{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:YIJ5EP6LIQR6J4UMTEH2JQAPJE","short_pith_number":"pith:YIJ5EP6L","canonical_record":{"source":{"id":"2207.02330","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2022-07-05T21:49:14Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"fec5f7d58c6b4f662f0a2a9d7bb403e0a76ad8b577340214dbf70a9ce39dd930","abstract_canon_sha256":"d3492edf274754e482fc585be067e3be2f842bb86865191d8bc9a2e012c4425d"},"schema_version":"1.0"},"canonical_sha256":"c213d23fcb4423e4f28c990fa4c00f49175b1a3c4cb1318cf9909f8163e975e4","source":{"kind":"arxiv","id":"2207.02330","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2207.02330","created_at":"2026-07-05T04:38:16Z"},{"alias_kind":"arxiv_version","alias_value":"2207.02330v2","created_at":"2026-07-05T04:38:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2207.02330","created_at":"2026-07-05T04:38:16Z"},{"alias_kind":"pith_short_12","alias_value":"YIJ5EP6LIQR6","created_at":"2026-07-05T04:38:16Z"},{"alias_kind":"pith_short_16","alias_value":"YIJ5EP6LIQR6J4UM","created_at":"2026-07-05T04:38:16Z"},{"alias_kind":"pith_short_8","alias_value":"YIJ5EP6L","created_at":"2026-07-05T04:38:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:YIJ5EP6LIQR6J4UMTEH2JQAPJE","target":"record","payload":{"canonical_record":{"source":{"id":"2207.02330","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2022-07-05T21:49:14Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"fec5f7d58c6b4f662f0a2a9d7bb403e0a76ad8b577340214dbf70a9ce39dd930","abstract_canon_sha256":"d3492edf274754e482fc585be067e3be2f842bb86865191d8bc9a2e012c4425d"},"schema_version":"1.0"},"canonical_sha256":"c213d23fcb4423e4f28c990fa4c00f49175b1a3c4cb1318cf9909f8163e975e4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:38:16.357053Z","signature_b64":"/NBAKPB//QrY5gPoBtx/+l5elGf7C08JJpXmCpHTaE7IieiZqOlu5LoU0JsfGKSB3L/RNARmStMS/7GhkKOKCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c213d23fcb4423e4f28c990fa4c00f49175b1a3c4cb1318cf9909f8163e975e4","last_reissued_at":"2026-07-05T04:38:16.356484Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:38:16.356484Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2207.02330","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":"2026-07-05T04:38:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6VdWk8sFhBiU0kSbmCDQmJcTx+joDqrXWYsuFKOx8ixxwx6/wzdlgiD7RXcy9vyi/2N1oetw7KS0YvhLx0RUCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T23:39:22.309849Z"},"content_sha256":"348819920405619518a34cde86808cc2b0624f08015e97bd6eb1da48344a0da9","schema_version":"1.0","event_id":"sha256:348819920405619518a34cde86808cc2b0624f08015e97bd6eb1da48344a0da9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:YIJ5EP6LIQR6J4UMTEH2JQAPJE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The shadow quandle cocycle invariant of knotoids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GT","authors_text":"Nicholas Cazet","submitted_at":"2022-07-05T21:49:14Z","abstract_excerpt":"This paper studies the chirality of knotoids using shadow quandle colorings and the shadow quandle cocycle invariant. The shadow coloring number and the shadow quandle cocycle invariant is shown to distinguish infinitely many knotoids from their mirrors. Specifically, the knot-type knotoid $3_1$ is shown to be chiral. The weight of a quandle 3-cocycle is used to calculate the crossing numbers of infinitely many multi-linkoids."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.02330","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2207.02330/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T04:38:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KM0bjdM/+bE8ovYwKR9zmT9vBA/VY+6ljj5hQN6zpGkhG5oDRsesQp1IXsF9l/STzpbOpvqQWfaw40eyhSBbDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T23:39:22.310715Z"},"content_sha256":"bd4782a5d85adde6f1f51fe2eec3551199166c2252a2b21e7eb6e919f576daa0","schema_version":"1.0","event_id":"sha256:bd4782a5d85adde6f1f51fe2eec3551199166c2252a2b21e7eb6e919f576daa0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YIJ5EP6LIQR6J4UMTEH2JQAPJE/bundle.json","state_url":"https://pith