{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:ILXGWQZ45U7IZ4UG6MDNZDHMK4","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":"f55da95691d65caa8988627a7c5320e288c6ced0640fd858f0447a4c6c614cc3","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-01-07T15:05:30Z","title_canon_sha256":"74ccd256131fe66916e55d04fdf9959fc7ffe6ea2555c2331c8a856d7a28cbbe"},"schema_version":"1.0","source":{"id":"1001.1080","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.1080","created_at":"2026-05-18T03:35:26Z"},{"alias_kind":"arxiv_version","alias_value":"1001.1080v3","created_at":"2026-05-18T03:35:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.1080","created_at":"2026-05-18T03:35:26Z"},{"alias_kind":"pith_short_12","alias_value":"ILXGWQZ45U7I","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"ILXGWQZ45U7IZ4UG","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"ILXGWQZ4","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:d9fbbf6f6859e114054535eb1deb14437600cd6bc09ad1aa88cebee03d780712","target":"graph","created_at":"2026-05-18T03:35:26Z","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 provide simple rules for the computation of Kazhdan--Lusztig polynomials in the maximal parabolic case. They are obtained by filling regions delimited by paths with \"Dyck strips\" obeying certain rules. We compare our results with those of Lascoux and Sch\\\"utzenberger.","authors_text":"K. Shigechi, P. Zinn-Justin","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-01-07T15:05:30Z","title":"Path representation of maximal parabolic Kazhdan-Lusztig polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.1080","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":"sha256:42b58d83dd57670204658a54b834e989fb76f018e1d028021e182f77fe9aed59","target":"record","created_at":"2026-05-18T03:35:26Z","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":"f55da95691d65caa8988627a7c5320e288c6ced0640fd858f0447a4c6c614cc3","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-01-07T15:05:30Z","title_canon_sha256":"74ccd256131fe66916e55d04fdf9959fc7ffe6ea2555c2331c8a856d7a28cbbe"},"schema_version":"1.0","source":{"id":"1001.1080","kind":"arxiv","version":3}},"canonical_sha256":"42ee6b433ced3e8cf286f306dc8cec570d8026882d42cb28d8287a37d9aa0057","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"42ee6b433ced3e8cf286f306dc8cec570d8026882d42cb28d8287a37d9aa0057","first_computed_at":"2026-05-18T03:35:26.663885Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:35:26.663885Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"w2kG84sDsL/3KmtMJ/V07l1uXfpZzV+ay90IKxuewoGd4u9KfNQBtiL7HRUloq1owLAEV7ghZPs5wCgC9VUsCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:35:26.665472Z","signed_message":"canonical_sha256_bytes"},"source_id":"1001.1080","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:42b58d83dd57670204658a54b834e989fb76f018e1d028021e182f77fe9aed59","sha256:d9fbbf6f6859e114054535eb1deb14437600cd6bc09ad1aa88cebee03d780712"],"state_sha256":"f11b41b836ef7b50dce54edc052a7625d3af5d453681b2142781676cb09fe4f8"}