{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:FKWL42LIGFD2FW5KOOG5EISUDH","short_pith_number":"pith:FKWL42LI","schema_version":"1.0","canonical_sha256":"2aacbe69683147a2dbaa738dd2225419c3fdf09088a42dc07eebedc8b05a138d","source":{"kind":"arxiv","id":"2407.01144","version":1},"attestation_state":"computed","paper":{"title":"Duality for the $\\mathfrak{sl}_2$ weight system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Polina Zakorko, Polina Zinova","submitted_at":"2024-07-01T10:12:25Z","abstract_excerpt":"The $\\mathfrak{sl}_2$ weight system, corresponding to the colored Jones polynomial of knots, is one of the the simplest weight system for chord diagrams. Recent works have led to explicit computations of this weight system on chord diagrams with complete and complete bipartite intersection graphs using $\\mathfrak{sl}_2$ weight systems on shares, i.e., on chord diagrams on two strands.\n  In this paper, we continue our study of shares. We prove a conjecture by Lando about a duality of values of the $\\mathfrak{sl}_2$ weight system on chord diagrams whose intersection graphs are joins of complemen"},"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":"2407.01144","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-07-01T10:12:25Z","cross_cats_sorted":[],"title_canon_sha256":"b3ca69f11cc95012f663c0f5e0696a377db80de631457facca9588468f07de22","abstract_canon_sha256":"eb8cee0a88cb498474d7d4ec2c07d94954056dfd9e3356a8bdf5afcc6f955d5e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:38:43.715557Z","signature_b64":"8kAXFjj3y+hi5Yev8zEK6ayQ5erhBosCMLNQlKNJq4DIBSz7l0Ek0Q57OxVQix5Ft88msUrCQyRSCc/SWCQ0AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2aacbe69683147a2dbaa738dd2225419c3fdf09088a42dc07eebedc8b05a138d","last_reissued_at":"2026-07-05T08:38:43.715060Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:38:43.715060Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Duality for the $\\mathfrak{sl}_2$ weight system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Polina Zakorko, Polina Zinova","submitted_at":"2024-07-01T10:12:25Z","abstract_excerpt":"The $\\mathfrak{sl}_2$ weight system, corresponding to the colored Jones polynomial of knots, is one of the the simplest weight system for chord diagrams. Recent works have led to explicit computations of this weight system on chord diagrams with complete and complete bipartite intersection graphs using $\\mathfrak{sl}_2$ weight systems on shares, i.e., on chord diagrams on two strands.\n  In this paper, we continue our study of shares. We prove a conjecture by Lando about a duality of values of the $\\mathfrak{sl}_2$ weight system on chord diagrams whose intersection graphs are joins of complemen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.01144","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/2407.01144/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":"2407.01144","created_at":"2026-07-05T08:38:43.715118+00:00"},{"alias_kind":"arxiv_version","alias_value":"2407.01144v1","created_at":"2026-07-05T08:38:43.715118+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.01144","created_at":"2026-07-05T08:38:43.715118+00:00"},{"alias_kind":"pith_short_12","alias_value":"FKWL42LIGFD2","created_at":"2026-07-05T08:38:43.715118+00:00"},{"alias_kind":"pith_short_16","alias_value":"FKWL42LIGFD2FW5K","created_at":"2026-07-05T08:38:43.715118+00:00"},{"alias_kind":"pith_short_8","alias_value":"FKWL42LI","created_at":"2026-07-05T08:38:43.715118+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/FKWL42LIGFD2FW5KOOG5EISUDH","json":"https://pith.science/pith/FKWL42LIGFD2FW5KOOG5EISUDH.json","graph_json":"https://pith.science/api/pith-number/FKWL42LIGFD2FW5KOOG5EISUDH/graph.json","events_json":"https://pith.science/api/pith-number/FKWL42LIGFD2FW5KOOG5EISUDH/events.json","paper":"https://pith.science/paper/FKWL42LI"},"agent_actions":{"view_html":"https://pith.science/pith/FKWL42LIGFD2FW5KOOG5EISUDH","download_json":"https://pith.science/pith/FKWL42LIGFD2FW5KOOG5EISUDH.json","view_paper":"https://pith.science/paper/FKWL42LI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2407.01144&json=true","fetch_graph":"https://pith.science/api/pith-number/FKWL42LIGFD2FW5KOOG5EISUDH/graph.json","fetch_events":"https://pith.science/api/pith-number/FKWL42LIGFD2FW5KOOG5EISUDH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FKWL42LIGFD2FW5KOOG5EISUDH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FKWL42LIGFD2FW5KOOG5EISUDH/action/storage_attestation","attest_author":"https://pith.science/pith/FKWL42LIGFD2FW5KOOG5EISUDH/action/author_attestation","sign_citation":"https://pith.science/pith/FKWL42LIGFD2FW5KOOG5EISUDH/action/citation_signature","submit_replication":"https://pith.science/pith/FKWL42LIGFD2FW5KOOG5EISUDH/action/replication_record"}},"created_at":"2026-07-05T08:38:43.715118+00:00","updated_at":"2026-07-05T08:38:43.715118+00:00"}