{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:KYTORS5TNPPF4B3FU242KP7FHB","short_pith_number":"pith:KYTORS5T","schema_version":"1.0","canonical_sha256":"5626e8cbb36bde5e0765a6b9a53fe5385596b64da4ed2c0782d62e22669d8dc2","source":{"kind":"arxiv","id":"1007.1207","version":2},"attestation_state":"computed","paper":{"title":"The sorting index","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"T. Kyle Petersen","submitted_at":"2010-07-07T17:57:55Z","abstract_excerpt":"We consider a bivariate polynomial that generalizes both the length and reflection length generating functions in a finite Coxeter group. In seeking a combinatorial description of the coefficients, we are led to the study of a new Mahonian statistic, which we call the sorting index. The sorting index of a permutation and its type B and type D analogues have natural combinatorial descriptions which we describe in detail."},"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":"1007.1207","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-07-07T17:57:55Z","cross_cats_sorted":[],"title_canon_sha256":"9239ad4fd576a626dc521120a4a33825afeccfd6c4cb125792538e39963d2605","abstract_canon_sha256":"a3ec21c46eabfa34e2804e987f5eebea89f8e7c38d6c45e5f8f6c19557a4757c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:38:58.072068Z","signature_b64":"4B0wmbiuQhytK1bxWC9f//QlCWdQ8QTwxUughFagY609/Y6Tp23uaDg4H4BUf2PPdCkVuO3N03k7Q/rdIG9PDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5626e8cbb36bde5e0765a6b9a53fe5385596b64da4ed2c0782d62e22669d8dc2","last_reissued_at":"2026-05-18T04:38:58.071427Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:38:58.071427Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The sorting index","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"T. Kyle Petersen","submitted_at":"2010-07-07T17:57:55Z","abstract_excerpt":"We consider a bivariate polynomial that generalizes both the length and reflection length generating functions in a finite Coxeter group. In seeking a combinatorial description of the coefficients, we are led to the study of a new Mahonian statistic, which we call the sorting index. The sorting index of a permutation and its type B and type D analogues have natural combinatorial descriptions which we describe in detail."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.1207","kind":"arxiv","version":2},"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":"1007.1207","created_at":"2026-05-18T04:38:58.071525+00:00"},{"alias_kind":"arxiv_version","alias_value":"1007.1207v2","created_at":"2026-05-18T04:38:58.071525+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.1207","created_at":"2026-05-18T04:38:58.071525+00:00"},{"alias_kind":"pith_short_12","alias_value":"KYTORS5TNPPF","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_16","alias_value":"KYTORS5TNPPF4B3F","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_8","alias_value":"KYTORS5T","created_at":"2026-05-18T12:26:09.077623+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/KYTORS5TNPPF4B3FU242KP7FHB","json":"https://pith.science/pith/KYTORS5TNPPF4B3FU242KP7FHB.json","graph_json":"https://pith.science/api/pith-number/KYTORS5TNPPF4B3FU242KP7FHB/graph.json","events_json":"https://pith.science/api/pith-number/KYTORS5TNPPF4B3FU242KP7FHB/events.json","paper":"https://pith.science/paper/KYTORS5T"},"agent_actions":{"view_html":"https://pith.science/pith/KYTORS5TNPPF4B3FU242KP7FHB","download_json":"https://pith.science/pith/KYTORS5TNPPF4B3FU242KP7FHB.json","view_paper":"https://pith.science/paper/KYTORS5T","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1007.1207&json=true","fetch_graph":"https://pith.science/api/pith-number/KYTORS5TNPPF4B3FU242KP7FHB/graph.json","fetch_events":"https://pith.science/api/pith-number/KYTORS5TNPPF4B3FU242KP7FHB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KYTORS5TNPPF4B3FU242KP7FHB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KYTORS5TNPPF4B3FU242KP7FHB/action/storage_attestation","attest_author":"https://pith.science/pith/KYTORS5TNPPF4B3FU242KP7FHB/action/author_attestation","sign_citation":"https://pith.science/pith/KYTORS5TNPPF4B3FU242KP7FHB/action/citation_signature","submit_replication":"https://pith.science/pith/KYTORS5TNPPF4B3FU242KP7FHB/action/replication_record"}},"created_at":"2026-05-18T04:38:58.071525+00:00","updated_at":"2026-05-18T04:38:58.071525+00:00"}