{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:BDC2QV4AVTFHYJ3IADRKM5PKAB","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":"4fcc58be9dfc22366439da4f29c5f840b8f13ed73b64e7e571f875c1757baa9e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-10-11T01:53:56Z","title_canon_sha256":"49bfedbed69d59a2a22f2df48fac4df2bbe792247f8364db85dac4f7c4c6000b"},"schema_version":"1.0","source":{"id":"1310.2996","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.2996","created_at":"2026-05-18T02:58:32Z"},{"alias_kind":"arxiv_version","alias_value":"1310.2996v2","created_at":"2026-05-18T02:58:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.2996","created_at":"2026-05-18T02:58:32Z"},{"alias_kind":"pith_short_12","alias_value":"BDC2QV4AVTFH","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"BDC2QV4AVTFHYJ3I","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"BDC2QV4A","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:1849c920417d08471634323124b545b9b0666e9f88f8727a6913dd4055f4da33","target":"graph","created_at":"2026-05-18T02:58:32Z","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":"We prove a generic vanishing type statement in positive characteristic and apply it to prove positive characteristic versions of Kawamata's theorems: a characterization of smooth varieties birational to ordinary abelian varieties and the surjectivity of the Albanese map when the Frobenius stable Kodaira dimension is zero.","authors_text":"Christopher D. Hacon, Zsolt Patakfalvi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-10-11T01:53:56Z","title":"Generic vanishing in characteristic $p>0$ and the characterization of ordinary abelian varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.2996","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:fe2f595754aa64d39985c13ab29f4928c00e55e108f6bfa5f545a4cd8e8410c9","target":"record","created_at":"2026-05-18T02:58:32Z","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":"4fcc58be9dfc22366439da4f29c5f840b8f13ed73b64e7e571f875c1757baa9e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-10-11T01:53:56Z","title_canon_sha256":"49bfedbed69d59a2a22f2df48fac4df2bbe792247f8364db85dac4f7c4c6000b"},"schema_version":"1.0","source":{"id":"1310.2996","kind":"arxiv","version":2}},"canonical_sha256":"08c5a85780acca7c276800e2a675ea004edf0bbdb0210f98feca961c100246ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"08c5a85780acca7c276800e2a675ea004edf0bbdb0210f98feca961c100246ef","first_computed_at":"2026-05-18T02:58:32.341631Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:32.341631Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"96wWWT2cbzDC3ahQkH4Sye0y55HUHOgJMbYZ0QeNK0xQB7NJ7XGhNCCGIYnFO1PTR9mYqylIHYf/c4YBsaLRAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:32.342247Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.2996","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fe2f595754aa64d39985c13ab29f4928c00e55e108f6bfa5f545a4cd8e8410c9","sha256:1849c920417d08471634323124b545b9b0666e9f88f8727a6913dd4055f4da33"],"state_sha256":"4ca68fc78a4c16a14f9f4090aa137cbe26f5eb276d4e0776f030507cd51d2800"}