{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:G4UYA6FJKWRU4NOLH6MQYC4JZ5","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":"8b9833a346b72a5efe46da47e4d4222c327f938fbd1fc5b8030853210c5a7fb4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-02-13T18:40:30Z","title_canon_sha256":"3b5be5dfbd496b11e5d3145ba15cd160c52608f776c87639d90f93900ee0260e"},"schema_version":"1.0","source":{"id":"1202.2813","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.2813","created_at":"2026-05-17T23:42:14Z"},{"alias_kind":"arxiv_version","alias_value":"1202.2813v2","created_at":"2026-05-17T23:42:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.2813","created_at":"2026-05-17T23:42:14Z"},{"alias_kind":"pith_short_12","alias_value":"G4UYA6FJKWRU","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"G4UYA6FJKWRU4NOL","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"G4UYA6FJ","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:396bc685f1dbb4460f9c836fd5e2dc751ea0bc773bc9b5188261efc00ef402f5","target":"graph","created_at":"2026-05-17T23:42:14Z","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 study geometric properties of varieties associated with invariant subspaces of nilpotent operators. There are reductive algebraic groups acting on these varieties. We give dimensions of orbits of these actions. Moreover, a combinatorial characterization of the partial order given by degenerations is described.","authors_text":"Justyna Kosakowska, Markus Schmidmeier","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-02-13T18:40:30Z","title":"Operations on Arc Diagrams and Degenerations for Invariant Subspaces of Linear Operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2813","kind":"arxiv","version":2},"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":"sha256:8537bcbfc7e295a380a815972f8be0b3e9798c821ab0932436fce5eae6b8aa9b","target":"record","created_at":"2026-05-17T23:42:14Z","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":"8b9833a346b72a5efe46da47e4d4222c327f938fbd1fc5b8030853210c5a7fb4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-02-13T18:40:30Z","title_canon_sha256":"3b5be5dfbd496b11e5d3145ba15cd160c52608f776c87639d90f93900ee0260e"},"schema_version":"1.0","source":{"id":"1202.2813","kind":"arxiv","version":2}},"canonical_sha256":"37298078a955a34e35cb3f990c0b89cf5df516864bb68059672c6c0a73f49493","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"37298078a955a34e35cb3f990c0b89cf5df516864bb68059672c6c0a73f49493","first_computed_at":"2026-05-17T23:42:14.636889Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:14.636889Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LEhBT9bEu0cZA99bprK4nvMGoW81p4Jk9tw5xwsoXCMO63A4RzpDCZ4k7cNeAk7Fd6zugViijrKDVC9rvy3eAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:14.637615Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.2813","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8537bcbfc7e295a380a815972f8be0b3e9798c821ab0932436fce5eae6b8aa9b","sha256:396bc685f1dbb4460f9c836fd5e2dc751ea0bc773bc9b5188261efc00ef402f5"],"state_sha256":"77dffc6ec26306d23b40a9e05d95eb39a9aaf8818431c3f47d9a7657f53c3a58"}