{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:I7TWI3W4GXRCNNOJSTGBAIEQVQ","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":"9b404545ac68167b1f90e8f9657abbe329a402253a0290e9a396520074341aa6","cross_cats_sorted":["math.AT","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-11-06T14:57:40Z","title_canon_sha256":"fbf882f21fec48f68e711038f323eff02b93e7e61862839c04a4ab904103fb17"},"schema_version":"1.0","source":{"id":"1511.02101","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.02101","created_at":"2026-05-18T00:49:52Z"},{"alias_kind":"arxiv_version","alias_value":"1511.02101v1","created_at":"2026-05-18T00:49:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.02101","created_at":"2026-05-18T00:49:52Z"},{"alias_kind":"pith_short_12","alias_value":"I7TWI3W4GXRC","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"I7TWI3W4GXRCNNOJ","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"I7TWI3W4","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:fa76b231f08d485d6e9ed553b810a374f7b87276d6d14828e5eb0be326519bbb","target":"graph","created_at":"2026-05-18T00:49:52Z","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 M be a surface, perhaps with boundary, and either compact, or with a finite number of points removed from the interior of the surface. We consider the inclusion i: F\\_n(M) --\\textgreater{} M^n of the nth configuration space F\\_n(M) of M into the n-fold Cartesian product of M, as well as the induced homomorphism i\\_\\#: P\\_n(M) --\\textgreater{} (\\pi\\_1(M))^n, where P\\_n(M) is the n-string pure braid group of M. Both i and i\\_\\# were studied initially by J.Birman who conjectured that Ker(i\\_\\#) is equal to the normal closure of the Artin pure braid group P\\_n in P\\_n(M). The conjecture was la","authors_text":"Daciberg Lima Gon\\c{c}alves, John Guaschi (LMNO)","cross_cats":["math.AT","math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-11-06T14:57:40Z","title":"The inclusion of configuration spaces of surfaces in Cartesian products, its induced homomorphism, and the virtual cohomological dimension of the braid groups of S^2 and RP^2"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.02101","kind":"arxiv","version":1},"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":"sha256:556b9873a0ce6d8c0e4c59c2a95337f0c2360779cf617e58052350b618a7701c","target":"record","created_at":"2026-05-18T00:49:52Z","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":"9b404545ac68167b1f90e8f9657abbe329a402253a0290e9a396520074341aa6","cross_cats_sorted":["math.AT","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-11-06T14:57:40Z","title_canon_sha256":"fbf882f21fec48f68e711038f323eff02b93e7e61862839c04a4ab904103fb17"},"schema_version":"1.0","source":{"id":"1511.02101","kind":"arxiv","version":1}},"canonical_sha256":"47e7646edc35e226b5c994cc102090ac0bb173cecab2a503422a2dcc1952ee28","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"47e7646edc35e226b5c994cc102090ac0bb173cecab2a503422a2dcc1952ee28","first_computed_at":"2026-05-18T00:49:52.525116Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:52.525116Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RatXj9/js0uL7zXRpMpYbyMXU6sL1hbOcAytGHL3E8N0XJlCNNsIIgoFkn2merDB8BAIWFYeNNa2GmuAsqeRBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:52.525549Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.02101","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:556b9873a0ce6d8c0e4c59c2a95337f0c2360779cf617e58052350b618a7701c","sha256:fa76b231f08d485d6e9ed553b810a374f7b87276d6d14828e5eb0be326519bbb"],"state_sha256":"51f0ef21fa1575f3b9ca0111ce494cdef8c84c0a7bdb1f99c7140543fb27fac8"}