{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:QNEWHDWAGKGAQ7WXR7T4CXIJBG","short_pith_number":"pith:QNEWHDWA","schema_version":"1.0","canonical_sha256":"8349638ec0328c087ed78fe7c15d0909ab7e09a7d268cb401a5bf09974b3c8e5","source":{"kind":"arxiv","id":"1304.1870","version":1},"attestation_state":"computed","paper":{"title":"Milnor invariants of length $2k+2$ for links with vanishing Milnor invariants of length $\\leq k$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Akira Yasuhara, Yuka Kotorii","submitted_at":"2013-04-06T09:57:41Z","abstract_excerpt":"J.-B. Meilhan and the second author showed that any Milnor $\\bar{\\mu}$-invariant of length between 3 and $2k+1$ can be represented as a combination of HOMFLYPT polynomial of knots obtained by certain band sum of the link components, if all $\\bar{\\mu}$-invariants of length $\\leq k$ vanish. They also showed that their formula does not hold for length $2k+2$. In this paper, we improve their formula to give the $\\bar{\\mu}$-invariants of length $2k+2$ by adding correction terms. The correction terms can be given by a combination of HOMFLYPT polynomial of knots determined by $\\bar{\\mu}$-invariants o"},"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":"1304.1870","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-04-06T09:57:41Z","cross_cats_sorted":[],"title_canon_sha256":"2df921a95e01b08bb98ce37d3e0350f2cddb7fcd0a461eaa449e73e98368182a","abstract_canon_sha256":"07f9d7f15b154a1757c02397cc2d70d5aa5ec3853267e063cfbf280feee34820"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:28:44.905006Z","signature_b64":"zpNtl8YgvDbIi6giLDx+LF2xue86/q/q+ZpJwJpyOmQp4BYFKEc7IyGhybWOzyEdI36dvwthYcpK5wTrp4gnDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8349638ec0328c087ed78fe7c15d0909ab7e09a7d268cb401a5bf09974b3c8e5","last_reissued_at":"2026-05-18T03:28:44.904443Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:28:44.904443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Milnor invariants of length $2k+2$ for links with vanishing Milnor invariants of length $\\leq k$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Akira Yasuhara, Yuka Kotorii","submitted_at":"2013-04-06T09:57:41Z","abstract_excerpt":"J.-B. Meilhan and the second author showed that any Milnor $\\bar{\\mu}$-invariant of length between 3 and $2k+1$ can be represented as a combination of HOMFLYPT polynomial of knots obtained by certain band sum of the link components, if all $\\bar{\\mu}$-invariants of length $\\leq k$ vanish. They also showed that their formula does not hold for length $2k+2$. In this paper, we improve their formula to give the $\\bar{\\mu}$-invariants of length $2k+2$ by adding correction terms. The correction terms can be given by a combination of HOMFLYPT polynomial of knots determined by $\\bar{\\mu}$-invariants o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.1870","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":"1304.1870","created_at":"2026-05-18T03:28:44.904526+00:00"},{"alias_kind":"arxiv_version","alias_value":"1304.1870v1","created_at":"2026-05-18T03:28:44.904526+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.1870","created_at":"2026-05-18T03:28:44.904526+00:00"},{"alias_kind":"pith_short_12","alias_value":"QNEWHDWAGKGA","created_at":"2026-05-18T12:27:57.521954+00:00"},{"alias_kind":"pith_short_16","alias_value":"QNEWHDWAGKGAQ7WX","created_at":"2026-05-18T12:27:57.521954+00:00"},{"alias_kind":"pith_short_8","alias_value":"QNEWHDWA","created_at":"2026-05-18T12:27:57.521954+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/QNEWHDWAGKGAQ7WXR7T4CXIJBG","json":"https://pith.science/pith/QNEWHDWAGKGAQ7WXR7T4CXIJBG.json","graph_json":"https://pith.science/api/pith-number/QNEWHDWAGKGAQ7WXR7T4CXIJBG/graph.json","events_json":"https://pith.science/api/pith-number/QNEWHDWAGKGAQ7WXR7T4CXIJBG/events.json","paper":"https://pith.science/paper/QNEWHDWA"},"agent_actions":{"view_html":"https://pith.science/pith/QNEWHDWAGKGAQ7WXR7T4CXIJBG","download_json":"https://pith.science/pith/QNEWHDWAGKGAQ7WXR7T4CXIJBG.json","view_paper":"https://pith.science/paper/QNEWHDWA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1304.1870&json=true","fetch_graph":"https://pith.science/api/pith-number/QNEWHDWAGKGAQ7WXR7T4CXIJBG/graph.json","fetch_events":"https://pith.science/api/pith-number/QNEWHDWAGKGAQ7WXR7T4CXIJBG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QNEWHDWAGKGAQ7WXR7T4CXIJBG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QNEWHDWAGKGAQ7WXR7T4CXIJBG/action/storage_attestation","attest_author":"https://pith.science/pith/QNEWHDWAGKGAQ7WXR7T4CXIJBG/action/author_attestation","sign_citation":"https://pith.science/pith/QNEWHDWAGKGAQ7WXR7T4CXIJBG/action/citation_signature","submit_replication":"https://pith.science/pith/QNEWHDWAGKGAQ7WXR7T4CXIJBG/action/replication_record"}},"created_at":"2026-05-18T03:28:44.904526+00:00","updated_at":"2026-05-18T03:28:44.904526+00:00"}