{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:3CZDW26LDF53TJTWJ26BVZUOUY","short_pith_number":"pith:3CZDW26L","canonical_record":{"source":{"id":"0909.4803","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-09-25T21:08:54Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"e304a865949446395f39792b49cd25174000669cd5665a47671f293bd2d9a6ae","abstract_canon_sha256":"edf10b18c253f4627388e094cc4d569f21b49493b60d12b958bf4fb64579c576"},"schema_version":"1.0"},"canonical_sha256":"d8b23b6bcb197bb9a6764ebc1ae68ea61c185361369ebf4872161a336114a85a","source":{"kind":"arxiv","id":"0909.4803","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.4803","created_at":"2026-05-18T04:40:08Z"},{"alias_kind":"arxiv_version","alias_value":"0909.4803v4","created_at":"2026-05-18T04:40:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.4803","created_at":"2026-05-18T04:40:08Z"},{"alias_kind":"pith_short_12","alias_value":"3CZDW26LDF53","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"3CZDW26LDF53TJTW","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"3CZDW26L","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:3CZDW26LDF53TJTWJ26BVZUOUY","target":"record","payload":{"canonical_record":{"source":{"id":"0909.4803","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-09-25T21:08:54Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"e304a865949446395f39792b49cd25174000669cd5665a47671f293bd2d9a6ae","abstract_canon_sha256":"edf10b18c253f4627388e094cc4d569f21b49493b60d12b958bf4fb64579c576"},"schema_version":"1.0"},"canonical_sha256":"d8b23b6bcb197bb9a6764ebc1ae68ea61c185361369ebf4872161a336114a85a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:40:08.362691Z","signature_b64":"hBbpQ5cJ21whx87LGC8uAqdInNqMkEku/eLuBBmaQwnDYc0fb9S+kW1KL9IpTTzchpIZ4Q5OoRwYLP5LAUUWBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d8b23b6bcb197bb9a6764ebc1ae68ea61c185361369ebf4872161a336114a85a","last_reissued_at":"2026-05-18T04:40:08.362229Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:40:08.362229Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0909.4803","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:40:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P77dRO37MKAoXed0JSFyxyPJPQHnKoWJ4fyAVmvxfmM53dI1gPHnclrDTIIRvs7qUJOsI/XOhFssdfbJV7QnBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T08:48:44.119178Z"},"content_sha256":"2d7db311c018ca4441172560c84b6f9367aea19c848b051057ed27de786cd828","schema_version":"1.0","event_id":"sha256:2d7db311c018ca4441172560c84b6f9367aea19c848b051057ed27de786cd828"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:3CZDW26LDF53TJTWJ26BVZUOUY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Neron class groups of abelian varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Cristian D. Gonzalez-Aviles","submitted_at":"2009-09-25T21:08:54Z","abstract_excerpt":"Let F be a global field and let S denote a nonempty finite set of primes of F containing the set S' of archimedean primes of F. In this paper we study the Neron S-class group C_{A,F,S} of an abelian variety A defined over F. In the well-known analogy that exists between the Birch and Swinnerton-Dyer conjecture for A over F and Dirichlet's analytic class number formula for the field F (in the number field case), the finite group C_{A,F,S'} (not the Tate-Shafarevich group of A) is a natural analog of the ideal class group of F."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.4803","kind":"arxiv","version":4},"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":"2026-05-18T04:40:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YI0qiM+fUrT5dTpwxoFnqYN53EfFUWeuQllwVXWO3fuFkoV45ZwVek0fFYVyiQkZOrOlBypfKMAq0JIeEDmRBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T08:48:44.119928Z"},"content_sha256":"7cb7230fa7ee510997321b1118dc978a8ca6bf3958a050d0c933bd409ad2dd59","schema_version":"1.0","event_id":"sha256:7cb7230fa7ee510997321b1118dc978a8ca6bf3958a050d0c933bd409ad2dd59"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3CZDW26LDF53TJTWJ26BVZUOUY/bundle.json","state_url":"https://pith.science/pith