{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:EF4ZVUNPKLTQRPEC4WWGVX2AFT","short_pith_number":"pith:EF4ZVUNP","canonical_record":{"source":{"id":"1806.06435","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-06-17T19:41:43Z","cross_cats_sorted":[],"title_canon_sha256":"21753e0944371784bd05673fdd4f0bcc4e11eda9292a86fb96e39b014c05d275","abstract_canon_sha256":"ffa770cd849a0a525450ddecaaf33d32d7fe79aa6720897a1d3b024fa3fc3dd3"},"schema_version":"1.0"},"canonical_sha256":"21799ad1af52e708bc82e5ac6adf402cfb0910b53a64f0bc7e926cb8d86e4f1e","source":{"kind":"arxiv","id":"1806.06435","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.06435","created_at":"2026-05-17T23:44:32Z"},{"alias_kind":"arxiv_version","alias_value":"1806.06435v2","created_at":"2026-05-17T23:44:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.06435","created_at":"2026-05-17T23:44:32Z"},{"alias_kind":"pith_short_12","alias_value":"EF4ZVUNPKLTQ","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EF4ZVUNPKLTQRPEC","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EF4ZVUNP","created_at":"2026-05-18T12:32:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:EF4ZVUNPKLTQRPEC4WWGVX2AFT","target":"record","payload":{"canonical_record":{"source":{"id":"1806.06435","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-06-17T19:41:43Z","cross_cats_sorted":[],"title_canon_sha256":"21753e0944371784bd05673fdd4f0bcc4e11eda9292a86fb96e39b014c05d275","abstract_canon_sha256":"ffa770cd849a0a525450ddecaaf33d32d7fe79aa6720897a1d3b024fa3fc3dd3"},"schema_version":"1.0"},"canonical_sha256":"21799ad1af52e708bc82e5ac6adf402cfb0910b53a64f0bc7e926cb8d86e4f1e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:32.432092Z","signature_b64":"/D5xO6zFQaS2tqKtR4trMgMejfOqH/dXXSFsWEb8tXv61PEoC+460vOakWFvaVwQtpHO8L1P5dp/hIm51rGhCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"21799ad1af52e708bc82e5ac6adf402cfb0910b53a64f0bc7e926cb8d86e4f1e","last_reissued_at":"2026-05-17T23:44:32.431411Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:32.431411Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.06435","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:44:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TkcAbVpjHlnbAwST6kxOID2qSUzP6iykL0QP1DNlMDKn5t8NxjHm7ocqFgFH6JlWYD6vbu3Y0FLFQVMD5995Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T18:25:05.466693Z"},"content_sha256":"b88fb36c7b95fc8a070f3d4761c6a8207fcce03a944d1365b74066c4872d06fe","schema_version":"1.0","event_id":"sha256:b88fb36c7b95fc8a070f3d4761c6a8207fcce03a944d1365b74066c4872d06fe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:EF4ZVUNPKLTQRPEC4WWGVX2AFT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Invariants for trivalent tangles and handlebody-tangles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Carmen Caprau","submitted_at":"2018-06-17T19:41:43Z","abstract_excerpt":"An enhanced trivalent tangle is a trivalent tangle with some of its edges labeled. We use enhanced trivalent tangles and classical knot theory to provide a recipe for constructing invariants for trivalent tangles, and in particular, for knotted trivalent graphs. Our method also yields invariants of, what we refer to as, enhanced handlebody-tangles and enhanced handlebody-links."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.06435","kind":"arxiv","version":2},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:44:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nPY1O/j8KIB58VZS/Ctmgii23sUJBJaDdpMbhJ1o2BJwy5arOUA6EgWq7CevetNbYLSnjQXw4HTL75LZvj1NDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T18:25:05.467042Z"},"content_sha256":"e0ebc46779d70f463938687bd8a201382b74f9b274f83f6a42c12d31c647bde7","schema_version":"1.0","event_id":"sha256:e0ebc46779d70f463938687bd8a201382b74f9b274f83f6a42c12d31c647bde7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EF4ZVUNPKLTQRPEC4WWGVX2AFT/bundle.json","state_url":