{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:H6E7IIS36EYNZOLP55OS6EUYST","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":"5876dd4c76e349cb906d155e036489a763c36b6165c1552a36698e3642bd7029","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-07-10T17:22:46Z","title_canon_sha256":"178b30cdedc14de436de9244653fc58dff6a79bb57671807870a0795165de7b2"},"schema_version":"1.0","source":{"id":"2607.09622","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.09622","created_at":"2026-07-13T01:20:24Z"},{"alias_kind":"arxiv_version","alias_value":"2607.09622v1","created_at":"2026-07-13T01:20:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.09622","created_at":"2026-07-13T01:20:24Z"},{"alias_kind":"pith_short_12","alias_value":"H6E7IIS36EYN","created_at":"2026-07-13T01:20:24Z"},{"alias_kind":"pith_short_16","alias_value":"H6E7IIS36EYNZOLP","created_at":"2026-07-13T01:20:24Z"},{"alias_kind":"pith_short_8","alias_value":"H6E7IIS3","created_at":"2026-07-13T01:20:24Z"}],"graph_snapshots":[{"event_id":"sha256:56de2e19b7e9a5edd2d9ca9604d630bc813c4ffc3608ed0d0391980e5b24c099","target":"graph","created_at":"2026-07-13T01:20:24Z","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/2607.09622/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this note, we explore the connection between hyperk\\\"ahler manifolds with large Picard numbers and abelian varieties. In particular, we are interested in Morrison's solution to the (modified) Oda's conjecture: every K3 surface whose Picard group is large enough (in a certain precise sense) must be related via an algebraic correspondence to an abelian surface. We generalize this theorem to the case of known examples of hyperk\\\"ahler manifolds such as pointed Hilbert schemes on K3 surfaces.","authors_text":"Abhinav Kumar, Ljudmila Kamenova","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-07-10T17:22:46Z","title":"Correspondences for hyperk\\\"ahler varieties with large Picard numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.09622","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:d2e102a130ded64a0f867e8326da15d8abff16bc368bcfc3371962d268b778c5","target":"record","created_at":"2026-07-13T01:20:24Z","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":"5876dd4c76e349cb906d155e036489a763c36b6165c1552a36698e3642bd7029","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-07-10T17:22:46Z","title_canon_sha256":"178b30cdedc14de436de9244653fc58dff6a79bb57671807870a0795165de7b2"},"schema_version":"1.0","source":{"id":"2607.09622","kind":"arxiv","version":1}},"canonical_sha256":"3f89f4225bf130dcb96fef5d2f129894c5175fe463accf5def61ecbcfb1eebd7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3f89f4225bf130dcb96fef5d2f129894c5175fe463accf5def61ecbcfb1eebd7","first_computed_at":"2026-07-13T01:20:24.785143Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-13T01:20:24.785143Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Lq56PoT2GblOHMnjsQnzvG08BKmzIuJfuh1ti8s8Pq4uVUDK7B+zS3l8OC1dvceQCZO5O4ehTnE6gD2uykwTBw==","signature_status":"signed_v1","signed_at":"2026-07-13T01:20:24.786537Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.09622","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d2e102a130ded64a0f867e8326da15d8abff16bc368bcfc3371962d268b778c5","sha256:56de2e19b7e9a5edd2d9ca9604d630bc813c4ffc3608ed0d0391980e5b24c099"],"state_sha256":"12e0babcfcd06975d40e1773d3bf221d985a38ea9775e9dbfeacec090c28703f"}