{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:TPC6ZUKYSMMP37EKW6TM5LAOCR","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":"c86332e77528442c14745b3d10385eb318c6a27cf77ff329c07268bc7a5dc11f","cross_cats_sorted":["hep-th","math-ph","math.MP","nlin.SI"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.RT","submitted_at":"2018-10-23T01:19:36Z","title_canon_sha256":"69daff6035cae598101a9f62258029d843db61b9e9b14f6974f5ba1cde724adf"},"schema_version":"1.0","source":{"id":"1810.09622","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.09622","created_at":"2026-07-05T01:51:16Z"},{"alias_kind":"arxiv_version","alias_value":"1810.09622v3","created_at":"2026-07-05T01:51:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.09622","created_at":"2026-07-05T01:51:16Z"},{"alias_kind":"pith_short_12","alias_value":"TPC6ZUKYSMMP","created_at":"2026-07-05T01:51:16Z"},{"alias_kind":"pith_short_16","alias_value":"TPC6ZUKYSMMP37EK","created_at":"2026-07-05T01:51:16Z"},{"alias_kind":"pith_short_8","alias_value":"TPC6ZUKY","created_at":"2026-07-05T01:51:16Z"}],"graph_snapshots":[{"event_id":"sha256:317a409de0ac33529b839512f15f81635a71fb2fbea08323027c7cf77e96bafa","target":"graph","created_at":"2026-07-05T01:51:16Z","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/1810.09622/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this short note we show that the Bruhat cells in real normal forms of semisimple Lie algebras enjoy the same property as their complex analogs: for any two elements $w$, $w'$ in the Weyl group $W(\\mathfrak g)$, the corresponding real Bruhat cell $X_w$ intersects with the dual Bruhat cell $Y_{w'}$ iff $w\\prec w'$ in the Bruhat order on $W(\\mathfrak g)$. Here $\\mathfrak g$ is a normal real form of a semisimple complex Lie algebra $\\mathfrak g_\\mathbb C$. Our reasoning is based on the properties of the Toda flows rather than on the analysis of the Weyl group action and geometric considerations","authors_text":"Alexander S. Sorin, Dmitry V. Talalaev, Georgy I. Sharygin, Yuri B. Chernyakov","cross_cats":["hep-th","math-ph","math.MP","nlin.SI"],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.RT","submitted_at":"2018-10-23T01:19:36Z","title":"The Full Symmetric Toda Flow and Intersections of Bruhat Cells"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.09622","kind":"arxiv","version":3},"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:dff97e23266c8a0784337de3fcebcd4e77fdce632a5da146858f16dd3b0cc08e","target":"record","created_at":"2026-07-05T01:51:16Z","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":"c86332e77528442c14745b3d10385eb318c6a27cf77ff329c07268bc7a5dc11f","cross_cats_sorted":["hep-th","math-ph","math.MP","nlin.SI"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.RT","submitted_at":"2018-10-23T01:19:36Z","title_canon_sha256":"69daff6035cae598101a9f62258029d843db61b9e9b14f6974f5ba1cde724adf"},"schema_version":"1.0","source":{"id":"1810.09622","kind":"arxiv","version":3}},"canonical_sha256":"9bc5ecd1589318fdfc8ab7a6ceac0e145fb7c5e2aaee864b483572fdcd7316fd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9bc5ecd1589318fdfc8ab7a6ceac0e145fb7c5e2aaee864b483572fdcd7316fd","first_computed_at":"2026-07-05T01:51:16.991286Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:51:16.991286Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"86hSP+zDZWBd9ACV3LsEyu09dSidNPWtusxTKEQaViWKNfOxSVigLIIrkZ6T5PgIl4FfpOmnbaCYCtBC0RN3DA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:51:16.991719Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.09622","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dff97e23266c8a0784337de3fcebcd4e77fdce632a5da146858f16dd3b0cc08e","sha256:317a409de0ac33529b839512f15f81635a71fb2fbea08323027c7cf77e96bafa"],"state_sha256":"8e4d5e1ebe6fc4ee0c783523eee1dbb6710ac4217cf80f9700bd4d89621ebc5b"}