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We utilize the Thom-Pontryagin construction to show that the Sato-Levine invariants $\\bar{\\mu}_{(iijj)}$ must vanish for 0.5-solvable links. Using this result, we show that the short exact sequence $0\\rightarrow \\mathcal{F}^m_0/\\mathcal{F}^m_{0.5} \\rightarrow \\mathcal{F}^m_{-0.5}/\\mathcal{F}^m_{0.5} \\rightarrow \\mathcal{F}^m_{-0.5}/\\mathcal{F}^m_0 \\rightarrow 0$ does not split for links of two or more comp"},"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":"1606.00481","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-06-01T22:03:44Z","cross_cats_sorted":[],"title_canon_sha256":"5b09402e43fb932b80d9e4a4faf917b9bda154fe45811eeeecb62f6096b2f411","abstract_canon_sha256":"6ecb4f5fccca223abd8cf27c104febb179559ce1aca5d9a3cf8e977408883a1c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:13:04.306849Z","signature_b64":"0ixO9+SJGY6aHUP73WEtUZTadE8t7kGKOswCEWSiVUyHSoPwdMaIekHgJKO6YUla3P1fiABEGWDB7hNci/03Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e978a225d8485018e5ae31c8c6f7c1b87219942838f44a519896340add3386a6","last_reissued_at":"2026-05-18T01:13:04.306474Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:13:04.306474Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Splittings of link concordance groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Carolyn Otto, Taylor E. Martin","submitted_at":"2016-06-01T22:03:44Z","abstract_excerpt":"We establish several results about two short exact sequences involving lower terms of the $n$-solvable filtration, $\\{\\mathcal{F}^m_n\\}$ of the string link concordance group $\\mathcal{C}^m$. We utilize the Thom-Pontryagin construction to show that the Sato-Levine invariants $\\bar{\\mu}_{(iijj)}$ must vanish for 0.5-solvable links. Using this result, we show that the short exact sequence $0\\rightarrow \\mathcal{F}^m_0/\\mathcal{F}^m_{0.5} \\rightarrow \\mathcal{F}^m_{-0.5}/\\mathcal{F}^m_{0.5} \\rightarrow \\mathcal{F}^m_{-0.5}/\\mathcal{F}^m_0 \\rightarrow 0$ does not split for links of two or more comp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.00481","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":"1606.00481","created_at":"2026-05-18T01:13:04.306527+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.00481v1","created_at":"2026-05-18T01:13:04.306527+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.00481","created_at":"2026-05-18T01:13:04.306527+00:00"},{"alias_kind":"pith_short_12","alias_value":"5F4KEJOYJBIB","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_16","alias_value":"5F4KEJOYJBIBRZNO","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_8","alias_value":"5F4KEJOY","created_at":"2026-05-18T12:30:01.593930+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/5F4KEJOYJBIBRZNOGHEMN56BXB","json":"https://pith.science/pith/5F4KEJOYJBIBRZNOGHEMN56BXB.json","graph_json":"https://pith.science/api/pith-number/5F4KEJOYJBIBRZNOGHEMN56BXB/graph.json","events_json":"https://pith.science/api/pith-number/5F4KEJOYJBIBRZNOGHEMN56BXB/events.json","paper":"https://pith.science/paper/5F4KEJOY"},"agent_actions":{"view_html":"https://pith.science/pith/5F4KEJOYJBIBRZNOGHEMN56BXB","download_json":"https://pith.science/pith/5F4KEJOYJBIBRZNOGHEMN56BXB.json","view_paper":"https://pith.science/paper/5F4KEJOY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.00481&json=true","fetch_graph":"https://pith.science/api/pith-number/5F4KEJOYJBIBRZNOGHEMN56BXB/graph.json","fetch_events":"https://pith.science/api/pith-number/5F4KEJOYJBIBRZNOGHEMN56BXB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5F4KEJOYJBIBRZNOGHEMN56BXB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5F4KEJOYJBIBRZNOGHEMN56BXB/action/storage_attestation","attest_author":"https://pith.science/pith/5F4KEJOYJBIBRZNOGHEMN56BXB/action/author_attestation","sign_citation":"https://pith.science/pith/5F4KEJOYJBIBRZNOGHEMN56BXB/action/citation_signature","submit_replication":"https://pith.science/pith/5F4KEJOYJBIBRZNOGHEMN56BXB/action/replication_record"}},"created_at":"2026-05-18T01:13:04.306527+00:00","updated_at":"2026-05-18T01:13:04.306527+00:00"}