{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:XMVRRASVQAHTNDIXVIZGHZXWOR","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":"4272ae3537459e7a0998b351d63de313d1a9a4fa7b42a49bdc73c910b9b7b9b6","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2021-04-11T05:19:09Z","title_canon_sha256":"061287f4420d8d72a4c4bd6e8ad98547a5d24c34c0f3dcdbfc4de7b40be896bf"},"schema_version":"1.0","source":{"id":"2104.04921","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2104.04921","created_at":"2026-07-05T03:42:00Z"},{"alias_kind":"arxiv_version","alias_value":"2104.04921v3","created_at":"2026-07-05T03:42:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2104.04921","created_at":"2026-07-05T03:42:00Z"},{"alias_kind":"pith_short_12","alias_value":"XMVRRASVQAHT","created_at":"2026-07-05T03:42:00Z"},{"alias_kind":"pith_short_16","alias_value":"XMVRRASVQAHTNDIX","created_at":"2026-07-05T03:42:00Z"},{"alias_kind":"pith_short_8","alias_value":"XMVRRASV","created_at":"2026-07-05T03:42:00Z"}],"graph_snapshots":[{"event_id":"sha256:fd00b98abb51add46fbd3c7465a4aebffa6c929ae104932ce474a828ea223e48","target":"graph","created_at":"2026-07-05T03:42:00Z","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/2104.04921/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper aims to give a one-to-one correspondence between $SU(2)$-representations of knot groups and colorings of knots with spherical quandles and give a geometric meaning of the \"trace-free\" condition we need to define Casson-Lin invariant.","authors_text":"Kentaro Yonemura","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2021-04-11T05:19:09Z","title":"Note on spherical quandles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.04921","kind":"arxiv","version":3},"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":"sha256:8d8f186d2116888347cdff5ea467a837d23e3921d4e23a21caaa56e8958ae843","target":"record","created_at":"2026-07-05T03:42:00Z","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":"4272ae3537459e7a0998b351d63de313d1a9a4fa7b42a49bdc73c910b9b7b9b6","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2021-04-11T05:19:09Z","title_canon_sha256":"061287f4420d8d72a4c4bd6e8ad98547a5d24c34c0f3dcdbfc4de7b40be896bf"},"schema_version":"1.0","source":{"id":"2104.04921","kind":"arxiv","version":3}},"canonical_sha256":"bb2b188255800f368d17aa3263e6f6744bcff4c305c70c8e7b5ccdfbf625dd8a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bb2b188255800f368d17aa3263e6f6744bcff4c305c70c8e7b5ccdfbf625dd8a","first_computed_at":"2026-07-05T03:42:00.536182Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:42:00.536182Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1OkZn5gJbkp6Jkkd8T2HntDYX3NThNBvpKAI25vJdFCjs1i7iRe3suMImgWC1vX3OU5SApAL2CSjoJrEduTtAA==","signature_status":"signed_v1","signed_at":"2026-07-05T03:42:00.536543Z","signed_message":"canonical_sha256_bytes"},"source_id":"2104.04921","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8d8f186d2116888347cdff5ea467a837d23e3921d4e23a21caaa56e8958ae843","sha256:fd00b98abb51add46fbd3c7465a4aebffa6c929ae104932ce474a828ea223e48"],"state_sha256":"975e730f88ec948cdd74dd87d7b0fa158ffc509b5e171796121b1c77cae6cc2e"}