{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:YGL42WJZ3JRBNXZUWI5HMMO35K","short_pith_number":"pith:YGL42WJZ","schema_version":"1.0","canonical_sha256":"c197cd5939da6216df34b23a7631dbeab54a5272ff318c2a60b002597e399553","source":{"kind":"arxiv","id":"1201.6482","version":1},"attestation_state":"computed","paper":{"title":"Minimal generating and normally generating sets for the braid and mapping class groups of the disc, the sphere and the projective plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Daciberg Lima Gon\\c{c}alves (IME), John Guaschi (LMNO)","submitted_at":"2012-01-31T09:17:54Z","abstract_excerpt":"We consider the (pure) braid groups B_{n}(M) and P_{n}(M), where M is the 2-sphere S^2 or the real projective plane RP^2. We determine the minimal cardinality of (normal) generating sets X of these groups, first when there is no restriction on X, and secondly when X consists of elements of finite order. This improves on results of Berrick and Matthey in the case of S^2, and extends them in the case of RP^2. We begin by recalling the situation for the Artin braid groups. As applications of our results, we answer the corresponding questions for the associated mapping class groups, and we show th"},"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":"1201.6482","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-01-31T09:17:54Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"280b735fef3f84254b5109774863540cf96dc87637fa26f1af2ccc880abf680f","abstract_canon_sha256":"44b22557e9014f5410d85a3a10d7c6184e9b0d438c83f83325f550e048a66bd9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:18.021592Z","signature_b64":"J/he1p4Fxa09rxwPLkRSoRGH4w9lOzXzei0YT6M5TCt4XKQsXmwXckdsh+3xt/y5Ab0Lq4Px2b8D1/IDXwncBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c197cd5939da6216df34b23a7631dbeab54a5272ff318c2a60b002597e399553","last_reissued_at":"2026-05-18T02:48:18.021133Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:18.021133Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Minimal generating and normally generating sets for the braid and mapping class groups of the disc, the sphere and the projective plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Daciberg Lima Gon\\c{c}alves (IME), John Guaschi (LMNO)","submitted_at":"2012-01-31T09:17:54Z","abstract_excerpt":"We consider the (pure) braid groups B_{n}(M) and P_{n}(M), where M is the 2-sphere S^2 or the real projective plane RP^2. We determine the minimal cardinality of (normal) generating sets X of these groups, first when there is no restriction on X, and secondly when X consists of elements of finite order. This improves on results of Berrick and Matthey in the case of S^2, and extends them in the case of RP^2. We begin by recalling the situation for the Artin braid groups. As applications of our results, we answer the corresponding questions for the associated mapping class groups, and we show th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.6482","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1201.6482","created_at":"2026-05-18T02:48:18.021198+00:00"},{"alias_kind":"arxiv_version","alias_value":"1201.6482v1","created_at":"2026-05-18T02:48:18.021198+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.6482","created_at":"2026-05-18T02:48:18.021198+00:00"},{"alias_kind":"pith_short_12","alias_value":"YGL42WJZ3JRB","created_at":"2026-05-18T12:27:27.928770+00:00"},{"alias_kind":"pith_short_16","alias_value":"YGL42WJZ3JRBNXZU","created_at":"2026-05-18T12:27:27.928770+00:00"},{"alias_kind":"pith_short_8","alias_value":"YGL42WJZ","created_at":"2026-05-18T12:27:27.928770+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YGL42WJZ3JRBNXZUWI5HMMO35K","json":"https://pith.science/pith/YGL42WJZ3JRBNXZUWI5HMMO35K.json","graph_json":"https://pith.science/api/pith-number/YGL42WJZ3JRBNXZUWI5HMMO35K/graph.json","events_json":"https://pith.science/api/pith-number/YGL42WJZ3JRBNXZUWI5HMMO35K/events.json","paper":"https://pith.science/paper/YGL42WJZ"},"agent_actions":{"view_html":"https://pith.science/pith/YGL42WJZ3JRBNXZUWI5HMMO35K","download_json":"https://pith.science/pith/YGL42WJZ3JRBNXZUWI5HMMO35K.json","view_paper":"https://pith.science/paper/YGL42WJZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1201.6482&json=true","fetch_graph":"https://pith.science/api/pith-number/YGL42WJZ3JRBNXZUWI5HMMO35K/graph.json","fetch_events":"https://pith.science/api/pith-number/YGL42WJZ3JRBNXZUWI5HMMO35K/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YGL42WJZ3JRBNXZUWI5HMMO35K/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YGL42WJZ3JRBNXZUWI5HMMO35K/action/storage_attestation","attest_author":"https://pith.science/pith/YGL42WJZ3JRBNXZUWI5HMMO35K/action/author_attestation","sign_citation":"https://pith.science/pith/YGL42WJZ3JRBNXZUWI5HMMO35K/action/citation_signature","submit_replication":"https://pith.science/pith/YGL42WJZ3JRBNXZUWI5HMMO35K/action/replication_record"}},"created_at":"2026-05-18T02:48:18.021198+00:00","updated_at":"2026-05-18T02:48:18.021198+00:00"}