fb958dc63e7965add75c9581935142999b2be2fd4","target":"graph","created_at":"2026-05-18T02:54:54Z","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":"Let k be an algebraically closed subfield of the complex numbers, and X a variety defined over k. One version of the Beilinson-Hodge conjecture that seems to survive scrutiny is the statement that the Betti cycle class map cl_{r,m} : H_M^{2r-m}(k(X),Q(r)) -> hom_{MHS}(Q(0),H^{2r-m}(k(X)(C),Q(r))) is surjective, that being equivalent to the Hodge conjecture in the case m=0. Now consider a smooth and proper map \\rho : X -> S of smooth quasi-projective varieties over k. We formulate a version of this conjecture for the generic fibre, expecting the corresponding cycle class map to be surjective. W","authors_text":"Deepam Patel, James D. Lewis, Rob de Jeu","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2014-04-03T20:29:02Z","title":"A relative version of the Beilinson-Hodge conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1092","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:d4ad1ffbb4f90e43976bc856724c7808614906c398ae5e609af1a46e2d3033c5","target":"record","created_at":"2026-05-18T02:54:54Z","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":"67f410708df08bbc7056a862fe9847a861761da43b80d1ec5bc9ebdb4fd0a6d4","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2014-04-03T20:29:02Z","title_canon_sha256":"73bad7aa4db90262e0c6bebfe40649d850782e6e82c593f5f9fb47bbc5a296c7"},"schema_version":"1.0","source":{"id":"1404.1092","kind":"arxiv","version":1}},"canonical_sha256":"4ae48c2bcb1f5a95ed1787cd483f307262f394240ff16e49e352708e071a2a88","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4ae48c2bcb1f5a95ed1787cd483f307262f394240ff16e49e352708e071a2a88","first_computed_at":"2026-05-18T02:54:54.227632Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:54.227632Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VDmAd2CjfXUrQFK2t3p1QN7bou54GEwwzAovJPw6QrCo31Kg/lt+ek9xtWHSvaYs/NcrYVZhrEaLcagESASoAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:54.228088Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.1092","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d4ad1ffbb4f90e43976bc856724c7808614906c398ae5e609af1a46e2d3033c5","sha256:a4f81417d9aef6fe6b18858fb958dc63e7965add75c9581935142999b2be2fd4"],"state_sha256":"427b88a9dd1ea4da52c93873a15554e1a85017f961e65930d4bb34bddc31ab42"}