{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:4BBQS2JOF447ZNXISOZBQYNUVP","short_pith_number":"pith:4BBQS2JO","canonical_record":{"source":{"id":"1805.11379","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-05-29T12:11:58Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"f4c478cb18a877feee966d74d3ea244883eb89dfba5b96a3bd3ec98ef53cfb92","abstract_canon_sha256":"0a238e9ad40bc8ef8046c9d87582628c061cf3a94f5becbb7705f54e40fa56dc"},"schema_version":"1.0"},"canonical_sha256":"e04309692e2f39fcb6e893b21861b4abe9e1cb1197cfb50f4aa262328dc57f83","source":{"kind":"arxiv","id":"1805.11379","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.11379","created_at":"2026-05-18T00:01:48Z"},{"alias_kind":"arxiv_version","alias_value":"1805.11379v4","created_at":"2026-05-18T00:01:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.11379","created_at":"2026-05-18T00:01:48Z"},{"alias_kind":"pith_short_12","alias_value":"4BBQS2JOF447","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4BBQS2JOF447ZNXI","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4BBQS2JO","created_at":"2026-05-18T12:32:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:4BBQS2JOF447ZNXISOZBQYNUVP","target":"record","payload":{"canonical_record":{"source":{"id":"1805.11379","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-05-29T12:11:58Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"f4c478cb18a877feee966d74d3ea244883eb89dfba5b96a3bd3ec98ef53cfb92","abstract_canon_sha256":"0a238e9ad40bc8ef8046c9d87582628c061cf3a94f5becbb7705f54e40fa56dc"},"schema_version":"1.0"},"canonical_sha256":"e04309692e2f39fcb6e893b21861b4abe9e1cb1197cfb50f4aa262328dc57f83","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:48.888470Z","signature_b64":"82y97KWQWtOHGWLbZmY98ljzMYg8i00mU9RVg42WfFnkzkwmn/h5BE9kq21DA2YBOc9u1iNkOFEYR6m5SeDSCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e04309692e2f39fcb6e893b21861b4abe9e1cb1197cfb50f4aa262328dc57f83","last_reissued_at":"2026-05-18T00:01:48.887885Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:48.887885Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.11379","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":"2026-05-18T00:01:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4OGqOQiI8H+U7IWIymEe3yzYdJ7NVcKxyFf1oNmnyHktTYkMhk7HdG0V2IcGj3/Os/UVpRZyhU1Wh85XDZo/CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T12:22:06.319534Z"},"content_sha256":"6645057171cd45b62e9954c334e2c3920b25e7f59985d5d8eadf1c50cd8ecb13","schema_version":"1.0","event_id":"sha256:6645057171cd45b62e9954c334e2c3920b25e7f59985d5d8eadf1c50cd8ecb13"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:4BBQS2JOF447ZNXISOZBQYNUVP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Embeddings of finite groups in $B_n/\\Gamma_k(P_n)$ for $k=2, 3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"CNRS, Daciberg Lima Gon\\c{c}alves (IME, John Guaschi (LMNO, NU), Oscar Ocampo (UFBA), UNICAEN, USP)","submitted_at":"2018-05-29T12:11:58Z","abstract_excerpt":"Let $n \\geq 3$. In this paper, we study the problem of whether a given finite group $G$ embeds in a quotient of the form $B_n/\\Gamma_k(P_n)$, where $B_n$ is the $n$-string Artin braid group, $k \\in \\{2, 3\\}$, and $\\{\\Gamma_l(P_n)\\}_{l\\in \\mathbb{N}}$ is the lower central series of the $n$-string pure braid group $P_n$. Previous results show that a necessary condition for such an embedding to exist is that $|G|$ is odd (resp. is relatively prime with $6$) if $k=2$ (resp. $k=3$), where $|G|$ denotes the order of $G$. We show that any finite group $G$ of odd order (resp. of order relatively prime"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.11379","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":"2026-05-18T00:01:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TiZ5h+F6kM+KBfvaud6C4gO8fqVM0n4Q0WVAVp2oqN+bwRaRAGc9i6d2heM1ZtPQgUBuvL4WXply/KgwwziUCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T12:22:06.319882Z"},"content_sha256":"4835a8d08387964494daf2e762844fa8253952fccddfd2f8803d2adead436460","schema_version":"1.0","event_id":"sha256:4835a8d08387964494daf2e762844fa8253952fccddfd2f8803d2adead436460"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4BBQS2JOF447ZNXISOZBQYNUVP/bundle.json","state_url":"https