{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:6GQLJTDSOUTOYZVEBW4IWUEUOS","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":"5ef12e69dc2b8f9affc6950194840c13419f2993b98b3398bad18369f8d15298","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-09-14T20:23:11Z","title_canon_sha256":"11b50b3070574d072e7c2ab3be50eed1be4d57035e2ce64f101b1ce6e47a1888"},"schema_version":"1.0","source":{"id":"1709.04967","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.04967","created_at":"2026-05-18T00:35:08Z"},{"alias_kind":"arxiv_version","alias_value":"1709.04967v1","created_at":"2026-05-18T00:35:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.04967","created_at":"2026-05-18T00:35:08Z"},{"alias_kind":"pith_short_12","alias_value":"6GQLJTDSOUTO","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6GQLJTDSOUTOYZVE","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6GQLJTDS","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:44a0d48ea8b5a6a468e4f0c53aae1a40087ba89003adef5adc22d4cd556557b9","target":"graph","created_at":"2026-05-18T00:35:08Z","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":"The paper concerns a certain subcategory of the category of representations for a semisimple algebraic group $G$ in characteristic $p$, which arise from the semisimple modules for the corresponding quantum group at a $p$-th root of unity. The subcategory, thus, records the cohomological difference between quantum groups and algebraic groups. We define translation functors in this category and use them to obtain information on the irreducible characters for $G$ when the Lusztig character formula does not hold.","authors_text":"Hankyung Ko","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-09-14T20:23:11Z","title":"Grade zero part of forced graded algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.04967","kind":"arxiv","version":1},"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":"sha256:8ff6b9fb0460f9845201b70b8a7a136a2cbf9be7b7c710214c60e17bf649df4b","target":"record","created_at":"2026-05-18T00:35:08Z","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":"5ef12e69dc2b8f9affc6950194840c13419f2993b98b3398bad18369f8d15298","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-09-14T20:23:11Z","title_canon_sha256":"11b50b3070574d072e7c2ab3be50eed1be4d57035e2ce64f101b1ce6e47a1888"},"schema_version":"1.0","source":{"id":"1709.04967","kind":"arxiv","version":1}},"canonical_sha256":"f1a0b4cc727526ec66a40db88b5094749a93d6670aa70f373c0a9a17dd5e095c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f1a0b4cc727526ec66a40db88b5094749a93d6670aa70f373c0a9a17dd5e095c","first_computed_at":"2026-05-18T00:35:08.737025Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:08.737025Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rfZnfHCc0zzTt9RUpnUoApc0dIB5NrItaBIPmR06IJGJ40pZqkKQabFAlEQC8GTSDsvCqDZRKkaINA1rejqRBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:08.737446Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.04967","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8ff6b9fb0460f9845201b70b8a7a136a2cbf9be7b7c710214c60e17bf649df4b","sha256:44a0d48ea8b5a6a468e4f0c53aae1a40087ba89003adef5adc22d4cd556557b9"],"state_sha256":"858771c500daba056f1d51b5ff8f674cc429d0f17bb344989718e6f4a382dc5b"}