{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:XB4QOCW7V36ZTNBBZRANUFAQB7","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":"57cb5e5f3d411cba167eb2c23031287854c4d4fb4ce2ded4b1df09224c8d8cef","cross_cats_sorted":["math.NT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2023-12-20T12:08:46Z","title_canon_sha256":"dac4ea5823923fc798ccc6709b49c827623963396a167575a638e0e72e9ea70c"},"schema_version":"1.0","source":{"id":"2312.12965","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.12965","created_at":"2026-07-05T09:51:30Z"},{"alias_kind":"arxiv_version","alias_value":"2312.12965v2","created_at":"2026-07-05T09:51:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.12965","created_at":"2026-07-05T09:51:30Z"},{"alias_kind":"pith_short_12","alias_value":"XB4QOCW7V36Z","created_at":"2026-07-05T09:51:30Z"},{"alias_kind":"pith_short_16","alias_value":"XB4QOCW7V36ZTNBB","created_at":"2026-07-05T09:51:30Z"},{"alias_kind":"pith_short_8","alias_value":"XB4QOCW7","created_at":"2026-07-05T09:51:30Z"}],"graph_snapshots":[{"event_id":"sha256:19ccd65e592a687a57308364c089b661e9c12b24200ea850344d8cc863e9c2f3","target":"graph","created_at":"2026-07-05T09:51:30Z","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/2312.12965/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that the Ceresa cycle $\\kappa(C_t)$ of the genus $3$ curve $C_t \\colon y^3 = x^4 + 2tx^2 + 1$ is torsion if and only if $Q_t=( \\sqrt[3]{t^2 -1},t)$ is a torsion point on the elliptic curve $y^2 = x^3 + 1$. This shows that there are infinitely many smooth plane quartic curves over $\\mathbb{C}$ (resp. $\\mathbb{Q}$) with torsion (resp. infinite order) Ceresa cycle. Over $\\overline{\\mathbb{Q}}$, we show that the Beilinson--Bloch height of $\\kappa(C_t)$ is proportional to the Neron--Tate height of $Q_t$. Thus, the height of $\\kappa(C_t)$ is nondegenerate and satisfies a Northcott property. ","authors_text":"Ari Shnidman, Jef Laga","cross_cats":["math.NT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2023-12-20T12:08:46Z","title":"Ceresa cycles of bielliptic Picard curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.12965","kind":"arxiv","version":2},"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:db13af3b3c8e3f0dada4258d8c30ad6c2a74f5ef8bc03ea661df62b37319fcba","target":"record","created_at":"2026-07-05T09:51:30Z","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":"57cb5e5f3d411cba167eb2c23031287854c4d4fb4ce2ded4b1df09224c8d8cef","cross_cats_sorted":["math.NT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2023-12-20T12:08:46Z","title_canon_sha256":"dac4ea5823923fc798ccc6709b49c827623963396a167575a638e0e72e9ea70c"},"schema_version":"1.0","source":{"id":"2312.12965","kind":"arxiv","version":2}},"canonical_sha256":"b879070adfaefd99b421cc40da14100ff183b8281a16c76f55194501b631c4bb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b879070adfaefd99b421cc40da14100ff183b8281a16c76f55194501b631c4bb","first_computed_at":"2026-07-05T09:51:30.092573Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:51:30.092573Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KlTRYypLztXsvNBGOpug54s9YNnFY0dgPffeXbViPoWwrE6FB+JqWBZOx9qVsr6qDQMBJKm8Q83SO1JnwcK1Bw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:51:30.093051Z","signed_message":"canonical_sha256_bytes"},"source_id":"2312.12965","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:db13af3b3c8e3f0dada4258d8c30ad6c2a74f5ef8bc03ea661df62b37319fcba","sha256:19ccd65e592a687a57308364c089b661e9c12b24200ea850344d8cc863e9c2f3"],"state_sha256":"ce624bc47ee503cc00cf51ed5f0691a1a1a3b08ae05044780abd76b5fd71e4e8"}