{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:V2O7RV7CWZLLTGNWZOINAHVAAT","short_pith_number":"pith:V2O7RV7C","schema_version":"1.0","canonical_sha256":"ae9df8d7e2b656b999b6cb90d01ea004d1ab1594055d4a8fc429c908b0a3452a","source":{"kind":"arxiv","id":"1202.4115","version":3},"attestation_state":"computed","paper":{"title":"On the equation N_{K/k}(\\Xi)=P(t)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Dasheng Wei","submitted_at":"2012-02-18T23:09:30Z","abstract_excerpt":"For varieties given by an equation N_{K/k}(\\Xi)=P(t), where N_{K/k} is the norm form attached to a field extension K/k and P(t) in k[t] is a polynomial, three topics have been investigated:\n  (1) computation of the unramified Brauer group of such varieties over arbitrary fields;\n  (2) rational points and Brauer-Manin obstruction over number fields (under Schinzel's hypothesis);\n  (3) zero-cycles and Brauer-Manin obstruction over number fields.\n  In this paper, we produce new results in each of three directions. We obtain quite general results under the assumption that K/k is abelian (as oppose"},"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":"1202.4115","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-02-18T23:09:30Z","cross_cats_sorted":[],"title_canon_sha256":"0f01fe8b4d537f423a7b167e0a14caa0e5244aa2a30d87ca7bc397ddd6d61a2d","abstract_canon_sha256":"1a59484989d37e9953bc97648c4bd640831c80c38a62b07cb3cebf84360533dd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:23.090865Z","signature_b64":"eusGk2FJy2KzEADThNpL4IxAI+MLp3y9r6t/VhGJJbhmNHl/pb6yGwtmYsWRJ/l4Z6lrW15LvJXAxo2ykMwMBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae9df8d7e2b656b999b6cb90d01ea004d1ab1594055d4a8fc429c908b0a3452a","last_reissued_at":"2026-05-18T02:50:23.090290Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:23.090290Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the equation N_{K/k}(\\Xi)=P(t)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Dasheng Wei","submitted_at":"2012-02-18T23:09:30Z","abstract_excerpt":"For varieties given by an equation N_{K/k}(\\Xi)=P(t), where N_{K/k} is the norm form attached to a field extension K/k and P(t) in k[t] is a polynomial, three topics have been investigated:\n  (1) computation of the unramified Brauer group of such varieties over arbitrary fields;\n  (2) rational points and Brauer-Manin obstruction over number fields (under Schinzel's hypothesis);\n  (3) zero-cycles and Brauer-Manin obstruction over number fields.\n  In this paper, we produce new results in each of three directions. We obtain quite general results under the assumption that K/k is abelian (as oppose"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.4115","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":"1202.4115","created_at":"2026-05-18T02:50:23.090381+00:00"},{"alias_kind":"arxiv_version","alias_value":"1202.4115v3","created_at":"2026-05-18T02:50:23.090381+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.4115","created_at":"2026-05-18T02:50:23.090381+00:00"},{"alias_kind":"pith_short_12","alias_value":"V2O7RV7CWZLL","created_at":"2026-05-18T12:27:25.539911+00:00"},{"alias_kind":"pith_short_16","alias_value":"V2O7RV7CWZLLTGNW","created_at":"2026-05-18T12:27:25.539911+00:00"},{"alias_kind":"pith_short_8","alias_value":"V2O7RV7C","created_at":"2026-05-18T12:27:25.539911+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/V2O7RV7CWZLLTGNWZOINAHVAAT","json":"https://pith.science/pith/V2O7RV7CWZLLTGNWZOINAHVAAT.json","graph_json":"https://pith.science/api/pith-number/V2O7RV7CWZLLTGNWZOINAHVAAT/graph.json","events_json":"https://pith.science/api/pith-number/V2O7RV7CWZLLTGNWZOINAHVAAT/events.json","paper":"https://pith.science/paper/V2O7RV7C"},"agent_actions":{"view_html":"https://pith.science/pith/V2O7RV7CWZLLTGNWZOINAHVAAT","download_json":"https://pith.science/pith/V2O7RV7CWZLLTGNWZOINAHVAAT.json","view_paper":"https://pith.science/paper/V2O7RV7C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1202.4115&json=true","fetch_graph":"https://pith.science/api/pith-number/V2O7RV7CWZLLTGNWZOINAHVAAT/graph.json","fetch_events":"https://pith.science/api/pith-number/V2O7RV7CWZLLTGNWZOINAHVAAT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/V2O7RV7CWZLLTGNWZOINAHVAAT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/V2O7RV7CWZLLTGNWZOINAHVAAT/action/storage_attestation","attest_author":"https://pith.science/pith/V2O7RV7CWZLLTGNWZOINAHVAAT/action/author_attestation","sign_citation":"https://pith.science/pith/V2O7RV7CWZLLTGNWZOINAHVAAT/action/citation_signature","submit_replication":"https://pith.science/pith/V2O7RV7CWZLLTGNWZOINAHVAAT/action/replication_record"}},"created_at":"2026-05-18T02:50:23.090381+00:00","updated_at":"2026-05-18T02:50:23.090381+00:00"}