{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:TM2IKFUK5AAKPDZGL6FPGWEKOT","short_pith_number":"pith:TM2IKFUK","canonical_record":{"source":{"id":"2406.12859","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.RA","submitted_at":"2024-03-06T09:25:17Z","cross_cats_sorted":[],"title_canon_sha256":"a3ada54a09cdb2ed325c73c8cd11e24b484cb31fa45bfc60806a6ce46928665c","abstract_canon_sha256":"b16e7f546112b74e30f8443369397a8a8244719bd8a4619224fd1aa3c9994a77"},"schema_version":"1.0"},"canonical_sha256":"9b3485168ae800a78f265f8af3588a74cffca6bf0b21985f4f27ddac3f41e64d","source":{"kind":"arxiv","id":"2406.12859","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.12859","created_at":"2026-07-05T08:33:52Z"},{"alias_kind":"arxiv_version","alias_value":"2406.12859v1","created_at":"2026-07-05T08:33:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.12859","created_at":"2026-07-05T08:33:52Z"},{"alias_kind":"pith_short_12","alias_value":"TM2IKFUK5AAK","created_at":"2026-07-05T08:33:52Z"},{"alias_kind":"pith_short_16","alias_value":"TM2IKFUK5AAKPDZG","created_at":"2026-07-05T08:33:52Z"},{"alias_kind":"pith_short_8","alias_value":"TM2IKFUK","created_at":"2026-07-05T08:33:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:TM2IKFUK5AAKPDZGL6FPGWEKOT","target":"record","payload":{"canonical_record":{"source":{"id":"2406.12859","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.RA","submitted_at":"2024-03-06T09:25:17Z","cross_cats_sorted":[],"title_canon_sha256":"a3ada54a09cdb2ed325c73c8cd11e24b484cb31fa45bfc60806a6ce46928665c","abstract_canon_sha256":"b16e7f546112b74e30f8443369397a8a8244719bd8a4619224fd1aa3c9994a77"},"schema_version":"1.0"},"canonical_sha256":"9b3485168ae800a78f265f8af3588a74cffca6bf0b21985f4f27ddac3f41e64d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:33:52.381006Z","signature_b64":"Gf6/QBDbkM8Dw6NkGMcKPoxgCoVW4lnkDFLGPDxWMkKGpTdjeJxcJOQxmXn/55A/HIacqBDTn7HXoRXNbeY5Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b3485168ae800a78f265f8af3588a74cffca6bf0b21985f4f27ddac3f41e64d","last_reissued_at":"2026-07-05T08:33:52.380624Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:33:52.380624Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2406.12859","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":"2026-07-05T08:33:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eFvWNw032KzXjnqcOD1epA2Aea0fTFjm2wclCqMvU6Z644eahWFb57JXXyR8GcgZjf08ILPcfkbAxDepPif9DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T18:08:30.480517Z"},"content_sha256":"851c61163082de1337146b7073b55f7a06eb4686e0545e95eb097af4ae8273ea","schema_version":"1.0","event_id":"sha256:851c61163082de1337146b7073b55f7a06eb4686e0545e95eb097af4ae8273ea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:TM2IKFUK5AAKPDZGL6FPGWEKOT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cohomologies of Reynolds Lie-Yamaguti algebras of any weight and applications","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Shuangjian Guo, Wen Teng","submitted_at":"2024-03-06T09:25:17Z","abstract_excerpt":"The purpose of the present paper is to investigate cohomologies of Reynolds Lie-Yamaguti algebras of any weight and provide some applications. First, we introduce the notion of Reynolds Lie-Yamaguti algebras and give some new examples. Moreover, cohomologies of Reynolds operators and Reynolds Lie-Yamaguti algebras with coefficients in a suitable representation are established. Finally, formal deformations and abelian extensions of Reynolds Lie-Yamaguti algebras are characterized in terms of lower degree cohomology groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.12859","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/2406.12859/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":"2026-07-05T08:33:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p9P6IrccTiggH55pMCXN3nYNAkLurF3rg2CkqSrtTDtY8lUokIqsShRRXX/eIFnLMhCKE2F/5Wx0zqHad4ZiDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T18:08:30.480875Z"},"content_sha256":"04bae4918e25b803ed84f22624034c72556c9b3afe221df5e2a6425ec7622c78","schema_version":"1.0","event_id":"sha256:04bae4918e25b803ed84f22624034c72556c9b3afe221df5e2a6425ec7622c78"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TM2IKFUK5AAKPDZGL6FPGWEKOT/bundle.json","state_url":"https://pith.science/pith/TM2IKFUK5AAKPDZGL6FPGWEKOT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TM2IKFUK5AAKPDZGL6FPGWEKOT/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":"2026-07-06T18:08:30Z","links":{"resolver":"https://pith.science/pith/TM2IKFUK5AAKPDZGL6FPGWEKOT","bundle":"https://pith.science/pith/TM2IKFUK5AAKPDZGL6FPGWEKOT/bundle.json","state":"https://pith.science/pith/TM2IKFUK5AAKPDZGL6FPGWEKOT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TM2IKFUK5AAKPDZGL6FPGWEKOT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:TM2IKFUK5AAKPDZGL6FPGWEKOT","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":"b16e7f546112b74e30f8443369397a8a8244719bd8a4619224fd1aa3c9994a77","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.RA","submitted_at":"2024-03-06T09:25:17Z","title_canon_sha256":"a3ada54a09cdb2ed325c73c8cd11e24b484cb31fa45bfc60806a6ce46928665c"},"schema_version":"1.0","source":{"id":"2406.12859","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.12859","created_at":"2026-07-05T08:33:52Z"},{"alias_kind":"arxiv_version","alias_value":"2406.12859v1","created_at":"2026-07-05T08:33:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.12859","created_at":"2026-07-05T08:33:52Z"},{"alias_kind":"pith_short_12","alias_value":"TM2IKFUK5AAK","created_at":"2026-07-05T08:33:52Z"},{"alias_kind":"pith_short_16","alias_value":"TM2IKFUK5AAKPDZG","created_at":"2026-07-05T08:33:52Z"},{"alias_kind":"pith_short_8","alias_value":"TM2IKFUK","created_at":"2026-07-05T08:33:52Z"}],"graph_snapshots":[{"event_id":"sha256:04bae4918e25b803ed84f22624034c72556c9b3afe221df5e2a6425ec7622c78","target":"graph","created_at":"2026-07-05T08:33:52Z","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/2406.12859/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The purpose of the present paper is to investigate cohomologies of Reynolds Lie-Yamaguti algebras of any weight and provide some applications. First, we introduce the notion of Reynolds Lie-Yamaguti algebras and give some new examples. Moreover, cohomologies of Reynolds operators and Reynolds Lie-Yamaguti algebras with coefficients in a suitable representation are established. Finally, formal deformations and abelian extensions of Reynolds Lie-Yamaguti algebras are characterized in terms of lower degree cohomology groups.","authors_text":"Shuangjian Guo, Wen Teng","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.RA","submitted_at":"2024-03-06T09:25:17Z","title":"Cohomologies of Reynolds Lie-Yamaguti algebras of any weight and applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.12859","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":"sha256:851c61163082de1337146b7073b55f7a06eb4686e0545e95eb097af4ae8273ea","target":"record","created_at":"2026-07-05T08:33:52Z","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":"b16e7f546112b74e30f8443369397a8a8244719bd8a4619224fd1aa3c9994a77","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.RA","submitted_at":"2024-03-06T09:25:17Z","title_canon_sha256":"a3ada54a09cdb2ed325c73c8cd11e24b484cb31fa45bfc60806a6ce46928665c"},"schema_version":"1.0","source":{"id":"2406.12859","kind":"arxiv","version":1}},"canonical_sha256":"9b3485168ae800a78f265f8af3588a74cffca6bf0b21985f4f27ddac3f41e64d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b3485168ae800a78f265f8af3588a74cffca6bf0b21985f4f27ddac3f41e64d","first_computed_at":"2026-07-05T08:33:52.380624Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:33:52.380624Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Gf6/QBDbkM8Dw6NkGMcKPoxgCoVW4lnkDFLGPDxWMkKGpTdjeJxcJOQxmXn/55A/HIacqBDTn7HXoRXNbeY5Cw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:33:52.381006Z","signed_message":"canonical_sha256_bytes"},"source_id":"2406.12859","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:851c61163082de1337146b7073b55f7a06eb4686e0545e95eb097af4ae8273ea","sha256:04bae4918e25b803ed84f22624034c72556c9b3afe221df5e2a6425ec7622c78"],"state_sha256":"6d45526102aaa17d5e978411c86cbd7ed90fdeb8a0cc885319cc78df6cc782d4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S1eOAr6egEKFxFlRiUKR78ZNd6lQfQ0+IKNGmkrU4s/ycDjTteRt/X57uQyLorftadW1BqrWt/dCi3JPrLIbDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T18:08:30.482770Z","bundle_sha256":"73e4844d0a34e79ef8a49f5dab67ff36e0ab93743ab37c5e3a9de0fbf23a17f2"}}