{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:2NNXK5AUKHM6KXKLGUFTQLTXRK","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":"568b27685ad502234b1e10414d1488f7b90bbce13bedef92bc134703dcf93b4e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-01-02T07:34:39Z","title_canon_sha256":"4c5aad35a0c6f069c72bd71c4e267d5de6d03b22e76587191f6b4c0a1cadb80e"},"schema_version":"1.0","source":{"id":"1401.0378","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.0378","created_at":"2026-05-18T03:03:23Z"},{"alias_kind":"arxiv_version","alias_value":"1401.0378v1","created_at":"2026-05-18T03:03:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.0378","created_at":"2026-05-18T03:03:23Z"},{"alias_kind":"pith_short_12","alias_value":"2NNXK5AUKHM6","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"2NNXK5AUKHM6KXKL","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"2NNXK5AU","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:9053de5295f4008f5597e8859a57b058f3146cfdd645c46314147542b17d53af","target":"graph","created_at":"2026-05-18T03:03:23Z","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":"In this paper, we discuss the representations of $n$-ary multiplicative Hom-Nambu-Lie superalgebras as a generalization of the notion of representations for $n$-ary multiplicative Hom-Nambu-Lie algebras. We also give the cohomology of an $n$-ary multiplicative Hom-Nambu-Lie superalgebra and obtain a relation between extensions of an $n$-ary multiplicative Hom-Nambu-Lie superalgebra $\\mathfrak{b}$ by an abelian one $\\mathfrak{a}$ and $Z^1(\\mathfrak{b}, \\mathfrak{a})_{\\bar{0}}$. We also introduce the notion of $T^*$-extensions of $n$-ary multiplicative Hom-Nambu-Lie superalgebras and prove that ","authors_text":"Baoling Guan, Liangyun Chen, Yao Ma","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-01-02T07:34:39Z","title":"On the cohomology and extensions of $n$-ary multiplicative Hom-Nambu-Lie superalgebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0378","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:fc811bf326276dfd179a4cdc86912c0ae195271198a918ab3ca5ad037872ca39","target":"record","created_at":"2026-05-18T03:03:23Z","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":"568b27685ad502234b1e10414d1488f7b90bbce13bedef92bc134703dcf93b4e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-01-02T07:34:39Z","title_canon_sha256":"4c5aad35a0c6f069c72bd71c4e267d5de6d03b22e76587191f6b4c0a1cadb80e"},"schema_version":"1.0","source":{"id":"1401.0378","kind":"arxiv","version":1}},"canonical_sha256":"d35b75741451d9e55d4b350b382e778a8bd9bc6cd9231c4215b35ffe853aa6e9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d35b75741451d9e55d4b350b382e778a8bd9bc6cd9231c4215b35ffe853aa6e9","first_computed_at":"2026-05-18T03:03:23.374786Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:03:23.374786Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"15W2zQOQT0PQcIV10UzevlsgZOxO/IBB75XoLGtVta2ITwLVrxjyQ5J1w5djkJ9Zc8bdqRx+BhRldYs8vcOcCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:03:23.375831Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.0378","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fc811bf326276dfd179a4cdc86912c0ae195271198a918ab3ca5ad037872ca39","sha256:9053de5295f4008f5597e8859a57b058f3146cfdd645c46314147542b17d53af"],"state_sha256":"20ed099fe460990b570a6547fd9ea5b416d0e0054ebcb6f8e6f24e1fb2ebe934"}