{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:XMVRRASVQAHTNDIXVIZGHZXWOR","short_pith_number":"pith:XMVRRASV","canonical_record":{"source":{"id":"2104.04921","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2021-04-11T05:19:09Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"061287f4420d8d72a4c4bd6e8ad98547a5d24c34c0f3dcdbfc4de7b40be896bf","abstract_canon_sha256":"4272ae3537459e7a0998b351d63de313d1a9a4fa7b42a49bdc73c910b9b7b9b6"},"schema_version":"1.0"},"canonical_sha256":"bb2b188255800f368d17aa3263e6f6744bcff4c305c70c8e7b5ccdfbf625dd8a","source":{"kind":"arxiv","id":"2104.04921","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:XMVRRASVQAHTNDIXVIZGHZXWOR","target":"record","payload":{"canonical_record":{"source":{"id":"2104.04921","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2021-04-11T05:19:09Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"061287f4420d8d72a4c4bd6e8ad98547a5d24c34c0f3dcdbfc4de7b40be896bf","abstract_canon_sha256":"4272ae3537459e7a0998b351d63de313d1a9a4fa7b42a49bdc73c910b9b7b9b6"},"schema_version":"1.0"},"canonical_sha256":"bb2b188255800f368d17aa3263e6f6744bcff4c305c70c8e7b5ccdfbf625dd8a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:42:00.536543Z","signature_b64":"1OkZn5gJbkp6Jkkd8T2HntDYX3NThNBvpKAI25vJdFCjs1i7iRe3suMImgWC1vX3OU5SApAL2CSjoJrEduTtAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bb2b188255800f368d17aa3263e6f6744bcff4c305c70c8e7b5ccdfbf625dd8a","last_reissued_at":"2026-07-05T03:42:00.536182Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:42:00.536182Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2104.04921","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:42:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FpJnUwu6jEGDH9KEdxHowmt2vRtJwFn0WHz0ZA7BFEQwvq8bMRC9oJaJTJ8Vstif+HrLSl50iwhLXVqic52uCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T10:39:28.377757Z"},"content_sha256":"8d8f186d2116888347cdff5ea467a837d23e3921d4e23a21caaa56e8958ae843","schema_version":"1.0","event_id":"sha256:8d8f186d2116888347cdff5ea467a837d23e3921d4e23a21caaa56e8958ae843"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:XMVRRASVQAHTNDIXVIZGHZXWOR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Note on spherical quandles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GT","authors_text":"Kentaro Yonemura","submitted_at":"2021-04-11T05:19:09Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.04921","kind":"arxiv","version":3},"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/2104.04921/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":"2026-07-05T03:42:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"azFo2ENOprfl9v7qxoqClsG6BaTdbhQdYigrhppWeI0TWa9TQt2f9UqYCnH35Aeu9rPMvulQNVZjMRoNEPS/Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T10:39:28.378241Z"},"content_sha256":"fd00b98abb51add46fbd3c7465a4aebffa6c929ae104932ce474a828ea223e48","schema_version":"1.0","event_id":"sha256:fd00b98abb51add46fbd3c7465a4aebffa6c929ae104932ce474a828ea223e48"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XMVRRASVQAHTNDIXVIZGHZXWOR/bundle.json","state_url":"https://pith.science/pith/XMVRRASVQAHTNDIXVIZGHZXWOR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XMVRRASVQAHTNDIXVIZGHZXWOR/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":"2026-08-23T10:39:28Z","links":{"resolver":"https://pith.science/pith/XMVRRASVQAHTNDIXVIZGHZXWOR","bundle":"https://pith.science/pith/XMVRRASVQAHTNDIXVIZGHZXWOR/bundle.json","state":"https://pith.science/pith/XMVRRASVQAHTNDIXVIZGHZXWOR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XMVRRASVQAHTNDIXVIZGHZXWOR/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MSQlWn7NpEIM0e32hAPOUUPwyKcWYw6nKDpomcHwJ7YvlcodInKgMXzeLhFVM3FlCINAfDDlMyV+3sSuUovhAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-23T10:39:28.382745Z","bundle_sha256":"54f244f6de6f374d0cd0db885e45b1e24a7aa4eed8dc4e47803796f58f0002e6"}}