{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:3XXY3UYZYAZPQAIVYOGIXDOBXA","short_pith_number":"pith:3XXY3UYZ","canonical_record":{"source":{"id":"1503.00761","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-12-11T06:19:37Z","cross_cats_sorted":[],"title_canon_sha256":"b35cc60ded965113439baf3ba8cdef6952613b0de4a957b2f30bf213a1a8d641","abstract_canon_sha256":"541ef0ecba0970434c59b6024affca6648221c9d6d4aa77765cc277528a71fec"},"schema_version":"1.0"},"canonical_sha256":"ddef8dd319c032f80115c38c8b8dc1b82cf971c889d06f15be7ea16eb3399341","source":{"kind":"arxiv","id":"1503.00761","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.00761","created_at":"2026-05-18T01:21:13Z"},{"alias_kind":"arxiv_version","alias_value":"1503.00761v2","created_at":"2026-05-18T01:21:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.00761","created_at":"2026-05-18T01:21:13Z"},{"alias_kind":"pith_short_12","alias_value":"3XXY3UYZYAZP","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3XXY3UYZYAZPQAIV","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3XXY3UYZ","created_at":"2026-05-18T12:28:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:3XXY3UYZYAZPQAIVYOGIXDOBXA","target":"record","payload":{"canonical_record":{"source":{"id":"1503.00761","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-12-11T06:19:37Z","cross_cats_sorted":[],"title_canon_sha256":"b35cc60ded965113439baf3ba8cdef6952613b0de4a957b2f30bf213a1a8d641","abstract_canon_sha256":"541ef0ecba0970434c59b6024affca6648221c9d6d4aa77765cc277528a71fec"},"schema_version":"1.0"},"canonical_sha256":"ddef8dd319c032f80115c38c8b8dc1b82cf971c889d06f15be7ea16eb3399341","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:13.496918Z","signature_b64":"kKIodwX9ghxtGuJb3atGKhNhUqRMWFM1YsGpNORvz5KhLO0F7DbbMhh3zb2DSerdeBVW1guiRRBvhyImnFo7BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ddef8dd319c032f80115c38c8b8dc1b82cf971c889d06f15be7ea16eb3399341","last_reissued_at":"2026-05-18T01:21:13.496258Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:13.496258Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.00761","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":"2026-05-18T01:21:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w+ZnAzDxVz2iGyv+5GjvwZi85cHtHJqxlD7pfOqYZVTN16fIAYtkP2PyLL/0A7pZWm4CBZBt5otMzmt/6HxgDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T05:19:10.070227Z"},"content_sha256":"c89105329812b0286ee80f877131be511d6555060c7be592f3ad68d8acc068ca","schema_version":"1.0","event_id":"sha256:c89105329812b0286ee80f877131be511d6555060c7be592f3ad68d8acc068ca"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:3XXY3UYZYAZPQAIVYOGIXDOBXA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exterior differential calculus in generalized Lie algebras(algebroids) category with applications to interior and exterior algebraic(differential) systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"C. M. Arcus, E. Peyghan","submitted_at":"2014-12-11T06:19:37Z","abstract_excerpt":"A new category of Lie algebras, called generalized Lie algebras, is presented such that classical Lie algebras and Lie-Rinehart algebras are objects of this new category. A new philosophy over generalized Lie algebroids theory is presented using the notion of generalized Lie algebra and examples of objects of the category of generalized Lie algebroids are presented. An exterior differential calculus on generalized Lie algebras is pre- sented and a theorem of Maurer-Cartan type is obtained. Supposing that any submodule(vector subbundle) of a generalized Lie algebra(algebroid) is an interior alg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.00761","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":"2026-05-18T01:21:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"da4tihMS+srMNVIkbwK46qsAFFGfA56OwIDq1hOzVU6bIjHi0zJA5dqa1iemyCoqlP7ejXFQ8rQFGCqiR5niCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T05:19:10.070993Z"},"content_sha256":"2297b542a90d470e8a6faa14e55dfe358feee7ff06fe3ad7f22c1c629d61e809","schema_version":"1.0","event_id":"sha256:2297b542a90d470e8a6faa14e55dfe358feee7ff06fe3ad7f22c1c629d61e809"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3XXY3UYZYAZPQAIVYOGIXDOBXA/bundle.json","state_url