{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:IHP27CHBH32CGPXQKYUDY7HZDB","short_pith_number":"pith:IHP27CHB","canonical_record":{"source":{"id":"1308.4528","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-08-21T10:10:50Z","cross_cats_sorted":[],"title_canon_sha256":"3e1bb47e096a5c69c9c8e15d5ec5c9ad0841d20ddc79f64cb8efe509f416bc8f","abstract_canon_sha256":"2b43c17c3f221753b3bc436966364369729052cf48ab88cf45f569334a21b7c5"},"schema_version":"1.0"},"canonical_sha256":"41dfaf88e13ef4233ef056283c7cf91847d21aa7781daa36be60e777c55d0735","source":{"kind":"arxiv","id":"1308.4528","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.4528","created_at":"2026-05-18T03:15:21Z"},{"alias_kind":"arxiv_version","alias_value":"1308.4528v1","created_at":"2026-05-18T03:15:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.4528","created_at":"2026-05-18T03:15:21Z"},{"alias_kind":"pith_short_12","alias_value":"IHP27CHBH32C","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"IHP27CHBH32CGPXQ","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"IHP27CHB","created_at":"2026-05-18T12:27:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:IHP27CHBH32CGPXQKYUDY7HZDB","target":"record","payload":{"canonical_record":{"source":{"id":"1308.4528","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-08-21T10:10:50Z","cross_cats_sorted":[],"title_canon_sha256":"3e1bb47e096a5c69c9c8e15d5ec5c9ad0841d20ddc79f64cb8efe509f416bc8f","abstract_canon_sha256":"2b43c17c3f221753b3bc436966364369729052cf48ab88cf45f569334a21b7c5"},"schema_version":"1.0"},"canonical_sha256":"41dfaf88e13ef4233ef056283c7cf91847d21aa7781daa36be60e777c55d0735","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:15:21.785113Z","signature_b64":"Qj2DRhbWNeUgDK8b2bF/yX5x0Rm/IZw/R9EN4wSWOec/GW1VBtRw2iXMsdBmdIorKp8EsiQWCSJecUDtwRgwCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"41dfaf88e13ef4233ef056283c7cf91847d21aa7781daa36be60e777c55d0735","last_reissued_at":"2026-05-18T03:15:21.784275Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:15:21.784275Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.4528","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:15:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ztR4tIBfCL/D2dj4bxT425PLrwFS9QnWM1Py5/cRZT0VRcgNO4nTwNerdjtzk+QRnTPrko/7qjRQ+RkAzOulAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T04:52:40.883425Z"},"content_sha256":"b9aa4b19ecf8018319faeed7f7440b8634a12f8fb9a8c283c5890c41c185f892","schema_version":"1.0","event_id":"sha256:b9aa4b19ecf8018319faeed7f7440b8634a12f8fb9a8c283c5890c41c185f892"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:IHP27CHBH32CGPXQKYUDY7HZDB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Weil-Ch\\^atelet divisible elements in Tate-Shafarevich groups II: On a question of Cassels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jakob Stix, Mirela \\c{C}iperiani","submitted_at":"2013-08-21T10:10:50Z","abstract_excerpt":"For an abelian variety A over a number field k we discuss the divisibility in H^1(k,A) of elements of the subgroup Sha(A/k). The results are most complete for elliptic curves over Q."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4528","kind":"arxiv","version":1},"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":"2026-05-18T03:15:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+GBigcZErjupIdKRtJ6Fmoxpovnpqckhe0m54GcJMfnZ0GSfOZTXP9zcLn9kbL8eI8cbVQDQmodWh/z8pK1nAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T04:52:40.884094Z"},"content_sha256":"cc9c06d1984b8a97cc34d273483e9abafe35db5a0adb5672bbf2d4f61f807627","schema_version":"1.0","event_id":"sha256:cc9c06d1984b8a97cc34d273483e9abafe35db5a0adb5672bbf2d4f61f807627"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IHP27CHBH32CGPXQKYUDY7HZDB/bundle.json","state