{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:WB7JZ3CYZA4TV7L6BZCMSEE3KQ","short_pith_number":"pith:WB7JZ3CY","canonical_record":{"source":{"id":"2303.12906","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2023-02-07T23:58:31Z","cross_cats_sorted":[],"title_canon_sha256":"ba8ef03ee1f6e3ab8a46973c14021e19cb24ff1e57701556f71a8a301f4ab545","abstract_canon_sha256":"40e33434fbd822f9bfdf6a8c3c35d7e304dd81b64998aca38d6f80898b2fce28"},"schema_version":"1.0"},"canonical_sha256":"b07e9cec58c8393afd7e0e44c9109b540827484f8bebfc64b43563f3d8520441","source":{"kind":"arxiv","id":"2303.12906","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2303.12906","created_at":"2026-07-05T05:53:55Z"},{"alias_kind":"arxiv_version","alias_value":"2303.12906v1","created_at":"2026-07-05T05:53:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.12906","created_at":"2026-07-05T05:53:55Z"},{"alias_kind":"pith_short_12","alias_value":"WB7JZ3CYZA4T","created_at":"2026-07-05T05:53:55Z"},{"alias_kind":"pith_short_16","alias_value":"WB7JZ3CYZA4TV7L6","created_at":"2026-07-05T05:53:55Z"},{"alias_kind":"pith_short_8","alias_value":"WB7JZ3CY","created_at":"2026-07-05T05:53:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:WB7JZ3CYZA4TV7L6BZCMSEE3KQ","target":"record","payload":{"canonical_record":{"source":{"id":"2303.12906","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2023-02-07T23:58:31Z","cross_cats_sorted":[],"title_canon_sha256":"ba8ef03ee1f6e3ab8a46973c14021e19cb24ff1e57701556f71a8a301f4ab545","abstract_canon_sha256":"40e33434fbd822f9bfdf6a8c3c35d7e304dd81b64998aca38d6f80898b2fce28"},"schema_version":"1.0"},"canonical_sha256":"b07e9cec58c8393afd7e0e44c9109b540827484f8bebfc64b43563f3d8520441","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:53:55.206798Z","signature_b64":"nteNcc8aoS5iTlH19cxzbhj48OxoiNrMSBTFMCENnsuykY+uqwye+2/q786X4/zbzDddTTMJgFpAAR5Blh9sAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b07e9cec58c8393afd7e0e44c9109b540827484f8bebfc64b43563f3d8520441","last_reissued_at":"2026-07-05T05:53:55.206261Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:53:55.206261Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2303.12906","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":"2026-07-05T05:53:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DSrB+db/+IK9kHRz5THrdbhAhHmFD4jfYUkYBK9au64sOFJhkTdz5By63n/jU5Ct7Chv3gyoSTRGhZcvWIBvAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T22:26:08.568744Z"},"content_sha256":"365107d6eaa43b6fdef2dc53769f0062d89b8067c09394c5b326fe3c8565c4c5","schema_version":"1.0","event_id":"sha256:365107d6eaa43b6fdef2dc53769f0062d89b8067c09394c5b326fe3c8565c4c5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:WB7JZ3CYZA4TV7L6BZCMSEE3KQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cohomology of compatible BiHom-Lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Asif Sania, Basdouri Imed, Bouzid Mosbahi, Nacib Saber","submitted_at":"2023-02-07T23:58:31Z","abstract_excerpt":"This paper defines compatible BiHom-Lie algebras by twisting the compatible Lie algebras by two linear commuting maps. We show the characterization of compatible BiHom-Lie algebra as a Maurer-Cartan element in a suitable bidifferential graded Lie algebra. We also define a cohomology theory for compatible BiHom-Lie algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.12906","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/2303.12906/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":"2026-07-05T05:53:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BEw8fgzYGdPL3PoId+VuOh0QPBi9Vyj8V6R6RXHsfLmhsCZgAaZcdqaeZqy/vuGiH8fZD8f4qj5yJBtKrg05BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T22:26:08.569293Z"},"content_sha256":"b5707d19468a3dd18536215db2894c0d825188b8a699e47d52ba066602ea4e88","schema_version":"1.0","event_id":"sha256:b5707d19468a3dd18536215db2894c0d825188b8a699e47d52ba066602ea4e88"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WB7JZ3CYZA4TV7L6BZCMSEE3KQ/bundle.json","state_url":"https://pith.science/pith/WB7JZ3CYZA4TV7L6BZCMSEE3KQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WB7JZ3CYZA4TV7L6BZCMSEE3KQ/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":"2026-08-13T22:26:08Z","links":{"resolver":"https://pith.science/pith/WB7JZ3CYZA4TV7L6BZCMSEE3KQ","bundle":"https://pith.science/pith/WB7JZ3CYZA4TV7L6BZCMSEE3KQ/bundle.json","state":"https://pith.science/pith/WB7JZ3CYZA4TV7L6BZCMSEE3KQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WB7JZ3CYZA4TV7L6BZCMSEE3KQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:WB7JZ3CYZA4TV7L6BZCMSEE3KQ","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":"40e33434fbd822f9bfdf6a8c3c35d7e304dd81b64998aca38d6f80898b2fce28","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2023-02-07T23:58:31Z","title_canon_sha256":"ba8ef03ee1f6e3ab8a46973c14021e19cb24ff1e57701556f71a8a301f4ab545"},"schema_version":"1.0","source":{"id":"2303.12906","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2303.12906","created_at":"2026-07-05T05:53:55Z"},{"alias_kind":"arxiv_version","alias_value":"2303.12906v1","created_at":"2026-07-05T05:53:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.12906","created_at":"2026-07-05T05:53:55Z"},{"alias_kind":"pith_short_12","alias_value":"WB7JZ3CYZA4T","created_at":"2026-07-05T05:53:55Z"},{"alias_kind":"pith_short_16","alias_value":"WB7JZ3CYZA4TV7L6","created_at":"2026-07-05T05:53:55Z"},{"alias_kind":"pith_short_8","alias_value":"WB7JZ3CY","created_at":"2026-07-05T05:53:55Z"}],"graph_snapshots":[{"event_id":"sha256:b5707d19468a3dd18536215db2894c0d825188b8a699e47d52ba066602ea4e88","target":"graph","created_at":"2026-07-05T05:53:55Z","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/2303.12906/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper defines compatible BiHom-Lie algebras by twisting the compatible Lie algebras by two linear commuting maps. We show the characterization of compatible BiHom-Lie algebra as a Maurer-Cartan element in a suitable bidifferential graded Lie algebra. We also define a cohomology theory for compatible BiHom-Lie algebras.","authors_text":"Asif Sania, Basdouri Imed, Bouzid Mosbahi, Nacib Saber","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2023-02-07T23:58:31Z","title":"Cohomology of compatible BiHom-Lie algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.12906","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":"sha256:365107d6eaa43b6fdef2dc53769f0062d89b8067c09394c5b326fe3c8565c4c5","target":"record","created_at":"2026-07-05T05:53:55Z","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":"40e33434fbd822f9bfdf6a8c3c35d7e304dd81b64998aca38d6f80898b2fce28","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2023-02-07T23:58:31Z","title_canon_sha256":"ba8ef03ee1f6e3ab8a46973c14021e19cb24ff1e57701556f71a8a301f4ab545"},"schema_version":"1.0","source":{"id":"2303.12906","kind":"arxiv","version":1}},"canonical_sha256":"b07e9cec58c8393afd7e0e44c9109b540827484f8bebfc64b43563f3d8520441","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b07e9cec58c8393afd7e0e44c9109b540827484f8bebfc64b43563f3d8520441","first_computed_at":"2026-07-05T05:53:55.206261Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:53:55.206261Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nteNcc8aoS5iTlH19cxzbhj48OxoiNrMSBTFMCENnsuykY+uqwye+2/q786X4/zbzDddTTMJgFpAAR5Blh9sAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T05:53:55.206798Z","signed_message":"canonical_sha256_bytes"},"source_id":"2303.12906","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:365107d6eaa43b6fdef2dc53769f0062d89b8067c09394c5b326fe3c8565c4c5","sha256:b5707d19468a3dd18536215db2894c0d825188b8a699e47d52ba066602ea4e88"],"state_sha256":"c56fc24252cf357fdc5e0c29193852d6d804a99ba528829752ce32f38b738d39"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O8NJDGED1+G9F7DbVe4nx3UG4qFgizkkq/AUqblKXxPvdS9yRPE7jOi3CRcvNezpD1kyhcl2VoxE+qfv9kJSBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T22:26:08.578620Z","bundle_sha256":"32d2cb8cd1f99d480cf485998608ddaedf360f5b6b3b2001fcfa4b98e3ded28b"}}