{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:LAYK6UQRYLXGNKQTRANKRALXLU","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"f4cb2f710bbfd8ecdcf1e23cf366be523e3b979473b0ca61612ac0de7f726427","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-12-24T17:56:48Z","title_canon_sha256":"f82564d64ed3ff409a661cb5aabafcd6bb2932dc2e4788f8744681e82aea4383"},"schema_version":"1.0","source":{"id":"1812.09960","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.09960","created_at":"2026-05-17T23:48:39Z"},{"alias_kind":"arxiv_version","alias_value":"1812.09960v2","created_at":"2026-05-17T23:48:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.09960","created_at":"2026-05-17T23:48:39Z"},{"alias_kind":"pith_short_12","alias_value":"LAYK6UQRYLXG","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"LAYK6UQRYLXGNKQT","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"LAYK6UQR","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:b33753f4c56b473017ef1ac2b8acf95332b36efed3d61ba8e4e65fce30f288fe","target":"graph","created_at":"2026-05-17T23:48:39Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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.","authors_text":"Pramod N. Achar, Simon Riche, William Hardesty","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-12-24T17:56:48Z","title":"Conjectures on tilting modules and antispherical $p$-cells"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.09960","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:61497cc2183194626cb322f741c9bd0281d8a2b484b69e02b4d955336927d96f","target":"record","created_at":"2026-05-17T23:48:39Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"f4cb2f710bbfd8ecdcf1e23cf366be523e3b979473b0ca61612ac0de7f726427","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-12-24T17:56:48Z","title_canon_sha256":"f82564d64ed3ff409a661cb5aabafcd6bb2932dc2e4788f8744681e82aea4383"},"schema_version":"1.0","source":{"id":"1812.09960","kind":"arxiv","version":2}},"canonical_sha256":"5830af5211c2ee66aa13881aa881775d0dd8f69a5740972278f72075e2994647","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5830af5211c2ee66aa13881aa881775d0dd8f69a5740972278f72075e2994647","first_computed_at":"2026-05-17T23:48:39.655751Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:39.655751Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f+Z5Y8qE42csjE74qVPZ8Ops1XJsRALyhWvHwiAIDGVBa9VlwxngAkSyJMSA4sK2Rld8K2ijBzoCZo6ZkzeECQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:39.656408Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.09960","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:61497cc2183194626cb322f741c9bd0281d8a2b484b69e02b4d955336927d96f","sha256:b33753f4c56b473017ef1ac2b8acf95332b36efed3d61ba8e4e65fce30f288fe"],"state_sha256":"d393c76f4e436e05fc340ae522ba1596f7c045f48ef520c0909f8819a111ab99"}