{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:QBBZMIOMV4TQGUIH6HKREJDWJK","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":"af40041280a9c60d8c03d63f8fa75482beaec56c3f566e4a3225a7a6b11a4d55","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-09-06T06:19:29Z","title_canon_sha256":"198279ce519dd533c7ed7794d7391c594b26044c511d34cc4791e2ef346e5083"},"schema_version":"1.0","source":{"id":"1209.1189","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.1189","created_at":"2026-05-18T03:10:26Z"},{"alias_kind":"arxiv_version","alias_value":"1209.1189v2","created_at":"2026-05-18T03:10:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.1189","created_at":"2026-05-18T03:10:26Z"},{"alias_kind":"pith_short_12","alias_value":"QBBZMIOMV4TQ","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QBBZMIOMV4TQGUIH","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QBBZMIOM","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:01d73917a33f8ce5e9b75006f71da4c3c3e207d8dc5a8c079fc5781ab41c506d","target":"graph","created_at":"2026-05-18T03:10:26Z","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":"Generalizing a method of Sutherland and the author for elliptic curves, we design a subexponential algorithm for computing the endomorphism rings of ordinary abelian varieties of dimension two over finite fields. Although its correctness and complexity analysis rest on several assumptions, we report on practical computations showing that it performs very well and can easily handle previously intractable cases.","authors_text":"Gaetan Bisson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-09-06T06:19:29Z","title":"Computing endomorphism rings of abelian varieties of dimension two"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.1189","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":"sha256:5c413192225d43c0546789f209d3872a068fd29b73da2caab709451d1125006d","target":"record","created_at":"2026-05-18T03:10:26Z","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":"af40041280a9c60d8c03d63f8fa75482beaec56c3f566e4a3225a7a6b11a4d55","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-09-06T06:19:29Z","title_canon_sha256":"198279ce519dd533c7ed7794d7391c594b26044c511d34cc4791e2ef346e5083"},"schema_version":"1.0","source":{"id":"1209.1189","kind":"arxiv","version":2}},"canonical_sha256":"80439621ccaf27035107f1d51224764a892089a028391b8ff076f9fa1361f746","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"80439621ccaf27035107f1d51224764a892089a028391b8ff076f9fa1361f746","first_computed_at":"2026-05-18T03:10:26.889277Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:10:26.889277Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PAdbELtUSKUMACPgjMSs7eiR2EQQY/pSZlFYQlX2YBo+udDTt0fEse+BgM1aMB4EGbxvVGsrYz3dg53Rt5FtDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:10:26.890143Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.1189","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5c413192225d43c0546789f209d3872a068fd29b73da2caab709451d1125006d","sha256:01d73917a33f8ce5e9b75006f71da4c3c3e207d8dc5a8c079fc5781ab41c506d"],"state_sha256":"107a2f2242c97dbc0035f637d26437531e7590a55f94d8b1a547d6d6f0e109c6"}