{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:LAYK6UQRYLXGNKQTRANKRALXLU","short_pith_number":"pith:LAYK6UQR","schema_version":"1.0","canonical_sha256":"5830af5211c2ee66aa13881aa881775d0dd8f69a5740972278f72075e2994647","source":{"kind":"arxiv","id":"1812.09960","version":2},"attestation_state":"computed","paper":{"title":"Conjectures on tilting modules and antispherical $p$-cells","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Pramod N. Achar, Simon Riche, William Hardesty","submitted_at":"2018-12-24T17:56:48Z","abstract_excerpt":"For quantum groups at a root of unity, there is a web of theorems (due to Bezrukavnikov and Ostrik, and relying on work of Lusztig) connecting the following topics: (i) tilting modules; (ii) vector bundles on nilpotent orbits; and (iii) Kazhdan-Lusztig cells in the affine Weyl group. In this paper, we propose a (partly conjectural) analogous picture for reductive algebraic groups over fields of positive characteristic, inspired by a conjecture of Humphreys."},"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":"1812.09960","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-12-24T17:56:48Z","cross_cats_sorted":[],"title_canon_sha256":"f82564d64ed3ff409a661cb5aabafcd6bb2932dc2e4788f8744681e82aea4383","abstract_canon_sha256":"f4cb2f710bbfd8ecdcf1e23cf366be523e3b979473b0ca61612ac0de7f726427"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:39.656408Z","signature_b64":"f+Z5Y8qE42csjE74qVPZ8Ops1XJsRALyhWvHwiAIDGVBa9VlwxngAkSyJMSA4sK2Rld8K2ijBzoCZo6ZkzeECQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5830af5211c2ee66aa13881aa881775d0dd8f69a5740972278f72075e2994647","last_reissued_at":"2026-05-17T23:48:39.655751Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:39.655751Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Conjectures on tilting modules and antispherical $p$-cells","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Pramod N. Achar, Simon Riche, William Hardesty","submitted_at":"2018-12-24T17:56:48Z","abstract_excerpt":"For quantum groups at a root of unity, there is a web of theorems (due to Bezrukavnikov and Ostrik, and relying on work of Lusztig) connecting the following topics: (i) tilting modules; (ii) vector bundles on nilpotent orbits; and (iii) Kazhdan-Lusztig cells in the affine Weyl group. In this paper, we propose a (partly conjectural) analogous picture for reductive algebraic groups over fields of positive characteristic, inspired by a conjecture of Humphreys."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.09960","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":"1812.09960","created_at":"2026-05-17T23:48:39.655847+00:00"},{"alias_kind":"arxiv_version","alias_value":"1812.09960v2","created_at":"2026-05-17T23:48:39.655847+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.09960","created_at":"2026-05-17T23:48:39.655847+00:00"},{"alias_kind":"pith_short_12","alias_value":"LAYK6UQRYLXG","created_at":"2026-05-18T12:32:33.847187+00:00"},{"alias_kind":"pith_short_16","alias_value":"LAYK6UQRYLXGNKQT","created_at":"2026-05-18T12:32:33.847187+00:00"},{"alias_kind":"pith_short_8","alias_value":"LAYK6UQR","created_at":"2026-05-18T12:32:33.847187+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/LAYK6UQRYLXGNKQTRANKRALXLU","json":"https://pith.science/pith/LAYK6UQRYLXGNKQTRANKRALXLU.json","graph_json":"https://pith.science/api/pith-number/LAYK6UQRYLXGNKQTRANKRALXLU/graph.json","events_json":"https://pith.science/api/pith-number/LAYK6UQRYLXGNKQTRANKRALXLU/events.json","paper":"https://pith.science/paper/LAYK6UQR"},"agent_actions":{"view_html":"https://pith.science/pith/LAYK6UQRYLXGNKQTRANKRALXLU","download_json":"https://pith.science/pith/LAYK6UQRYLXGNKQTRANKRALXLU.json","view_paper":"https://pith.science/paper/LAYK6UQR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1812.09960&json=true","fetch_graph":"https://pith.science/api/pith-number/LAYK6UQRYLXGNKQTRANKRALXLU/graph.json","fetch_events":"https://pith.science/api/pith-number/LAYK6UQRYLXGNKQTRANKRALXLU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LAYK6UQRYLXGNKQTRANKRALXLU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LAYK6UQRYLXGNKQTRANKRALXLU/action/storage_attestation","attest_author":"https://pith.science/pith/LAYK6UQRYLXGNKQTRANKRALXLU/action/author_attestation","sign_citation":"https://pith.science/pith/LAYK6UQRYLXGNKQTRANKRALXLU/action/citation_signature","submit_replication":"https://pith.science/pith/LAYK6UQRYLXGNKQTRANKRALXLU/action/replication_record"}},"created_at":"2026-05-17T23:48:39.655847+00:00","updated_at":"2026-05-17T23:48:39.655847+00:00"}