{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:KNRE4YDHV4UW75ALI2PQ62HU2D","short_pith_number":"pith:KNRE4YDH","canonical_record":{"source":{"id":"0902.4277","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-02-25T01:41:21Z","cross_cats_sorted":[],"title_canon_sha256":"9ce4471885c89e6afb2931852322d17f266a5db47c43f5ee113b647b92781590","abstract_canon_sha256":"066b2b253db9e847405803e6a3c5f692d66ce8da6c989908f1fd3be1a320b50c"},"schema_version":"1.0"},"canonical_sha256":"53624e6067af296ff40b469f0f68f4d0cdd1add7fe6ebb419a25755de828fe0e","source":{"kind":"arxiv","id":"0902.4277","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.4277","created_at":"2026-05-18T01:23:45Z"},{"alias_kind":"arxiv_version","alias_value":"0902.4277v1","created_at":"2026-05-18T01:23:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.4277","created_at":"2026-05-18T01:23:45Z"},{"alias_kind":"pith_short_12","alias_value":"KNRE4YDHV4UW","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"KNRE4YDHV4UW75AL","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"KNRE4YDH","created_at":"2026-05-18T12:26:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:KNRE4YDHV4UW75ALI2PQ62HU2D","target":"record","payload":{"canonical_record":{"source":{"id":"0902.4277","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-02-25T01:41:21Z","cross_cats_sorted":[],"title_canon_sha256":"9ce4471885c89e6afb2931852322d17f266a5db47c43f5ee113b647b92781590","abstract_canon_sha256":"066b2b253db9e847405803e6a3c5f692d66ce8da6c989908f1fd3be1a320b50c"},"schema_version":"1.0"},"canonical_sha256":"53624e6067af296ff40b469f0f68f4d0cdd1add7fe6ebb419a25755de828fe0e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:45.790082Z","signature_b64":"hP10S2+T8xduRzCLvfnd2DKJ3F6+BOosiziT/kODKI+ASS/wDrhj33JMQsISsrPVlV36wGhK9syGyjxWBbvmBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"53624e6067af296ff40b469f0f68f4d0cdd1add7fe6ebb419a25755de828fe0e","last_reissued_at":"2026-05-18T01:23:45.789376Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:45.789376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0902.4277","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":"2026-05-18T01:23:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Il40qYoO31ZmOtK4Dh/0vCHa3eS7Y79WFjCxsFrtEHx5+0lbXL7GEPfj/7oz4ancB/rOxwPiuzUeeX7XZEfnBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T22:12:40.761436Z"},"content_sha256":"8ccb040cb21f9eb253245261b9d0f96a18950a91ebda5cb407f5f52d0db0adf9","schema_version":"1.0","event_id":"sha256:8ccb040cb21f9eb253245261b9d0f96a18950a91ebda5cb407f5f52d0db0adf9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:KNRE4YDHV4UW75ALI2PQ62HU2D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Homology Groups of Symmetric Quandles and Cocycle Invariants of Links and Surface-links","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Kanako Oshiro, Seiichi Kamada","submitted_at":"2009-02-25T01:41:21Z","abstract_excerpt":"We introduce the notion of a quandle with a good involution and its homology groups. Carter et al. defined quandle cocycle invariants for oriented links and oriented surface-links. By use of good involutions, quandle cocyle invariants can be defined for links and surface-links which are not necessarily oriented or orientable. The invariants can be used in order to estimate the minimal triple point numbers of non-orientable surface-links."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.4277","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":"2026-05-18T01:23:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0WD63zdCLqCQy2YpdCTGoqQtf139jDc7TQqnzTZABlHXM8tim2KdYeSWkNxztL1K8gNNFUHUshP+Pc6JnbpYCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T22:12:40.761773Z"},"content_sha256":"b643a97ddc12fbbec1701c64a6ed3ce61b4bf811aa4ed6898dca9726d2cd3fc6","schema_version":"1.0","event_id":"sha256:b643a97ddc12fbbec1701c64a6ed3ce61b4bf811aa4ed6898dca9726d2cd3fc6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KNRE4YDHV4UW75ALI2PQ62HU2D/bundle.json","state_url":