{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:OGLLAI3OH4CZGMATY6PWRO5ICV","short_pith_number":"pith:OGLLAI3O","canonical_record":{"source":{"id":"1110.1849","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-10-09T15:25:00Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"1994ceb1b4e0f55237d314e6d93d41d1bda4c2fe7195527aeeee9b7c5243b629","abstract_canon_sha256":"de69b131b143bbbe0a9d37a8f5e14a14bf583529686c9a1f6fed47c5b8cbefe9"},"schema_version":"1.0"},"canonical_sha256":"7196b0236e3f05933013c79f68bba8157a795a40965c30a69f623c77f37c7e8b","source":{"kind":"arxiv","id":"1110.1849","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.1849","created_at":"2026-05-18T04:11:19Z"},{"alias_kind":"arxiv_version","alias_value":"1110.1849v1","created_at":"2026-05-18T04:11:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.1849","created_at":"2026-05-18T04:11:19Z"},{"alias_kind":"pith_short_12","alias_value":"OGLLAI3OH4CZ","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"OGLLAI3OH4CZGMAT","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"OGLLAI3O","created_at":"2026-05-18T12:26:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:OGLLAI3OH4CZGMATY6PWRO5ICV","target":"record","payload":{"canonical_record":{"source":{"id":"1110.1849","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-10-09T15:25:00Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"1994ceb1b4e0f55237d314e6d93d41d1bda4c2fe7195527aeeee9b7c5243b629","abstract_canon_sha256":"de69b131b143bbbe0a9d37a8f5e14a14bf583529686c9a1f6fed47c5b8cbefe9"},"schema_version":"1.0"},"canonical_sha256":"7196b0236e3f05933013c79f68bba8157a795a40965c30a69f623c77f37c7e8b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:11:19.529576Z","signature_b64":"c0i+UOh4Etr+I6NENW7JbevKrjjvJfuO3rscjAvN+tFWLQbBLwFlCHEVk7jEn3Qj6Q9TgqTaEoTu84EGZgGPAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7196b0236e3f05933013c79f68bba8157a795a40965c30a69f623c77f37c7e8b","last_reissued_at":"2026-05-18T04:11:19.529100Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:11:19.529100Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.1849","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":"2026-05-18T04:11:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+YGGa13lk+lbWPPYm5TekkTar/kVCesW3Itb1sVEN5n1kcRVm9pWXn7jWBbQ32z3sI0UuOA8s+nxJM/MyVt7CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T19:57:27.629726Z"},"content_sha256":"9668493d95d4f11efd6392af0a559e6ceb61def620b1c605999dff317a99a3b1","schema_version":"1.0","event_id":"sha256:9668493d95d4f11efd6392af0a559e6ceb61def620b1c605999dff317a99a3b1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:OGLLAI3OH4CZGMATY6PWRO5ICV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Canonical forms for operation tables of finiate connected quandles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Chuichiro Hayashi","submitted_at":"2011-10-09T15:25:00Z","abstract_excerpt":"We introduce a notion of natural orderings of elements of finite connected quandles of order $n$. When the elements of such a quandle $Q$ are already ordered naturally, any automophism on $Q$ is a natural ordering. Although there are many natural orderings, the operation tables for such orderings coincide when the permutation $*q$ is a cycle of length $n-1$. This leads to the classification of automorphisms on such a quandle. Moreover, it is also shown that every row and column of the operation table of such a quandle contains all the elements of $Q$, which is due to K. Oshiro. We also conside"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1849","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":"2026-05-18T04:11:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K0+yeEXtLO8uKdC1dDpifuj4I2zaqE8W59xZc4b0IJSZ4ypR2ORVVhn/5rXX/Ddn2WnZBqTADEclEHe2MwNSDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T19:57:27.630077Z"},"content_sha256":"9dee730fe8aabcac54c18443fa0b2650498592ec533de4b1b7cd4a4c1716902c","schema_version":"1.0","event_id":"sha256:9dee730fe8aabcac54c18443fa0b2650498592ec533de4b1b7cd4a4c1716902c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OGLLAI3OH4CZGMATY6PWRO5ICV/bundle.json","state_