/3CZDW26LDF53TJTWJ26BVZUOUY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3CZDW26LDF53TJTWJ26BVZUOUY/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":"2026-06-11T08:48:44Z","links":{"resolver":"https://pith.science/pith/3CZDW26LDF53TJTWJ26BVZUOUY","bundle":"https://pith.science/pith/3CZDW26LDF53TJTWJ26BVZUOUY/bundle.json","state":"https://pith.science/pith/3CZDW26LDF53TJTWJ26BVZUOUY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3CZDW26LDF53TJTWJ26BVZUOUY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:3CZDW26LDF53TJTWJ26BVZUOUY","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":"edf10b18c253f4627388e094cc4d569f21b49493b60d12b958bf4fb64579c576","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-09-25T21:08:54Z","title_canon_sha256":"e304a865949446395f39792b49cd25174000669cd5665a47671f293bd2d9a6ae"},"schema_version":"1.0","source":{"id":"0909.4803","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.4803","created_at":"2026-05-18T04:40:08Z"},{"alias_kind":"arxiv_version","alias_value":"0909.4803v4","created_at":"2026-05-18T04:40:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.4803","created_at":"2026-05-18T04:40:08Z"},{"alias_kind":"pith_short_12","alias_value":"3CZDW26LDF53","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"3CZDW26LDF53TJTW","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"3CZDW26L","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:7cb7230fa7ee510997321b1118dc978a8ca6bf3958a050d0c933bd409ad2dd59","target":"graph","created_at":"2026-05-18T04:40:08Z","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 F be a global field and let S denote a nonempty finite set of primes of F containing the set S' of archimedean primes of F. In this paper we study the Neron S-class group C_{A,F,S} of an abelian variety A defined over F. In the well-known analogy that exists between the Birch and Swinnerton-Dyer conjecture for A over F and Dirichlet's analytic class number formula for the field F (in the number field case), the finite group C_{A,F,S'} (not the Tate-Shafarevich group of A) is a natural analog of the ideal class group of F.","authors_text":"Cristian D. Gonzalez-Aviles","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-09-25T21:08:54Z","title":"On Neron class groups of abelian varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.4803","kind":"arxiv","version":4},"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":"sha256:2d7db311c018ca4441172560c84b6f9367aea19c848b051057ed27de786cd828","target":"record","created_at":"2026-05-18T04:40:08Z","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":"edf10b18c253f4627388e094cc4d569f21b49493b60d12b958bf4fb64579c576","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-09-25T21:08:54Z","title_canon_sha256":"e304a865949446395f39792b49cd25174000669cd5665a47671f293bd2d9a6ae"},"schema_version":"1.0","source":{"id":"0909.4803","kind":"arxiv","version":4}},"canonical_sha256":"d8b23b6bcb197bb9a6764ebc1ae68ea61c185361369ebf4872161a336114a85a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d8b23b6bcb197bb9a6764ebc1ae68ea61c185361369ebf4872161a336114a85a","first_computed_at":"2026-05-18T04:40:08.362229Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:40:08.362229Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hBbpQ5cJ21whx87LGC8uAqdInNqMkEku/eLuBBmaQwnDYc0fb9S+kW1KL9IpTTzchpIZ4Q5OoRwYLP5LAUUWBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:40:08.362691Z","signed_message":"canonical_sha256_bytes"},"source_id":"0909.4803","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d7db311c018ca4441172560c84b6f9367aea19c848b051057ed27de786cd828","sha256:7cb7230fa7ee510997321b1118dc978a8ca6bf3958a050d0c933bd409ad2dd59"],"state_sha256":"cc203c22c32b016d71e5d42b7dc778fa2d33e02254dd5af87ede8ba92e01a6df"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lnd8BQ/6ProUDgUefBSdF/US23sY9W5BXu+n8q+IZWEKdwoScM2rDVf5fiQXeshHor3+gnGlX9En11RVuyQFCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T08:48:44.124235Z","bundle_sha256":"38b8e1f8ca887094a8b02b8d486f66bec31aa9c34148dab80eef535a92f46831"}}