{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:RBK2ZZCP7BTHD26OW7RPADKOFS","short_pith_number":"pith:RBK2ZZCP","canonical_record":{"source":{"id":"2306.12425","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2023-03-08T07:05:46Z","cross_cats_sorted":[],"title_canon_sha256":"017238da9d54ec19de503fba33e939c1940a5f1744894132ca7c5539b5e34847","abstract_canon_sha256":"b26bbdafc4e9d0e8cde22c6ba08e80fe79d24c10ce54d8a509f825044cffa783"},"schema_version":"1.0"},"canonical_sha256":"8855ace44ff86671ebceb7e2f00d4e2c9ab69f4ab272f670b572caa2a85bcc05","source":{"kind":"arxiv","id":"2306.12425","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2306.12425","created_at":"2026-07-05T06:23:38Z"},{"alias_kind":"arxiv_version","alias_value":"2306.12425v1","created_at":"2026-07-05T06:23:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.12425","created_at":"2026-07-05T06:23:38Z"},{"alias_kind":"pith_short_12","alias_value":"RBK2ZZCP7BTH","created_at":"2026-07-05T06:23:38Z"},{"alias_kind":"pith_short_16","alias_value":"RBK2ZZCP7BTHD26O","created_at":"2026-07-05T06:23:38Z"},{"alias_kind":"pith_short_8","alias_value":"RBK2ZZCP","created_at":"2026-07-05T06:23:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:RBK2ZZCP7BTHD26OW7RPADKOFS","target":"record","payload":{"canonical_record":{"source":{"id":"2306.12425","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2023-03-08T07:05:46Z","cross_cats_sorted":[],"title_canon_sha256":"017238da9d54ec19de503fba33e939c1940a5f1744894132ca7c5539b5e34847","abstract_canon_sha256":"b26bbdafc4e9d0e8cde22c6ba08e80fe79d24c10ce54d8a509f825044cffa783"},"schema_version":"1.0"},"canonical_sha256":"8855ace44ff86671ebceb7e2f00d4e2c9ab69f4ab272f670b572caa2a85bcc05","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:23:38.559942Z","signature_b64":"2knIzLxFGRFE//MoAM3SXO5O3R4+OpvkkMWxX/iE4Mq0Th4GcUGW+4xurcn7Za7ZNVfQ4lNe+ZEyiZozrGJ8BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8855ace44ff86671ebceb7e2f00d4e2c9ab69f4ab272f670b572caa2a85bcc05","last_reissued_at":"2026-07-05T06:23:38.559537Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:23:38.559537Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2306.12425","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":"2026-07-05T06:23:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XSFKrFGlENP8KylCKWhgK1OXrMe9El8Hsd1mGQYGyRO9tJnc2q+876fHXJnyQiNGQJcLqBuju6L53u4F8KnmAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T20:22:35.387758Z"},"content_sha256":"c87f3e97cb5c4702df458a4c8a28149d2357e9b76799cd6077dae839fe8d4e33","schema_version":"1.0","event_id":"sha256:c87f3e97cb5c4702df458a4c8a28149d2357e9b76799cd6077dae839fe8d4e33"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:RBK2ZZCP7BTHD26OW7RPADKOFS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cohomologies of pre-LieDer pairs and applications","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Liangyun Chen, Shanshan Liu","submitted_at":"2023-03-08T07:05:46Z","abstract_excerpt":"In this paper, we use the higher derived bracket to give the controlling algebra of pre-LieDer pairs. We give the cohomology of pre-LieDer pairs by using the twist $L_\\infty$-algebra of this controlling algebra. In particular, we define the cohomology of regular pre-LieDer pairs. We study infinitesimal deformations of pre-LieDer pairs, which are characterized by the second cohomology group of pre-LieDer pairs. We also define the cohomology of regular pre-LieDer pairs with coefficients in arbitrary representation and using the second cohomology group to classify abelian extensions of regular pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.12425","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/2306.12425/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":"2026-07-05T06:23:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nTIU6/KP8wE5E8vwjRWPJPuXVBUY4bqLdMEJzvWI2ltnW1dJbI1st5ja9cTuCFzCeHTLbzLAfXSaGKVF6cEVCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T20:22:35.388234Z"},"content_sha256":"03194b20eaffaf9c4a40869473b6a722d3f131859e155de7a6526e613df2c3a3","schema_version":"1.0","event_id":"sha256:03194b20eaffaf9c4a40869473b6a722d3f131859e155de7a6526e613df2c3a3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RBK2ZZCP7BTHD26OW7RPADKOFS/bundle.json","state_url":"https