.science/pith/YIJ5EP6LIQR6J4UMTEH2JQAPJE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YIJ5EP6LIQR6J4UMTEH2JQAPJE/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":"2026-08-14T23:39:22Z","links":{"resolver":"https://pith.science/pith/YIJ5EP6LIQR6J4UMTEH2JQAPJE","bundle":"https://pith.science/pith/YIJ5EP6LIQR6J4UMTEH2JQAPJE/bundle.json","state":"https://pith.science/pith/YIJ5EP6LIQR6J4UMTEH2JQAPJE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YIJ5EP6LIQR6J4UMTEH2JQAPJE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:YIJ5EP6LIQR6J4UMTEH2JQAPJE","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":"d3492edf274754e482fc585be067e3be2f842bb86865191d8bc9a2e012c4425d","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2022-07-05T21:49:14Z","title_canon_sha256":"fec5f7d58c6b4f662f0a2a9d7bb403e0a76ad8b577340214dbf70a9ce39dd930"},"schema_version":"1.0","source":{"id":"2207.02330","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2207.02330","created_at":"2026-07-05T04:38:16Z"},{"alias_kind":"arxiv_version","alias_value":"2207.02330v2","created_at":"2026-07-05T04:38:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2207.02330","created_at":"2026-07-05T04:38:16Z"},{"alias_kind":"pith_short_12","alias_value":"YIJ5EP6LIQR6","created_at":"2026-07-05T04:38:16Z"},{"alias_kind":"pith_short_16","alias_value":"YIJ5EP6LIQR6J4UM","created_at":"2026-07-05T04:38:16Z"},{"alias_kind":"pith_short_8","alias_value":"YIJ5EP6L","created_at":"2026-07-05T04:38:16Z"}],"graph_snapshots":[{"event_id":"sha256:bd4782a5d85adde6f1f51fe2eec3551199166c2252a2b21e7eb6e919f576daa0","target":"graph","created_at":"2026-07-05T04:38:16Z","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/2207.02330/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper studies the chirality of knotoids using shadow quandle colorings and the shadow quandle cocycle invariant. The shadow coloring number and the shadow quandle cocycle invariant is shown to distinguish infinitely many knotoids from their mirrors. Specifically, the knot-type knotoid $3_1$ is shown to be chiral. The weight of a quandle 3-cocycle is used to calculate the crossing numbers of infinitely many multi-linkoids.","authors_text":"Nicholas Cazet","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2022-07-05T21:49:14Z","title":"The shadow quandle cocycle invariant of knotoids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.02330","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":"sha256:348819920405619518a34cde86808cc2b0624f08015e97bd6eb1da48344a0da9","target":"record","created_at":"2026-07-05T04:38:16Z","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":"d3492edf274754e482fc585be067e3be2f842bb86865191d8bc9a2e012c4425d","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2022-07-05T21:49:14Z","title_canon_sha256":"fec5f7d58c6b4f662f0a2a9d7bb403e0a76ad8b577340214dbf70a9ce39dd930"},"schema_version":"1.0","source":{"id":"2207.02330","kind":"arxiv","version":2}},"canonical_sha256":"c213d23fcb4423e4f28c990fa4c00f49175b1a3c4cb1318cf9909f8163e975e4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c213d23fcb4423e4f28c990fa4c00f49175b1a3c4cb1318cf9909f8163e975e4","first_computed_at":"2026-07-05T04:38:16.356484Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:38:16.356484Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/NBAKPB//QrY5gPoBtx/+l5elGf7C08JJpXmCpHTaE7IieiZqOlu5LoU0JsfGKSB3L/RNARmStMS/7GhkKOKCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:38:16.357053Z","signed_message":"canonical_sha256_bytes"},"source_id":"2207.02330","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:348819920405619518a34cde86808cc2b0624f08015e97bd6eb1da48344a0da9","sha256:bd4782a5d85adde6f1f51fe2eec3551199166c2252a2b21e7eb6e919f576daa0"],"state_sha256":"92e2621cf3edb24e6946513618242748026c6fc21045a76d98ae5cad9fa9ff9b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"br3Jqub8DM4XzjQxBcF3vEsdBhbIsOSRcBSCzZU/NKl9DKMobZHP0gx8N88Gn2JlsXPPs+HCfACHp/pdzOdjCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T23:39:22.316057Z","bundle_sha256":"764b244df55118535114d03281fbfadedd059b18de59628043a4b1435c73b0d1"}}