://pith.science/pith/4BBQS2JOF447ZNXISOZBQYNUVP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4BBQS2JOF447ZNXISOZBQYNUVP/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":"2026-06-09T12:22:06Z","links":{"resolver":"https://pith.science/pith/4BBQS2JOF447ZNXISOZBQYNUVP","bundle":"https://pith.science/pith/4BBQS2JOF447ZNXISOZBQYNUVP/bundle.json","state":"https://pith.science/pith/4BBQS2JOF447ZNXISOZBQYNUVP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4BBQS2JOF447ZNXISOZBQYNUVP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:4BBQS2JOF447ZNXISOZBQYNUVP","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":"0a238e9ad40bc8ef8046c9d87582628c061cf3a94f5becbb7705f54e40fa56dc","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-05-29T12:11:58Z","title_canon_sha256":"f4c478cb18a877feee966d74d3ea244883eb89dfba5b96a3bd3ec98ef53cfb92"},"schema_version":"1.0","source":{"id":"1805.11379","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.11379","created_at":"2026-05-18T00:01:48Z"},{"alias_kind":"arxiv_version","alias_value":"1805.11379v4","created_at":"2026-05-18T00:01:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.11379","created_at":"2026-05-18T00:01:48Z"},{"alias_kind":"pith_short_12","alias_value":"4BBQS2JOF447","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4BBQS2JOF447ZNXI","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4BBQS2JO","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:4835a8d08387964494daf2e762844fa8253952fccddfd2f8803d2adead436460","target":"graph","created_at":"2026-05-18T00:01:48Z","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":"Let $n \\geq 3$. In this paper, we study the problem of whether a given finite group $G$ embeds in a quotient of the form $B_n/\\Gamma_k(P_n)$, where $B_n$ is the $n$-string Artin braid group, $k \\in \\{2, 3\\}$, and $\\{\\Gamma_l(P_n)\\}_{l\\in \\mathbb{N}}$ is the lower central series of the $n$-string pure braid group $P_n$. Previous results show that a necessary condition for such an embedding to exist is that $|G|$ is odd (resp. is relatively prime with $6$) if $k=2$ (resp. $k=3$), where $|G|$ denotes the order of $G$. We show that any finite group $G$ of odd order (resp. of order relatively prime","authors_text":"CNRS, Daciberg Lima Gon\\c{c}alves (IME, John Guaschi (LMNO, NU), Oscar Ocampo (UFBA), UNICAEN, USP)","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-05-29T12:11:58Z","title":"Embeddings of finite groups in $B_n/\\Gamma_k(P_n)$ for $k=2, 3$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.11379","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":"sha256:6645057171cd45b62e9954c334e2c3920b25e7f59985d5d8eadf1c50cd8ecb13","target":"record","created_at":"2026-05-18T00:01:48Z","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":"0a238e9ad40bc8ef8046c9d87582628c061cf3a94f5becbb7705f54e40fa56dc","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-05-29T12:11:58Z","title_canon_sha256":"f4c478cb18a877feee966d74d3ea244883eb89dfba5b96a3bd3ec98ef53cfb92"},"schema_version":"1.0","source":{"id":"1805.11379","kind":"arxiv","version":4}},"canonical_sha256":"e04309692e2f39fcb6e893b21861b4abe9e1cb1197cfb50f4aa262328dc57f83","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e04309692e2f39fcb6e893b21861b4abe9e1cb1197cfb50f4aa262328dc57f83","first_computed_at":"2026-05-18T00:01:48.887885Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:48.887885Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"82y97KWQWtOHGWLbZmY98ljzMYg8i00mU9RVg42WfFnkzkwmn/h5BE9kq21DA2YBOc9u1iNkOFEYR6m5SeDSCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:48.888470Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.11379","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6645057171cd45b62e9954c334e2c3920b25e7f59985d5d8eadf1c50cd8ecb13","sha256:4835a8d08387964494daf2e762844fa8253952fccddfd2f8803d2adead436460"],"state_sha256":"e6fd4986c90c0a673467ca558620c23b508693d44906d05475a796fb485cfe35"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ti8aOiXJuVnfB5n7Sa1VVr3jVmjHS2TmE5ZicsiXbfOMSEfLy7AZfO7WyLO0ENBFlbJVYQgv85aIxpMPhG67BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T12:22:06.322039Z","bundle_sha256":"0bc7c75854cd9f244d0a4840ac2e8f46e6eac2e0a4b5daed8139ad561836f9ff"}}