{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:S6PK4QCP3AO5RHVB3MNT75Y5QT","short_pith_number":"pith:S6PK4QCP","schema_version":"1.0","canonical_sha256":"979eae404fd81dd89ea1db1b3ff71d84e4f84767b0f41242c37bd47ce1f494a0","source":{"kind":"arxiv","id":"2506.17706","version":1},"attestation_state":"computed","paper":{"title":"Quantum $\\mathfrak{gl}$-weight system and its average values","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.CO","authors_text":"Mikhail Zaitsev","submitted_at":"2025-06-21T12:54:09Z","abstract_excerpt":"We present a proof of a recent conjecture due to M. Kazarian, E. Krasilnikov, S. Lando, and M. Shapiro, which describes the average value of the universal $\\mathfrak{gl}$-weight system on permutations. The proof uses a quantum analogue of the $\\mathfrak{gl}$-weight system on Hecke algebras of type $A$, which leads to a one-parameter deformation of the average value of the universal ${\\mathfrak{gl}}$-weight system. We show that the average value of the quantum weight system is a linear combination of one-part Schur functions, with coefficients being $q$-analogues of Bernoulli polynomials."},"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":"2506.17706","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-06-21T12:54:09Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"124bb8462c9d32b33ae3caa55caabdc8fde10565226e1b5170a058f1d470816c","abstract_canon_sha256":"be37f2811b71b97b71300ac59b58236f2dee440ced10f84c4dabcff1617678ad"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:25:22.197901Z","signature_b64":"QL1OHouoIv3jkzBa7wo9YjDD8oa+Y2IGGDG+mQMnvKwJizKd/b8/JYTud2Gisoo1l17NEu55ot4gOyi077fUBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"979eae404fd81dd89ea1db1b3ff71d84e4f84767b0f41242c37bd47ce1f494a0","last_reissued_at":"2026-07-05T11:25:22.197375Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:25:22.197375Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quantum $\\mathfrak{gl}$-weight system and its average values","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.CO","authors_text":"Mikhail Zaitsev","submitted_at":"2025-06-21T12:54:09Z","abstract_excerpt":"We present a proof of a recent conjecture due to M. Kazarian, E. Krasilnikov, S. Lando, and M. Shapiro, which describes the average value of the universal $\\mathfrak{gl}$-weight system on permutations. The proof uses a quantum analogue of the $\\mathfrak{gl}$-weight system on Hecke algebras of type $A$, which leads to a one-parameter deformation of the average value of the universal ${\\mathfrak{gl}}$-weight system. We show that the average value of the quantum weight system is a linear combination of one-part Schur functions, with coefficients being $q$-analogues of Bernoulli polynomials."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.17706","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.17706/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2506.17706","created_at":"2026-07-05T11:25:22.197434+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.17706v1","created_at":"2026-07-05T11:25:22.197434+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.17706","created_at":"2026-07-05T11:25:22.197434+00:00"},{"alias_kind":"pith_short_12","alias_value":"S6PK4QCP3AO5","created_at":"2026-07-05T11:25:22.197434+00:00"},{"alias_kind":"pith_short_16","alias_value":"S6PK4QCP3AO5RHVB","created_at":"2026-07-05T11:25:22.197434+00:00"},{"alias_kind":"pith_short_8","alias_value":"S6PK4QCP","created_at":"2026-07-05T11:25:22.197434+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/S6PK4QCP3AO5RHVB3MNT75Y5QT","json":"https://pith.science/pith/S6PK4QCP3AO5RHVB3MNT75Y5QT.json","graph_json":"https://pith.science/api/pith-number/S6PK4QCP3AO5RHVB3MNT75Y5QT/graph.json","events_json":"https://pith.science/api/pith-number/S6PK4QCP3AO5RHVB3MNT75Y5QT/events.json","paper":"https://pith.science/paper/S6PK4QCP"},"agent_actions":{"view_html":"https://pith.science/pith/S6PK4QCP3AO5RHVB3MNT75Y5QT","download_json":"https://pith.science/pith/S6PK4QCP3AO5RHVB3MNT75Y5QT.json","view_paper":"https://pith.science/paper/S6PK4QCP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.17706&json=true","fetch_graph":"https://pith.science/api/pith-number/S6PK4QCP3AO5RHVB3MNT75Y5QT/graph.json","fetch_events":"https://pith.science/api/pith-number/S6PK4QCP3AO5RHVB3MNT75Y5QT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S6PK4QCP3AO5RHVB3MNT75Y5QT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S6PK4QCP3AO5RHVB3MNT75Y5QT/action/storage_attestation","attest_author":"https://pith.science/pith/S6PK4QCP3AO5RHVB3MNT75Y5QT/action/author_attestation","sign_citation":"https://pith.science/pith/S6PK4QCP3AO5RHVB3MNT75Y5QT/action/citation_signature","submit_replication":"https://pith.science/pith/S6PK4QCP3AO5RHVB3MNT75Y5QT/action/replication_record"}},"created_at":"2026-07-05T11:25:22.197434+00:00","updated_at":"2026-07-05T11:25:22.197434+00:00"}