{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:Y756JH5BV2M44MYWMYXFWYVH4M","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":"9fcb885224716ef0bb80da3bae47195d78896478c3dfa0905f44735ec2d11d2a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-08-14T20:40:01Z","title_canon_sha256":"ff1043d2a9fbcdfe55958dce2cd85bb132e8621abffe503700fd3fdc96845b9f"},"schema_version":"1.0","source":{"id":"2408.07809","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2408.07809","created_at":"2026-07-05T11:41:19Z"},{"alias_kind":"arxiv_version","alias_value":"2408.07809v4","created_at":"2026-07-05T11:41:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.07809","created_at":"2026-07-05T11:41:19Z"},{"alias_kind":"pith_short_12","alias_value":"Y756JH5BV2M4","created_at":"2026-07-05T11:41:19Z"},{"alias_kind":"pith_short_16","alias_value":"Y756JH5BV2M44MYW","created_at":"2026-07-05T11:41:19Z"},{"alias_kind":"pith_short_8","alias_value":"Y756JH5B","created_at":"2026-07-05T11:41:19Z"}],"graph_snapshots":[{"event_id":"sha256:23fc674723d4b669e86a3af47a613414d22a76de6a4cac3d43084950e30ecd94","target":"graph","created_at":"2026-07-05T11:41:19Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2408.07809/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The main result is that when the genus is at least 3, the rank of the normal function function of the Ceresa cycle over the moduli space of curves has maximal rank. This result was proved independently by Z. Gao and S.-W. Zhang (arXiv:2407.01304) by different methods. In genus 3 we show that the Green--Griffiths invariant of this normal function is a Teichmuller modular form of weight (4,0,-1) and use this to show that the rank of the Ceresa normal function is exactly 1 along the hyperelliptic locus.","authors_text":"Richard Hain","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-08-14T20:40:01Z","title":"The Rank of the Normal Functions of the Ceresa and Gross--Schoen Cycles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.07809","kind":"arxiv","version":4},"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:f3bc485b4bc6d3c516e679f0f50853e682d7c6a52fee177581b45579a088da80","target":"record","created_at":"2026-07-05T11:41:19Z","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":"9fcb885224716ef0bb80da3bae47195d78896478c3dfa0905f44735ec2d11d2a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-08-14T20:40:01Z","title_canon_sha256":"ff1043d2a9fbcdfe55958dce2cd85bb132e8621abffe503700fd3fdc96845b9f"},"schema_version":"1.0","source":{"id":"2408.07809","kind":"arxiv","version":4}},"canonical_sha256":"c7fbe49fa1ae99ce3316662e5b62a7e319f9dcf2192c850f9da7144670fd800f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c7fbe49fa1ae99ce3316662e5b62a7e319f9dcf2192c850f9da7144670fd800f","first_computed_at":"2026-07-05T11:41:19.058775Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:41:19.058775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lZEG2ehsaGfSq3RR/hpmdhtHCWtzTaBlRHOxwwZSD7AYq+M+0OiVk1w1wg02dealMCn411t6zbzyjo1afJPECA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:41:19.059290Z","signed_message":"canonical_sha256_bytes"},"source_id":"2408.07809","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f3bc485b4bc6d3c516e679f0f50853e682d7c6a52fee177581b45579a088da80","sha256:23fc674723d4b669e86a3af47a613414d22a76de6a4cac3d43084950e30ecd94"],"state_sha256":"7e4cca6e0ec856685da95515eb726a505e00aeee5e49c43b9a2e9110303ce960"}