{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:3IZSBAYE4N3SWPRPYE77BKUJTT","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":"d5a00687c4920252771110dd48a6753b350a11f5db0070d106def0095064c31c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.GR","submitted_at":"2023-10-06T11:00:16Z","title_canon_sha256":"176d451648d895b4ad6ca71b2acabbe56e651f9d88157e1c26c5c62f1764f02e"},"schema_version":"1.0","source":{"id":"2310.04154","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2310.04154","created_at":"2026-07-05T06:57:59Z"},{"alias_kind":"arxiv_version","alias_value":"2310.04154v1","created_at":"2026-07-05T06:57:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.04154","created_at":"2026-07-05T06:57:59Z"},{"alias_kind":"pith_short_12","alias_value":"3IZSBAYE4N3S","created_at":"2026-07-05T06:57:59Z"},{"alias_kind":"pith_short_16","alias_value":"3IZSBAYE4N3SWPRP","created_at":"2026-07-05T06:57:59Z"},{"alias_kind":"pith_short_8","alias_value":"3IZSBAYE","created_at":"2026-07-05T06:57:59Z"}],"graph_snapshots":[{"event_id":"sha256:8828bb641f0ab45943cad596782e3c3c7fd13c9007b613cc627c702cfac88112","target":"graph","created_at":"2026-07-05T06:57:59Z","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/2310.04154/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we study some subgroups and their decompositions in semi-direct product of the twisted virtual braid group $TVB_n$. In particular, the twisted virtual pure braid group $TVP_n$ is the kernel of an epimorphism of $TVB_n$ onto the symmetric group $S_n$. We find the set of generators and defining relations for $TVP_n$ and show that $TVB_n = TVP_n \\rtimes S_n$. Further we prove that $TVP_n$ is a semi-direct product of some subgroup and abelian group $\\mathbb{Z}_2^n$. As corollary we get that the virtual pure braid group $VP_n$ is a subgroup of $TVP_n$. Also, we construct some other ep","authors_text":"Komal Negi, Madeti Prabhakar, Tatyana A. Kozlovskaya, Valeriy G. Bardakov","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.GR","submitted_at":"2023-10-06T11:00:16Z","title":"Twisted Virtual Braid Group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.04154","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:ac7cf08e199f4890459f7030feaf1ca71fdf86047200a7d9b689a7bee6e2dcb3","target":"record","created_at":"2026-07-05T06:57:59Z","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":"d5a00687c4920252771110dd48a6753b350a11f5db0070d106def0095064c31c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.GR","submitted_at":"2023-10-06T11:00:16Z","title_canon_sha256":"176d451648d895b4ad6ca71b2acabbe56e651f9d88157e1c26c5c62f1764f02e"},"schema_version":"1.0","source":{"id":"2310.04154","kind":"arxiv","version":1}},"canonical_sha256":"da33208304e3772b3e2fc13ff0aa899cc5c4779c207c625c3e50ba579afb3177","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"da33208304e3772b3e2fc13ff0aa899cc5c4779c207c625c3e50ba579afb3177","first_computed_at":"2026-07-05T06:57:59.145359Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:57:59.145359Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LCqUxiQ+TWLuWPvVSivVUgRbmUS//BBbJ9OPBdQTtDNDcHWJkIoha3c9Rc0BlXlwfA290GH//+PX+xafzJK7Dg==","signature_status":"signed_v1","signed_at":"2026-07-05T06:57:59.145809Z","signed_message":"canonical_sha256_bytes"},"source_id":"2310.04154","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ac7cf08e199f4890459f7030feaf1ca71fdf86047200a7d9b689a7bee6e2dcb3","sha256:8828bb641f0ab45943cad596782e3c3c7fd13c9007b613cc627c702cfac88112"],"state_sha256":"c7b26f6470d1c83964d08dae2401dac9cc6eaffb1bad903031595aba9cc6ca4f"}