{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:HHINIX3LRBTQ77JDPKS2OFEDUM","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":"b52ad79e5c866cbead3c6189569507d53606a66a101eaa8422ad060eed2f1e5b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-07-08T06:28:59Z","title_canon_sha256":"c93bf28f375d3a1b9519c79d760c5049427aa874837d30c6ef0208b4d3c11624"},"schema_version":"1.0","source":{"id":"2607.07053","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.07053","created_at":"2026-07-09T01:20:13Z"},{"alias_kind":"arxiv_version","alias_value":"2607.07053v1","created_at":"2026-07-09T01:20:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.07053","created_at":"2026-07-09T01:20:13Z"},{"alias_kind":"pith_short_12","alias_value":"HHINIX3LRBTQ","created_at":"2026-07-09T01:20:13Z"},{"alias_kind":"pith_short_16","alias_value":"HHINIX3LRBTQ77JD","created_at":"2026-07-09T01:20:13Z"},{"alias_kind":"pith_short_8","alias_value":"HHINIX3L","created_at":"2026-07-09T01:20:13Z"}],"graph_snapshots":[{"event_id":"sha256:aeb4dc1f7c16a6274e6ac66cc872d072239a152ec9a8870d872818a80f2894ba","target":"graph","created_at":"2026-07-09T01:20:13Z","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/2607.07053/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that for a very general abelian variety of dimension $\\geq 4$, a divisor $D\\in {\\rm CH}^1(A)$ that satisfies $D^2=0$ in ${\\rm CH}^2(A)$ is of torsion. The same result is also established for a very general Jacobian in genus $4$. We use then the second statement in order to prove a conjecture of Pirola, which states that any rational section of the Kummer fibration $K=J/\\pm {\\rm Id}\\rightarrow \\mathcal{M}_4$, where $J\\rightarrow \\mathcal{M}_4 $ is the Jacobian fibration, must be a multiple of the Griffiths-Pirola section given by the difference of the two trigonal divisors.","authors_text":"Claire Voisin","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-07-08T06:28:59Z","title":"On the Chow ring of very general abelian varieties and a question of Pirola"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.07053","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:cd2276e01ae24ac9f29e96a03ff70005d6a8d753cb800f6abd6a96ea3ed1950d","target":"record","created_at":"2026-07-09T01:20:13Z","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":"b52ad79e5c866cbead3c6189569507d53606a66a101eaa8422ad060eed2f1e5b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-07-08T06:28:59Z","title_canon_sha256":"c93bf28f375d3a1b9519c79d760c5049427aa874837d30c6ef0208b4d3c11624"},"schema_version":"1.0","source":{"id":"2607.07053","kind":"arxiv","version":1}},"canonical_sha256":"39d0d45f6b88670ffd237aa5a71483a30d97a9ce0eed073f4bcc203a779d95d6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"39d0d45f6b88670ffd237aa5a71483a30d97a9ce0eed073f4bcc203a779d95d6","first_computed_at":"2026-07-09T01:20:13.335214Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-09T01:20:13.335214Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B/FgsinMr0MeQWllOamZ18eNwEfOdHqZ8wcJfmM7A2uj15iAKMZT7IktcqbGrLfBeiB+gSTTbTW1HPfjErasCg==","signature_status":"signed_v1","signed_at":"2026-07-09T01:20:13.335589Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.07053","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd2276e01ae24ac9f29e96a03ff70005d6a8d753cb800f6abd6a96ea3ed1950d","sha256:aeb4dc1f7c16a6274e6ac66cc872d072239a152ec9a8870d872818a80f2894ba"],"state_sha256":"89b1993448c379a5d424b115a8c38583c361aced533b9919ce1a5164e8bfe486"}