{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:2QMUQXRWTI5U6IRD5FI3GIUE63","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":"857514347d117682aa35327985d21b5dcd32a21cd56b20ea4a0409863cbdbd70","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-01-11T11:24:10Z","title_canon_sha256":"cc5f5b649820054c200c5e012d14771142669ea4855f3e59f8165ce28dde9bb9"},"schema_version":"1.0","source":{"id":"1501.02446","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.02446","created_at":"2026-05-18T02:29:37Z"},{"alias_kind":"arxiv_version","alias_value":"1501.02446v1","created_at":"2026-05-18T02:29:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.02446","created_at":"2026-05-18T02:29:37Z"},{"alias_kind":"pith_short_12","alias_value":"2QMUQXRWTI5U","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2QMUQXRWTI5U6IRD","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2QMUQXRW","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:703f1c56bae94ec6a22d988b006b2aca8c4b8d1fb6a72af25805c0b98190fea3","target":"graph","created_at":"2026-05-18T02:29:37Z","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 assign functorially a $\\mathbb{Z}$-lattice with semisimple Frobenius action to each abelian variety over $\\mathbb{F}_p$. This establishes an equivalence of categories that describes abelian varieties over $\\mathbb{F}_p$ avoiding $\\sqrt{p}$ as an eigenvalue of Frobenius in terms of simple commutative algebra. The result extends the isomorphism classification of Waterhouse and Deligne's equivalence for ordinary abelian varieties.","authors_text":"Jakob Stix, Tommaso Giorgio Centeleghe","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-01-11T11:24:10Z","title":"Categories of abelian varieties over finite fields I. Abelian varieties over $\\mathbb{F}_p$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.02446","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:d4e6ae99564e2d81043a15f9562387c88c7f2888f58ee193234ebaf96c1568b1","target":"record","created_at":"2026-05-18T02:29:37Z","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":"857514347d117682aa35327985d21b5dcd32a21cd56b20ea4a0409863cbdbd70","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-01-11T11:24:10Z","title_canon_sha256":"cc5f5b649820054c200c5e012d14771142669ea4855f3e59f8165ce28dde9bb9"},"schema_version":"1.0","source":{"id":"1501.02446","kind":"arxiv","version":1}},"canonical_sha256":"d419485e369a3b4f2223e951b32284f6fe8a384a40ed234f88642832fc833ed4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d419485e369a3b4f2223e951b32284f6fe8a384a40ed234f88642832fc833ed4","first_computed_at":"2026-05-18T02:29:37.947883Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:37.947883Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"do5Qz1w/kPImIW437dBhTYlxSZGFYiTPfg+FGL8Kl3XAsr50+ZemEysq3YFfbCLAJKS+lUOeUIqtj6HfTuGQCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:37.948249Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.02446","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d4e6ae99564e2d81043a15f9562387c88c7f2888f58ee193234ebaf96c1568b1","sha256:703f1c56bae94ec6a22d988b006b2aca8c4b8d1fb6a72af25805c0b98190fea3"],"state_sha256":"52769b2964130467ebda6c68166297593bff3c8a7511900d78a7a8b9854520bb"}