"https://pith.science/pith/EF4ZVUNPKLTQRPEC4WWGVX2AFT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EF4ZVUNPKLTQRPEC4WWGVX2AFT/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-24T18:25:05Z","links":{"resolver":"https://pith.science/pith/EF4ZVUNPKLTQRPEC4WWGVX2AFT","bundle":"https://pith.science/pith/EF4ZVUNPKLTQRPEC4WWGVX2AFT/bundle.json","state":"https://pith.science/pith/EF4ZVUNPKLTQRPEC4WWGVX2AFT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EF4ZVUNPKLTQRPEC4WWGVX2AFT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:EF4ZVUNPKLTQRPEC4WWGVX2AFT","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":"ffa770cd849a0a525450ddecaaf33d32d7fe79aa6720897a1d3b024fa3fc3dd3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-06-17T19:41:43Z","title_canon_sha256":"21753e0944371784bd05673fdd4f0bcc4e11eda9292a86fb96e39b014c05d275"},"schema_version":"1.0","source":{"id":"1806.06435","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.06435","created_at":"2026-05-17T23:44:32Z"},{"alias_kind":"arxiv_version","alias_value":"1806.06435v2","created_at":"2026-05-17T23:44:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.06435","created_at":"2026-05-17T23:44:32Z"},{"alias_kind":"pith_short_12","alias_value":"EF4ZVUNPKLTQ","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EF4ZVUNPKLTQRPEC","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EF4ZVUNP","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:e0ebc46779d70f463938687bd8a201382b74f9b274f83f6a42c12d31c647bde7","target":"graph","created_at":"2026-05-17T23:44:32Z","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":"An enhanced trivalent tangle is a trivalent tangle with some of its edges labeled. We use enhanced trivalent tangles and classical knot theory to provide a recipe for constructing invariants for trivalent tangles, and in particular, for knotted trivalent graphs. Our method also yields invariants of, what we refer to as, enhanced handlebody-tangles and enhanced handlebody-links.","authors_text":"Carmen Caprau","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-06-17T19:41:43Z","title":"Invariants for trivalent tangles and handlebody-tangles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.06435","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:b88fb36c7b95fc8a070f3d4761c6a8207fcce03a944d1365b74066c4872d06fe","target":"record","created_at":"2026-05-17T23:44:32Z","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":"ffa770cd849a0a525450ddecaaf33d32d7fe79aa6720897a1d3b024fa3fc3dd3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-06-17T19:41:43Z","title_canon_sha256":"21753e0944371784bd05673fdd4f0bcc4e11eda9292a86fb96e39b014c05d275"},"schema_version":"1.0","source":{"id":"1806.06435","kind":"arxiv","version":2}},"canonical_sha256":"21799ad1af52e708bc82e5ac6adf402cfb0910b53a64f0bc7e926cb8d86e4f1e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"21799ad1af52e708bc82e5ac6adf402cfb0910b53a64f0bc7e926cb8d86e4f1e","first_computed_at":"2026-05-17T23:44:32.431411Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:32.431411Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/D5xO6zFQaS2tqKtR4trMgMejfOqH/dXXSFsWEb8tXv61PEoC+460vOakWFvaVwQtpHO8L1P5dp/hIm51rGhCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:32.432092Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.06435","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b88fb36c7b95fc8a070f3d4761c6a8207fcce03a944d1365b74066c4872d06fe","sha256:e0ebc46779d70f463938687bd8a201382b74f9b274f83f6a42c12d31c647bde7"],"state_sha256":"f5292c346586cbcfcda2983fb73e04299ab0169ed353705686c75c5d6309867d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lWYjeJ5ZHTEXi0bV5eUQiYbvDXFI3WPwgSKr+oCCBXGxOdzfP+RGH6AMmHDgt1I+DGQUgRpRkGwCkdpBBRjOAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T18:25:05.468910Z","bundle_sha256":"11013eb6aec1aa91b0984ce301b6e3a81dce09436f32f43106a5cefc95a0a379"}}