{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:RZX6IATJNNGI4JSE2JEZL5UY7N","short_pith_number":"pith:RZX6IATJ","canonical_record":{"source":{"id":"1904.12030","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-04-26T20:02:38Z","cross_cats_sorted":[],"title_canon_sha256":"4b30ea0f3cf4ea99dedbda3947f04dad1f8acd50b596ac77d8d80070e403d523","abstract_canon_sha256":"ad1227fdb000f1eb9513339833216fa8c931fcd34a81320cc91c0fa51f803c5b"},"schema_version":"1.0"},"canonical_sha256":"8e6fe402696b4c8e2644d24995f698fb5d0012f4b6fb85ab9c9c7d84b2840946","source":{"kind":"arxiv","id":"1904.12030","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.12030","created_at":"2026-05-17T23:47:39Z"},{"alias_kind":"arxiv_version","alias_value":"1904.12030v1","created_at":"2026-05-17T23:47:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.12030","created_at":"2026-05-17T23:47:39Z"},{"alias_kind":"pith_short_12","alias_value":"RZX6IATJNNGI","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"RZX6IATJNNGI4JSE","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"RZX6IATJ","created_at":"2026-05-18T12:33:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:RZX6IATJNNGI4JSE2JEZL5UY7N","target":"record","payload":{"canonical_record":{"source":{"id":"1904.12030","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-04-26T20:02:38Z","cross_cats_sorted":[],"title_canon_sha256":"4b30ea0f3cf4ea99dedbda3947f04dad1f8acd50b596ac77d8d80070e403d523","abstract_canon_sha256":"ad1227fdb000f1eb9513339833216fa8c931fcd34a81320cc91c0fa51f803c5b"},"schema_version":"1.0"},"canonical_sha256":"8e6fe402696b4c8e2644d24995f698fb5d0012f4b6fb85ab9c9c7d84b2840946","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:39.044108Z","signature_b64":"C5Wxmi6xnEprRj8hq3r9exmcKe26lGHVhPMSOjods8uvhdjdx3l6UoYo0OpLVCuWRM1GcBuH3NYFv8R+b4taAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8e6fe402696b4c8e2644d24995f698fb5d0012f4b6fb85ab9c9c7d84b2840946","last_reissued_at":"2026-05-17T23:47:39.043587Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:39.043587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.12030","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":"2026-05-17T23:47:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lko/DenE6nzCZpYxkxO517F5EsHgpvxfu3jLixmHxt/GyyMDUlg6f498TeemWpHrMAUomwyRoMmCNsXDd+OECQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T23:42:12.445573Z"},"content_sha256":"2026ce486b476f70dabd735a34b4eb210ec2edeb9912600880477965fd0d7e1c","schema_version":"1.0","event_id":"sha256:2026ce486b476f70dabd735a34b4eb210ec2edeb9912600880477965fd0d7e1c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:RZX6IATJNNGI4JSE2JEZL5UY7N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"From Trigroups To Leibniz 3-Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Calvin Tcheka, Guy R. Biyogmam","submitted_at":"2019-04-26T20:02:38Z","abstract_excerpt":"In this paper, we study the category of trigroups as a generalization of the notion of digroup [4] and analyze their relationship with 3-racks [1] and Leibniz 3-algebras [6]. Trigroups are essentially associative trioids in which there are bar-units and bar-inverses. We prove that 3-racks can be constructed by conjugating trigroups. We also prove that trigroups equipped with a smooth manifold structure produce Leibniz 3-algebras via their associated Lie 3-racks."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.12030","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":"2026-05-17T23:47:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"woL8YqQ+xMYy/4eG3jjSACfACcpH39Z6LKzlgGkosQGR3xGnTrsmiGK1OAdE+AZFsy7gUjzoYaAd36YeUQ3PAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T23:42:12.445934Z"},"content_sha256":"077db3a34f9ce24a3e774035d024e3c5f0f491630ac3c002aa634ea89243c27e","schema_version":"1.0","event_id":"sha256:077db3a34f9ce24a3e774035d024e3c5f0f491630ac3c002aa634ea89243c27e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RZX6IATJNNGI4JSE2JEZL5UY7N/bundle.json","state_url":"https