{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:5LZ4SSOVF5AMTO62HLLVJIWDIR","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":"6c49040f803290ce8afbb3c4bfb89e4679accb2005e9d29037c8ded0f30b9ac3","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-08-22T10:45:24Z","title_canon_sha256":"591f965c04d0cc308420b4f630a4b1e4b1f6edf7424d87d1de568e6d1b624ac1"},"schema_version":"1.0","source":{"id":"1908.08301","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.08301","created_at":"2026-07-04T23:59:11Z"},{"alias_kind":"arxiv_version","alias_value":"1908.08301v1","created_at":"2026-07-04T23:59:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.08301","created_at":"2026-07-04T23:59:11Z"},{"alias_kind":"pith_short_12","alias_value":"5LZ4SSOVF5AM","created_at":"2026-07-04T23:59:11Z"},{"alias_kind":"pith_short_16","alias_value":"5LZ4SSOVF5AMTO62","created_at":"2026-07-04T23:59:11Z"},{"alias_kind":"pith_short_8","alias_value":"5LZ4SSOV","created_at":"2026-07-04T23:59:11Z"}],"graph_snapshots":[{"event_id":"sha256:5270ba4039412e7ff7097a60ec9f5c174819086188d54b969d957a7d769dbfb1","target":"graph","created_at":"2026-07-04T23:59:11Z","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/1908.08301/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Biquandles are algebraic objects with two binary operations whose axioms encode the generalized Reidemeister moves for virtual knots and links. These objects also provide set-theoretic solutions of the well-known Yang-Baxter equation. The first half of this paper proposes some natural constructions of biquandles from groups and from their simpler counterparts, namely, quandles. We completely determine all words in the free group on two generators that give rise to (bi)quandle structures on all groups. We give some novel constructions of biquandles on unions and products of quandles, including ","authors_text":"Mahender Singh, Timur Nasybullov, Valeriy Bardakov","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-08-22T10:45:24Z","title":"General constructions of biquandles and their symmetries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.08301","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:f89a630d4bc2af7287e195aa7f3599d343e548af380ff52614fd90a034b5531f","target":"record","created_at":"2026-07-04T23:59:11Z","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":"6c49040f803290ce8afbb3c4bfb89e4679accb2005e9d29037c8ded0f30b9ac3","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-08-22T10:45:24Z","title_canon_sha256":"591f965c04d0cc308420b4f630a4b1e4b1f6edf7424d87d1de568e6d1b624ac1"},"schema_version":"1.0","source":{"id":"1908.08301","kind":"arxiv","version":1}},"canonical_sha256":"eaf3c949d52f40c9bbda3ad754a2c3444da86921d808413b91d0e8d0215fc496","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eaf3c949d52f40c9bbda3ad754a2c3444da86921d808413b91d0e8d0215fc496","first_computed_at":"2026-07-04T23:59:11.599344Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:59:11.599344Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XDku6Iwfz3UyT7BpqyZEAZliP++ik0JI3qdtHucZEB2umG9dZS/szZBC6CbZZmdduNsbFGLgc/B+hDq5azHxDQ==","signature_status":"signed_v1","signed_at":"2026-07-04T23:59:11.599732Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.08301","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f89a630d4bc2af7287e195aa7f3599d343e548af380ff52614fd90a034b5531f","sha256:5270ba4039412e7ff7097a60ec9f5c174819086188d54b969d957a7d769dbfb1"],"state_sha256":"ebae5505fd7b75032e322cf9c2d033f4d16569b6e8c775794280c36c0376e2e6"}