{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:CHSZESUGFBKJN42KHXJG5NOYJO","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":"e68c826468c07ef928acab67adbccdf3312c31c72745861cd145190ac3a9d53c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-01-03T15:41:16Z","title_canon_sha256":"d540c31940c9974807101f2c8bf540d993ccb77b4f18ec68372073e5eedd9183"},"schema_version":"1.0","source":{"id":"1601.00305","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.00305","created_at":"2026-05-18T00:50:01Z"},{"alias_kind":"arxiv_version","alias_value":"1601.00305v2","created_at":"2026-05-18T00:50:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.00305","created_at":"2026-05-18T00:50:01Z"},{"alias_kind":"pith_short_12","alias_value":"CHSZESUGFBKJ","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CHSZESUGFBKJN42K","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CHSZESUG","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:10af40cbc76b3ab214a7941adc1f2c5287311db63500a703f40fccdc458cff24","target":"graph","created_at":"2026-05-18T00:50:01Z","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":"In 2000, Dergachev and Kirillov introduced subalgebras of \"seaweed type\" in $\\mathfrak{gl}(n)$ and computed their index using certain graphs. In this article, those graphs are called type-A meander graphs. Then the subalgebras of seaweed type, or just \"seaweeds\", have been defined by Panyushev (2001) for arbitrary simple Lie algebras. Namely, if $\\mathfrak p_1,\\mathfrak p_2\\subset\\mathfrak g$ are parabolic subalgebras such that $\\mathfrak p_1+\\mathfrak p_2=\\mathfrak g$, then $\\mathfrak q=\\mathfrak p_1\\cap\\mathfrak p_2$ is a seaweed in $\\mathfrak g$. A general algebraic formula for the index of","authors_text":"Dmitri Panyushev, Oksana Yakimova","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-01-03T15:41:16Z","title":"On seaweed subalgebras and meander graphs in type C"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.00305","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:d03049bcd73f825cf7c489dbba8e513544c20d19658e2eba7275888133675abd","target":"record","created_at":"2026-05-18T00:50:01Z","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":"e68c826468c07ef928acab67adbccdf3312c31c72745861cd145190ac3a9d53c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-01-03T15:41:16Z","title_canon_sha256":"d540c31940c9974807101f2c8bf540d993ccb77b4f18ec68372073e5eedd9183"},"schema_version":"1.0","source":{"id":"1601.00305","kind":"arxiv","version":2}},"canonical_sha256":"11e5924a86285496f34a3dd26eb5d84bbd07ad35939887ceee252a72f5131356","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"11e5924a86285496f34a3dd26eb5d84bbd07ad35939887ceee252a72f5131356","first_computed_at":"2026-05-18T00:50:01.707825Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:01.707825Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yM9NJtsSGsxwCakK8vdfVGxwgBELp0pI3c4wE7CaZ3XsAFRyLoPW1kooyLhpXRSO+yYValsZ4k22ZXpxqDDsBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:01.708613Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.00305","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d03049bcd73f825cf7c489dbba8e513544c20d19658e2eba7275888133675abd","sha256:10af40cbc76b3ab214a7941adc1f2c5287311db63500a703f40fccdc458cff24"],"state_sha256":"41adbc70dbf13ef6eb8065136f32ed9703756927f41e52d6dce390a4b4c38745"}