{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:VKAILLWPH3YFKQSLNHTPOYVECZ","short_pith_number":"pith:VKAILLWP","canonical_record":{"source":{"id":"1404.2511","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-04-09T15:02:46Z","cross_cats_sorted":[],"title_canon_sha256":"12c4b8b5d4c0803668e03ab9b09ad0733bff85adb62571eadcfb8a2a5b882247","abstract_canon_sha256":"5e9e60a65d096c2f3e517394fa541cc0484ae66ac2b56828b63d47d6ac7d24f2"},"schema_version":"1.0"},"canonical_sha256":"aa8085aecf3ef055424b69e6f762a4166a8cf8df99d07f6a879f6ab3daccb7b5","source":{"kind":"arxiv","id":"1404.2511","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.2511","created_at":"2026-05-18T00:02:14Z"},{"alias_kind":"arxiv_version","alias_value":"1404.2511v4","created_at":"2026-05-18T00:02:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.2511","created_at":"2026-05-18T00:02:14Z"},{"alias_kind":"pith_short_12","alias_value":"VKAILLWPH3YF","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"VKAILLWPH3YFKQSL","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"VKAILLWP","created_at":"2026-05-18T12:28:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:VKAILLWPH3YFKQSLNHTPOYVECZ","target":"record","payload":{"canonical_record":{"source":{"id":"1404.2511","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-04-09T15:02:46Z","cross_cats_sorted":[],"title_canon_sha256":"12c4b8b5d4c0803668e03ab9b09ad0733bff85adb62571eadcfb8a2a5b882247","abstract_canon_sha256":"5e9e60a65d096c2f3e517394fa541cc0484ae66ac2b56828b63d47d6ac7d24f2"},"schema_version":"1.0"},"canonical_sha256":"aa8085aecf3ef055424b69e6f762a4166a8cf8df99d07f6a879f6ab3daccb7b5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:14.066805Z","signature_b64":"hiHefJqQ7ttRS0s9QfoVxSB39RDkEnnCO4gpeorzhl0a4SbyYefeTM2J4GPqqjCxvefwpSCEPTo7MkC4ZQVXCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aa8085aecf3ef055424b69e6f762a4166a8cf8df99d07f6a879f6ab3daccb7b5","last_reissued_at":"2026-05-18T00:02:14.066332Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:14.066332Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.2511","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:02:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TrVMHN7PTOLPWxyCYcbh8lh55Y+sO8RNK8/4+eCcrjKJiKvMmDZqdOZS+bXhfujT9h02iqx5nF5hH3hAw0IACQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T07:37:24.749610Z"},"content_sha256":"a958f7d95a96681538b0fab3a4b6c89c67b61466fef8b407a6e785d1ffcbf99b","schema_version":"1.0","event_id":"sha256:a958f7d95a96681538b0fab3a4b6c89c67b61466fef8b407a6e785d1ffcbf99b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:VKAILLWPH3YFKQSLNHTPOYVECZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The braid group of a necklace","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Arnaud Bodin, Paolo Bellingeri","submitted_at":"2014-04-09T15:02:46Z","abstract_excerpt":"We show several geometric and algebraic aspects of a necklace: a link composed with a core circle and a series of circles linked to this core. We first prove that the fundamental group of the configuration space of necklaces (that we will call braid group of a necklace) is isomorphic to the braid group over an annulus quotiented by the square of the center. We then define braid groups of necklaces and affine braid groups of type A in terms of automorphisms of free groups and characterize these automorphisms among all automorphisms of free groups. In the case of affine braid groups of type A su"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.2511","kind":"arxiv","version":4},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:02:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C6DYlcdjR8AQ8b1jh/Jzv7nA+lySQebgDO3Zd7lL5ak51FgSr0pW+S6F6J3I4yO8NpqLUPi7C7YK10SHwDanDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T07:37:24.749953Z"},"content_sha256":"f9a2f0ad857127cb0ecf547410cac185117e208dc72d961ce421a9e2a104614c","schema_version":"1.0","event_id":"sha256:f9a2f0ad857127cb0ecf547410cac185117e208dc72d961ce421a9e2a104614c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VKAILLWPH3YFKQSLNHTPOYVECZ/bundle.json","state_url":"https://pith