{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:FO32WKG62E5DLQEI2QWTQ7SIYZ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"230c3b91cc5bfc9541920ff25e62519d70f6cc93fdd4eae10a5e16c97f0ba0f7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2026-05-06T02:53:44Z","title_canon_sha256":"13bc2b904219cadab444bd5a0920392d9086d3c76e683d2495f66a54206ff79c"},"schema_version":"1.0","source":{"id":"2605.04433","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.04433","created_at":"2026-05-20T00:03:13Z"},{"alias_kind":"arxiv_version","alias_value":"2605.04433v2","created_at":"2026-05-20T00:03:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.04433","created_at":"2026-05-20T00:03:13Z"},{"alias_kind":"pith_short_12","alias_value":"FO32WKG62E5D","created_at":"2026-05-20T00:03:13Z"},{"alias_kind":"pith_short_16","alias_value":"FO32WKG62E5DLQEI","created_at":"2026-05-20T00:03:13Z"},{"alias_kind":"pith_short_8","alias_value":"FO32WKG6","created_at":"2026-05-20T00:03:13Z"}],"graph_snapshots":[{"event_id":"sha256:b9034259df1189095e7fb4ac6a3a97aee140b24d798dd1ed9ba23fe7bde864d5","target":"graph","created_at":"2026-05-20T00:03:13Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"we present an implementation of this algorithm, which is available at [KMcode], and exhibit new pairs of links that are not link-homotopic yet cannot be distinguished by Milnor's link-homotopy invariants, called μ-bar-invariants."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The explicit computations of the group actions on string links for the 4- and 5-component cases, reported in the authors' prior paper [KM4], are correct and complete."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Implementation of the Habegger-Lin decision algorithm for link-homotopy of 4- and 5-component links, together with new pairs not distinguished by Milnor invariants."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Implementation of the Habegger-Lin algorithm decides link-homotopy for four- and five-component links and finds new examples beyond Milnor invariants."}],"snapshot_sha256":"c7efbb159fc832f49618f7590be2e99a6bf40457499269fc585c32adf69f09ac"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[{"findings_count":0,"name":"doi_title_agreement","ran_at":"2026-05-19T23:01:19.943706Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"doi_compliance","ran_at":"2026-05-19T14:28:24.895085Z","status":"completed","version":"1.0.0"}],"endpoint":"/pith/2605.04433/integrity.json","findings":[],"snapshot_sha256":"4d2c6751ee2c24b1cce681b9fb53612a77a4ce16f20f30bff9a3ec87e1549a59","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Habegger and Lin gave a classification of link-homotopy classes of links in terms of that of string links modulo certain group actions. As an application, they constructed an algorithm for determining whether given two links are link-homotopic. In \\cite{KM4}, we explicitly computed these group actions for the 4- and 5-component cases. Consequently, the Habegger--Lin algorithm can be effectively applied in these cases. In this paper, we present an implementation of this algorithm, which is available at \\cite{KMcode}, and exhibit new pairs of links that are not link-homotopic yet cannot be disti","authors_text":"Atsuhiko Mizusawa, Yuka Kotorii","cross_cats":[],"headline":"Implementation of the Habegger-Lin algorithm decides link-homotopy for four- and five-component links and finds new examples beyond Milnor invariants.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2026-05-06T02:53:44Z","title":"Implementation of the Habegger--Lin decision algorithm"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.04433","kind":"arxiv","version":2},"verdict":{"created_at":"2026-05-08T17:26:30.309736Z","id":"e3c80c4f-26bc-47fe-b48a-3495df7f72a1","model_set":{"reader":"grok-4.3"},"one_line_summary":"Implementation of the Habegger-Lin decision algorithm for link-homotopy of 4- and 5-component links, together with new pairs not distinguished by Milnor invariants.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Implementation of the Habegger-Lin algorithm decides link-homotopy for four- and five-component links and finds new examples beyond Milnor invariants.","strongest_claim":"we present an implementation of this algorithm, which is available at [KMcode], and exhibit new pairs of links that are not link-homotopic yet cannot be distinguished by Milnor's link-homotopy invariants, called μ-bar-invariants.","weakest_assumption":"The explicit computations of the group actions on string links for the 4- and 5-component cases, reported in the authors' prior paper [KM4], are correct and complete."}},"verdict_id":"e3c80c4f-26bc-47fe-b48a-3495df7f72a1"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:f4fdf54befc84d06a5bfaa5c76cd072b5013895c7d4596949b0b706fbf947c90","target":"record","created_at":"2026-05-20T00:03:13Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"230c3b91cc5bfc9541920ff25e62519d70f6cc93fdd4eae10a5e16c97f0ba0f7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2026-05-06T02:53:44Z","title_canon_sha256":"13bc2b904219cadab444bd5a0920392d9086d3c76e683d2495f66a54206ff79c"},"schema_version":"1.0","source":{"id":"2605.04433","kind":"arxiv","version":2}},"canonical_sha256":"2bb7ab28ded13a35c088d42d387e48c6545804906d49f276e711bd80b4dec3fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2bb7ab28ded13a35c088d42d387e48c6545804906d49f276e711bd80b4dec3fe","first_computed_at":"2026-05-20T00:03:13.988262Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:03:13.988262Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G+lDQg/tKsYBF9vkjb1CpiQrvHUED8J0G3H1D/OOy2ZSEwJwIPQ4UhkRA1La9krJgKINyoVuXVJDvNOWtQCGBw==","signature_status":"signed_v1","signed_at":"2026-05-20T00:03:13.989133Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.04433","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f4fdf54befc84d06a5bfaa5c76cd072b5013895c7d4596949b0b706fbf947c90","sha256:b9034259df1189095e7fb4ac6a3a97aee140b24d798dd1ed9ba23fe7bde864d5"],"state_sha256":"a67ca3b793ec43519d15dffa67d509c8e46dfbb6333fdf503660493a88a35f97"}