{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:HVLASOP76RPFCFLPEXANA5YB4X","short_pith_number":"pith:HVLASOP7","canonical_record":{"source":{"id":"1805.10550","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-05-26T22:44:41Z","cross_cats_sorted":[],"title_canon_sha256":"e047342099f43046b5092cea9f75ddebb9a77e12dfe39649f131f2500220914c","abstract_canon_sha256":"10e38b0a2518dbd07efd93193dbb97990b4207c4b7f64357f5e4766ad78f396e"},"schema_version":"1.0"},"canonical_sha256":"3d560939fff45e51156f25c0d07701e5da97ce9d75f613b8ec2e6e636cd840d2","source":{"kind":"arxiv","id":"1805.10550","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.10550","created_at":"2026-05-18T00:14:52Z"},{"alias_kind":"arxiv_version","alias_value":"1805.10550v1","created_at":"2026-05-18T00:14:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.10550","created_at":"2026-05-18T00:14:52Z"},{"alias_kind":"pith_short_12","alias_value":"HVLASOP76RPF","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HVLASOP76RPFCFLP","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HVLASOP7","created_at":"2026-05-18T12:32:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:HVLASOP76RPFCFLPEXANA5YB4X","target":"record","payload":{"canonical_record":{"source":{"id":"1805.10550","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-05-26T22:44:41Z","cross_cats_sorted":[],"title_canon_sha256":"e047342099f43046b5092cea9f75ddebb9a77e12dfe39649f131f2500220914c","abstract_canon_sha256":"10e38b0a2518dbd07efd93193dbb97990b4207c4b7f64357f5e4766ad78f396e"},"schema_version":"1.0"},"canonical_sha256":"3d560939fff45e51156f25c0d07701e5da97ce9d75f613b8ec2e6e636cd840d2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:52.189101Z","signature_b64":"lJgtdhluV1uF+L1GSZV2nlcy0q2cY+jAMf0hHS04IsAAm2wRDCW5ljqPbxc3hS6PYmVgh6Np8lk/GaixKRf0Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3d560939fff45e51156f25c0d07701e5da97ce9d75f613b8ec2e6e636cd840d2","last_reissued_at":"2026-05-18T00:14:52.188428Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:52.188428Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.10550","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:14:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/3+IYanFrUSP2bZehkhZjXBY6nSlCBbhpx5m8y4jlCEu4T/4nWyagePiIz/ZRgK2eVcK/aD9Uak0oWV7eruVBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T17:17:50.802832Z"},"content_sha256":"5ea9a5008198b277193ca0f010c3889941e58d29af54f10c8885c8d135e38459","schema_version":"1.0","event_id":"sha256:5ea9a5008198b277193ca0f010c3889941e58d29af54f10c8885c8d135e38459"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:HVLASOP76RPFCFLPEXANA5YB4X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Z/m-graded Lie algebras and perverse sheaves, IV","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"George Lusztig, Zhiwei Yun","submitted_at":"2018-05-26T22:44:41Z","abstract_excerpt":"Let G be a reductive group over C. Assume that the Lie algebra g of G has a given grading (g_j) indexed by a cyclic group Z/m such that g_0 contains a Cartan subalgebra of g. The subgroup G_0 of G corresponding to g_0 acts on the variety of nilpotent elements in g_1 with finitely many orbits. We are interested in computing the local intersection cohomology of the closures of these orbits with coefficients in irreducible G-equivariant local systems which are in the \"principal block\". We show that these can be computed by a purely combinatorial algorithm."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.10550","kind":"arxiv","version":1},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:14:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jauFtDu0qgVM8DYThqzfF8U3iaTiToLsNnAY1iAAsN6SncPWvcJxFweURNHNZ7zRQEAzcKD4Ff1n2LEZg4XmAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T17:17:50.803546Z"},"content_sha256":"2c809f69ce6dc289fbbcdebf3df1a570045cfd913c401fa83ba528aa34f004bf","schema_version":"1.0","event_id":"sha256:2c809f69ce6dc289fbbcdebf3df1a570045cfd913c401fa83ba528aa34f004bf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HVLASOP76RPFCFLPEXANA5YB4X/bundle.json","state_url