{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:4ZQXATQC5MFJH3OGT45R2BSOS4","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":"1c2928664e53e89bdcf41b70983da791fa803576ae9d8747ef2f56eef732998a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-07-02T00:46:08Z","title_canon_sha256":"6987944d5a4e41a3b754f4139c5c051ca39ad614b427b1af2553c8347b39b49f"},"schema_version":"1.0","source":{"id":"1507.00401","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.00401","created_at":"2026-05-18T00:35:44Z"},{"alias_kind":"arxiv_version","alias_value":"1507.00401v3","created_at":"2026-05-18T00:35:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.00401","created_at":"2026-05-18T00:35:44Z"},{"alias_kind":"pith_short_12","alias_value":"4ZQXATQC5MFJ","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4ZQXATQC5MFJH3OG","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4ZQXATQC","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:c1cede302f3f606cc00cd316de2412b7ce2b95e0ab4f2b5ad463c4e70636954b","target":"graph","created_at":"2026-05-18T00:35:44Z","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":"We complete the construction of the modular generalized Springer correspondence for an arbitrary connected reductive group, with a uniform proof of the disjointness of induction series that avoids the case-by-case arguments for classical groups used in previous papers in the series. We show that the induction series containing the trivial local system on the regular nilpotent orbit is determined by the Sylow subgroups of the Weyl group. Under some assumptions, we give an algorithm for determining the induction series associated to the minimal cuspidal datum with a given central character. We a","authors_text":"Anthony Henderson, Daniel Juteau, Pramod N. Achar, Simon Riche","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-07-02T00:46:08Z","title":"Modular generalized Springer correspondence III: exceptional groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.00401","kind":"arxiv","version":3},"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":"sha256:01e032bf1e09f046e88320e42ad3d8bceeb8126d6fa3e208cb1c91e2d1a466e0","target":"record","created_at":"2026-05-18T00:35:44Z","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":"1c2928664e53e89bdcf41b70983da791fa803576ae9d8747ef2f56eef732998a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-07-02T00:46:08Z","title_canon_sha256":"6987944d5a4e41a3b754f4139c5c051ca39ad614b427b1af2553c8347b39b49f"},"schema_version":"1.0","source":{"id":"1507.00401","kind":"arxiv","version":3}},"canonical_sha256":"e661704e02eb0a93edc69f3b1d064e973a13e43e2cb6f2145274d068a1182b31","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e661704e02eb0a93edc69f3b1d064e973a13e43e2cb6f2145274d068a1182b31","first_computed_at":"2026-05-18T00:35:44.484610Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:44.484610Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CLNiUYlgBmAgS3xh/tebFSoXUXRgmlKObY5OC9Mt9qOGFO9NZXRpzJXvR1NDPaA6DxYMK2cbxjHEhr1nxjLmCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:44.485203Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.00401","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:01e032bf1e09f046e88320e42ad3d8bceeb8126d6fa3e208cb1c91e2d1a466e0","sha256:c1cede302f3f606cc00cd316de2412b7ce2b95e0ab4f2b5ad463c4e70636954b"],"state_sha256":"9584b95e1225e568e186629f821d96f698f25e4dcd70489084fe2b7806d523f2"}