url":"https://pith.science/pith/OGLLAI3OH4CZGMATY6PWRO5ICV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OGLLAI3OH4CZGMATY6PWRO5ICV/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":"2026-06-23T19:57:27Z","links":{"resolver":"https://pith.science/pith/OGLLAI3OH4CZGMATY6PWRO5ICV","bundle":"https://pith.science/pith/OGLLAI3OH4CZGMATY6PWRO5ICV/bundle.json","state":"https://pith.science/pith/OGLLAI3OH4CZGMATY6PWRO5ICV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OGLLAI3OH4CZGMATY6PWRO5ICV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:OGLLAI3OH4CZGMATY6PWRO5ICV","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":"de69b131b143bbbe0a9d37a8f5e14a14bf583529686c9a1f6fed47c5b8cbefe9","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-10-09T15:25:00Z","title_canon_sha256":"1994ceb1b4e0f55237d314e6d93d41d1bda4c2fe7195527aeeee9b7c5243b629"},"schema_version":"1.0","source":{"id":"1110.1849","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.1849","created_at":"2026-05-18T04:11:19Z"},{"alias_kind":"arxiv_version","alias_value":"1110.1849v1","created_at":"2026-05-18T04:11:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.1849","created_at":"2026-05-18T04:11:19Z"},{"alias_kind":"pith_short_12","alias_value":"OGLLAI3OH4CZ","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"OGLLAI3OH4CZGMAT","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"OGLLAI3O","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:9dee730fe8aabcac54c18443fa0b2650498592ec533de4b1b7cd4a4c1716902c","target":"graph","created_at":"2026-05-18T04:11:19Z","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 a notion of natural orderings of elements of finite connected quandles of order $n$. When the elements of such a quandle $Q$ are already ordered naturally, any automophism on $Q$ is a natural ordering. Although there are many natural orderings, the operation tables for such orderings coincide when the permutation $*q$ is a cycle of length $n-1$. This leads to the classification of automorphisms on such a quandle. Moreover, it is also shown that every row and column of the operation table of such a quandle contains all the elements of $Q$, which is due to K. Oshiro. We also conside","authors_text":"Chuichiro Hayashi","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-10-09T15:25:00Z","title":"Canonical forms for operation tables of finiate connected quandles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1849","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":"sha256:9668493d95d4f11efd6392af0a559e6ceb61def620b1c605999dff317a99a3b1","target":"record","created_at":"2026-05-18T04:11:19Z","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":"de69b131b143bbbe0a9d37a8f5e14a14bf583529686c9a1f6fed47c5b8cbefe9","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-10-09T15:25:00Z","title_canon_sha256":"1994ceb1b4e0f55237d314e6d93d41d1bda4c2fe7195527aeeee9b7c5243b629"},"schema_version":"1.0","source":{"id":"1110.1849","kind":"arxiv","version":1}},"canonical_sha256":"7196b0236e3f05933013c79f68bba8157a795a40965c30a69f623c77f37c7e8b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7196b0236e3f05933013c79f68bba8157a795a40965c30a69f623c77f37c7e8b","first_computed_at":"2026-05-18T04:11:19.529100Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:11:19.529100Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c0i+UOh4Etr+I6NENW7JbevKrjjvJfuO3rscjAvN+tFWLQbBLwFlCHEVk7jEn3Qj6Q9TgqTaEoTu84EGZgGPAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:11:19.529576Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.1849","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9668493d95d4f11efd6392af0a559e6ceb61def620b1c605999dff317a99a3b1","sha256:9dee730fe8aabcac54c18443fa0b2650498592ec533de4b1b7cd4a4c1716902c"],"state_sha256":"fd1a322c6a8185b22f9e83823890d3423f477e4abbd5d6eb0b4e7194dead3816"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gYTPZIgwhJY90ki5+AIqJNxiNKmhevjJNFfm7tFpKJtt85qkejWtJs8jFv+lf8IyDOLCWbPswXY/gT/bsjh8Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T19:57:27.632018Z","bundle_sha256":"5394caabe2da81b605952818c2dce58ebb8f7a7b9fec00d037ef4fa9803f4322"}}