{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:QDN7K3JIGWET4XPPLSS6FUPB3W","short_pith_number":"pith:QDN7K3JI","canonical_record":{"source":{"id":"1805.00104","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-04-30T21:18:23Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"691eefa35d496441bd9f0cfd51e723e3f28622d071b0978dc1ec276cfe42ad87","abstract_canon_sha256":"19ca6b503b44f27ad8b264cfe64e44366471616b2491463f00a6702c1a8909a6"},"schema_version":"1.0"},"canonical_sha256":"80dbf56d2835893e5def5ca5e2d1e1ddb7be13c409ebffacb7aeedbb680488f6","source":{"kind":"arxiv","id":"1805.00104","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.00104","created_at":"2026-05-18T00:17:10Z"},{"alias_kind":"arxiv_version","alias_value":"1805.00104v1","created_at":"2026-05-18T00:17:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.00104","created_at":"2026-05-18T00:17:10Z"},{"alias_kind":"pith_short_12","alias_value":"QDN7K3JIGWET","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"QDN7K3JIGWET4XPP","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"QDN7K3JI","created_at":"2026-05-18T12:32:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:QDN7K3JIGWET4XPPLSS6FUPB3W","target":"record","payload":{"canonical_record":{"source":{"id":"1805.00104","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-04-30T21:18:23Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"691eefa35d496441bd9f0cfd51e723e3f28622d071b0978dc1ec276cfe42ad87","abstract_canon_sha256":"19ca6b503b44f27ad8b264cfe64e44366471616b2491463f00a6702c1a8909a6"},"schema_version":"1.0"},"canonical_sha256":"80dbf56d2835893e5def5ca5e2d1e1ddb7be13c409ebffacb7aeedbb680488f6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:17:10.549105Z","signature_b64":"+xPnsyNkZImwUrJXa96hGVGlv4jWrNANlKcsvpaLLCi3q5HMVFjh7s8Z0xiFEQjZ5SOUrnZCT4aFhfreVmphAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"80dbf56d2835893e5def5ca5e2d1e1ddb7be13c409ebffacb7aeedbb680488f6","last_reissued_at":"2026-05-18T00:17:10.548446Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:17:10.548446Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.00104","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:17:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tttDyLiT+oied5MX0dNcox915bq00GnGyheW43clz6maiDK8TP+AuLOZPnV9GjGLaK9g8kbmI1ne39cW5TdPCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T19:05:18.206030Z"},"content_sha256":"58d8e471080700cbeb6df9df64790dd4bccd5464d1ff436c9423ca589e2f874f","schema_version":"1.0","event_id":"sha256:58d8e471080700cbeb6df9df64790dd4bccd5464d1ff436c9423ca589e2f874f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:QDN7K3JIGWET4XPPLSS6FUPB3W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Niebrzydowski Algebras and Trivalent Spatial Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.GT","authors_text":"Paige Graves, Sam Nelson, Sherilyn Tamagawa","submitted_at":"2018-04-30T21:18:23Z","abstract_excerpt":"We introduce \\textit{Niebrzydowski algebras}, algebraic structures with a ternary operation and a partially defined multiplication, with axioms motivated by the Reidemeister moves for $Y$-oriented trivalent spatial graphs and handlebody-links. As part of this definition, we identify generating sets of $Y$-oriented Reidemeister moves. We give some examples to demonstrate that the counting invariant can distinguish some $Y$-oriented trivalent spatial graphs and handlebody-links."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.00104","kind":"arxiv","version":1},"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":"2026-05-18T00:17:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FhC4QAXAOjpKRrcxN+wz0MQnmHPrJAhwkALwmgSLp4UThhakNb4Y0XiZHIp/gSFgY3ltUeywL2hvsYf9g5wpAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T19:05:18.206390Z"},"content_sha256":"1e3d0d54112503f770b18aee2c91100e86efcac4a0faa5f5b1ebd0c62a92e5ed","schema_version":"1.0","event_id":"sha256:1e3d0d54112503f770b18aee2c91100e86efcac4a0faa5f5b1ebd0c62a92e5ed"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QDN7K3JIGWET4XPPLSS6FUPB3W/bundle.