{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:QYLBZMQCL6XH4W6PSTCVK2SGZT","short_pith_number":"pith:QYLBZMQC","canonical_record":{"source":{"id":"0802.3471","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2008-02-25T16:53:34Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"895c0ed1dffc66d310a0ae18103e4be527cc028e44d8dbebf5ae3c4cb7600253","abstract_canon_sha256":"d77ff075b93195628ee75f1b7c104833f3ce873a13b738d06ae513ca9631eef1"},"schema_version":"1.0"},"canonical_sha256":"86161cb2025fae7e5bcf94c5556a46ccedd96ce63a16b3c72b272c9f0de77975","source":{"kind":"arxiv","id":"0802.3471","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0802.3471","created_at":"2026-05-18T01:17:10Z"},{"alias_kind":"arxiv_version","alias_value":"0802.3471v2","created_at":"2026-05-18T01:17:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0802.3471","created_at":"2026-05-18T01:17:10Z"},{"alias_kind":"pith_short_12","alias_value":"QYLBZMQCL6XH","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"QYLBZMQCL6XH4W6P","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"QYLBZMQC","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:QYLBZMQCL6XH4W6PSTCVK2SGZT","target":"record","payload":{"canonical_record":{"source":{"id":"0802.3471","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2008-02-25T16:53:34Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"895c0ed1dffc66d310a0ae18103e4be527cc028e44d8dbebf5ae3c4cb7600253","abstract_canon_sha256":"d77ff075b93195628ee75f1b7c104833f3ce873a13b738d06ae513ca9631eef1"},"schema_version":"1.0"},"canonical_sha256":"86161cb2025fae7e5bcf94c5556a46ccedd96ce63a16b3c72b272c9f0de77975","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:10.622288Z","signature_b64":"AhbPOTVTFUqjf8JmBRnk9ZEKQ508NCQlzXPEQp6WzrXe9+Wbf1M4lhXegz0Lr6UeiOBFRIoKC2mj/JL/EKgiBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"86161cb2025fae7e5bcf94c5556a46ccedd96ce63a16b3c72b272c9f0de77975","last_reissued_at":"2026-05-18T01:17:10.621422Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:10.621422Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0802.3471","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:17:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0vUI5IvHWg3SCmKWNhpQT9E+VM9JV5i1ZpZttmLIp4qQtN7iR109ytcQiDve49iyaYKckmP1wESOEX16q5dvCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T11:01:22.067398Z"},"content_sha256":"0d21004c4390edebec6c5e1190039fe0776d6d3312e4efddda3a31ad4f3546e9","schema_version":"1.0","event_id":"sha256:0d21004c4390edebec6c5e1190039fe0776d6d3312e4efddda3a31ad4f3546e9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:QYLBZMQCL6XH4W6PSTCVK2SGZT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Moufang symmetry I. Generalized Lie and Maurer-Cartan equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.RT","authors_text":"Eugen Paal","submitted_at":"2008-02-25T16:53:34Z","abstract_excerpt":"The continuous Moufang loops are characterized as the algebraic systems where the associativity law is perturbed minimally. The minimal perturbation of associativity is characterized by the first- order partial differential equations, which in a natural way generalize the Lie and Maurer-Cartan equations from the theory of Lie groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0802.3471","kind":"arxiv","version":2},"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":"2026-05-18T01:17:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZXXDph0xB/R1FWnw+fh5M+JFyEDj/wj04Bk9b4iGLjP3KFn4+dwev5mHLWteQkA7ccaMqYDKgyYnbZ53nL3sCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T11:01:22.067931Z"},"content_sha256":"cbfff12168d2c7ea0ba13a33da9e6f4556c807207dbd62cf6d5f15d6991c3a96","schema_version":"1.0","event_id":"sha256:cbfff12168d2c7ea0ba13a33da9e6f4556c807207dbd62cf6d5f15d6991c3a96"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QYLBZMQCL6XH4W6PSTCVK2SGZT/bundle.json","state_url":"https://pith.science/pith/QYLBZMQCL6XH4W6PSTCVK2SGZT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QYLBZMQCL6XH4W6PSTCVK2SGZT/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":"2026-06-05T11:01:22Z","links":{"resolver":"https://pith.science/pith/QYLBZMQCL6XH4W6PSTCVK2SGZT","bundle":"https://pith.science/pith/QYLBZMQCL6XH4W6PSTCVK2SGZT/bundle.json","state":"https://pith.science/pith/QYLBZMQCL6XH4W6PSTCVK2SGZT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QYLBZMQCL6XH4W6PSTCVK2SGZT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:QYLBZMQCL6XH4W6PSTCVK2SGZT","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":"d77ff075b93195628ee75f1b7c104833f3ce873a13b738d06ae513ca9631eef1","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2008-02-25T16:53:34Z","title_canon_sha256":"895c0ed1dffc66d310a0ae18103e4be527cc028e44d8dbebf5ae3c4cb7600253"},"schema_version":"1.0","source":{"id":"0802.3471","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0802.3471","created_at":"2026-05-18T01:17:10Z"},{"alias_kind":"arxiv_version","alias_value":"0802.3471v2","created_at":"2026-05-18T01:17:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0802.3471","created_at":"2026-05-18T01:17:10Z"},{"alias_kind":"pith_short_12","alias_value":"QYLBZMQCL6XH","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"QYLBZMQCL6XH4W6P","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"QYLBZMQC","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:cbfff12168d2c7ea0ba13a33da9e6f4556c807207dbd62cf6d5f15d6991c3a96","target":"graph","created_at":"2026-05-18T01:17:10Z","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":"The continuous Moufang loops are characterized as the algebraic systems where the associativity law is perturbed minimally. The minimal perturbation of associativity is characterized by the first- order partial differential equations, which in a natural way generalize the Lie and Maurer-Cartan equations from the theory of Lie groups.","authors_text":"Eugen Paal","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2008-02-25T16:53:34Z","title":"Moufang symmetry I. Generalized Lie and Maurer-Cartan equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0802.3471","kind":"arxiv","version":2},"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":"sha256:0d21004c4390edebec6c5e1190039fe0776d6d3312e4efddda3a31ad4f3546e9","target":"record","created_at":"2026-05-18T01:17:10Z","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":"d77ff075b93195628ee75f1b7c104833f3ce873a13b738d06ae513ca9631eef1","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2008-02-25T16:53:34Z","title_canon_sha256":"895c0ed1dffc66d310a0ae18103e4be527cc028e44d8dbebf5ae3c4cb7600253"},"schema_version":"1.0","source":{"id":"0802.3471","kind":"arxiv","version":2}},"canonical_sha256":"86161cb2025fae7e5bcf94c5556a46ccedd96ce63a16b3c72b272c9f0de77975","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"86161cb2025fae7e5bcf94c5556a46ccedd96ce63a16b3c72b272c9f0de77975","first_computed_at":"2026-05-18T01:17:10.621422Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:10.621422Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AhbPOTVTFUqjf8JmBRnk9ZEKQ508NCQlzXPEQp6WzrXe9+Wbf1M4lhXegz0Lr6UeiOBFRIoKC2mj/JL/EKgiBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:10.622288Z","signed_message":"canonical_sha256_bytes"},"source_id":"0802.3471","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0d21004c4390edebec6c5e1190039fe0776d6d3312e4efddda3a31ad4f3546e9","sha256:cbfff12168d2c7ea0ba13a33da9e6f4556c807207dbd62cf6d5f15d6991c3a96"],"state_sha256":"7050f26bd454401a26e8cfca68dd94f104497e27b15cb7baf77fb603eec06473"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z1r14Mv7LGBpA1R4mf+DtZx8en6aUqv1FiqUbaLWkJocNcK+AU9YjfamID245wM+ha/36PmI5+LJ3vwcITYJBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T11:01:22.070402Z","bundle_sha256":"825eda0dd132f918393e294ba795a50a3e20a0216d1609073de5121ecb5917b9"}}