":"https://pith.science/pith/3XXY3UYZYAZPQAIVYOGIXDOBXA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3XXY3UYZYAZPQAIVYOGIXDOBXA/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":"2026-05-31T05:19:10Z","links":{"resolver":"https://pith.science/pith/3XXY3UYZYAZPQAIVYOGIXDOBXA","bundle":"https://pith.science/pith/3XXY3UYZYAZPQAIVYOGIXDOBXA/bundle.json","state":"https://pith.science/pith/3XXY3UYZYAZPQAIVYOGIXDOBXA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3XXY3UYZYAZPQAIVYOGIXDOBXA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:3XXY3UYZYAZPQAIVYOGIXDOBXA","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":"541ef0ecba0970434c59b6024affca6648221c9d6d4aa77765cc277528a71fec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-12-11T06:19:37Z","title_canon_sha256":"b35cc60ded965113439baf3ba8cdef6952613b0de4a957b2f30bf213a1a8d641"},"schema_version":"1.0","source":{"id":"1503.00761","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.00761","created_at":"2026-05-18T01:21:13Z"},{"alias_kind":"arxiv_version","alias_value":"1503.00761v2","created_at":"2026-05-18T01:21:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.00761","created_at":"2026-05-18T01:21:13Z"},{"alias_kind":"pith_short_12","alias_value":"3XXY3UYZYAZP","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3XXY3UYZYAZPQAIV","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3XXY3UYZ","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:2297b542a90d470e8a6faa14e55dfe358feee7ff06fe3ad7f22c1c629d61e809","target":"graph","created_at":"2026-05-18T01:21:13Z","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":"A new category of Lie algebras, called generalized Lie algebras, is presented such that classical Lie algebras and Lie-Rinehart algebras are objects of this new category. A new philosophy over generalized Lie algebroids theory is presented using the notion of generalized Lie algebra and examples of objects of the category of generalized Lie algebroids are presented. An exterior differential calculus on generalized Lie algebras is pre- sented and a theorem of Maurer-Cartan type is obtained. Supposing that any submodule(vector subbundle) of a generalized Lie algebra(algebroid) is an interior alg","authors_text":"C. M. Arcus, E. Peyghan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-12-11T06:19:37Z","title":"Exterior differential calculus in generalized Lie algebras(algebroids) category with applications to interior and exterior algebraic(differential) systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.00761","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:c89105329812b0286ee80f877131be511d6555060c7be592f3ad68d8acc068ca","target":"record","created_at":"2026-05-18T01:21:13Z","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":"541ef0ecba0970434c59b6024affca6648221c9d6d4aa77765cc277528a71fec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-12-11T06:19:37Z","title_canon_sha256":"b35cc60ded965113439baf3ba8cdef6952613b0de4a957b2f30bf213a1a8d641"},"schema_version":"1.0","source":{"id":"1503.00761","kind":"arxiv","version":2}},"canonical_sha256":"ddef8dd319c032f80115c38c8b8dc1b82cf971c889d06f15be7ea16eb3399341","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ddef8dd319c032f80115c38c8b8dc1b82cf971c889d06f15be7ea16eb3399341","first_computed_at":"2026-05-18T01:21:13.496258Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:13.496258Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kKIodwX9ghxtGuJb3atGKhNhUqRMWFM1YsGpNORvz5KhLO0F7DbbMhh3zb2DSerdeBVW1guiRRBvhyImnFo7BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:13.496918Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.00761","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c89105329812b0286ee80f877131be511d6555060c7be592f3ad68d8acc068ca","sha256:2297b542a90d470e8a6faa14e55dfe358feee7ff06fe3ad7f22c1c629d61e809"],"state_sha256":"638ff1bede365ed5c1af27deee0c6ac8511e6498aa619200fe4b3472425535be"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LYA9d6oi3ARQqEwuz7n6xIIhDNod3cvT9laQwuwK4ZRjlNjpSGr/vF/CNTqPUym7dyThc3ic3FLasxVCfSk0CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T05:19:10.074916Z","bundle_sha256":"82bff00f62e4eb4ef8ec99991d89aa0eb6b0fd92a7bb354db6385e84033523c8"}}