://pith.science/pith/RBK2ZZCP7BTHD26OW7RPADKOFS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RBK2ZZCP7BTHD26OW7RPADKOFS/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":"2026-08-06T20:22:35Z","links":{"resolver":"https://pith.science/pith/RBK2ZZCP7BTHD26OW7RPADKOFS","bundle":"https://pith.science/pith/RBK2ZZCP7BTHD26OW7RPADKOFS/bundle.json","state":"https://pith.science/pith/RBK2ZZCP7BTHD26OW7RPADKOFS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RBK2ZZCP7BTHD26OW7RPADKOFS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:RBK2ZZCP7BTHD26OW7RPADKOFS","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":"b26bbdafc4e9d0e8cde22c6ba08e80fe79d24c10ce54d8a509f825044cffa783","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2023-03-08T07:05:46Z","title_canon_sha256":"017238da9d54ec19de503fba33e939c1940a5f1744894132ca7c5539b5e34847"},"schema_version":"1.0","source":{"id":"2306.12425","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2306.12425","created_at":"2026-07-05T06:23:38Z"},{"alias_kind":"arxiv_version","alias_value":"2306.12425v1","created_at":"2026-07-05T06:23:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.12425","created_at":"2026-07-05T06:23:38Z"},{"alias_kind":"pith_short_12","alias_value":"RBK2ZZCP7BTH","created_at":"2026-07-05T06:23:38Z"},{"alias_kind":"pith_short_16","alias_value":"RBK2ZZCP7BTHD26O","created_at":"2026-07-05T06:23:38Z"},{"alias_kind":"pith_short_8","alias_value":"RBK2ZZCP","created_at":"2026-07-05T06:23:38Z"}],"graph_snapshots":[{"event_id":"sha256:03194b20eaffaf9c4a40869473b6a722d3f131859e155de7a6526e613df2c3a3","target":"graph","created_at":"2026-07-05T06:23:38Z","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/2306.12425/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we use the higher derived bracket to give the controlling algebra of pre-LieDer pairs. We give the cohomology of pre-LieDer pairs by using the twist $L_\\infty$-algebra of this controlling algebra. In particular, we define the cohomology of regular pre-LieDer pairs. We study infinitesimal deformations of pre-LieDer pairs, which are characterized by the second cohomology group of pre-LieDer pairs. We also define the cohomology of regular pre-LieDer pairs with coefficients in arbitrary representation and using the second cohomology group to classify abelian extensions of regular pr","authors_text":"Liangyun Chen, Shanshan Liu","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2023-03-08T07:05:46Z","title":"Cohomologies of pre-LieDer pairs and applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.12425","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:c87f3e97cb5c4702df458a4c8a28149d2357e9b76799cd6077dae839fe8d4e33","target":"record","created_at":"2026-07-05T06:23:38Z","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":"b26bbdafc4e9d0e8cde22c6ba08e80fe79d24c10ce54d8a509f825044cffa783","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2023-03-08T07:05:46Z","title_canon_sha256":"017238da9d54ec19de503fba33e939c1940a5f1744894132ca7c5539b5e34847"},"schema_version":"1.0","source":{"id":"2306.12425","kind":"arxiv","version":1}},"canonical_sha256":"8855ace44ff86671ebceb7e2f00d4e2c9ab69f4ab272f670b572caa2a85bcc05","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8855ace44ff86671ebceb7e2f00d4e2c9ab69f4ab272f670b572caa2a85bcc05","first_computed_at":"2026-07-05T06:23:38.559537Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:23:38.559537Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2knIzLxFGRFE//MoAM3SXO5O3R4+OpvkkMWxX/iE4Mq0Th4GcUGW+4xurcn7Za7ZNVfQ4lNe+ZEyiZozrGJ8BA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:23:38.559942Z","signed_message":"canonical_sha256_bytes"},"source_id":"2306.12425","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c87f3e97cb5c4702df458a4c8a28149d2357e9b76799cd6077dae839fe8d4e33","sha256:03194b20eaffaf9c4a40869473b6a722d3f131859e155de7a6526e613df2c3a3"],"state_sha256":"b5be0c9603e3ea04b0901b1c223354bbfcf73b4e540d7cc4882942c23b487230"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tXFUR3qJOj/QVs2ITubdtq3fbTNR0DvmzZDigc0cTz7GiKn8joy1KhajlewkeStMbjHMMDnS0QmAuXIyQOCQDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T20:22:35.391496Z","bundle_sha256":"ff890b0ba545de2145d60c17544294952455c2f158b787a470c7f22ad417b748"}}