{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:HMGN3N3NQIIFD5IGJS34EVBHWS","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":"83d9035cad5091dec3e1d0b6a323372cf0e03c3841c21fa8742ed9afe353b89f","cross_cats_sorted":["math.GT"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.GR","submitted_at":"2021-09-01T13:53:32Z","title_canon_sha256":"ce4ea999f3794b70e78614098c8931b40049beea12e79aae8c240d5fda062015"},"schema_version":"1.0","source":{"id":"2109.00390","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.00390","created_at":"2026-07-05T03:10:46Z"},{"alias_kind":"arxiv_version","alias_value":"2109.00390v1","created_at":"2026-07-05T03:10:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.00390","created_at":"2026-07-05T03:10:46Z"},{"alias_kind":"pith_short_12","alias_value":"HMGN3N3NQIIF","created_at":"2026-07-05T03:10:46Z"},{"alias_kind":"pith_short_16","alias_value":"HMGN3N3NQIIFD5IG","created_at":"2026-07-05T03:10:46Z"},{"alias_kind":"pith_short_8","alias_value":"HMGN3N3N","created_at":"2026-07-05T03:10:46Z"}],"graph_snapshots":[{"event_id":"sha256:228c59f709edda809292ac069c0eadbdf523b7c9d6ab5ec473af9e927e4151e3","target":"graph","created_at":"2026-07-05T03:10:46Z","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/2109.00390/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $n\\geq 3$. In this paper we deal with the conjugacy problem in the Artin braid group quotient $B_n/[P_n,P_n]$. To solve it we use systems of equations over the integers arising from the action of $B_n/[P_n,P_n]$ over the abelianization of the pure Artin braid group $P_n/[P_n,P_n]$. Using this technique we also realize explicitly infinite virtually cyclic subgroups in $B_n/[P_n,P_n]$.","authors_text":"Oscar Ocampo, Paulo Cesar Cerqueira dos Santos J\\'unior","cross_cats":["math.GT"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.GR","submitted_at":"2021-09-01T13:53:32Z","title":"The conjugacy problem and virtually cyclic subgroups in the Artin braid group quotient $B_n/[P_n,P_n]$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.00390","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:d164395cb9c7d11754a6d4731a4f2b5d4e6dbee3ccdadc1e6476c793526cc168","target":"record","created_at":"2026-07-05T03:10:46Z","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":"83d9035cad5091dec3e1d0b6a323372cf0e03c3841c21fa8742ed9afe353b89f","cross_cats_sorted":["math.GT"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.GR","submitted_at":"2021-09-01T13:53:32Z","title_canon_sha256":"ce4ea999f3794b70e78614098c8931b40049beea12e79aae8c240d5fda062015"},"schema_version":"1.0","source":{"id":"2109.00390","kind":"arxiv","version":1}},"canonical_sha256":"3b0cddb76d821051f5064cb7c25427b4beda383a9cebfe7bd65aaf15cd8d1f30","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b0cddb76d821051f5064cb7c25427b4beda383a9cebfe7bd65aaf15cd8d1f30","first_computed_at":"2026-07-05T03:10:46.120043Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:10:46.120043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v8GeaCY0PjLYjr1/zXBHxB3yGuQtK7Xk1WWCwbA53jFclEQ6SVK+wTQrKXjSQU8RlvqbRi/Kog1ZWhlj2sw6Bw==","signature_status":"signed_v1","signed_at":"2026-07-05T03:10:46.120409Z","signed_message":"canonical_sha256_bytes"},"source_id":"2109.00390","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d164395cb9c7d11754a6d4731a4f2b5d4e6dbee3ccdadc1e6476c793526cc168","sha256:228c59f709edda809292ac069c0eadbdf523b7c9d6ab5ec473af9e927e4151e3"],"state_sha256":"dfe8214f11532af9300265721a861afa686214741ca8f8c20b38460ce799ee56"}