{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:2GMPOAYV6GCU3MI4K2477PYT6A","short_pith_number":"pith:2GMPOAYV","schema_version":"1.0","canonical_sha256":"d198f70315f1854db11c56b9ffbf13f0229bbe25c672d0dac8e2ec6abb4756ca","source":{"kind":"arxiv","id":"0809.2374","version":1},"attestation_state":"computed","paper":{"title":"Permutations with Kazhdan-Lusztig polynomial P_{id,w}(q) = 1 + q^h","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Alexander Woo, Jonathan Weed, Sara Billey","submitted_at":"2008-09-13T23:15:35Z","abstract_excerpt":"Using resolutions of singularities introduced by Cortez and a method for calculating Kazhdan-Lusztig polynomials due to Polo, we prove the conjecture of Billey and Braden characterizing permutations w with Kazhdan-Lusztig polynomial P_{id,w}(q)=1+q^h for some h."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0809.2374","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-09-13T23:15:35Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"405ffbf41774a1ef86239546c75bb3a0a9a2a293d3bc609c22877115d3373b40","abstract_canon_sha256":"3ffeebb31115b0e7522b23812e1271a8971073d96b870a4888bd06a88a01edd6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:03:44.055513Z","signature_b64":"+mD5V8hfH66CTHMqvQKFWJxFTW2JEk/VYXq28VphtOhULrEFfT/LhA1Wt7ULLNxtug0lBIY3K2UNcsAIKqclBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d198f70315f1854db11c56b9ffbf13f0229bbe25c672d0dac8e2ec6abb4756ca","last_reissued_at":"2026-05-18T04:03:44.054940Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:03:44.054940Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Permutations with Kazhdan-Lusztig polynomial P_{id,w}(q) = 1 + q^h","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Alexander Woo, Jonathan Weed, Sara Billey","submitted_at":"2008-09-13T23:15:35Z","abstract_excerpt":"Using resolutions of singularities introduced by Cortez and a method for calculating Kazhdan-Lusztig polynomials due to Polo, we prove the conjecture of Billey and Braden characterizing permutations w with Kazhdan-Lusztig polynomial P_{id,w}(q)=1+q^h for some h."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.2374","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"0809.2374","created_at":"2026-05-18T04:03:44.055033+00:00"},{"alias_kind":"arxiv_version","alias_value":"0809.2374v1","created_at":"2026-05-18T04:03:44.055033+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0809.2374","created_at":"2026-05-18T04:03:44.055033+00:00"},{"alias_kind":"pith_short_12","alias_value":"2GMPOAYV6GCU","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_16","alias_value":"2GMPOAYV6GCU3MI4","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_8","alias_value":"2GMPOAYV","created_at":"2026-05-18T12:25:56.245647+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2GMPOAYV6GCU3MI4K2477PYT6A","json":"https://pith.science/pith/2GMPOAYV6GCU3MI4K2477PYT6A.json","graph_json":"https://pith.science/api/pith-number/2GMPOAYV6GCU3MI4K2477PYT6A/graph.json","events_json":"https://pith.science/api/pith-number/2GMPOAYV6GCU3MI4K2477PYT6A/events.json","paper":"https://pith.science/paper/2GMPOAYV"},"agent_actions":{"view_html":"https://pith.science/pith/2GMPOAYV6GCU3MI4K2477PYT6A","download_json":"https://pith.science/pith/2GMPOAYV6GCU3MI4K2477PYT6A.json","view_paper":"https://pith.science/paper/2GMPOAYV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0809.2374&json=true","fetch_graph":"https://pith.science/api/pith-number/2GMPOAYV6GCU3MI4K2477PYT6A/graph.json","fetch_events":"https://pith.science/api/pith-number/2GMPOAYV6GCU3MI4K2477PYT6A/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2GMPOAYV6GCU3MI4K2477PYT6A/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2GMPOAYV6GCU3MI4K2477PYT6A/action/storage_attestation","attest_author":"https://pith.science/pith/2GMPOAYV6GCU3MI4K2477PYT6A/action/author_attestation","sign_citation":"https://pith.science/pith/2GMPOAYV6GCU3MI4K2477PYT6A/action/citation_signature","submit_replication":"https://pith.science/pith/2GMPOAYV6GCU3MI4K2477PYT6A/action/replication_record"}},"created_at":"2026-05-18T04:03:44.055033+00:00","updated_at":"2026-05-18T04:03:44.055033+00:00"}