{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:KNGPRM4NBQGEIYWFFUXM2GVXSG","short_pith_number":"pith:KNGPRM4N","schema_version":"1.0","canonical_sha256":"534cf8b38d0c0c4462c52d2ecd1ab791972f7c359112cc658621c1ca867d1601","source":{"kind":"arxiv","id":"2207.00619","version":2},"attestation_state":"computed","paper":{"title":"Embedding spaces of split links","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AT","math.GR"],"primary_cat":"math.GT","authors_text":"Corey Bregman, Rachael Boyd","submitted_at":"2022-07-01T18:45:08Z","abstract_excerpt":"We study the homotopy type of the space $E(L)$ of unparametrised embeddings of a split link $L=L_1\\sqcup \\ldots \\sqcup L_n$ in $\\mathbb{R}^3$. Our main result is a simple description of the fundamental group, or motion group, of $E(L)$, and we extend this to a description of the motion group of embeddings in $S^3$. The main tool we build is a semi-simplicial space of separating systems, which we show is homotopy equivalent to $E(L)$. This combinatorial object provides a gateway to studying the homotopy type of $E(L)$ via the homotopy type of the spaces $E(L_i)$."},"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":"2207.00619","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2022-07-01T18:45:08Z","cross_cats_sorted":["math.AT","math.GR"],"title_canon_sha256":"a6b34c48f15f835d1e6a622115f11dd12d1378e5407dece0e3239a7d6ab461f8","abstract_canon_sha256":"7a25842615c14436301f21cb4e7e721c0c765a688c363e8c9ffba55634dd58e4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:35:28.531165Z","signature_b64":"PA/emvLhL1n3r07lHh+6FLKu3OdFhEDQCWCu7ch+sC5ahu+X70WX9kHyVdCsLs0UzBozW/qAiRuyGGcNlpYSBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"534cf8b38d0c0c4462c52d2ecd1ab791972f7c359112cc658621c1ca867d1601","last_reissued_at":"2026-07-05T10:35:28.530348Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:35:28.530348Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Embedding spaces of split links","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AT","math.GR"],"primary_cat":"math.GT","authors_text":"Corey Bregman, Rachael Boyd","submitted_at":"2022-07-01T18:45:08Z","abstract_excerpt":"We study the homotopy type of the space $E(L)$ of unparametrised embeddings of a split link $L=L_1\\sqcup \\ldots \\sqcup L_n$ in $\\mathbb{R}^3$. Our main result is a simple description of the fundamental group, or motion group, of $E(L)$, and we extend this to a description of the motion group of embeddings in $S^3$. The main tool we build is a semi-simplicial space of separating systems, which we show is homotopy equivalent to $E(L)$. This combinatorial object provides a gateway to studying the homotopy type of $E(L)$ via the homotopy type of the spaces $E(L_i)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.00619","kind":"arxiv","version":2},"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/2207.00619/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":"2207.00619","created_at":"2026-07-05T10:35:28.530428+00:00"},{"alias_kind":"arxiv_version","alias_value":"2207.00619v2","created_at":"2026-07-05T10:35:28.530428+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2207.00619","created_at":"2026-07-05T10:35:28.530428+00:00"},{"alias_kind":"pith_short_12","alias_value":"KNGPRM4NBQGE","created_at":"2026-07-05T10:35:28.530428+00:00"},{"alias_kind":"pith_short_16","alias_value":"KNGPRM4NBQGEIYWF","created_at":"2026-07-05T10:35:28.530428+00:00"},{"alias_kind":"pith_short_8","alias_value":"KNGPRM4N","created_at":"2026-07-05T10:35:28.530428+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.13749","citing_title":"Cohomology of the pure symmetric automorphisms of right-angled Artin groups","ref_index":3,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KNGPRM4NBQGEIYWFFUXM2GVXSG","json":"https://pith.science/pith/KNGPRM4NBQGEIYWFFUXM2GVXSG.json","graph_json":"https://pith.science/api/pith-number/KNGPRM4NBQGEIYWFFUXM2GVXSG/graph.json","events_json":"https://pith.science/api/pith-number/KNGPRM4NBQGEIYWFFUXM2GVXSG/events.json","paper":"https://pith.science/paper/KNGPRM4N"},"agent_actions":{"view_html":"https://pith.science/pith/KNGPRM4NBQGEIYWFFUXM2GVXSG","download_json":"https://pith.science/pith/KNGPRM4NBQGEIYWFFUXM2GVXSG.json","view_paper":"https://pith.science/paper/KNGPRM4N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2207.00619&json=true","fetch_graph":"https://pith.science/api/pith-number/KNGPRM4NBQGEIYWFFUXM2GVXSG/graph.json","fetch_events":"https://pith.science/api/pith-number/KNGPRM4NBQGEIYWFFUXM2GVXSG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KNGPRM4NBQGEIYWFFUXM2GVXSG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KNGPRM4NBQGEIYWFFUXM2GVXSG/action/storage_attestation","attest_author":"https://pith.science/pith/KNGPRM4NBQGEIYWFFUXM2GVXSG/action/author_attestation","sign_citation":"https://pith.science/pith/KNGPRM4NBQGEIYWFFUXM2GVXSG/action/citation_signature","submit_replication":"https://pith.science/pith/KNGPRM4NBQGEIYWFFUXM2GVXSG/action/replication_record"}},"created_at":"2026-07-05T10:35:28.530428+00:00","updated_at":"2026-07-05T10:35:28.530428+00:00"}