{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:UD66N5A77GGER4WR6WLLZ44CM3","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":"d1e99a4ac38875dba7f64730b209d9a5ad50b57e139863ce1d34b9f8a4e1ba81","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2007-04-23T21:24:47Z","title_canon_sha256":"02e987361260763bf207accafa6722d039758fdf0204cb5031efe71724880f08"},"schema_version":"1.0","source":{"id":"0704.3093","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0704.3093","created_at":"2026-05-18T04:01:13Z"},{"alias_kind":"arxiv_version","alias_value":"0704.3093v2","created_at":"2026-05-18T04:01:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0704.3093","created_at":"2026-05-18T04:01:13Z"},{"alias_kind":"pith_short_12","alias_value":"UD66N5A77GGE","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"UD66N5A77GGER4WR","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"UD66N5A7","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:4244de360fd6a76e9615a64741736d261e50b561e02c85418647a7b14b20a09a","target":"graph","created_at":"2026-05-18T04:01:13Z","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":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We consider the operation of Whitehead double on a component of a link and study the behavior of Milnor invariants under this operation. We show that this operation turns a link whose Milnor invariants of length < k are all zero into a link with vanishing Milnor invariants of length < 2k, and we provide formulas for the first non-vanishing ones.\n  As a consequence, we obtain statements relating the notions of link-homotopy and self Delta-equivalence via the Whitehead double operation. By using our result, we show that a Brunnian link L is link-homotopic to the unlink if and only if a link L wi","authors_text":"Akira Yasuhara, Jean-Baptiste Meilhan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2007-04-23T21:24:47Z","title":"Whitehead double and Milnor invariants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0704.3093","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:def0af5238329e2895cdefaeffcd6fc82ae704a70c0d37ba2ca438fba665ea08","target":"record","created_at":"2026-05-18T04:01:13Z","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":"d1e99a4ac38875dba7f64730b209d9a5ad50b57e139863ce1d34b9f8a4e1ba81","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2007-04-23T21:24:47Z","title_canon_sha256":"02e987361260763bf207accafa6722d039758fdf0204cb5031efe71724880f08"},"schema_version":"1.0","source":{"id":"0704.3093","kind":"arxiv","version":2}},"canonical_sha256":"a0fde6f41ff98c48f2d1f596bcf38266d3f3f14b39d4ba1525bb5a28e58395e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a0fde6f41ff98c48f2d1f596bcf38266d3f3f14b39d4ba1525bb5a28e58395e0","first_computed_at":"2026-05-18T04:01:13.555654Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:01:13.555654Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nDM1UPGFwdbO38vOdMseThcFrljajpCK+5yRypUcgY2Ca8HPR9dSuIvbz18kjvVLEv4p++cueGTGd+cH8cYMDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:01:13.556405Z","signed_message":"canonical_sha256_bytes"},"source_id":"0704.3093","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:def0af5238329e2895cdefaeffcd6fc82ae704a70c0d37ba2ca438fba665ea08","sha256:4244de360fd6a76e9615a64741736d261e50b561e02c85418647a7b14b20a09a"],"state_sha256":"a50ceffcd269e8715351b675ec35397efd9af7ae0b6f6747f579d0f1b3ad2f90"}