{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:X77Q32B5AJ4SMOC664CGLCRP7Z","short_pith_number":"pith:X77Q32B5","canonical_record":{"source":{"id":"2503.22157","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-03-28T05:22:57Z","cross_cats_sorted":[],"title_canon_sha256":"a06d8cd7412d34323ef01667898df0ec056d530bf09f5088e98b72436644dffc","abstract_canon_sha256":"e8964da5975fed72a906b03b583abaa3810b2598c5239d5002cd91063ddc7719"},"schema_version":"1.0"},"canonical_sha256":"bfff0de83d027926385ef704658a2ffe4f79d4a3cbd89a714ab14f12e41c71ce","source":{"kind":"arxiv","id":"2503.22157","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.22157","created_at":"2026-07-05T10:40:48Z"},{"alias_kind":"arxiv_version","alias_value":"2503.22157v1","created_at":"2026-07-05T10:40:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.22157","created_at":"2026-07-05T10:40:48Z"},{"alias_kind":"pith_short_12","alias_value":"X77Q32B5AJ4S","created_at":"2026-07-05T10:40:48Z"},{"alias_kind":"pith_short_16","alias_value":"X77Q32B5AJ4SMOC6","created_at":"2026-07-05T10:40:48Z"},{"alias_kind":"pith_short_8","alias_value":"X77Q32B5","created_at":"2026-07-05T10:40:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:X77Q32B5AJ4SMOC664CGLCRP7Z","target":"record","payload":{"canonical_record":{"source":{"id":"2503.22157","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-03-28T05:22:57Z","cross_cats_sorted":[],"title_canon_sha256":"a06d8cd7412d34323ef01667898df0ec056d530bf09f5088e98b72436644dffc","abstract_canon_sha256":"e8964da5975fed72a906b03b583abaa3810b2598c5239d5002cd91063ddc7719"},"schema_version":"1.0"},"canonical_sha256":"bfff0de83d027926385ef704658a2ffe4f79d4a3cbd89a714ab14f12e41c71ce","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:40:48.492443Z","signature_b64":"PlvB15Uo4s/g8/4NHfZajMhANvYtKCFYjL4/FIECAuZSburuLHmWUJJlUryP5ZOuQskNQpZLRAB2vNgntKtRCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bfff0de83d027926385ef704658a2ffe4f79d4a3cbd89a714ab14f12e41c71ce","last_reissued_at":"2026-07-05T10:40:48.491935Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:40:48.491935Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2503.22157","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":"2026-07-05T10:40:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KRPtiBkMYGedEeUaMxZgoApNVrD4zzXaDKBQs6qE4S8oYi7XBDE/v57riC7DBeR3ESdBA8CjSMBUx7DiTEj+AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T00:19:56.268738Z"},"content_sha256":"b4aa627d9dfdc72275ab62dbc380824a8bce1e070449a43f831d20bc93cb153e","schema_version":"1.0","event_id":"sha256:b4aa627d9dfdc72275ab62dbc380824a8bce1e070449a43f831d20bc93cb153e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:X77Q32B5AJ4SMOC664CGLCRP7Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Deformations of Nijenhuis Lie algebras and Nijenhuis Lie algebroids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Chao Song, Guodong Zhou, Kai Wang, Yuanyuan Zhang","submitted_at":"2025-03-28T05:22:57Z","abstract_excerpt":"This paper is the second in a series dedicated to the operadic study of Nijenhuis structures, focusing on Nijenhuis Lie algebras and Nijenhuis geometry. We introduce the concept of homotopy Nijenhuis Lie algebras and establish that the differential graded (=dg) operad $\\mathfrak{NjL}_{\\infty}$ governing these structures serves as the minimal model of the operad $\\mathfrak{NjL}$ for Nijenhuis Lie algebras. We construct an $L_\\infty$-algebra that encodes the simultaneous deformations of Lie brackets and Nijenhuis operators, leading to the deformation cochain complex and an associated cohomology "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.22157","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2503.22157/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T10:40:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cGo7h0tbrvaJE5eqZDRdOod9h0ZnRNqhGQhOwhYyfvSNxjzunBFLTmSwD7UsptQnBWDykg0dkhzVNi41axSwDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T00:19:56.269498Z"},"content_sha256":"5b89a7b9250ac2b6684c02e6a0a4ca90a7c67519af8344bca9b8981c959311bb","schema_version":"1.0","event_id":"sha256:5b89a7b9250ac2b6684c02e6a0a4ca90a7c67519af8344bca9b8981c959311bb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X77Q32B5AJ4SMOC664CGLCRP7Z/bundle.json","state_url":"https