{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2002:O6LWIU67ZJEIRVKMXD5DSZJZIH","short_pith_number":"pith:O6LWIU67","schema_version":"1.0","canonical_sha256":"77976453dfca4888d54cb8fa39653941eef6e669f36c091588d23824adff2938","source":{"kind":"arxiv","id":"math/0208118","version":1},"attestation_state":"computed","paper":{"title":"Kummer theory of abelian varieties and reductions of Mordell-Weil groups","license":"","headline":"","cross_cats":["math.AC"],"primary_cat":"math.NT","authors_text":"Tom Weston","submitted_at":"2002-08-14T22:18:51Z","abstract_excerpt":"Let A be an abelian variety over a number field F with End(A/F) commutative. Let S be a subgroup of A(F) and let x be a point of A(F). Suppose that for almost all places v of F the reduction of x modulo v lies in the reduction of S modulo v. In this paper we prove that x must then lie in S + A(F)_tors. This provides a partial answer to a generalization (due to W. Gajda) of the support problem of Erdos."},"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":"math/0208118","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.NT","submitted_at":"2002-08-14T22:18:51Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"f8dd2c2cc587c59c6bdba589c11cc8eca126d6f92e0ee4e7e41bb0f6b45e36a3","abstract_canon_sha256":"7ab0e40ffeef8d2de3d0f37fdacefda678628d5f107ee1cb08bbc6284bbc96f1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:29.447298Z","signature_b64":"i4MsS/WH2PXKxHtQ0LfZIw1mVQyaeWn3EeAm4RHI3GcEir/DMUWhokdkhMLcWPegNxrqDrUFgSC0ELQSc2NlAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"77976453dfca4888d54cb8fa39653941eef6e669f36c091588d23824adff2938","last_reissued_at":"2026-05-18T01:38:29.446654Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:29.446654Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Kummer theory of abelian varieties and reductions of Mordell-Weil groups","license":"","headline":"","cross_cats":["math.AC"],"primary_cat":"math.NT","authors_text":"Tom Weston","submitted_at":"2002-08-14T22:18:51Z","abstract_excerpt":"Let A be an abelian variety over a number field F with End(A/F) commutative. Let S be a subgroup of A(F) and let x be a point of A(F). Suppose that for almost all places v of F the reduction of x modulo v lies in the reduction of S modulo v. In this paper we prove that x must then lie in S + A(F)_tors. This provides a partial answer to a generalization (due to W. Gajda) of the support problem of Erdos."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0208118","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":"math/0208118","created_at":"2026-05-18T01:38:29.446753+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0208118v1","created_at":"2026-05-18T01:38:29.446753+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0208118","created_at":"2026-05-18T01:38:29.446753+00:00"},{"alias_kind":"pith_short_12","alias_value":"O6LWIU67ZJEI","created_at":"2026-05-18T12:25:51.375804+00:00"},{"alias_kind":"pith_short_16","alias_value":"O6LWIU67ZJEIRVKM","created_at":"2026-05-18T12:25:51.375804+00:00"},{"alias_kind":"pith_short_8","alias_value":"O6LWIU67","created_at":"2026-05-18T12:25:51.375804+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/O6LWIU67ZJEIRVKMXD5DSZJZIH","json":"https://pith.science/pith/O6LWIU67ZJEIRVKMXD5DSZJZIH.json","graph_json":"https://pith.science/api/pith-number/O6LWIU67ZJEIRVKMXD5DSZJZIH/graph.json","events_json":"https://pith.science/api/pith-number/O6LWIU67ZJEIRVKMXD5DSZJZIH/events.json","paper":"https://pith.science/paper/O6LWIU67"},"agent_actions":{"view_html":"https://pith.science/pith/O6LWIU67ZJEIRVKMXD5DSZJZIH","download_json":"https://pith.science/pith/O6LWIU67ZJEIRVKMXD5DSZJZIH.json","view_paper":"https://pith.science/paper/O6LWIU67","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0208118&json=true","fetch_graph":"https://pith.science/api/pith-number/O6LWIU67ZJEIRVKMXD5DSZJZIH/graph.json","fetch_events":"https://pith.science/api/pith-number/O6LWIU67ZJEIRVKMXD5DSZJZIH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/O6LWIU67ZJEIRVKMXD5DSZJZIH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/O6LWIU67ZJEIRVKMXD5DSZJZIH/action/storage_attestation","attest_author":"https://pith.science/pith/O6LWIU67ZJEIRVKMXD5DSZJZIH/action/author_attestation","sign_citation":"https://pith.science/pith/O6LWIU67ZJEIRVKMXD5DSZJZIH/action/citation_signature","submit_replication":"https://pith.science/pith/O6LWIU67ZJEIRVKMXD5DSZJZIH/action/replication_record"}},"created_at":"2026-05-18T01:38:29.446753+00:00","updated_at":"2026-05-18T01:38:29.446753+00:00"}