{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:LJVLEVTRL4XUOUXWAK5DO5JV6V","short_pith_number":"pith:LJVLEVTR","schema_version":"1.0","canonical_sha256":"5a6ab256715f2f4752f602ba377535f55b0f15ae0c98f9dcaa6fe2aeb23c8669","source":{"kind":"arxiv","id":"1309.1658","version":2},"attestation_state":"computed","paper":{"title":"The Breuil-Mezard conjecture for non-scalar split residual representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Fucheng Tan, Yongquan Hu","submitted_at":"2013-09-06T14:46:16Z","abstract_excerpt":"We prove the Breuil-Mezard conjecture for split non-scalar residual representations of Gal(Qp/Qp) by local methods. Combined with the cases previously proved in [18] and [24], this completes the proof of the conjecture (when p>3). As a consequence, the local restriction in the proof of the Fontaine-Mazur conjecture in [18] is removed."},"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":"1309.1658","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-09-06T14:46:16Z","cross_cats_sorted":[],"title_canon_sha256":"4f53b8eb12f416c49faff1554f3b74e3966d2d29ecd5471ec4e688bcaee8c392","abstract_canon_sha256":"cf1ea47a337056f359bee74384f787c0dba7a4e64871a7cd9043ef8304dea99c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:37:42.998422Z","signature_b64":"O8pG3ZpMNnJm9+k79uZ7WASYBvOPc9o6hwwqJjpIxqIF9+kFqw9ywj3wKShh8SoFbaMny/xZUdusZwELyfRnBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5a6ab256715f2f4752f602ba377535f55b0f15ae0c98f9dcaa6fe2aeb23c8669","last_reissued_at":"2026-05-18T02:37:42.998034Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:37:42.998034Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Breuil-Mezard conjecture for non-scalar split residual representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Fucheng Tan, Yongquan Hu","submitted_at":"2013-09-06T14:46:16Z","abstract_excerpt":"We prove the Breuil-Mezard conjecture for split non-scalar residual representations of Gal(Qp/Qp) by local methods. Combined with the cases previously proved in [18] and [24], this completes the proof of the conjecture (when p>3). As a consequence, the local restriction in the proof of the Fontaine-Mazur conjecture in [18] is removed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1658","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":"1309.1658","created_at":"2026-05-18T02:37:42.998095+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.1658v2","created_at":"2026-05-18T02:37:42.998095+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.1658","created_at":"2026-05-18T02:37:42.998095+00:00"},{"alias_kind":"pith_short_12","alias_value":"LJVLEVTRL4XU","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_16","alias_value":"LJVLEVTRL4XUOUXW","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_8","alias_value":"LJVLEVTR","created_at":"2026-05-18T12:27:51.066281+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/LJVLEVTRL4XUOUXWAK5DO5JV6V","json":"https://pith.science/pith/LJVLEVTRL4XUOUXWAK5DO5JV6V.json","graph_json":"https://pith.science/api/pith-number/LJVLEVTRL4XUOUXWAK5DO5JV6V/graph.json","events_json":"https://pith.science/api/pith-number/LJVLEVTRL4XUOUXWAK5DO5JV6V/events.json","paper":"https://pith.science/paper/LJVLEVTR"},"agent_actions":{"view_html":"https://pith.science/pith/LJVLEVTRL4XUOUXWAK5DO5JV6V","download_json":"https://pith.science/pith/LJVLEVTRL4XUOUXWAK5DO5JV6V.json","view_paper":"https://pith.science/paper/LJVLEVTR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.1658&json=true","fetch_graph":"https://pith.science/api/pith-number/LJVLEVTRL4XUOUXWAK5DO5JV6V/graph.json","fetch_events":"https://pith.science/api/pith-number/LJVLEVTRL4XUOUXWAK5DO5JV6V/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LJVLEVTRL4XUOUXWAK5DO5JV6V/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LJVLEVTRL4XUOUXWAK5DO5JV6V/action/storage_attestation","attest_author":"https://pith.science/pith/LJVLEVTRL4XUOUXWAK5DO5JV6V/action/author_attestation","sign_citation":"https://pith.science/pith/LJVLEVTRL4XUOUXWAK5DO5JV6V/action/citation_signature","submit_replication":"https://pith.science/pith/LJVLEVTRL4XUOUXWAK5DO5JV6V/action/replication_record"}},"created_at":"2026-05-18T02:37:42.998095+00:00","updated_at":"2026-05-18T02:37:42.998095+00:00"}