{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:T4CX2DGEO2Z7KW5HVKKSYDEXHZ","short_pith_number":"pith:T4CX2DGE","schema_version":"1.0","canonical_sha256":"9f057d0cc476b3f55ba7aa952c0c973e67542816ae55fb6219e5b29886d1c398","source":{"kind":"arxiv","id":"2606.06095","version":1},"attestation_state":"computed","paper":{"title":"Forbidden relations in universal virtual braid groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Charalampos Stylianakis, Oscar Ocampo","submitted_at":"2026-06-04T12:32:53Z","abstract_excerpt":"We study natural automorphisms of the universal virtual braid group $UV_n(k)$. These automorphisms induce commuting involutions in the outer automorphism group and generate a subgroup isomorphic to $\\mathbb{Z}_2^k\\times\\mathbb{Z}_2$. We then show that the two one-forbidden quotients of $UV_n(k)$ are isomorphic. Furthermore, we introduce the universal unrestricted virtual braid group $UUV_n(k)$ obtained by imposing simultaneously the two forbidden relations, and derive several structural properties inherited from the universal setting. Since the multi-virtual braid group $M_kVB_n$ is a quotient"},"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":"2606.06095","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2026-06-04T12:32:53Z","cross_cats_sorted":[],"title_canon_sha256":"0d604325fb95b7694d1526ea29a5ef7a5675b149662d20c32a40ccf9241016bd","abstract_canon_sha256":"b835ab51228bef83d9f63428cee64243ad662325ccc8d611a3180a8dd5ad9c77"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-05T01:15:33.133119Z","signature_b64":"tKOuIF58d/v7H+boI3cUWOxLQEeLgLJjPHCyEhWE9jWwtn8/lyJbjMGkqf526zVqAn/VcndAtSJ81tsiPP3xAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f057d0cc476b3f55ba7aa952c0c973e67542816ae55fb6219e5b29886d1c398","last_reissued_at":"2026-06-05T01:15:33.132537Z","signature_status":"signed_v1","first_computed_at":"2026-06-05T01:15:33.132537Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Forbidden relations in universal virtual braid groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Charalampos Stylianakis, Oscar Ocampo","submitted_at":"2026-06-04T12:32:53Z","abstract_excerpt":"We study natural automorphisms of the universal virtual braid group $UV_n(k)$. These automorphisms induce commuting involutions in the outer automorphism group and generate a subgroup isomorphic to $\\mathbb{Z}_2^k\\times\\mathbb{Z}_2$. We then show that the two one-forbidden quotients of $UV_n(k)$ are isomorphic. Furthermore, we introduce the universal unrestricted virtual braid group $UUV_n(k)$ obtained by imposing simultaneously the two forbidden relations, and derive several structural properties inherited from the universal setting. Since the multi-virtual braid group $M_kVB_n$ is a quotient"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.06095","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.06095/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2606.06095","created_at":"2026-06-05T01:15:33.132641+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.06095v1","created_at":"2026-06-05T01:15:33.132641+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.06095","created_at":"2026-06-05T01:15:33.132641+00:00"},{"alias_kind":"pith_short_12","alias_value":"T4CX2DGEO2Z7","created_at":"2026-06-05T01:15:33.132641+00:00"},{"alias_kind":"pith_short_16","alias_value":"T4CX2DGEO2Z7KW5H","created_at":"2026-06-05T01:15:33.132641+00:00"},{"alias_kind":"pith_short_8","alias_value":"T4CX2DGE","created_at":"2026-06-05T01:15:33.132641+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/T4CX2DGEO2Z7KW5HVKKSYDEXHZ","json":"https://pith.science/pith/T4CX2DGEO2Z7KW5HVKKSYDEXHZ.json","graph_json":"https://pith.science/api/pith-number/T4CX2DGEO2Z7KW5HVKKSYDEXHZ/graph.json","events_json":"https://pith.science/api/pith-number/T4CX2DGEO2Z7KW5HVKKSYDEXHZ/events.json","paper":"https://pith.science/paper/T4CX2DGE"},"agent_actions":{"view_html":"https://pith.science/pith/T4CX2DGEO2Z7KW5HVKKSYDEXHZ","download_json":"https://pith.science/pith/T4CX2DGEO2Z7KW5HVKKSYDEXHZ.json","view_paper":"https://pith.science/paper/T4CX2DGE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.06095&json=true","fetch_graph":"https://pith.science/api/pith-number/T4CX2DGEO2Z7KW5HVKKSYDEXHZ/graph.json","fetch_events":"https://pith.science/api/pith-number/T4CX2DGEO2Z7KW5HVKKSYDEXHZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/T4CX2DGEO2Z7KW5HVKKSYDEXHZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/T4CX2DGEO2Z7KW5HVKKSYDEXHZ/action/storage_attestation","attest_author":"https://pith.science/pith/T4CX2DGEO2Z7KW5HVKKSYDEXHZ/action/author_attestation","sign_citation":"https://pith.science/pith/T4CX2DGEO2Z7KW5HVKKSYDEXHZ/action/citation_signature","submit_replication":"https://pith.science/pith/T4CX2DGEO2Z7KW5HVKKSYDEXHZ/action/replication_record"}},"created_at":"2026-06-05T01:15:33.132641+00:00","updated_at":"2026-06-05T01:15:33.132641+00:00"}