{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:7CK4ZO3GRILQT2HNKZC6D7TJLI","short_pith_number":"pith:7CK4ZO3G","schema_version":"1.0","canonical_sha256":"f895ccbb668a1709e8ed5645e1fe695a0956b5033cc658a2e139c4cd1d4d661e","source":{"kind":"arxiv","id":"2601.16975","version":2},"attestation_state":"computed","paper":{"title":"Explicit Brauer-Manin obstructions on plane quartics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A method makes Brauer-Manin obstructions explicit on plane quartics without computing full S-unit groups of étale algebras.","cross_cats":[],"primary_cat":"math.NT","authors_text":"Brendan Creutz, Nils Bruin","submitted_at":"2026-01-23T18:53:19Z","abstract_excerpt":"We describe a method to show a plane quartic over a number field has no rational points. The method can be adapted to show that a curve does not have divisors of degree 1 or 2 and can be generalized to arbitrary smooth projective curves. Our approach significantly improves on the applicability over previous 2-cover descent methods by not requiring the computation of the full $S$-unit group of the \\'etale algebras involved. We illustrate the practicality with several examples, including examples where we determine plane quartics to be of index 2 or 4 when the maximum local index is strictly sma"},"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":true},"canonical_record":{"source":{"id":"2601.16975","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-01-23T18:53:19Z","cross_cats_sorted":[],"title_canon_sha256":"08c57f6c63df42473d4fa7819c2bab012418e9d08a3fe73d82c133b970516b7c","abstract_canon_sha256":"0e5d136767db5fd63f11247357e1c72832925c461eaed93fbdd0c97495adf5a5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:16.597844Z","signature_b64":"JDGstL4Y4NrWyOcM93h5W0X53VkzR5JrcQJFlHbINd84wqN2L+NS/Af1M+1UVlWrKXOsCHigDqIpgMnPU4UiCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f895ccbb668a1709e8ed5645e1fe695a0956b5033cc658a2e139c4cd1d4d661e","last_reissued_at":"2026-05-17T23:39:16.597088Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:16.597088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Explicit Brauer-Manin obstructions on plane quartics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A method makes Brauer-Manin obstructions explicit on plane quartics without computing full S-unit groups of étale algebras.","cross_cats":[],"primary_cat":"math.NT","authors_text":"Brendan Creutz, Nils Bruin","submitted_at":"2026-01-23T18:53:19Z","abstract_excerpt":"We describe a method to show a plane quartic over a number field has no rational points. The method can be adapted to show that a curve does not have divisors of degree 1 or 2 and can be generalized to arbitrary smooth projective curves. Our approach significantly improves on the applicability over previous 2-cover descent methods by not requiring the computation of the full $S$-unit group of the \\'etale algebras involved. We illustrate the practicality with several examples, including examples where we determine plane quartics to be of index 2 or 4 when the maximum local index is strictly sma"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Our approach significantly improves on the applicability over previous 2-cover descent methods by not requiring the computation of the full S-unit group of the étale algebras involved.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The Brauer-Manin obstruction is assumed to be the dominant or only obstruction that needs to be made explicit, and the adaptation to divisors of degree 1 or 2 is presumed to work without introducing new computational bottlenecks or unaccounted local obstructions.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A computational method uses explicit Brauer-Manin obstructions to obstruct rational points on plane quartics without requiring full S-unit group calculations.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A method makes Brauer-Manin obstructions explicit on plane quartics without computing full S-unit groups of étale algebras.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"4a4adae5c736ef3581b29fbb6a78e8f53e300bc2086f5d40aed1a927fcc9398f"},"source":{"id":"2601.16975","kind":"arxiv","version":2},"verdict":{"id":"5d3a0aad-ae2e-4ad9-9f4c-36f073c35213","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-16T11:30:08.329096Z","strongest_claim":"Our approach significantly improves on the applicability over previous 2-cover descent methods by not requiring the computation of the full S-unit group of the étale algebras involved.","one_line_summary":"A computational method uses explicit Brauer-Manin obstructions to obstruct rational points on plane quartics without requiring full S-unit group calculations.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The Brauer-Manin obstruction is assumed to be the dominant or only obstruction that needs to be made explicit, and the adaptation to divisors of degree 1 or 2 is presumed to work without introducing new computational bottlenecks or unaccounted local obstructions.","pith_extraction_headline":"A method makes Brauer-Manin obstructions explicit on plane quartics without computing full S-unit groups of étale algebras."},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"9275738a975ea2c210837bb212e6dc735561fc1fc122411423d454505195627c"},"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":"2601.16975","created_at":"2026-05-17T23:39:16.597219+00:00"},{"alias_kind":"arxiv_version","alias_value":"2601.16975v2","created_at":"2026-05-17T23:39:16.597219+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.16975","created_at":"2026-05-17T23:39:16.597219+00:00"},{"alias_kind":"pith_short_12","alias_value":"7CK4ZO3GRILQ","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_16","alias_value":"7CK4ZO3GRILQT2HN","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_8","alias_value":"7CK4ZO3G","created_at":"2026-05-18T12:33:37.589309+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":2,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7CK4ZO3GRILQT2HNKZC6D7TJLI","json":"https://pith.science/pith/7CK4ZO3GRILQT2HNKZC6D7TJLI.json","graph_json":"https://pith.science/api/pith-number/7CK4ZO3GRILQT2HNKZC6D7TJLI/graph.json","events_json":"https://pith.science/api/pith-number/7CK4ZO3GRILQT2HNKZC6D7TJLI/events.json","paper":"https://pith.science/paper/7CK4ZO3G"},"agent_actions":{"view_html":"https://pith.science/pith/7CK4ZO3GRILQT2HNKZC6D7TJLI","download_json":"https://pith.science/pith/7CK4ZO3GRILQT2HNKZC6D7TJLI.json","view_paper":"https://pith.science/paper/7CK4ZO3G","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2601.16975&json=true","fetch_graph":"https://pith.science/api/pith-number/7CK4ZO3GRILQT2HNKZC6D7TJLI/graph.json","fetch_events":"https://pith.science/api/pith-number/7CK4ZO3GRILQT2HNKZC6D7TJLI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7CK4ZO3GRILQT2HNKZC6D7TJLI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7CK4ZO3GRILQT2HNKZC6D7TJLI/action/storage_attestation","attest_author":"https://pith.science/pith/7CK4ZO3GRILQT2HNKZC6D7TJLI/action/author_attestation","sign_citation":"https://pith.science/pith/7CK4ZO3GRILQT2HNKZC6D7TJLI/action/citation_signature","submit_replication":"https://pith.science/pith/7CK4ZO3GRILQT2HNKZC6D7TJLI/action/replication_record"}},"created_at":"2026-05-17T23:39:16.597219+00:00","updated_at":"2026-05-17T23:39:16.597219+00:00"}