{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:SC27HVG5WP2ROX7F2UPDQLGJPN","short_pith_number":"pith:SC27HVG5","canonical_record":{"source":{"id":"1007.0115","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-07-01T09:56:05Z","cross_cats_sorted":[],"title_canon_sha256":"4d0a0bd7a110732f005de5aa5e7e17e79a3a84fef1b9987f711f05dee620a83f","abstract_canon_sha256":"96ba4313b0309ab31791a68682ea9600d6215f783c5e19e86d50719a13658d0c"},"schema_version":"1.0"},"canonical_sha256":"90b5f3d4ddb3f5175fe5d51e382cc97b4375d0a593dcc350956dbe9fe8723da7","source":{"kind":"arxiv","id":"1007.0115","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.0115","created_at":"2026-05-18T03:55:25Z"},{"alias_kind":"arxiv_version","alias_value":"1007.0115v2","created_at":"2026-05-18T03:55:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.0115","created_at":"2026-05-18T03:55:25Z"},{"alias_kind":"pith_short_12","alias_value":"SC27HVG5WP2R","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"SC27HVG5WP2ROX7F","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"SC27HVG5","created_at":"2026-05-18T12:26:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:SC27HVG5WP2ROX7F2UPDQLGJPN","target":"record","payload":{"canonical_record":{"source":{"id":"1007.0115","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-07-01T09:56:05Z","cross_cats_sorted":[],"title_canon_sha256":"4d0a0bd7a110732f005de5aa5e7e17e79a3a84fef1b9987f711f05dee620a83f","abstract_canon_sha256":"96ba4313b0309ab31791a68682ea9600d6215f783c5e19e86d50719a13658d0c"},"schema_version":"1.0"},"canonical_sha256":"90b5f3d4ddb3f5175fe5d51e382cc97b4375d0a593dcc350956dbe9fe8723da7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:55:25.110957Z","signature_b64":"oJeCJgBjEfXBxgv89ct/5jWs3IMc6wPTEg01CFaQ3xaNoV3ycY6BNYUU+YTKPrEVDQzYe9CVUuZYUX87XrHMDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"90b5f3d4ddb3f5175fe5d51e382cc97b4375d0a593dcc350956dbe9fe8723da7","last_reissued_at":"2026-05-18T03:55:25.110145Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:55:25.110145Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1007.0115","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:55:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"99Ek+S6iN/8ienOSskebLZ7+Qp0EqVlu/gy9KYONHDxyh1Hepmk9CF7nAxcrAXasJe1rrw0IiKizW32J+zsrCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T15:55:34.529291Z"},"content_sha256":"9007aaaa71b14480e1578cea4e2797110b08291677e3e5cf15d1616c38feae6c","schema_version":"1.0","event_id":"sha256:9007aaaa71b14480e1578cea4e2797110b08291677e3e5cf15d1616c38feae6c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:SC27HVG5WP2ROX7F2UPDQLGJPN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The groups of points on abelian surfaces over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Sergey Rybakov","submitted_at":"2010-07-01T09:56:05Z","abstract_excerpt":"Let $A$ be an abelian surface over a finite field $k$. The $k$-isogeny class of $A$ is uniquely determined by a Weil polynomial $f_A$ of degree 4. We give a classification of the groups of $k$-rational points on varieties from this class in terms of $f_A$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.0115","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:55:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HFkQPkQ4WlUpNBsjiFtvlXLYG8iMu02wZ64xqo1cx3Ea6jwOS85G9NcjobjMNxrFLIXnFfobSjoqWiZWARwJCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T15:55:34.530027Z"},"content_sha256":"eea2e44a61773524d4a01d08c0b2905bcbfc2390397aba955efee9aa026581c7","schema_version":"1.0","event_id":"sha256:eea2e44a61773524d4a01d08c0b2905bcbfc2390397aba955efee9aa026581c7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SC27HVG5WP2ROX7F2UPDQLGJPN/bundle.json","state_url":"https://pith.science