_url":"https://pith.science/pith/IHP27CHBH32CGPXQKYUDY7HZDB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IHP27CHBH32CGPXQKYUDY7HZDB/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":"2026-06-05T04:52:40Z","links":{"resolver":"https://pith.science/pith/IHP27CHBH32CGPXQKYUDY7HZDB","bundle":"https://pith.science/pith/IHP27CHBH32CGPXQKYUDY7HZDB/bundle.json","state":"https://pith.science/pith/IHP27CHBH32CGPXQKYUDY7HZDB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IHP27CHBH32CGPXQKYUDY7HZDB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:IHP27CHBH32CGPXQKYUDY7HZDB","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":"2b43c17c3f221753b3bc436966364369729052cf48ab88cf45f569334a21b7c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-08-21T10:10:50Z","title_canon_sha256":"3e1bb47e096a5c69c9c8e15d5ec5c9ad0841d20ddc79f64cb8efe509f416bc8f"},"schema_version":"1.0","source":{"id":"1308.4528","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.4528","created_at":"2026-05-18T03:15:21Z"},{"alias_kind":"arxiv_version","alias_value":"1308.4528v1","created_at":"2026-05-18T03:15:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.4528","created_at":"2026-05-18T03:15:21Z"},{"alias_kind":"pith_short_12","alias_value":"IHP27CHBH32C","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"IHP27CHBH32CGPXQ","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"IHP27CHB","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:cc9c06d1984b8a97cc34d273483e9abafe35db5a0adb5672bbf2d4f61f807627","target":"graph","created_at":"2026-05-18T03:15:21Z","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 an abelian variety A over a number field k we discuss the divisibility in H^1(k,A) of elements of the subgroup Sha(A/k). The results are most complete for elliptic curves over Q.","authors_text":"Jakob Stix, Mirela \\c{C}iperiani","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-08-21T10:10:50Z","title":"Weil-Ch\\^atelet divisible elements in Tate-Shafarevich groups II: On a question of Cassels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4528","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:b9aa4b19ecf8018319faeed7f7440b8634a12f8fb9a8c283c5890c41c185f892","target":"record","created_at":"2026-05-18T03:15:21Z","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":"2b43c17c3f221753b3bc436966364369729052cf48ab88cf45f569334a21b7c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-08-21T10:10:50Z","title_canon_sha256":"3e1bb47e096a5c69c9c8e15d5ec5c9ad0841d20ddc79f64cb8efe509f416bc8f"},"schema_version":"1.0","source":{"id":"1308.4528","kind":"arxiv","version":1}},"canonical_sha256":"41dfaf88e13ef4233ef056283c7cf91847d21aa7781daa36be60e777c55d0735","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"41dfaf88e13ef4233ef056283c7cf91847d21aa7781daa36be60e777c55d0735","first_computed_at":"2026-05-18T03:15:21.784275Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:15:21.784275Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Qj2DRhbWNeUgDK8b2bF/yX5x0Rm/IZw/R9EN4wSWOec/GW1VBtRw2iXMsdBmdIorKp8EsiQWCSJecUDtwRgwCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:15:21.785113Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.4528","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b9aa4b19ecf8018319faeed7f7440b8634a12f8fb9a8c283c5890c41c185f892","sha256:cc9c06d1984b8a97cc34d273483e9abafe35db5a0adb5672bbf2d4f61f807627"],"state_sha256":"a2176c1f83e8b85faeb0b892a101051125344f781fff1a75176b158e98354481"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/VTFjlUwUypundafmas+Dp3P/eNfOBI91GQ4V02hnU+L9KAjv6N7/ZOiRjbTzILxdspLLfe1kyBh/St0rhDnAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T04:52:40.887548Z","bundle_sha256":"77187f68b100ceb5245f8da9f33650a5f54d35f3074a106edd1c3b1dda41bf6a"}}