{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ZS5VQKEIP7E23C7TCJSGBLGSQU","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":"64914ad845c5506b5bed0ec2faafc53264d1b43d69d9e9eaed894254faa3c581","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-08-21T17:57:39Z","title_canon_sha256":"6af9fe574193b7afabc8470033605f0621ed0a1d218a940e8a3a9ec1b00ae464"},"schema_version":"1.0","source":{"id":"1708.06341","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.06341","created_at":"2026-05-18T00:37:42Z"},{"alias_kind":"arxiv_version","alias_value":"1708.06341v1","created_at":"2026-05-18T00:37:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.06341","created_at":"2026-05-18T00:37:42Z"},{"alias_kind":"pith_short_12","alias_value":"ZS5VQKEIP7E2","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZS5VQKEIP7E23C7T","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZS5VQKEI","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:0328fa08aa327946856626f7e8cf67532b199bcd7d8f9ba0951c4837a6364b9a","target":"graph","created_at":"2026-05-18T00:37:42Z","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":"Consider a simple complex Lie group $G$ acting diagonally on a triple flag variety $G/P_1\\times G/P_2\\times G/P_3$, where $P_i$ is parabolic subgroup of $G$. We provide an algorithm for systematically checking when this action has finitely many orbits. We then use this method to give a complete classification for when $G$ is of type $F_4$. The $E_6, E_7,$ and $E_8$ cases will be treated in a subsequent paper.","authors_text":"Bal\\'azs Elek, Dan Barbasch, Gautam Gopal Krishnan, Sergio Da Silva","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-08-21T17:57:39Z","title":"Finite type multiple flag varieties of exceptional groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.06341","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":"sha256:55fcfa0863f823707ebe33ce3640771f20ea3b9f73e1bc92c131320b60de3c64","target":"record","created_at":"2026-05-18T00:37:42Z","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":"64914ad845c5506b5bed0ec2faafc53264d1b43d69d9e9eaed894254faa3c581","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-08-21T17:57:39Z","title_canon_sha256":"6af9fe574193b7afabc8470033605f0621ed0a1d218a940e8a3a9ec1b00ae464"},"schema_version":"1.0","source":{"id":"1708.06341","kind":"arxiv","version":1}},"canonical_sha256":"ccbb5828887fc9ad8bf3126460acd28528eef9019b895c5ac06616a230952fb1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ccbb5828887fc9ad8bf3126460acd28528eef9019b895c5ac06616a230952fb1","first_computed_at":"2026-05-18T00:37:42.540532Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:37:42.540532Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XmgpVIoi0YHpMgZux5Gew2PhDRg9ggRatPje9X7Cw0OO0xXNBURH5NhMn299ZgLAUYQfaiTdof41T/0OFvJXBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:37:42.541157Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.06341","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:55fcfa0863f823707ebe33ce3640771f20ea3b9f73e1bc92c131320b60de3c64","sha256:0328fa08aa327946856626f7e8cf67532b199bcd7d8f9ba0951c4837a6364b9a"],"state_sha256":"7a819b2800a8581f92f3c47ef9e95dc75295dc1d710eee9e4538cb0afeb02d89"}