{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:7TQ44O2BREWYL42DLCYZEMO3XD","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":"dac54f0fc6dab199ebd1142d601471faef29621882f59b0845f08f36fa90a12b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.RT","submitted_at":"2026-07-01T06:53:37Z","title_canon_sha256":"39f3ac169fd3b237dffb486498a51aba2e6e2a8bb7ca23ddbc4b11d986c59ad5"},"schema_version":"1.0","source":{"id":"2607.00515","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.00515","created_at":"2026-07-02T01:17:46Z"},{"alias_kind":"arxiv_version","alias_value":"2607.00515v1","created_at":"2026-07-02T01:17:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.00515","created_at":"2026-07-02T01:17:46Z"},{"alias_kind":"pith_short_12","alias_value":"7TQ44O2BREWY","created_at":"2026-07-02T01:17:46Z"},{"alias_kind":"pith_short_16","alias_value":"7TQ44O2BREWYL42D","created_at":"2026-07-02T01:17:46Z"},{"alias_kind":"pith_short_8","alias_value":"7TQ44O2B","created_at":"2026-07-02T01:17:46Z"}],"graph_snapshots":[{"event_id":"sha256:2d85555527b598279b31d98f0c68ab3f77e53f9e09d7212e293aaa9f48970b49","target":"graph","created_at":"2026-07-02T01:17:46Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.00515/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"It has been shown that the theory of unipotent characters of finite reductive groups admits a generalisation to objects whose Weyl group is a spetsial complex reflection group, called spetses. In this paper we prove several natural properties satisfied by the unipotent characters of spetses, in particular the validity of all Harish-Chandra theories as well as the existence of Ennola $d$-alities for all integers $d$, Alvis--Curtis duality, and compatibility with Rouquier blocks of relative Hecke algebras.","authors_text":"Gunter Malle","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.RT","submitted_at":"2026-07-01T06:53:37Z","title":"Harish-Chandra theories, Ennola $d$-ality and Rouquier blocks for spetses"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.00515","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:d42c2e84804866f1360623e40e23c62d3b0e1f4f359360b960521f760f593a88","target":"record","created_at":"2026-07-02T01:17:46Z","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":"dac54f0fc6dab199ebd1142d601471faef29621882f59b0845f08f36fa90a12b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.RT","submitted_at":"2026-07-01T06:53:37Z","title_canon_sha256":"39f3ac169fd3b237dffb486498a51aba2e6e2a8bb7ca23ddbc4b11d986c59ad5"},"schema_version":"1.0","source":{"id":"2607.00515","kind":"arxiv","version":1}},"canonical_sha256":"fce1ce3b41892d85f34358b19231dbb8dddc7d643cc5a3faa71e03cc0b65d5b3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fce1ce3b41892d85f34358b19231dbb8dddc7d643cc5a3faa71e03cc0b65d5b3","first_computed_at":"2026-07-02T01:17:46.407434Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-02T01:17:46.407434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K5CPc7BaaL5BLDZj28BalCnoaizh1/YEZdpbS5VrYUhEhDOMJonrc2HoRHHEyrj2V12F7QIbrOX4/axLy1NkDw==","signature_status":"signed_v1","signed_at":"2026-07-02T01:17:46.407832Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.00515","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d42c2e84804866f1360623e40e23c62d3b0e1f4f359360b960521f760f593a88","sha256:2d85555527b598279b31d98f0c68ab3f77e53f9e09d7212e293aaa9f48970b49"],"state_sha256":"376d04f590b4a893b67e6e5e96cc0a280c929d0c9471ef17dfdb2c8ca2d196c9"}