"https://pith.science/pith/KNRE4YDHV4UW75ALI2PQ62HU2D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KNRE4YDHV4UW75ALI2PQ62HU2D/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":"2026-06-20T22:12:40Z","links":{"resolver":"https://pith.science/pith/KNRE4YDHV4UW75ALI2PQ62HU2D","bundle":"https://pith.science/pith/KNRE4YDHV4UW75ALI2PQ62HU2D/bundle.json","state":"https://pith.science/pith/KNRE4YDHV4UW75ALI2PQ62HU2D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KNRE4YDHV4UW75ALI2PQ62HU2D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:KNRE4YDHV4UW75ALI2PQ62HU2D","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":"066b2b253db9e847405803e6a3c5f692d66ce8da6c989908f1fd3be1a320b50c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-02-25T01:41:21Z","title_canon_sha256":"9ce4471885c89e6afb2931852322d17f266a5db47c43f5ee113b647b92781590"},"schema_version":"1.0","source":{"id":"0902.4277","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.4277","created_at":"2026-05-18T01:23:45Z"},{"alias_kind":"arxiv_version","alias_value":"0902.4277v1","created_at":"2026-05-18T01:23:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.4277","created_at":"2026-05-18T01:23:45Z"},{"alias_kind":"pith_short_12","alias_value":"KNRE4YDHV4UW","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"KNRE4YDHV4UW75AL","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"KNRE4YDH","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:b643a97ddc12fbbec1701c64a6ed3ce61b4bf811aa4ed6898dca9726d2cd3fc6","target":"graph","created_at":"2026-05-18T01:23:45Z","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 the notion of a quandle with a good involution and its homology groups. Carter et al. defined quandle cocycle invariants for oriented links and oriented surface-links. By use of good involutions, quandle cocyle invariants can be defined for links and surface-links which are not necessarily oriented or orientable. The invariants can be used in order to estimate the minimal triple point numbers of non-orientable surface-links.","authors_text":"Kanako Oshiro, Seiichi Kamada","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-02-25T01:41:21Z","title":"Homology Groups of Symmetric Quandles and Cocycle Invariants of Links and Surface-links"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.4277","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":"sha256:8ccb040cb21f9eb253245261b9d0f96a18950a91ebda5cb407f5f52d0db0adf9","target":"record","created_at":"2026-05-18T01:23:45Z","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":"066b2b253db9e847405803e6a3c5f692d66ce8da6c989908f1fd3be1a320b50c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-02-25T01:41:21Z","title_canon_sha256":"9ce4471885c89e6afb2931852322d17f266a5db47c43f5ee113b647b92781590"},"schema_version":"1.0","source":{"id":"0902.4277","kind":"arxiv","version":1}},"canonical_sha256":"53624e6067af296ff40b469f0f68f4d0cdd1add7fe6ebb419a25755de828fe0e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"53624e6067af296ff40b469f0f68f4d0cdd1add7fe6ebb419a25755de828fe0e","first_computed_at":"2026-05-18T01:23:45.789376Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:45.789376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hP10S2+T8xduRzCLvfnd2DKJ3F6+BOosiziT/kODKI+ASS/wDrhj33JMQsISsrPVlV36wGhK9syGyjxWBbvmBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:45.790082Z","signed_message":"canonical_sha256_bytes"},"source_id":"0902.4277","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8ccb040cb21f9eb253245261b9d0f96a18950a91ebda5cb407f5f52d0db0adf9","sha256:b643a97ddc12fbbec1701c64a6ed3ce61b4bf811aa4ed6898dca9726d2cd3fc6"],"state_sha256":"fb213ad107a471596f687b260a69705d3c21155c4545759a2de69f5771e49ae8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h9RdeHmDepQ8Um78kaZsZAIQ1dgcpKdaV1LbP1pTtVETpISANP8PMm4+myzO3yXMlV4FQxYToeVZCnR/iIPcCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T22:12:40.763758Z","bundle_sha256":"600c85a24cbe51debda0c5516a8e734af3e52e1a681d0bbe6e46b39cf42d3383"}}