{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:Z5S43ROZYXZANBOO42Q7HWWCJO","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":"53c0f6944d37ea63366618825e435a6378b0450c1a926b31bd7d18ffb385b32a","cross_cats_sorted":["math.AG","math.CO"],"license":"","primary_cat":"math.RT","submitted_at":"2002-02-24T18:49:56Z","title_canon_sha256":"05dfcae2ccc270a6c6a451cd502ca176165fcacf9d32f48ca3090181317b5734"},"schema_version":"1.0","source":{"id":"math/0202252","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0202252","created_at":"2026-07-04T14:35:56Z"},{"alias_kind":"arxiv_version","alias_value":"math/0202252v5","created_at":"2026-07-04T14:35:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0202252","created_at":"2026-07-04T14:35:56Z"},{"alias_kind":"pith_short_12","alias_value":"Z5S43ROZYXZA","created_at":"2026-07-04T14:35:56Z"},{"alias_kind":"pith_short_16","alias_value":"Z5S43ROZYXZANBOO","created_at":"2026-07-04T14:35:56Z"},{"alias_kind":"pith_short_8","alias_value":"Z5S43ROZ","created_at":"2026-07-04T14:35:56Z"}],"graph_snapshots":[{"event_id":"sha256:0c4a54eeedfefdfc24df8c866ae6c783d6b66ea0b1b5b02710a5868f776430d8","target":"graph","created_at":"2026-07-04T14:35:56Z","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/0202252/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give a lower bound for the value at q=1 of a Kazhdan-Lustig polynomial in a Weyl group W in terms of \"patterns''. This is expressed by a \"pattern map\" from W to W' for any parabloic subgroup W'. This notion generalizes the concept of patterns and pattern avoidance for permutations to all Weyl groups. The main tool of the proof is a \"hyperbolic localization\" on intersection cohomology; see the related paper http://front.math.ucdavis.edu/math.AG/0202251","authors_text":"Sara Billey, Tom Braden","cross_cats":["math.AG","math.CO"],"headline":"","license":"","primary_cat":"math.RT","submitted_at":"2002-02-24T18:49:56Z","title":"Lower bounds for Kazhdan-Lusztig polynomials from patterns"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0202252","kind":"arxiv","version":5},"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":"sha256:0512066ed98ecb3115c8cc466cedc6734a92b78f08b49313b774395714314495","target":"record","created_at":"2026-07-04T14:35:56Z","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":"53c0f6944d37ea63366618825e435a6378b0450c1a926b31bd7d18ffb385b32a","cross_cats_sorted":["math.AG","math.CO"],"license":"","primary_cat":"math.RT","submitted_at":"2002-02-24T18:49:56Z","title_canon_sha256":"05dfcae2ccc270a6c6a451cd502ca176165fcacf9d32f48ca3090181317b5734"},"schema_version":"1.0","source":{"id":"math/0202252","kind":"arxiv","version":5}},"canonical_sha256":"cf65cdc5d9c5f20685cee6a1f3dac24bb931d5e190ee2d048036ff1ac6f495bf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf65cdc5d9c5f20685cee6a1f3dac24bb931d5e190ee2d048036ff1ac6f495bf","first_computed_at":"2026-07-04T14:35:56.406569Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:35:56.406569Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+qiuySoeIKHjx0OvXqyO9NLyjcMn6EYmyCuxU+aWZ3jf9jJ8mJAA0nbUJoGH5uWi5AQAwVPqFNUfJuulbigOCg==","signature_status":"signed_v1","signed_at":"2026-07-04T14:35:56.406907Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0202252","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0512066ed98ecb3115c8cc466cedc6734a92b78f08b49313b774395714314495","sha256:0c4a54eeedfefdfc24df8c866ae6c783d6b66ea0b1b5b02710a5868f776430d8"],"state_sha256":"2d921ef854f35068fed9db80124891fe08dfe673556222ed5615829d55d49109"}