{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:L6NO5X2TYBB5MAUWBUMY52G2LB","short_pith_number":"pith:L6NO5X2T","canonical_record":{"source":{"id":"1309.5204","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-09-20T08:28:01Z","cross_cats_sorted":[],"title_canon_sha256":"e0f9cb7e1e80dca093ba18136b9c841eb8fe401920bed7e67d9198dd87331dbc","abstract_canon_sha256":"b2bce5b5696cb9ca790fd0f7b8600e044be1b2f17d112c9d0349756100a2b702"},"schema_version":"1.0"},"canonical_sha256":"5f9aeedf53c043d602960d198ee8da5851dfaf41b4e10da3b9a0041706577138","source":{"kind":"arxiv","id":"1309.5204","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.5204","created_at":"2026-05-18T03:12:47Z"},{"alias_kind":"arxiv_version","alias_value":"1309.5204v1","created_at":"2026-05-18T03:12:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.5204","created_at":"2026-05-18T03:12:47Z"},{"alias_kind":"pith_short_12","alias_value":"L6NO5X2TYBB5","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"L6NO5X2TYBB5MAUW","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"L6NO5X2T","created_at":"2026-05-18T12:27:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:L6NO5X2TYBB5MAUWBUMY52G2LB","target":"record","payload":{"canonical_record":{"source":{"id":"1309.5204","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-09-20T08:28:01Z","cross_cats_sorted":[],"title_canon_sha256":"e0f9cb7e1e80dca093ba18136b9c841eb8fe401920bed7e67d9198dd87331dbc","abstract_canon_sha256":"b2bce5b5696cb9ca790fd0f7b8600e044be1b2f17d112c9d0349756100a2b702"},"schema_version":"1.0"},"canonical_sha256":"5f9aeedf53c043d602960d198ee8da5851dfaf41b4e10da3b9a0041706577138","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:47.263717Z","signature_b64":"sPTYONwiuXDucU8uObAAqLPr5UN21GeyXV8PoXtTf7dGXWQjLWjcnrA8xcahwvbHe+6QAVyiQ5K8jVCmUOurCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5f9aeedf53c043d602960d198ee8da5851dfaf41b4e10da3b9a0041706577138","last_reissued_at":"2026-05-18T03:12:47.262927Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:47.262927Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.5204","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":"2026-05-18T03:12:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gBkPbTIyrTQzsImPTDuAXBNnvnXBv6ATP/8/tPXITD4Z/1cv/mYsWCl5UXyzb1ayvOWPVgRAEwt5UhRsS5/PBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T12:40:45.170869Z"},"content_sha256":"f7420824bf9756ed8ba802ea7b12264b55ff746f5db9346ed57c2140f4a6649e","schema_version":"1.0","event_id":"sha256:f7420824bf9756ed8ba802ea7b12264b55ff746f5db9346ed57c2140f4a6649e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:L6NO5X2TYBB5MAUWBUMY52G2LB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the univeral \\alpha-central extensions of the semi-direct product of Hom-Leibniz algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"J. M. Casas, N Pacheco Regon","submitted_at":"2013-09-20T08:28:01Z","abstract_excerpt":"We introduce Hom-actions, semi-direct product and establish the equivalence between split extensions and the semi-direct product extension of Hom-Leibniz algebras. We analyze the functorial properties of the universal ({\\alpha})-central extensions of ({\\alpha})-perfect Hom-Leibniz algebras. We establish under what conditions an automorphism or a derivation can be lifted in an {\\alpha}-cover and we analyze the universal {\\alpha}-central extension of the semi-direct product of two {\\alpha}-perfect Hom-Leibniz algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5204","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":"2026-05-18T03:12:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lv4NINbS4fQWJohRl+TIgDO22Jnmw4As3Xz5lEqGGrbP8B7zKL+vxTzLvuXsd/w6C5yHb61UFo5k1z6q7KyLCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T12:40:45.171206Z"},"content_sha256":"ec0aeb7c343e84c6ad6fa205d104e933c93af56077ba036c41c599c564b175ff","schema_version":"1.0","event_id":"sha256:ec0aeb7c343e84c6ad6fa205d104e933c93af56077ba036c41c599c564b175ff"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L6NO5X2TYBB5MAUWBUMY52G2LB/bundle.json","state_url":"https://