{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:QBQOSSHIZTYI7JTOSOGA22MS6Q","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":"14eae6302dca360e96b75332c5bfc1a42c1237672684eebb3cf1684ca6c3afc5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-01-04T06:24:45Z","title_canon_sha256":"d194356a3605ae76a700c794c43ac42db0191b3ca3ae5795fc5ef95c2648acaa"},"schema_version":"1.0","source":{"id":"1501.00640","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.00640","created_at":"2026-05-18T01:32:50Z"},{"alias_kind":"arxiv_version","alias_value":"1501.00640v1","created_at":"2026-05-18T01:32:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.00640","created_at":"2026-05-18T01:32:50Z"},{"alias_kind":"pith_short_12","alias_value":"QBQOSSHIZTYI","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"QBQOSSHIZTYI7JTO","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"QBQOSSHI","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:8b8b4e5ad5378001f86185b8178620c51a9143607d26d29bdfeb7d6ff546b100","target":"graph","created_at":"2026-05-18T01:32:50Z","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":"For any abelian variety $A$ over a number field, we construct an extension of the Tate-Shafarevich group by the Bloch-Tamagawa space using the recent work of Lichtenbaum and Flach. This gives a new example of a Zagier sequence for the Selmer group of $A$.","authors_text":"Niranjan Ramachandran","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-01-04T06:24:45Z","title":"A note on the Bloch-Tamagawa space and Selmer groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.00640","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:be8283bdd0a6a2a66f39d12429a77e0196a54f7866aa5954290d419d1b5a2cd8","target":"record","created_at":"2026-05-18T01:32:50Z","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":"14eae6302dca360e96b75332c5bfc1a42c1237672684eebb3cf1684ca6c3afc5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-01-04T06:24:45Z","title_canon_sha256":"d194356a3605ae76a700c794c43ac42db0191b3ca3ae5795fc5ef95c2648acaa"},"schema_version":"1.0","source":{"id":"1501.00640","kind":"arxiv","version":1}},"canonical_sha256":"8060e948e8ccf08fa66e938c0d6992f40dde761645661c809b6e91bce8a84197","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8060e948e8ccf08fa66e938c0d6992f40dde761645661c809b6e91bce8a84197","first_computed_at":"2026-05-18T01:32:50.605042Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:50.605042Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uHVtOsi/zRmEpsn7d4yFYVTkSNG8ZM2YMZ6+S+TSD1tMZQXalp5ZpGUhN0JVg/Fnmed0jR6w+FBqM/twiemoAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:50.605596Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.00640","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:be8283bdd0a6a2a66f39d12429a77e0196a54f7866aa5954290d419d1b5a2cd8","sha256:8b8b4e5ad5378001f86185b8178620c51a9143607d26d29bdfeb7d6ff546b100"],"state_sha256":"d05173b66742fa2f4ea05c9a74cffeffded7e53cddadaaf15a07a8f767a6b867"}