{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:J5QK5J3DR24YUXJUHKTNRUGCEV","short_pith_number":"pith:J5QK5J3D","canonical_record":{"source":{"id":"2504.19109","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2025-04-27T05:00:40Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"a1b30ad94aa791ef08157df790599a1e25606b714f5baecff1f8a57910bd8ad3","abstract_canon_sha256":"0a20762da4a0f36acdd60e2673b5461cf8f08483d17d5215311c00af00527436"},"schema_version":"1.0"},"canonical_sha256":"4f60aea7638eb98a5d343aa6d8d0c2257325bd4a4ba22d17a0e0ad4f3aa03e22","source":{"kind":"arxiv","id":"2504.19109","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.19109","created_at":"2026-07-05T10:54:52Z"},{"alias_kind":"arxiv_version","alias_value":"2504.19109v1","created_at":"2026-07-05T10:54:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.19109","created_at":"2026-07-05T10:54:52Z"},{"alias_kind":"pith_short_12","alias_value":"J5QK5J3DR24Y","created_at":"2026-07-05T10:54:52Z"},{"alias_kind":"pith_short_16","alias_value":"J5QK5J3DR24YUXJU","created_at":"2026-07-05T10:54:52Z"},{"alias_kind":"pith_short_8","alias_value":"J5QK5J3D","created_at":"2026-07-05T10:54:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:J5QK5J3DR24YUXJUHKTNRUGCEV","target":"record","payload":{"canonical_record":{"source":{"id":"2504.19109","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2025-04-27T05:00:40Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"a1b30ad94aa791ef08157df790599a1e25606b714f5baecff1f8a57910bd8ad3","abstract_canon_sha256":"0a20762da4a0f36acdd60e2673b5461cf8f08483d17d5215311c00af00527436"},"schema_version":"1.0"},"canonical_sha256":"4f60aea7638eb98a5d343aa6d8d0c2257325bd4a4ba22d17a0e0ad4f3aa03e22","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:54:52.206037Z","signature_b64":"Z2+urAI5LnjnFWi0iS7JdYsQpQbs/VKK0Qk1T2+bCNfkmvEeLtm/ZVBCwqu5QPwmCwRDutavKGKsrFvms/8JDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f60aea7638eb98a5d343aa6d8d0c2257325bd4a4ba22d17a0e0ad4f3aa03e22","last_reissued_at":"2026-07-05T10:54:52.205556Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:54:52.205556Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2504.19109","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":"2026-07-05T10:54:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wou9JOG3lEY0mm+XffyCBMRRI2k2+bFK2hUWRetXNYFXu2OpVSgvIMVCVEbRWPJ/FdLWqhX6n95B79hTAlo0BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T10:47:56.569965Z"},"content_sha256":"80fb14a63ea239b28ee98d4020bb83f97e02165d9076756da31e97a92e57f848","schema_version":"1.0","event_id":"sha256:80fb14a63ea239b28ee98d4020bb83f97e02165d9076756da31e97a92e57f848"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:J5QK5J3DR24YUXJUHKTNRUGCEV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Simply Connected Quandles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Marco Bonatto","submitted_at":"2025-04-27T05:00:40Z","abstract_excerpt":"In this paper we provide an alternative characterization of finite simply connected quandles involving only cocycles with values in abelian groups of prime size. As a corollary of such a characterization and the classification of connected quandles of size $p^2$ and $p^3$ we obtain a classification of simply connected quandles of size $p^2$ (already obtained with a different method in \\cite{VV}) and $p^3$ for $p>3$ using a method that works for quandles of size $p^n$ for arbitrary $n$. We also classify the simply connected quandles within two subclasses of finite involutory quandles: nilpotent"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.19109","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2504.19109/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":"2026-07-05T10:54:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a9d0SZ37fRuMo7Kzk5P/cGdZtXJJXbMLTwr93uGlhPWc92MY2W4GjBRjB8xCE8LR1m5QSjtE8TfWZ9cY0L61CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T10:47:56.570460Z"},"content_sha256":"0c32184d212883e6d1ff95747d0f51276b4261c96e1dac20a574c3a54af01b5f","schema_version":"1.0","event_id":"sha256:0c32184d212883e6d1ff95747d0f51276b4261c96e1dac20a574c3a54af01b5f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J5QK5J3DR24YUXJUHKTNRUGCEV/bundle.json","state_url":"https://