":"https://pith.science/pith/HVLASOP76RPFCFLPEXANA5YB4X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HVLASOP76RPFCFLPEXANA5YB4X/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-07T17:17:50Z","links":{"resolver":"https://pith.science/pith/HVLASOP76RPFCFLPEXANA5YB4X","bundle":"https://pith.science/pith/HVLASOP76RPFCFLPEXANA5YB4X/bundle.json","state":"https://pith.science/pith/HVLASOP76RPFCFLPEXANA5YB4X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HVLASOP76RPFCFLPEXANA5YB4X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:HVLASOP76RPFCFLPEXANA5YB4X","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":"10e38b0a2518dbd07efd93193dbb97990b4207c4b7f64357f5e4766ad78f396e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-05-26T22:44:41Z","title_canon_sha256":"e047342099f43046b5092cea9f75ddebb9a77e12dfe39649f131f2500220914c"},"schema_version":"1.0","source":{"id":"1805.10550","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.10550","created_at":"2026-05-18T00:14:52Z"},{"alias_kind":"arxiv_version","alias_value":"1805.10550v1","created_at":"2026-05-18T00:14:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.10550","created_at":"2026-05-18T00:14:52Z"},{"alias_kind":"pith_short_12","alias_value":"HVLASOP76RPF","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HVLASOP76RPFCFLP","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HVLASOP7","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:2c809f69ce6dc289fbbcdebf3df1a570045cfd913c401fa83ba528aa34f004bf","target":"graph","created_at":"2026-05-18T00:14:52Z","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":"Let G be a reductive group over C. Assume that the Lie algebra g of G has a given grading (g_j) indexed by a cyclic group Z/m such that g_0 contains a Cartan subalgebra of g. The subgroup G_0 of G corresponding to g_0 acts on the variety of nilpotent elements in g_1 with finitely many orbits. We are interested in computing the local intersection cohomology of the closures of these orbits with coefficients in irreducible G-equivariant local systems which are in the \"principal block\". We show that these can be computed by a purely combinatorial algorithm.","authors_text":"George Lusztig, Zhiwei Yun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-05-26T22:44:41Z","title":"Z/m-graded Lie algebras and perverse sheaves, IV"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.10550","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":"sha256:5ea9a5008198b277193ca0f010c3889941e58d29af54f10c8885c8d135e38459","target":"record","created_at":"2026-05-18T00:14:52Z","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":"10e38b0a2518dbd07efd93193dbb97990b4207c4b7f64357f5e4766ad78f396e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-05-26T22:44:41Z","title_canon_sha256":"e047342099f43046b5092cea9f75ddebb9a77e12dfe39649f131f2500220914c"},"schema_version":"1.0","source":{"id":"1805.10550","kind":"arxiv","version":1}},"canonical_sha256":"3d560939fff45e51156f25c0d07701e5da97ce9d75f613b8ec2e6e636cd840d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3d560939fff45e51156f25c0d07701e5da97ce9d75f613b8ec2e6e636cd840d2","first_computed_at":"2026-05-18T00:14:52.188428Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:52.188428Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lJgtdhluV1uF+L1GSZV2nlcy0q2cY+jAMf0hHS04IsAAm2wRDCW5ljqPbxc3hS6PYmVgh6Np8lk/GaixKRf0Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:52.189101Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.10550","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ea9a5008198b277193ca0f010c3889941e58d29af54f10c8885c8d135e38459","sha256:2c809f69ce6dc289fbbcdebf3df1a570045cfd913c401fa83ba528aa34f004bf"],"state_sha256":"c551ae8f1ab5c3821bc5e2e0514524a4c3629711d34d8f97ba25c85da4108ffa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P0aC3USg5rMeMhn0PChC81abeXsETQpTyv2KGHaSNYBRMI6AJLLWH9CRXZfbSz8n79EjUj4OdAAv65cF6S4HDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T17:17:50.807270Z","bundle_sha256":"4bcbcdd05d5124ef8e39fcde8b8526f0d0f31b05a5181622aa727c84bdae2470"}}