://pith.science/pith/RZX6IATJNNGI4JSE2JEZL5UY7N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RZX6IATJNNGI4JSE2JEZL5UY7N/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":"2026-06-30T23:42:12Z","links":{"resolver":"https://pith.science/pith/RZX6IATJNNGI4JSE2JEZL5UY7N","bundle":"https://pith.science/pith/RZX6IATJNNGI4JSE2JEZL5UY7N/bundle.json","state":"https://pith.science/pith/RZX6IATJNNGI4JSE2JEZL5UY7N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RZX6IATJNNGI4JSE2JEZL5UY7N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:RZX6IATJNNGI4JSE2JEZL5UY7N","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":"ad1227fdb000f1eb9513339833216fa8c931fcd34a81320cc91c0fa51f803c5b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-04-26T20:02:38Z","title_canon_sha256":"4b30ea0f3cf4ea99dedbda3947f04dad1f8acd50b596ac77d8d80070e403d523"},"schema_version":"1.0","source":{"id":"1904.12030","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.12030","created_at":"2026-05-17T23:47:39Z"},{"alias_kind":"arxiv_version","alias_value":"1904.12030v1","created_at":"2026-05-17T23:47:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.12030","created_at":"2026-05-17T23:47:39Z"},{"alias_kind":"pith_short_12","alias_value":"RZX6IATJNNGI","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"RZX6IATJNNGI4JSE","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"RZX6IATJ","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:077db3a34f9ce24a3e774035d024e3c5f0f491630ac3c002aa634ea89243c27e","target":"graph","created_at":"2026-05-17T23:47:39Z","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":"In this paper, we study the category of trigroups as a generalization of the notion of digroup [4] and analyze their relationship with 3-racks [1] and Leibniz 3-algebras [6]. Trigroups are essentially associative trioids in which there are bar-units and bar-inverses. We prove that 3-racks can be constructed by conjugating trigroups. We also prove that trigroups equipped with a smooth manifold structure produce Leibniz 3-algebras via their associated Lie 3-racks.","authors_text":"Calvin Tcheka, Guy R. Biyogmam","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-04-26T20:02:38Z","title":"From Trigroups To Leibniz 3-Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.12030","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":"sha256:2026ce486b476f70dabd735a34b4eb210ec2edeb9912600880477965fd0d7e1c","target":"record","created_at":"2026-05-17T23:47:39Z","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":"ad1227fdb000f1eb9513339833216fa8c931fcd34a81320cc91c0fa51f803c5b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-04-26T20:02:38Z","title_canon_sha256":"4b30ea0f3cf4ea99dedbda3947f04dad1f8acd50b596ac77d8d80070e403d523"},"schema_version":"1.0","source":{"id":"1904.12030","kind":"arxiv","version":1}},"canonical_sha256":"8e6fe402696b4c8e2644d24995f698fb5d0012f4b6fb85ab9c9c7d84b2840946","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8e6fe402696b4c8e2644d24995f698fb5d0012f4b6fb85ab9c9c7d84b2840946","first_computed_at":"2026-05-17T23:47:39.043587Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:39.043587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C5Wxmi6xnEprRj8hq3r9exmcKe26lGHVhPMSOjods8uvhdjdx3l6UoYo0OpLVCuWRM1GcBuH3NYFv8R+b4taAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:39.044108Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.12030","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2026ce486b476f70dabd735a34b4eb210ec2edeb9912600880477965fd0d7e1c","sha256:077db3a34f9ce24a3e774035d024e3c5f0f491630ac3c002aa634ea89243c27e"],"state_sha256":"24d9cb4c665d572e86e4ae76357acc43ff1c2046d72efdbe4560e85acf4c80d8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0KUWfupX9jSVklN+7DqFvPgxPYGCJhVHrQO/Eu8LCs1YmgGvgQ5RZnnKLru3zY+b16sJqhBIpfpNElr4yYo2DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T23:42:12.447920Z","bundle_sha256":"3ce4bc1546b953145d62fd71f79fecf86bcb49838110482570cdd229c6d2049e"}}