json","state_url":"https://pith.science/pith/QDN7K3JIGWET4XPPLSS6FUPB3W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QDN7K3JIGWET4XPPLSS6FUPB3W/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":"2026-06-20T19:05:18Z","links":{"resolver":"https://pith.science/pith/QDN7K3JIGWET4XPPLSS6FUPB3W","bundle":"https://pith.science/pith/QDN7K3JIGWET4XPPLSS6FUPB3W/bundle.json","state":"https://pith.science/pith/QDN7K3JIGWET4XPPLSS6FUPB3W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QDN7K3JIGWET4XPPLSS6FUPB3W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:QDN7K3JIGWET4XPPLSS6FUPB3W","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":"19ca6b503b44f27ad8b264cfe64e44366471616b2491463f00a6702c1a8909a6","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-04-30T21:18:23Z","title_canon_sha256":"691eefa35d496441bd9f0cfd51e723e3f28622d071b0978dc1ec276cfe42ad87"},"schema_version":"1.0","source":{"id":"1805.00104","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.00104","created_at":"2026-05-18T00:17:10Z"},{"alias_kind":"arxiv_version","alias_value":"1805.00104v1","created_at":"2026-05-18T00:17:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.00104","created_at":"2026-05-18T00:17:10Z"},{"alias_kind":"pith_short_12","alias_value":"QDN7K3JIGWET","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"QDN7K3JIGWET4XPP","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"QDN7K3JI","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:1e3d0d54112503f770b18aee2c91100e86efcac4a0faa5f5b1ebd0c62a92e5ed","target":"graph","created_at":"2026-05-18T00:17:10Z","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":"We introduce \\textit{Niebrzydowski algebras}, algebraic structures with a ternary operation and a partially defined multiplication, with axioms motivated by the Reidemeister moves for $Y$-oriented trivalent spatial graphs and handlebody-links. As part of this definition, we identify generating sets of $Y$-oriented Reidemeister moves. We give some examples to demonstrate that the counting invariant can distinguish some $Y$-oriented trivalent spatial graphs and handlebody-links.","authors_text":"Paige Graves, Sam Nelson, Sherilyn Tamagawa","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-04-30T21:18:23Z","title":"Niebrzydowski Algebras and Trivalent Spatial Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.00104","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":"sha256:58d8e471080700cbeb6df9df64790dd4bccd5464d1ff436c9423ca589e2f874f","target":"record","created_at":"2026-05-18T00:17:10Z","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":"19ca6b503b44f27ad8b264cfe64e44366471616b2491463f00a6702c1a8909a6","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-04-30T21:18:23Z","title_canon_sha256":"691eefa35d496441bd9f0cfd51e723e3f28622d071b0978dc1ec276cfe42ad87"},"schema_version":"1.0","source":{"id":"1805.00104","kind":"arxiv","version":1}},"canonical_sha256":"80dbf56d2835893e5def5ca5e2d1e1ddb7be13c409ebffacb7aeedbb680488f6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"80dbf56d2835893e5def5ca5e2d1e1ddb7be13c409ebffacb7aeedbb680488f6","first_computed_at":"2026-05-18T00:17:10.548446Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:10.548446Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+xPnsyNkZImwUrJXa96hGVGlv4jWrNANlKcsvpaLLCi3q5HMVFjh7s8Z0xiFEQjZ5SOUrnZCT4aFhfreVmphAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:10.549105Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.00104","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:58d8e471080700cbeb6df9df64790dd4bccd5464d1ff436c9423ca589e2f874f","sha256:1e3d0d54112503f770b18aee2c91100e86efcac4a0faa5f5b1ebd0c62a92e5ed"],"state_sha256":"4960720ffea35e7bd3ff6895a41a05f522173497542085875fc83e7c40aaa03e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+yIZCXax2ysxlqk6C6PiY06Er5D+dHWY+jTcyG+t7TuRE3oVd2IWpbSywO5M9IXAnGRiePDBjK7Ahe1WfjEZBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T19:05:18.208356Z","bundle_sha256":"dbb33213daab1af85f0ab584ea1eb985acda487febc338fb6cc4398f3d59f23e"}}