{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:S6PILHQKJH6OHQ7VOHII2SWOJR","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":"bff13bb8c65e79e18de659745d4a9daa1462f462b36f39c9b7b7839aa02bedf1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-08-02T20:01:24Z","title_canon_sha256":"64f375fd521bedc58972df1f89ab9f6c931a8bebf6b32ba33902e9a98059afe9"},"schema_version":"1.0","source":{"id":"1708.00913","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.00913","created_at":"2026-05-18T00:38:41Z"},{"alias_kind":"arxiv_version","alias_value":"1708.00913v1","created_at":"2026-05-18T00:38:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.00913","created_at":"2026-05-18T00:38:41Z"},{"alias_kind":"pith_short_12","alias_value":"S6PILHQKJH6O","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"S6PILHQKJH6OHQ7V","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"S6PILHQK","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:f24136243139ef663a9b89140ca6598aabc37b28c068b95af4b3f4d56e1b9659","target":"graph","created_at":"2026-05-18T00:38:41Z","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":"Oshima's Lemma describes the orbits of parabolic subgroups of irreducible finite Weyl groups on crystallographic root systems. This note generalises that result to all root systems of finite Coxeter groups, and provides a self contained proof, independent of the representation theory of semisimple complex Lie algebras.","authors_text":"G. I. Lehrer, M. J. Dyer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-08-02T20:01:24Z","title":"Parabolic subgroup orbits on finite root systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.00913","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":"sha256:2de41d68bf7cf49917c7c2e7c13290d22b2f259ba2d344ba709d23e72e3f5787","target":"record","created_at":"2026-05-18T00:38:41Z","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":"bff13bb8c65e79e18de659745d4a9daa1462f462b36f39c9b7b7839aa02bedf1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-08-02T20:01:24Z","title_canon_sha256":"64f375fd521bedc58972df1f89ab9f6c931a8bebf6b32ba33902e9a98059afe9"},"schema_version":"1.0","source":{"id":"1708.00913","kind":"arxiv","version":1}},"canonical_sha256":"979e859e0a49fce3c3f571d08d4ace4c7e71d411ab56983a7c1f1d716b11151f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"979e859e0a49fce3c3f571d08d4ace4c7e71d411ab56983a7c1f1d716b11151f","first_computed_at":"2026-05-18T00:38:41.175856Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:41.175856Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lw0LwxFrcNynRhPdHgkd124b/3BgHmknQngHNPpatb/8sn3N7pH0bjcaiKOzDHF843OPd03lErGpLhLMm4RbDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:41.176306Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.00913","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2de41d68bf7cf49917c7c2e7c13290d22b2f259ba2d344ba709d23e72e3f5787","sha256:f24136243139ef663a9b89140ca6598aabc37b28c068b95af4b3f4d56e1b9659"],"state_sha256":"a36e079b44fa4ca4279013e2b3d4a11f3d8ab015a6d244913b35034e203c4ee1"}