{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:ZN7F4QYQCIFCFEU537O2PXZHYK","short_pith_number":"pith:ZN7F4QYQ","canonical_record":{"source":{"id":"1506.00084","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-05-30T07:22:38Z","cross_cats_sorted":["math.AT","math.QA","math.RA"],"title_canon_sha256":"0d465cf65d4f813bc7e64bf45edccfc86ada9da4952f9916a80d7c72d2b37ee7","abstract_canon_sha256":"4aa5d7bcbbcfd6498dd775e9882b01ff3a55501ae59a85c9426273a7af9c4b1c"},"schema_version":"1.0"},"canonical_sha256":"cb7e5e4310120a22929ddfdda7df27c29648456aa30bbe734a4e523dcd60e579","source":{"kind":"arxiv","id":"1506.00084","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.00084","created_at":"2026-05-18T01:59:55Z"},{"alias_kind":"arxiv_version","alias_value":"1506.00084v1","created_at":"2026-05-18T01:59:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.00084","created_at":"2026-05-18T01:59:55Z"},{"alias_kind":"pith_short_12","alias_value":"ZN7F4QYQCIFC","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZN7F4QYQCIFCFEU5","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZN7F4QYQ","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:ZN7F4QYQCIFCFEU537O2PXZHYK","target":"record","payload":{"canonical_record":{"source":{"id":"1506.00084","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-05-30T07:22:38Z","cross_cats_sorted":["math.AT","math.QA","math.RA"],"title_canon_sha256":"0d465cf65d4f813bc7e64bf45edccfc86ada9da4952f9916a80d7c72d2b37ee7","abstract_canon_sha256":"4aa5d7bcbbcfd6498dd775e9882b01ff3a55501ae59a85c9426273a7af9c4b1c"},"schema_version":"1.0"},"canonical_sha256":"cb7e5e4310120a22929ddfdda7df27c29648456aa30bbe734a4e523dcd60e579","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:59:55.529978Z","signature_b64":"3w1dalDKISY3t3mq2mpmFEZ3/RxNvG3WBFVXephk/YV8/1tLlMrVpnn6vDTzlVQ4s8UWOd723Rzy1S8lzW0EBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cb7e5e4310120a22929ddfdda7df27c29648456aa30bbe734a4e523dcd60e579","last_reissued_at":"2026-05-18T01:59:55.529412Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:59:55.529412Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.00084","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":"2026-05-18T01:59:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uqnhJ38YCl2YDy33Z1/9S3Wqnh0HzCxPgJk8e3+N6zYZ5h/ysobnTHCfnlKi3KhhDfmVRqPD0lrZEEnR7d7MDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T15:02:33.395036Z"},"content_sha256":"4e02d72712d2123c58f15730a1b5de2f81f78786999dbabd3dc4a95fd25eb61d","schema_version":"1.0","event_id":"sha256:4e02d72712d2123c58f15730a1b5de2f81f78786999dbabd3dc4a95fd25eb61d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:ZN7F4QYQCIFCFEU537O2PXZHYK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Foundations of topological racks and quandles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.QA","math.RA"],"primary_cat":"math.GT","authors_text":"El-ka\\\"ioum M. Moutuou, Mohamed Elhamdadi","submitted_at":"2015-05-30T07:22:38Z","abstract_excerpt":"We give a foundational account on topological racks and quandles. Specifically, we define the notions of ideals, kernels, units, and inner automorphism group in the context of topological racks. Further, we investigate topological rack modules and principal rack bundles. Central extensions of topological racks are then introduced providing a first step towards a general continuous cohomology theory for topological racks and quandles."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.00084","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":"2026-05-18T01:59:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3Mk7wOuPLL8y7wtT+5xnczM+4JTw5qWSFyWQy3CqarukpRcle0BRUW4dVU/CP/9mKnFBkBdUdfWZme/HL2p1Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T15:02:33.395804Z"},"content_sha256":"30644d3e847fcd42d3f9eb0dda3d93288e059342ef9b3eb0405ebd7838eae472","schema_version":"1.0","event_id":"sha256:30644d3e847fcd42d3f9eb0dda3d93288e059342ef9b3eb0405ebd7838eae472"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZN7F4QYQCIFCFEU537O2PXZHYK/bundle.json","state_url":"https://pith.science/