{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:JKL2VOJUZSTBQZKLOKC6LQLA2S","short_pith_number":"pith:JKL2VOJU","schema_version":"1.0","canonical_sha256":"4a97aab934cca618654b7285e5c160d4a95c560b9dc420d19c57e4c7dcba69c0","source":{"kind":"arxiv","id":"1901.06687","version":2},"attestation_state":"computed","paper":{"title":"Counterexamples to the Tilting and $(p,r)$-Filtration Conjectures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Christopher P. Bendel, Cornelius Pillen, Daniel K. Nakano, Paul Sobaje","submitted_at":"2019-01-20T15:00:35Z","abstract_excerpt":"In this paper the authors produce a projective indecomposable module for the Frobenius kernel of a simple algebraic group in characteristic $p$ that is not the restriction of an indecomposable tilting module. This yields a counterexample to Donkin's longstanding Tilting Module Conjecture. The authors also produce a Weyl module that does not admit a $p$-Weyl filtration. This answers an old question of Jantzen, and also provides a counterexample to the $(p,r)$-Filtration Conjecture."},"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":"1901.06687","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-01-20T15:00:35Z","cross_cats_sorted":[],"title_canon_sha256":"6c1c52c305bdb699acef34c26695a410c59325c688c36a39df7be87d325ba50c","abstract_canon_sha256":"c786f6df48c8dad9470c0d1694e2baf646fd7c32459438b37ac78c8d01c6b753"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:41.171067Z","signature_b64":"OslfijI+nO+v0lLaiEwobLuA7QQG0MYmPp6uMq30tf7Dy1YYXiPu/hTixISkZHXky4jmdY5tIfaOMWfhOHl7Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4a97aab934cca618654b7285e5c160d4a95c560b9dc420d19c57e4c7dcba69c0","last_reissued_at":"2026-05-17T23:53:41.170641Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:41.170641Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Counterexamples to the Tilting and $(p,r)$-Filtration Conjectures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Christopher P. Bendel, Cornelius Pillen, Daniel K. Nakano, Paul Sobaje","submitted_at":"2019-01-20T15:00:35Z","abstract_excerpt":"In this paper the authors produce a projective indecomposable module for the Frobenius kernel of a simple algebraic group in characteristic $p$ that is not the restriction of an indecomposable tilting module. This yields a counterexample to Donkin's longstanding Tilting Module Conjecture. The authors also produce a Weyl module that does not admit a $p$-Weyl filtration. This answers an old question of Jantzen, and also provides a counterexample to the $(p,r)$-Filtration Conjecture."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.06687","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":"1901.06687","created_at":"2026-05-17T23:53:41.170702+00:00"},{"alias_kind":"arxiv_version","alias_value":"1901.06687v2","created_at":"2026-05-17T23:53:41.170702+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.06687","created_at":"2026-05-17T23:53:41.170702+00:00"},{"alias_kind":"pith_short_12","alias_value":"JKL2VOJUZSTB","created_at":"2026-05-18T12:33:21.387695+00:00"},{"alias_kind":"pith_short_16","alias_value":"JKL2VOJUZSTBQZKL","created_at":"2026-05-18T12:33:21.387695+00:00"},{"alias_kind":"pith_short_8","alias_value":"JKL2VOJU","created_at":"2026-05-18T12:33:21.387695+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/JKL2VOJUZSTBQZKLOKC6LQLA2S","json":"https://pith.science/pith/JKL2VOJUZSTBQZKLOKC6LQLA2S.json","graph_json":"https://pith.science/api/pith-number/JKL2VOJUZSTBQZKLOKC6LQLA2S/graph.json","events_json":"https://pith.science/api/pith-number/JKL2VOJUZSTBQZKLOKC6LQLA2S/events.json","paper":"https://pith.science/paper/JKL2VOJU"},"agent_actions":{"view_html":"https://pith.science/pith/JKL2VOJUZSTBQZKLOKC6LQLA2S","download_json":"https://pith.science/pith/JKL2VOJUZSTBQZKLOKC6LQLA2S.json","view_paper":"https://pith.science/paper/JKL2VOJU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1901.06687&json=true","fetch_graph":"https://pith.science/api/pith-number/JKL2VOJUZSTBQZKLOKC6LQLA2S/graph.json","fetch_events":"https://pith.science/api/pith-number/JKL2VOJUZSTBQZKLOKC6LQLA2S/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JKL2VOJUZSTBQZKLOKC6LQLA2S/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JKL2VOJUZSTBQZKLOKC6LQLA2S/action/storage_attestation","attest_author":"https://pith.science/pith/JKL2VOJUZSTBQZKLOKC6LQLA2S/action/author_attestation","sign_citation":"https://pith.science/pith/JKL2VOJUZSTBQZKLOKC6LQLA2S/action/citation_signature","submit_replication":"https://pith.science/pith/JKL2VOJUZSTBQZKLOKC6LQLA2S/action/replication_record"}},"created_at":"2026-05-17T23:53:41.170702+00:00","updated_at":"2026-05-17T23:53:41.170702+00:00"}