{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:IZGXAMITEOC5CMU2T6Y6KCYTKK","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":"68a0517e27b8b259b29ba7b8e57659b1ea2e2bfeb490e4a3e1ea9cfecb6a3efb","cross_cats_sorted":[],"license":"","primary_cat":"math.RT","submitted_at":"2003-07-02T12:09:54Z","title_canon_sha256":"9f01f64c16a254a0f8216d8f65dae9884e55d32ec8c8e24a8b13089a6fbe14af"},"schema_version":"1.0","source":{"id":"math/0307017","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0307017","created_at":"2026-07-05T02:00:39Z"},{"alias_kind":"arxiv_version","alias_value":"math/0307017v2","created_at":"2026-07-05T02:00:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0307017","created_at":"2026-07-05T02:00:39Z"},{"alias_kind":"pith_short_12","alias_value":"IZGXAMITEOC5","created_at":"2026-07-05T02:00:39Z"},{"alias_kind":"pith_short_16","alias_value":"IZGXAMITEOC5CMU2","created_at":"2026-07-05T02:00:39Z"},{"alias_kind":"pith_short_8","alias_value":"IZGXAMIT","created_at":"2026-07-05T02:00:39Z"}],"graph_snapshots":[{"event_id":"sha256:584fce8a66b9fef7b6f93d485a0acb46ae39703db7616e790b070c9b791a275d","target":"graph","created_at":"2026-07-05T02:00:39Z","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/math/0307017/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For the flag variety G/B of a reductive algebraic group G we define a certain (set-theoretical) cross-section phi from G/B to G, which depends on a choice of reduced expression for the longest element in the Weyl group. This cross-section is continuous along the components of Deodhar's decomposition of G/B and assigns to any flag gB a representative phi(gB) in G which comes with a natural factorization into simple root subgroups and simple reflections. We introduce a generalization of the Chamber Ansatz of Berenstein, Fomin and Zelevinsky and use it to obtain formulas for the factors of phi(gB","authors_text":"Bethany Marsh, K. Rietsch","cross_cats":[],"headline":"","license":"","primary_cat":"math.RT","submitted_at":"2003-07-02T12:09:54Z","title":"Parametrizations of flag varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0307017","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":"sha256:2e3542f185dcf30cbe5778bb8d84c9a940d75d8886510fe2135e06428c735a5f","target":"record","created_at":"2026-07-05T02:00:39Z","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":"68a0517e27b8b259b29ba7b8e57659b1ea2e2bfeb490e4a3e1ea9cfecb6a3efb","cross_cats_sorted":[],"license":"","primary_cat":"math.RT","submitted_at":"2003-07-02T12:09:54Z","title_canon_sha256":"9f01f64c16a254a0f8216d8f65dae9884e55d32ec8c8e24a8b13089a6fbe14af"},"schema_version":"1.0","source":{"id":"math/0307017","kind":"arxiv","version":2}},"canonical_sha256":"464d7031132385d1329a9fb1e50b1352a27c31360811ab1714909a870e301040","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"464d7031132385d1329a9fb1e50b1352a27c31360811ab1714909a870e301040","first_computed_at":"2026-07-05T02:00:39.387433Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:00:39.387433Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qvnD+YuQ/PpjyVVWToIhc1gPtJFgbMNAM4I6N3rix2ON6FpspBhIUt3QcOdf6oBY37fHJju9LboYCyZjPppkDg==","signature_status":"signed_v1","signed_at":"2026-07-05T02:00:39.387898Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0307017","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2e3542f185dcf30cbe5778bb8d84c9a940d75d8886510fe2135e06428c735a5f","sha256:584fce8a66b9fef7b6f93d485a0acb46ae39703db7616e790b070c9b791a275d"],"state_sha256":"2d00b7b3752d48504d800b08c42cd62209f5801925d301e98d6aca2d38c701de"}