{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:CW4BTMFVQMUD4CTHXHSFSETBSQ","short_pith_number":"pith:CW4BTMFV","schema_version":"1.0","canonical_sha256":"15b819b0b583283e0a67b9e459126194245f38e892cd6dc19011b43a37ecaa31","source":{"kind":"arxiv","id":"1705.10490","version":4},"attestation_state":"computed","paper":{"title":"Goussarov-Polyak-Viro's $n$-equivalence and the pure virtual braid group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Yuka Kotorii","submitted_at":"2017-05-30T07:41:59Z","abstract_excerpt":"In the context of finite type invariants, Stanford introduced a family of equivalence relations on knots defined by the lower central series of the pure braid groups and characterized the finite type invariants in terms of the structure of the braid groups. It is known that this equivalence and Ohyama's equivalence defined by a local move are equivalent. On the other hand, in the virtual knot theory, the concept of Ohyama's equivalence was extended by Goussarov-Polyak-Viro, which called an $n$-equivalence. In this paper we extend Stanford's equivalence to virtual knots and virtual string links"},"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":"1705.10490","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-05-30T07:41:59Z","cross_cats_sorted":[],"title_canon_sha256":"4662a48e356f357d618a75482f4b1c12e088edd7b66ec77015ef831982fa5dbd","abstract_canon_sha256":"0722fee46e50b91090f319bd0f7934b016c4669ac556c011eac82591aaa17533"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:03.868970Z","signature_b64":"jADtoYVuExfJhg45KVigoKLBCCr68T/LodyEO8ccX7wLIbxLlFoz8noyYTBEdaTuOErKuoN2tSvlmYoAqWWkBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"15b819b0b583283e0a67b9e459126194245f38e892cd6dc19011b43a37ecaa31","last_reissued_at":"2026-05-17T23:47:03.868225Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:03.868225Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Goussarov-Polyak-Viro's $n$-equivalence and the pure virtual braid group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Yuka Kotorii","submitted_at":"2017-05-30T07:41:59Z","abstract_excerpt":"In the context of finite type invariants, Stanford introduced a family of equivalence relations on knots defined by the lower central series of the pure braid groups and characterized the finite type invariants in terms of the structure of the braid groups. It is known that this equivalence and Ohyama's equivalence defined by a local move are equivalent. On the other hand, in the virtual knot theory, the concept of Ohyama's equivalence was extended by Goussarov-Polyak-Viro, which called an $n$-equivalence. In this paper we extend Stanford's equivalence to virtual knots and virtual string links"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.10490","kind":"arxiv","version":4},"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":"1705.10490","created_at":"2026-05-17T23:47:03.868376+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.10490v4","created_at":"2026-05-17T23:47:03.868376+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.10490","created_at":"2026-05-17T23:47:03.868376+00:00"},{"alias_kind":"pith_short_12","alias_value":"CW4BTMFVQMUD","created_at":"2026-05-18T12:31:10.602751+00:00"},{"alias_kind":"pith_short_16","alias_value":"CW4BTMFVQMUD4CTH","created_at":"2026-05-18T12:31:10.602751+00:00"},{"alias_kind":"pith_short_8","alias_value":"CW4BTMFV","created_at":"2026-05-18T12:31:10.602751+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/CW4BTMFVQMUD4CTHXHSFSETBSQ","json":"https://pith.science/pith/CW4BTMFVQMUD4CTHXHSFSETBSQ.json","graph_json":"https://pith.science/api/pith-number/CW4BTMFVQMUD4CTHXHSFSETBSQ/graph.json","events_json":"https://pith.science/api/pith-number/CW4BTMFVQMUD4CTHXHSFSETBSQ/events.json","paper":"https://pith.science/paper/CW4BTMFV"},"agent_actions":{"view_html":"https://pith.science/pith/CW4BTMFVQMUD4CTHXHSFSETBSQ","download_json":"https://pith.science/pith/CW4BTMFVQMUD4CTHXHSFSETBSQ.json","view_paper":"https://pith.science/paper/CW4BTMFV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.10490&json=true","fetch_graph":"https://pith.science/api/pith-number/CW4BTMFVQMUD4CTHXHSFSETBSQ/graph.json","fetch_events":"https://pith.science/api/pith-number/CW4BTMFVQMUD4CTHXHSFSETBSQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CW4BTMFVQMUD4CTHXHSFSETBSQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CW4BTMFVQMUD4CTHXHSFSETBSQ/action/storage_attestation","attest_author":"https://pith.science/pith/CW4BTMFVQMUD4CTHXHSFSETBSQ/action/author_attestation","sign_citation":"https://pith.science/pith/CW4BTMFVQMUD4CTHXHSFSETBSQ/action/citation_signature","submit_replication":"https://pith.science/pith/CW4BTMFVQMUD4CTHXHSFSETBSQ/action/replication_record"}},"created_at":"2026-05-17T23:47:03.868376+00:00","updated_at":"2026-05-17T23:47:03.868376+00:00"}