pith/ZN7F4QYQCIFCFEU537O2PXZHYK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZN7F4QYQCIFCFEU537O2PXZHYK/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":"2026-06-10T15:02:33Z","links":{"resolver":"https://pith.science/pith/ZN7F4QYQCIFCFEU537O2PXZHYK","bundle":"https://pith.science/pith/ZN7F4QYQCIFCFEU537O2PXZHYK/bundle.json","state":"https://pith.science/pith/ZN7F4QYQCIFCFEU537O2PXZHYK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZN7F4QYQCIFCFEU537O2PXZHYK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ZN7F4QYQCIFCFEU537O2PXZHYK","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":"4aa5d7bcbbcfd6498dd775e9882b01ff3a55501ae59a85c9426273a7af9c4b1c","cross_cats_sorted":["math.AT","math.QA","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-05-30T07:22:38Z","title_canon_sha256":"0d465cf65d4f813bc7e64bf45edccfc86ada9da4952f9916a80d7c72d2b37ee7"},"schema_version":"1.0","source":{"id":"1506.00084","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.00084","created_at":"2026-05-18T01:59:55Z"},{"alias_kind":"arxiv_version","alias_value":"1506.00084v1","created_at":"2026-05-18T01:59:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.00084","created_at":"2026-05-18T01:59:55Z"},{"alias_kind":"pith_short_12","alias_value":"ZN7F4QYQCIFC","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZN7F4QYQCIFCFEU5","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZN7F4QYQ","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:30644d3e847fcd42d3f9eb0dda3d93288e059342ef9b3eb0405ebd7838eae472","target":"graph","created_at":"2026-05-18T01:59:55Z","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 give a foundational account on topological racks and quandles. Specifically, we define the notions of ideals, kernels, units, and inner automorphism group in the context of topological racks. Further, we investigate topological rack modules and principal rack bundles. Central extensions of topological racks are then introduced providing a first step towards a general continuous cohomology theory for topological racks and quandles.","authors_text":"El-ka\\\"ioum M. Moutuou, Mohamed Elhamdadi","cross_cats":["math.AT","math.QA","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-05-30T07:22:38Z","title":"Foundations of topological racks and quandles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.00084","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":"sha256:4e02d72712d2123c58f15730a1b5de2f81f78786999dbabd3dc4a95fd25eb61d","target":"record","created_at":"2026-05-18T01:59:55Z","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":"4aa5d7bcbbcfd6498dd775e9882b01ff3a55501ae59a85c9426273a7af9c4b1c","cross_cats_sorted":["math.AT","math.QA","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-05-30T07:22:38Z","title_canon_sha256":"0d465cf65d4f813bc7e64bf45edccfc86ada9da4952f9916a80d7c72d2b37ee7"},"schema_version":"1.0","source":{"id":"1506.00084","kind":"arxiv","version":1}},"canonical_sha256":"cb7e5e4310120a22929ddfdda7df27c29648456aa30bbe734a4e523dcd60e579","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cb7e5e4310120a22929ddfdda7df27c29648456aa30bbe734a4e523dcd60e579","first_computed_at":"2026-05-18T01:59:55.529412Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:59:55.529412Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3w1dalDKISY3t3mq2mpmFEZ3/RxNvG3WBFVXephk/YV8/1tLlMrVpnn6vDTzlVQ4s8UWOd723Rzy1S8lzW0EBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:59:55.529978Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.00084","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4e02d72712d2123c58f15730a1b5de2f81f78786999dbabd3dc4a95fd25eb61d","sha256:30644d3e847fcd42d3f9eb0dda3d93288e059342ef9b3eb0405ebd7838eae472"],"state_sha256":"73ca5700da01907d341df3c1e8e906e1d63e6f6caeb949439767dc0ed78127fa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p4grXNP/1rhH90Yg8C/6A9Fgiuj7t/fi/LqBbf0KEMPLDF/VTCgTxGKoARlOghfWjEku1D2DGAwvBaU4XkmODw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T15:02:33.399776Z","bundle_sha256":"80b601a84c1412f01dc84b7bb2d679f839ab660646e486d55c1c750247f3b2d5"}}