/pith/SC27HVG5WP2ROX7F2UPDQLGJPN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SC27HVG5WP2ROX7F2UPDQLGJPN/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T15:55:34Z","links":{"resolver":"https://pith.science/pith/SC27HVG5WP2ROX7F2UPDQLGJPN","bundle":"https://pith.science/pith/SC27HVG5WP2ROX7F2UPDQLGJPN/bundle.json","state":"https://pith.science/pith/SC27HVG5WP2ROX7F2UPDQLGJPN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SC27HVG5WP2ROX7F2UPDQLGJPN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:SC27HVG5WP2ROX7F2UPDQLGJPN","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":"96ba4313b0309ab31791a68682ea9600d6215f783c5e19e86d50719a13658d0c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-07-01T09:56:05Z","title_canon_sha256":"4d0a0bd7a110732f005de5aa5e7e17e79a3a84fef1b9987f711f05dee620a83f"},"schema_version":"1.0","source":{"id":"1007.0115","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.0115","created_at":"2026-05-18T03:55:25Z"},{"alias_kind":"arxiv_version","alias_value":"1007.0115v2","created_at":"2026-05-18T03:55:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.0115","created_at":"2026-05-18T03:55:25Z"},{"alias_kind":"pith_short_12","alias_value":"SC27HVG5WP2R","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"SC27HVG5WP2ROX7F","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"SC27HVG5","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:eea2e44a61773524d4a01d08c0b2905bcbfc2390397aba955efee9aa026581c7","target":"graph","created_at":"2026-05-18T03:55:25Z","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":"Let $A$ be an abelian surface over a finite field $k$. The $k$-isogeny class of $A$ is uniquely determined by a Weil polynomial $f_A$ of degree 4. We give a classification of the groups of $k$-rational points on varieties from this class in terms of $f_A$.","authors_text":"Sergey Rybakov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-07-01T09:56:05Z","title":"The groups of points on abelian surfaces over finite fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.0115","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":"sha256:9007aaaa71b14480e1578cea4e2797110b08291677e3e5cf15d1616c38feae6c","target":"record","created_at":"2026-05-18T03:55:25Z","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":"96ba4313b0309ab31791a68682ea9600d6215f783c5e19e86d50719a13658d0c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-07-01T09:56:05Z","title_canon_sha256":"4d0a0bd7a110732f005de5aa5e7e17e79a3a84fef1b9987f711f05dee620a83f"},"schema_version":"1.0","source":{"id":"1007.0115","kind":"arxiv","version":2}},"canonical_sha256":"90b5f3d4ddb3f5175fe5d51e382cc97b4375d0a593dcc350956dbe9fe8723da7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"90b5f3d4ddb3f5175fe5d51e382cc97b4375d0a593dcc350956dbe9fe8723da7","first_computed_at":"2026-05-18T03:55:25.110145Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:55:25.110145Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oJeCJgBjEfXBxgv89ct/5jWs3IMc6wPTEg01CFaQ3xaNoV3ycY6BNYUU+YTKPrEVDQzYe9CVUuZYUX87XrHMDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:55:25.110957Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.0115","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9007aaaa71b14480e1578cea4e2797110b08291677e3e5cf15d1616c38feae6c","sha256:eea2e44a61773524d4a01d08c0b2905bcbfc2390397aba955efee9aa026581c7"],"state_sha256":"d3ecbb1acd5403bb1b66e5c2b29ac53342e60415b5e1d58f61039e2af7607bc8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aSVliNtjdot1mwhWYGYZwgaX9JfOABWlBRGQaIDYlBgxS6X0si7IZ3eDNXx6pvfPUM+vx9GIZvatyAZuXp+GDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T15:55:34.532809Z","bundle_sha256":"e8305a60e2ca890fe8ac0ab78bceddd79f5ed546e218836fa8c1f235a5ef0380"}}