{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:P64UVFIKY6MHIQNEI73FIB5DX3","short_pith_number":"pith:P64UVFIK","schema_version":"1.0","canonical_sha256":"7fb94a950ac7987441a447f65407a3bed3054c49dfd5d4732f850b9fd1bfd802","source":{"kind":"arxiv","id":"1305.5881","version":1},"attestation_state":"computed","paper":{"title":"On the local-global principle for divisibility in the cohomology of elliptic curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Brendan Creutz","submitted_at":"2013-05-25T02:24:14Z","abstract_excerpt":"For every prime power p^n with p = 2 or 3 and n > 1 we give an example of an elliptic curve over Q containing a rational point which is locally divisible by p^n but is not divisible by p^n. For these same prime powers we construct examples showing that the analogous local-global principle for divisibility in the Weil-Ch\\^atelet group can also fail."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1305.5881","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-05-25T02:24:14Z","cross_cats_sorted":[],"title_canon_sha256":"0af90068285bfa54ae43f22e908cfbf144e056d958abdb83978d36cddb4fae5f","abstract_canon_sha256":"306af917c9abd119595a1a6d4f6bb97698f513047f1d1ee40f676935eddb30ad"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:11.439038Z","signature_b64":"5ucnsGk21Yf/egOkMxx1tnyx4nKAsSPjxz3vPnglX83jGIs07L7/dsfarIe0NJG1z6ueKaqRFIOFY0JeXPZWBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7fb94a950ac7987441a447f65407a3bed3054c49dfd5d4732f850b9fd1bfd802","last_reissued_at":"2026-05-18T01:24:11.438490Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:11.438490Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the local-global principle for divisibility in the cohomology of elliptic curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Brendan Creutz","submitted_at":"2013-05-25T02:24:14Z","abstract_excerpt":"For every prime power p^n with p = 2 or 3 and n > 1 we give an example of an elliptic curve over Q containing a rational point which is locally divisible by p^n but is not divisible by p^n. For these same prime powers we construct examples showing that the analogous local-global principle for divisibility in the Weil-Ch\\^atelet group can also fail."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.5881","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1305.5881","created_at":"2026-05-18T01:24:11.438562+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.5881v1","created_at":"2026-05-18T01:24:11.438562+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.5881","created_at":"2026-05-18T01:24:11.438562+00:00"},{"alias_kind":"pith_short_12","alias_value":"P64UVFIKY6MH","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_16","alias_value":"P64UVFIKY6MHIQNE","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_8","alias_value":"P64UVFIK","created_at":"2026-05-18T12:27:54.935989+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/P64UVFIKY6MHIQNEI73FIB5DX3","json":"https://pith.science/pith/P64UVFIKY6MHIQNEI73FIB5DX3.json","graph_json":"https://pith.science/api/pith-number/P64UVFIKY6MHIQNEI73FIB5DX3/graph.json","events_json":"https://pith.science/api/pith-number/P64UVFIKY6MHIQNEI73FIB5DX3/events.json","paper":"https://pith.science/paper/P64UVFIK"},"agent_actions":{"view_html":"https://pith.science/pith/P64UVFIKY6MHIQNEI73FIB5DX3","download_json":"https://pith.science/pith/P64UVFIKY6MHIQNEI73FIB5DX3.json","view_paper":"https://pith.science/paper/P64UVFIK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.5881&json=true","fetch_graph":"https://pith.science/api/pith-number/P64UVFIKY6MHIQNEI73FIB5DX3/graph.json","fetch_events":"https://pith.science/api/pith-number/P64UVFIKY6MHIQNEI73FIB5DX3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/P64UVFIKY6MHIQNEI73FIB5DX3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/P64UVFIKY6MHIQNEI73FIB5DX3/action/storage_attestation","attest_author":"https://pith.science/pith/P64UVFIKY6MHIQNEI73FIB5DX3/action/author_attestation","sign_citation":"https://pith.science/pith/P64UVFIKY6MHIQNEI73FIB5DX3/action/citation_signature","submit_replication":"https://pith.science/pith/P64UVFIKY6MHIQNEI73FIB5DX3/action/replication_record"}},"created_at":"2026-05-18T01:24:11.438562+00:00","updated_at":"2026-05-18T01:24:11.438562+00:00"}