{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:JN3HJ2NGSLJY6BGMU6VX2TQAP7","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":"b59189a83d0c8e8145fab39df2ea3e3ad6e1cb3efae45502d21829dcfd17620e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-07-07T16:13:07Z","title_canon_sha256":"f16af242780d64e9d94b0abe49337a6d0d4244bea8f631981ca953719ab7bbe8"},"schema_version":"1.0","source":{"id":"1707.02250","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.02250","created_at":"2026-05-18T00:36:38Z"},{"alias_kind":"arxiv_version","alias_value":"1707.02250v2","created_at":"2026-05-18T00:36:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.02250","created_at":"2026-05-18T00:36:38Z"},{"alias_kind":"pith_short_12","alias_value":"JN3HJ2NGSLJY","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"JN3HJ2NGSLJY6BGM","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"JN3HJ2NG","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:f424b5c0b3c3b1692ce842676206077555263572ed5cdef51f60461d7a51543b","target":"graph","created_at":"2026-05-18T00:36:38Z","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":"For a given $(X,S,\\beta)$, where $S,\\beta\\colon X\\times X\\to X\\times X$ are set theoretical solutions of Yang-Baxter equation with a compatibility condition, we define an invariant for virtual (or classical) knots/links using non commutative 2-cocycles pairs $(f,g)$ that generalizes the one defined in [FG2]. We also define, a group $U_{nc}^{fg}=U_{nc}^{fg}(X,S,\\beta)$ and functions $\\pi_f, \\pi_g\\colon X\\times X\\to U_{nc}^{fg}(X)$ governing all 2-cocycles in $X$. We exhibit examples of computations achieved using GAP.","authors_text":"Juliana Garc\\'ia Galofre, Marco Farinati","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-07-07T16:13:07Z","title":"Virtual link and knot invariants from non-abelian Yang-Baxter 2-cocycle pairs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.02250","kind":"arxiv","version":2},"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":"sha256:5f18fe3ff686cf68398db708e40c054c475c676910ffafe6e848ba77ec5614bb","target":"record","created_at":"2026-05-18T00:36:38Z","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":"b59189a83d0c8e8145fab39df2ea3e3ad6e1cb3efae45502d21829dcfd17620e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-07-07T16:13:07Z","title_canon_sha256":"f16af242780d64e9d94b0abe49337a6d0d4244bea8f631981ca953719ab7bbe8"},"schema_version":"1.0","source":{"id":"1707.02250","kind":"arxiv","version":2}},"canonical_sha256":"4b7674e9a692d38f04cca7ab7d4e007ff39cefb2c7b863b51f9a334e24fa81f6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b7674e9a692d38f04cca7ab7d4e007ff39cefb2c7b863b51f9a334e24fa81f6","first_computed_at":"2026-05-18T00:36:38.285868Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:38.285868Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EEpz+O1L4opqZMZAQRmebBKVceQcuqW2NZMG/RmBQknnk19J1bIMXYKXx5aYWsPUREhMlv/Oo6JzLDQPzllOCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:38.286525Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.02250","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5f18fe3ff686cf68398db708e40c054c475c676910ffafe6e848ba77ec5614bb","sha256:f424b5c0b3c3b1692ce842676206077555263572ed5cdef51f60461d7a51543b"],"state_sha256":"3df6b29b018984f8b951774e3dcd976fae35ca3d02692213d3287cd9477a9a67"}