pith.science/pith/J5QK5J3DR24YUXJUHKTNRUGCEV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J5QK5J3DR24YUXJUHKTNRUGCEV/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":"2026-08-23T10:47:56Z","links":{"resolver":"https://pith.science/pith/J5QK5J3DR24YUXJUHKTNRUGCEV","bundle":"https://pith.science/pith/J5QK5J3DR24YUXJUHKTNRUGCEV/bundle.json","state":"https://pith.science/pith/J5QK5J3DR24YUXJUHKTNRUGCEV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J5QK5J3DR24YUXJUHKTNRUGCEV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:J5QK5J3DR24YUXJUHKTNRUGCEV","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":"0a20762da4a0f36acdd60e2673b5461cf8f08483d17d5215311c00af00527436","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2025-04-27T05:00:40Z","title_canon_sha256":"a1b30ad94aa791ef08157df790599a1e25606b714f5baecff1f8a57910bd8ad3"},"schema_version":"1.0","source":{"id":"2504.19109","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.19109","created_at":"2026-07-05T10:54:52Z"},{"alias_kind":"arxiv_version","alias_value":"2504.19109v1","created_at":"2026-07-05T10:54:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.19109","created_at":"2026-07-05T10:54:52Z"},{"alias_kind":"pith_short_12","alias_value":"J5QK5J3DR24Y","created_at":"2026-07-05T10:54:52Z"},{"alias_kind":"pith_short_16","alias_value":"J5QK5J3DR24YUXJU","created_at":"2026-07-05T10:54:52Z"},{"alias_kind":"pith_short_8","alias_value":"J5QK5J3D","created_at":"2026-07-05T10:54:52Z"}],"graph_snapshots":[{"event_id":"sha256:0c32184d212883e6d1ff95747d0f51276b4261c96e1dac20a574c3a54af01b5f","target":"graph","created_at":"2026-07-05T10:54:52Z","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/2504.19109/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we provide an alternative characterization of finite simply connected quandles involving only cocycles with values in abelian groups of prime size. As a corollary of such a characterization and the classification of connected quandles of size $p^2$ and $p^3$ we obtain a classification of simply connected quandles of size $p^2$ (already obtained with a different method in \\cite{VV}) and $p^3$ for $p>3$ using a method that works for quandles of size $p^n$ for arbitrary $n$. We also classify the simply connected quandles within two subclasses of finite involutory quandles: nilpotent","authors_text":"Marco Bonatto","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2025-04-27T05:00:40Z","title":"On Simply Connected Quandles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.19109","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":"sha256:80fb14a63ea239b28ee98d4020bb83f97e02165d9076756da31e97a92e57f848","target":"record","created_at":"2026-07-05T10:54:52Z","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":"0a20762da4a0f36acdd60e2673b5461cf8f08483d17d5215311c00af00527436","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2025-04-27T05:00:40Z","title_canon_sha256":"a1b30ad94aa791ef08157df790599a1e25606b714f5baecff1f8a57910bd8ad3"},"schema_version":"1.0","source":{"id":"2504.19109","kind":"arxiv","version":1}},"canonical_sha256":"4f60aea7638eb98a5d343aa6d8d0c2257325bd4a4ba22d17a0e0ad4f3aa03e22","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f60aea7638eb98a5d343aa6d8d0c2257325bd4a4ba22d17a0e0ad4f3aa03e22","first_computed_at":"2026-07-05T10:54:52.205556Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:54:52.205556Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Z2+urAI5LnjnFWi0iS7JdYsQpQbs/VKK0Qk1T2+bCNfkmvEeLtm/ZVBCwqu5QPwmCwRDutavKGKsrFvms/8JDw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:54:52.206037Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.19109","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:80fb14a63ea239b28ee98d4020bb83f97e02165d9076756da31e97a92e57f848","sha256:0c32184d212883e6d1ff95747d0f51276b4261c96e1dac20a574c3a54af01b5f"],"state_sha256":"0cfc84ea9fff5b049337294390ae80391820a54a43c407895f3d16f1230ce774"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2Qh5iV/N7D8//0GP/NjGfY+bZ2TScNm42A06Ey+UubD6p1rbdkHuQ+nD5ht3KSo7Z764+FK2/fHJBFr9Zty/Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-23T10:47:56.575430Z","bundle_sha256":"273e31c2ef66ae364a379024a4bcb7a03470dbeb297ec792f4c4d3fd49ada0ed"}}