{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:S74RBVJS6XW6KSAZ74PZF3WR5Z","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":"f3c44e200fce3a275ad536fbd7026357a42bcc3f0f165f3bfea09c75afcd6905","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-02-26T20:33:01Z","title_canon_sha256":"cff2e95cda742099c0ac05eb74222f468d43e9740fa7f53da0e1d9ba0a2e7e2a"},"schema_version":"1.0","source":{"id":"1402.6673","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.6673","created_at":"2026-05-18T02:57:43Z"},{"alias_kind":"arxiv_version","alias_value":"1402.6673v1","created_at":"2026-05-18T02:57:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.6673","created_at":"2026-05-18T02:57:43Z"},{"alias_kind":"pith_short_12","alias_value":"S74RBVJS6XW6","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"S74RBVJS6XW6KSAZ","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"S74RBVJS","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:f367c1ed78aab20c660d3e624a0fcd6da3ce1db6ebc7c7fdb75855721856e05c","target":"graph","created_at":"2026-05-18T02:57:43Z","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":"This paper is devoted to qualgebras and squandles, which are quandles enriched with a compatible binary/unary operation. Algebraically, they are modeled after groups with conjugation and multiplication/squaring operations. Topologically, qualgebras emerge as an algebraic counterpart of knotted 3-valent graphs, just like quandles can be seen as an \"algebraization\" of knots; squandles in turn simplify the qualgebra algebraization of graphs. Knotted 3-valent graph invariants are constructed by counting qualgebra/squandle colorings of graph diagrams, and are further enhanced using qualgebra/squand","authors_text":"Victoria Lebed (OCAMI)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-02-26T20:33:01Z","title":"Qualgebras and knotted 3-valent graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.6673","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:d8758d83828054421709ef30d1bc3dad1b0abcd7f192ff0cd147cccfecd6e229","target":"record","created_at":"2026-05-18T02:57:43Z","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":"f3c44e200fce3a275ad536fbd7026357a42bcc3f0f165f3bfea09c75afcd6905","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-02-26T20:33:01Z","title_canon_sha256":"cff2e95cda742099c0ac05eb74222f468d43e9740fa7f53da0e1d9ba0a2e7e2a"},"schema_version":"1.0","source":{"id":"1402.6673","kind":"arxiv","version":1}},"canonical_sha256":"97f910d532f5ede54819ff1f92eed1ee6a3123798f004a5cebf856580aa9a2df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"97f910d532f5ede54819ff1f92eed1ee6a3123798f004a5cebf856580aa9a2df","first_computed_at":"2026-05-18T02:57:43.885287Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:43.885287Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5VpcKFwRqMroDWpWBuiaspXiQ3SjDXHNsZG6k6MQOwkUR98imtffgUVhUXSZFdwSJADXZnBIjt5pFut0c5IGDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:43.885734Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.6673","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d8758d83828054421709ef30d1bc3dad1b0abcd7f192ff0cd147cccfecd6e229","sha256:f367c1ed78aab20c660d3e624a0fcd6da3ce1db6ebc7c7fdb75855721856e05c"],"state_sha256":"2a9e6d44a04fba19b82fe365ed50043ba460980d58c3af1ce0a6069508e4a655"}