.science/pith/VKAILLWPH3YFKQSLNHTPOYVECZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VKAILLWPH3YFKQSLNHTPOYVECZ/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":"2026-06-27T07:37:24Z","links":{"resolver":"https://pith.science/pith/VKAILLWPH3YFKQSLNHTPOYVECZ","bundle":"https://pith.science/pith/VKAILLWPH3YFKQSLNHTPOYVECZ/bundle.json","state":"https://pith.science/pith/VKAILLWPH3YFKQSLNHTPOYVECZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VKAILLWPH3YFKQSLNHTPOYVECZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:VKAILLWPH3YFKQSLNHTPOYVECZ","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":"5e9e60a65d096c2f3e517394fa541cc0484ae66ac2b56828b63d47d6ac7d24f2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-04-09T15:02:46Z","title_canon_sha256":"12c4b8b5d4c0803668e03ab9b09ad0733bff85adb62571eadcfb8a2a5b882247"},"schema_version":"1.0","source":{"id":"1404.2511","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.2511","created_at":"2026-05-18T00:02:14Z"},{"alias_kind":"arxiv_version","alias_value":"1404.2511v4","created_at":"2026-05-18T00:02:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.2511","created_at":"2026-05-18T00:02:14Z"},{"alias_kind":"pith_short_12","alias_value":"VKAILLWPH3YF","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"VKAILLWPH3YFKQSL","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"VKAILLWP","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:f9a2f0ad857127cb0ecf547410cac185117e208dc72d961ce421a9e2a104614c","target":"graph","created_at":"2026-05-18T00:02:14Z","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 show several geometric and algebraic aspects of a necklace: a link composed with a core circle and a series of circles linked to this core. We first prove that the fundamental group of the configuration space of necklaces (that we will call braid group of a necklace) is isomorphic to the braid group over an annulus quotiented by the square of the center. We then define braid groups of necklaces and affine braid groups of type A in terms of automorphisms of free groups and characterize these automorphisms among all automorphisms of free groups. In the case of affine braid groups of type A su","authors_text":"Arnaud Bodin, Paolo Bellingeri","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-04-09T15:02:46Z","title":"The braid group of a necklace"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.2511","kind":"arxiv","version":4},"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:a958f7d95a96681538b0fab3a4b6c89c67b61466fef8b407a6e785d1ffcbf99b","target":"record","created_at":"2026-05-18T00:02:14Z","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":"5e9e60a65d096c2f3e517394fa541cc0484ae66ac2b56828b63d47d6ac7d24f2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-04-09T15:02:46Z","title_canon_sha256":"12c4b8b5d4c0803668e03ab9b09ad0733bff85adb62571eadcfb8a2a5b882247"},"schema_version":"1.0","source":{"id":"1404.2511","kind":"arxiv","version":4}},"canonical_sha256":"aa8085aecf3ef055424b69e6f762a4166a8cf8df99d07f6a879f6ab3daccb7b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aa8085aecf3ef055424b69e6f762a4166a8cf8df99d07f6a879f6ab3daccb7b5","first_computed_at":"2026-05-18T00:02:14.066332Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:14.066332Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hiHefJqQ7ttRS0s9QfoVxSB39RDkEnnCO4gpeorzhl0a4SbyYefeTM2J4GPqqjCxvefwpSCEPTo7MkC4ZQVXCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:14.066805Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.2511","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a958f7d95a96681538b0fab3a4b6c89c67b61466fef8b407a6e785d1ffcbf99b","sha256:f9a2f0ad857127cb0ecf547410cac185117e208dc72d961ce421a9e2a104614c"],"state_sha256":"7f50ca698fc3a26aecbaf0c220ffcc6e1cbde558477dc040388640ab2b0afcc6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lr6YlHE96//fnwDWdIeC+R5H/ZsDuo8HHTf2KXjWCiS6vu9Y8104RzacCQ1AHm9jyobFV5OlfPOT57+5m4scBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T07:37:24.751745Z","bundle_sha256":"fc4a39c4768c20a6c8914eeae38951c4fafe1b9e394191231d2715f8cb3ff4f1"}}