pith.science/pith/L6NO5X2TYBB5MAUWBUMY52G2LB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L6NO5X2TYBB5MAUWBUMY52G2LB/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":"2026-06-29T12:40:45Z","links":{"resolver":"https://pith.science/pith/L6NO5X2TYBB5MAUWBUMY52G2LB","bundle":"https://pith.science/pith/L6NO5X2TYBB5MAUWBUMY52G2LB/bundle.json","state":"https://pith.science/pith/L6NO5X2TYBB5MAUWBUMY52G2LB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L6NO5X2TYBB5MAUWBUMY52G2LB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:L6NO5X2TYBB5MAUWBUMY52G2LB","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":"b2bce5b5696cb9ca790fd0f7b8600e044be1b2f17d112c9d0349756100a2b702","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-09-20T08:28:01Z","title_canon_sha256":"e0f9cb7e1e80dca093ba18136b9c841eb8fe401920bed7e67d9198dd87331dbc"},"schema_version":"1.0","source":{"id":"1309.5204","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.5204","created_at":"2026-05-18T03:12:47Z"},{"alias_kind":"arxiv_version","alias_value":"1309.5204v1","created_at":"2026-05-18T03:12:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.5204","created_at":"2026-05-18T03:12:47Z"},{"alias_kind":"pith_short_12","alias_value":"L6NO5X2TYBB5","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"L6NO5X2TYBB5MAUW","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"L6NO5X2T","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:ec0aeb7c343e84c6ad6fa205d104e933c93af56077ba036c41c599c564b175ff","target":"graph","created_at":"2026-05-18T03:12:47Z","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 introduce Hom-actions, semi-direct product and establish the equivalence between split extensions and the semi-direct product extension of Hom-Leibniz algebras. We analyze the functorial properties of the universal ({\\alpha})-central extensions of ({\\alpha})-perfect Hom-Leibniz algebras. We establish under what conditions an automorphism or a derivation can be lifted in an {\\alpha}-cover and we analyze the universal {\\alpha}-central extension of the semi-direct product of two {\\alpha}-perfect Hom-Leibniz algebras.","authors_text":"J. M. Casas, N Pacheco Regon","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-09-20T08:28:01Z","title":"On the univeral \\alpha-central extensions of the semi-direct product of Hom-Leibniz algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5204","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:f7420824bf9756ed8ba802ea7b12264b55ff746f5db9346ed57c2140f4a6649e","target":"record","created_at":"2026-05-18T03:12:47Z","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":"b2bce5b5696cb9ca790fd0f7b8600e044be1b2f17d112c9d0349756100a2b702","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-09-20T08:28:01Z","title_canon_sha256":"e0f9cb7e1e80dca093ba18136b9c841eb8fe401920bed7e67d9198dd87331dbc"},"schema_version":"1.0","source":{"id":"1309.5204","kind":"arxiv","version":1}},"canonical_sha256":"5f9aeedf53c043d602960d198ee8da5851dfaf41b4e10da3b9a0041706577138","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5f9aeedf53c043d602960d198ee8da5851dfaf41b4e10da3b9a0041706577138","first_computed_at":"2026-05-18T03:12:47.262927Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:12:47.262927Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sPTYONwiuXDucU8uObAAqLPr5UN21GeyXV8PoXtTf7dGXWQjLWjcnrA8xcahwvbHe+6QAVyiQ5K8jVCmUOurCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:12:47.263717Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.5204","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f7420824bf9756ed8ba802ea7b12264b55ff746f5db9346ed57c2140f4a6649e","sha256:ec0aeb7c343e84c6ad6fa205d104e933c93af56077ba036c41c599c564b175ff"],"state_sha256":"d61c1ae29286cdb96012dd37d64a981a93aece979887d3e6b14ffd378a3ee2fd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9GdRUhRHOEiQ6RML9FMDf7MSs9S0BIBtxM1zI3g+QAINSq+xOcIhGkyNF1CXQ3K850OVjDO64i2JDPFswOULDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T12:40:45.173020Z","bundle_sha256":"78500898633e74d15db9a0a0cd45abc6ec11a1368bb7e8ee1c78ea046d2147a8"}}