{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:K4SF7XXMX5CRVQPAGARNQPIWH5","short_pith_number":"pith:K4SF7XXM","schema_version":"1.0","canonical_sha256":"57245fdeecbf451ac1e03022d83d163f4cc25728ff84900b33a80cffe89b61a6","source":{"kind":"arxiv","id":"1009.3546","version":3},"attestation_state":"computed","paper":{"title":"A Grunwald-Wang type theorem for abelian varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Brendan Creutz","submitted_at":"2010-09-18T10:18:29Z","abstract_excerpt":"Let A be an abelian variety over a number field k. We show that weak approximation holds in the Weil-Ch\\^atelet group of A/k but that it may fail when one restricts to the n-torsion subgroup. This failure is however relatively mild; we show that weak approximation holds outside a finite set of primes which is generically empty. This proves a conjecture of Lang and Tate that can be seen as an analog of the Grunwald-Wang theorem in class field theory. The methods apply, for the most part, to arbitrary finite Galois modules and so may be of interest in their own right."},"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":"1009.3546","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-09-18T10:18:29Z","cross_cats_sorted":[],"title_canon_sha256":"da6342138d8a48746be1f5e2a3e2844a6e88c473ebed4c9c7c20c16d9a164969","abstract_canon_sha256":"c41179cf03296b3772cb6b3127498919cc2ef61895fe12025305df62fd74aa89"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:13.076350Z","signature_b64":"ncxh6vl9dtjpEtSCEATsXtztuuccBvdxY1CT4BPjGV16k89by55jMYxQnXUqDIGB9lggNqd+4tfMn3DlHJGhCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"57245fdeecbf451ac1e03022d83d163f4cc25728ff84900b33a80cffe89b61a6","last_reissued_at":"2026-05-18T01:24:13.075882Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:13.075882Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Grunwald-Wang type theorem for abelian varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Brendan Creutz","submitted_at":"2010-09-18T10:18:29Z","abstract_excerpt":"Let A be an abelian variety over a number field k. We show that weak approximation holds in the Weil-Ch\\^atelet group of A/k but that it may fail when one restricts to the n-torsion subgroup. This failure is however relatively mild; we show that weak approximation holds outside a finite set of primes which is generically empty. This proves a conjecture of Lang and Tate that can be seen as an analog of the Grunwald-Wang theorem in class field theory. The methods apply, for the most part, to arbitrary finite Galois modules and so may be of interest in their own right."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.3546","kind":"arxiv","version":3},"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":"1009.3546","created_at":"2026-05-18T01:24:13.075965+00:00"},{"alias_kind":"arxiv_version","alias_value":"1009.3546v3","created_at":"2026-05-18T01:24:13.075965+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.3546","created_at":"2026-05-18T01:24:13.075965+00:00"},{"alias_kind":"pith_short_12","alias_value":"K4SF7XXMX5CR","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_16","alias_value":"K4SF7XXMX5CRVQPA","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_8","alias_value":"K4SF7XXM","created_at":"2026-05-18T12:26:09.077623+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/K4SF7XXMX5CRVQPAGARNQPIWH5","json":"https://pith.science/pith/K4SF7XXMX5CRVQPAGARNQPIWH5.json","graph_json":"https://pith.science/api/pith-number/K4SF7XXMX5CRVQPAGARNQPIWH5/graph.json","events_json":"https://pith.science/api/pith-number/K4SF7XXMX5CRVQPAGARNQPIWH5/events.json","paper":"https://pith.science/paper/K4SF7XXM"},"agent_actions":{"view_html":"https://pith.science/pith/K4SF7XXMX5CRVQPAGARNQPIWH5","download_json":"https://pith.science/pith/K4SF7XXMX5CRVQPAGARNQPIWH5.json","view_paper":"https://pith.science/paper/K4SF7XXM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1009.3546&json=true","fetch_graph":"https://pith.science/api/pith-number/K4SF7XXMX5CRVQPAGARNQPIWH5/graph.json","fetch_events":"https://pith.science/api/pith-number/K4SF7XXMX5CRVQPAGARNQPIWH5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/K4SF7XXMX5CRVQPAGARNQPIWH5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/K4SF7XXMX5CRVQPAGARNQPIWH5/action/storage_attestation","attest_author":"https://pith.science/pith/K4SF7XXMX5CRVQPAGARNQPIWH5/action/author_attestation","sign_citation":"https://pith.science/pith/K4SF7XXMX5CRVQPAGARNQPIWH5/action/citation_signature","submit_replication":"https://pith.science/pith/K4SF7XXMX5CRVQPAGARNQPIWH5/action/replication_record"}},"created_at":"2026-05-18T01:24:13.075965+00:00","updated_at":"2026-05-18T01:24:13.075965+00:00"}