{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:KNGPRM4NBQGEIYWFFUXM2GVXSG","short_pith_number":"pith:KNGPRM4N","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"},"canonical_sha256":"534cf8b38d0c0c4462c52d2ecd1ab791972f7c359112cc658621c1ca867d1601","source":{"kind":"arxiv","id":"2207.00619","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2207.00619","created_at":"2026-07-05T10:35:28Z"},{"alias_kind":"arxiv_version","alias_value":"2207.00619v2","created_at":"2026-07-05T10:35:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2207.00619","created_at":"2026-07-05T10:35:28Z"},{"alias_kind":"pith_short_12","alias_value":"KNGPRM4NBQGE","created_at":"2026-07-05T10:35:28Z"},{"alias_kind":"pith_short_16","alias_value":"KNGPRM4NBQGEIYWF","created_at":"2026-07-05T10:35:28Z"},{"alias_kind":"pith_short_8","alias_value":"KNGPRM4N","created_at":"2026-07-05T10:35:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:KNGPRM4NBQGEIYWFFUXM2GVXSG","target":"record","payload":{"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"},"canonical_sha256":"534cf8b38d0c0c4462c52d2ecd1ab791972f7c359112cc658621c1ca867d1601","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"},"source_kind":"arxiv","source_id":"2207.00619","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:35:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KpUJsOaCZIWQYqdn0/33w7MOy+fe/o66cOgdynE9ibwY5o6P0s6yJMVm45t6t5xCemnLz3yh9C4OaXDqDEe+DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T10:22:06.396406Z"},"content_sha256":"86e77dec39200e7a0acb2a630cd0c7c6d98375e28d163fd6e5e3f8f5b94231f7","schema_version":"1.0","event_id":"sha256:86e77dec39200e7a0acb2a630cd0c7c6d98375e28d163fd6e5e3f8f5b94231f7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:KNGPRM4NBQGEIYWFFUXM2GVXSG","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:35:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ovvkkA4X7qnEpEKQbr4dh2bvUSW7fI0FHCihRKJe4TTDfHFq2WtGiZewdMR3QMAvEQkgkAAgemXfvbzgvQkpCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T10:22:06.396906Z"},"content_sha256":"84ab9a4a394a92221d15bf5f0cbccd8bb88dbecb52825b719beab4fab891d083","schema_version":"1.0","event_id":"sha256:84ab9a4a394a92221d15bf5f0cbccd8bb88dbecb52825b719beab4fab891d083"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KNGPRM4NBQGEIYWFFUXM2GVXSG/bundle.json","state_url":"https://pith.science/pith/KNGPRM4NBQGEIYWFFUXM2GVXSG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KNGPRM4NBQGEIYWFFUXM2GVXSG/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-08T10:22:06Z","links":{"resolver":"https://pith.science/pith/KNGPRM4NBQGEIYWFFUXM2GVXSG","bundle":"https://pith.science/pith/KNGPRM4NBQGEIYWFFUXM2GVXSG/bundle.json","state":"https://pith.science/pith/KNGPRM4NBQGEIYWFFUXM2GVXSG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KNGPRM4NBQGEIYWFFUXM2GVXSG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:KNGPRM4NBQGEIYWFFUXM2GVXSG","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":"7a25842615c14436301f21cb4e7e721c0c765a688c363e8c9ffba55634dd58e4","cross_cats_sorted":["math.AT","math.GR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2022-07-01T18:45:08Z","title_canon_sha256":"a6b34c48f15f835d1e6a622115f11dd12d1378e5407dece0e3239a7d6ab461f8"},"schema_version":"1.0","source":{"id":"2207.00619","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2207.00619","created_at":"2026-07-05T10:35:28Z"},{"alias_kind":"arxiv_version","alias_value":"2207.00619v2","created_at":"2026-07-05T10:35:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2207.00619","created_at":"2026-07-05T10:35:28Z"},{"alias_kind":"pith_short_12","alias_value":"KNGPRM4NBQGE","created_at":"2026-07-05T10:35:28Z"},{"alias_kind":"pith_short_16","alias_value":"KNGPRM4NBQGEIYWF","created_at":"2026-07-05T10:35:28Z"},{"alias_kind":"pith_short_8","alias_value":"KNGPRM4N","created_at":"2026-07-05T10:35:28Z"}],"graph_snapshots":[{"event_id":"sha256:84ab9a4a394a92221d15bf5f0cbccd8bb88dbecb52825b719beab4fab891d083","target":"graph","created_at":"2026-07-05T10:35:28Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2207.00619/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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 $E(L_i)$.","authors_text":"Corey Bregman, Rachael Boyd","cross_cats":["math.AT","math.GR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2022-07-01T18:45:08Z","title":"Embedding spaces of split links"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.00619","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":"sha256:86e77dec39200e7a0acb2a630cd0c7c6d98375e28d163fd6e5e3f8f5b94231f7","target":"record","created_at":"2026-07-05T10:35:28Z","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":"7a25842615c14436301f21cb4e7e721c0c765a688c363e8c9ffba55634dd58e4","cross_cats_sorted":["math.AT","math.GR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2022-07-01T18:45:08Z","title_canon_sha256":"a6b34c48f15f835d1e6a622115f11dd12d1378e5407dece0e3239a7d6ab461f8"},"schema_version":"1.0","source":{"id":"2207.00619","kind":"arxiv","version":2}},"canonical_sha256":"534cf8b38d0c0c4462c52d2ecd1ab791972f7c359112cc658621c1ca867d1601","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"534cf8b38d0c0c4462c52d2ecd1ab791972f7c359112cc658621c1ca867d1601","first_computed_at":"2026-07-05T10:35:28.530348Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:35:28.530348Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PA/emvLhL1n3r07lHh+6FLKu3OdFhEDQCWCu7ch+sC5ahu+X70WX9kHyVdCsLs0UzBozW/qAiRuyGGcNlpYSBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:35:28.531165Z","signed_message":"canonical_sha256_bytes"},"source_id":"2207.00619","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:86e77dec39200e7a0acb2a630cd0c7c6d98375e28d163fd6e5e3f8f5b94231f7","sha256:84ab9a4a394a92221d15bf5f0cbccd8bb88dbecb52825b719beab4fab891d083"],"state_sha256":"bc1f5eaa33a3d10678eccbf9af07145efc390db780414313b92275dd1c679e4a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ix/CV2QUEYkqmwrx3wY8KaSwrvpdxCuOc7eat8Nips13VRI3mScn/c837KpAietj9fodfeDfSqlFfDVaIKZuCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T10:22:06.402176Z","bundle_sha256":"fc40716193a8d1adf8703808854c22ff47d5ad0aaf56d05c992b2e849cdd6c28"}}