{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:FMTGTFB4FTL2P62NVCXNJID36T","short_pith_number":"pith:FMTGTFB4","schema_version":"1.0","canonical_sha256":"2b2669943c2cd7a7fb4da8aed4a07bf4fe0e1b267bc4ed1e40c1fee3b112fba5","source":{"kind":"arxiv","id":"1608.01371","version":2},"attestation_state":"computed","paper":{"title":"Local-global principles for Weil-Ch\\^atelet divisibility in positive characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Brendan Creutz, Jos\\'e Felipe Voloch","submitted_at":"2016-08-03T21:57:44Z","abstract_excerpt":"We extend existing results characterizing Weil-Ch\\^atelet divisibility of locally trivial torsors over number fields to global fields of positive characteristic. Building on work of Gonz\\'alez-Avil\\'es and Tan, we characterize when local-global divisibility holds in such contexts, providing examples showing that these results are optimal. We give an example of an elliptic curve over a global field of characteristic $2$ containing a rational point which is locally divisible by $8$, but is not divisible by $8$ as well as examples showing that the analogous local-global principle for divisibility"},"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":"1608.01371","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-08-03T21:57:44Z","cross_cats_sorted":[],"title_canon_sha256":"eca971dbe13c36e68e2722fb50cbe2d5250a1ef8b215f8d4afe5ad546313d122","abstract_canon_sha256":"4087bbee380890517e27e2070f6105acdfd373ca73da5c6c7587d8b148871513"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:23.260332Z","signature_b64":"Uxak1zMJjqX4Wn9f63eunXJ9NPMH9bVYV8ufTjIgcivZopnM9ucNP2GBP8gjxAr+S+HyYXuEb81FSjcvN5obBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b2669943c2cd7a7fb4da8aed4a07bf4fe0e1b267bc4ed1e40c1fee3b112fba5","last_reissued_at":"2026-05-18T00:33:23.259643Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:23.259643Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Local-global principles for Weil-Ch\\^atelet divisibility in positive characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Brendan Creutz, Jos\\'e Felipe Voloch","submitted_at":"2016-08-03T21:57:44Z","abstract_excerpt":"We extend existing results characterizing Weil-Ch\\^atelet divisibility of locally trivial torsors over number fields to global fields of positive characteristic. Building on work of Gonz\\'alez-Avil\\'es and Tan, we characterize when local-global divisibility holds in such contexts, providing examples showing that these results are optimal. We give an example of an elliptic curve over a global field of characteristic $2$ containing a rational point which is locally divisible by $8$, but is not divisible by $8$ as well as examples showing that the analogous local-global principle for divisibility"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.01371","kind":"arxiv","version":2},"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":"1608.01371","created_at":"2026-05-18T00:33:23.259751+00:00"},{"alias_kind":"arxiv_version","alias_value":"1608.01371v2","created_at":"2026-05-18T00:33:23.259751+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.01371","created_at":"2026-05-18T00:33:23.259751+00:00"},{"alias_kind":"pith_short_12","alias_value":"FMTGTFB4FTL2","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_16","alias_value":"FMTGTFB4FTL2P62N","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_8","alias_value":"FMTGTFB4","created_at":"2026-05-18T12:30:15.759754+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/FMTGTFB4FTL2P62NVCXNJID36T","json":"https://pith.science/pith/FMTGTFB4FTL2P62NVCXNJID36T.json","graph_json":"https://pith.science/api/pith-number/FMTGTFB4FTL2P62NVCXNJID36T/graph.json","events_json":"https://pith.science/api/pith-number/FMTGTFB4FTL2P62NVCXNJID36T/events.json","paper":"https://pith.science/paper/FMTGTFB4"},"agent_actions":{"view_html":"https://pith.science/pith/FMTGTFB4FTL2P62NVCXNJID36T","download_json":"https://pith.science/pith/FMTGTFB4FTL2P62NVCXNJID36T.json","view_paper":"https://pith.science/paper/FMTGTFB4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1608.01371&json=true","fetch_graph":"https://pith.science/api/pith-number/FMTGTFB4FTL2P62NVCXNJID36T/graph.json","fetch_events":"https://pith.science/api/pith-number/FMTGTFB4FTL2P62NVCXNJID36T/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FMTGTFB4FTL2P62NVCXNJID36T/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FMTGTFB4FTL2P62NVCXNJID36T/action/storage_attestation","attest_author":"https://pith.science/pith/FMTGTFB4FTL2P62NVCXNJID36T/action/author_attestation","sign_citation":"https://pith.science/pith/FMTGTFB4FTL2P62NVCXNJID36T/action/citation_signature","submit_replication":"https://pith.science/pith/FMTGTFB4FTL2P62NVCXNJID36T/action/replication_record"}},"created_at":"2026-05-18T00:33:23.259751+00:00","updated_at":"2026-05-18T00:33:23.259751+00:00"}