://pith.science/pith/X77Q32B5AJ4SMOC664CGLCRP7Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X77Q32B5AJ4SMOC664CGLCRP7Z/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":"2026-08-09T00:19:56Z","links":{"resolver":"https://pith.science/pith/X77Q32B5AJ4SMOC664CGLCRP7Z","bundle":"https://pith.science/pith/X77Q32B5AJ4SMOC664CGLCRP7Z/bundle.json","state":"https://pith.science/pith/X77Q32B5AJ4SMOC664CGLCRP7Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X77Q32B5AJ4SMOC664CGLCRP7Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:X77Q32B5AJ4SMOC664CGLCRP7Z","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":"e8964da5975fed72a906b03b583abaa3810b2598c5239d5002cd91063ddc7719","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-03-28T05:22:57Z","title_canon_sha256":"a06d8cd7412d34323ef01667898df0ec056d530bf09f5088e98b72436644dffc"},"schema_version":"1.0","source":{"id":"2503.22157","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.22157","created_at":"2026-07-05T10:40:48Z"},{"alias_kind":"arxiv_version","alias_value":"2503.22157v1","created_at":"2026-07-05T10:40:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.22157","created_at":"2026-07-05T10:40:48Z"},{"alias_kind":"pith_short_12","alias_value":"X77Q32B5AJ4S","created_at":"2026-07-05T10:40:48Z"},{"alias_kind":"pith_short_16","alias_value":"X77Q32B5AJ4SMOC6","created_at":"2026-07-05T10:40:48Z"},{"alias_kind":"pith_short_8","alias_value":"X77Q32B5","created_at":"2026-07-05T10:40:48Z"}],"graph_snapshots":[{"event_id":"sha256:5b89a7b9250ac2b6684c02e6a0a4ca90a7c67519af8344bca9b8981c959311bb","target":"graph","created_at":"2026-07-05T10:40:48Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2503.22157/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper is the second in a series dedicated to the operadic study of Nijenhuis structures, focusing on Nijenhuis Lie algebras and Nijenhuis geometry. We introduce the concept of homotopy Nijenhuis Lie algebras and establish that the differential graded (=dg) operad $\\mathfrak{NjL}_{\\infty}$ governing these structures serves as the minimal model of the operad $\\mathfrak{NjL}$ for Nijenhuis Lie algebras. We construct an $L_\\infty$-algebra that encodes the simultaneous deformations of Lie brackets and Nijenhuis operators, leading to the deformation cochain complex and an associated cohomology ","authors_text":"Chao Song, Guodong Zhou, Kai Wang, Yuanyuan Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-03-28T05:22:57Z","title":"Deformations of Nijenhuis Lie algebras and Nijenhuis Lie algebroids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.22157","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:b4aa627d9dfdc72275ab62dbc380824a8bce1e070449a43f831d20bc93cb153e","target":"record","created_at":"2026-07-05T10:40:48Z","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":"e8964da5975fed72a906b03b583abaa3810b2598c5239d5002cd91063ddc7719","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-03-28T05:22:57Z","title_canon_sha256":"a06d8cd7412d34323ef01667898df0ec056d530bf09f5088e98b72436644dffc"},"schema_version":"1.0","source":{"id":"2503.22157","kind":"arxiv","version":1}},"canonical_sha256":"bfff0de83d027926385ef704658a2ffe4f79d4a3cbd89a714ab14f12e41c71ce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bfff0de83d027926385ef704658a2ffe4f79d4a3cbd89a714ab14f12e41c71ce","first_computed_at":"2026-07-05T10:40:48.491935Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:40:48.491935Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PlvB15Uo4s/g8/4NHfZajMhANvYtKCFYjL4/FIECAuZSburuLHmWUJJlUryP5ZOuQskNQpZLRAB2vNgntKtRCA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:40:48.492443Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.22157","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b4aa627d9dfdc72275ab62dbc380824a8bce1e070449a43f831d20bc93cb153e","sha256:5b89a7b9250ac2b6684c02e6a0a4ca90a7c67519af8344bca9b8981c959311bb"],"state_sha256":"08e1933c1c191b30aa3bb5cf4adf3c4404f952ab45091185aed7452052e9009e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FQN5dN51jNvPKLZ1qqzbhSgm6++sibmJPNFp4uh5xqFq2tDtAVWnNVDym4WurctNiV3N1dLmbKWFDl76eXF3BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T00:19:56.275055Z","bundle_sha256":"4f831cc19df5719297f9188a29776765b49e473cb7d63a35cd4036534e59acd0"}}