{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:GUUM4WB42Q425OY2L7JMJ7L7ED","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":"c73a9f22f960dc384d8a790ada31680603185596090142c8317400b23c2a2087","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-10-10T15:36:41Z","title_canon_sha256":"11e7a386ccfea574b66ebdbf7d839fb80cd47aec96b0749e2099f0b864aa648b"},"schema_version":"1.0","source":{"id":"1110.2078","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.2078","created_at":"2026-05-18T04:11:19Z"},{"alias_kind":"arxiv_version","alias_value":"1110.2078v1","created_at":"2026-05-18T04:11:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.2078","created_at":"2026-05-18T04:11:19Z"},{"alias_kind":"pith_short_12","alias_value":"GUUM4WB42Q42","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"GUUM4WB42Q425OY2","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"GUUM4WB4","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:faaf30a2194121802f0f5341611b1352e31116b90f45741bae2b3e9d8fa9daa3","target":"graph","created_at":"2026-05-18T04:11:19Z","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":"The purpose of this paper is to introduce and study quadratic $n$-ary Hom-Nambu algebras, which are $n$-ary Hom-Nambu algebras with an invariant, nondegenerate and symmetric bilinear forms that are also $\\alpha$-symmetric and $\\beta$-invariant where $\\alpha$ and $\\beta$ are twisting maps. We provide constructions of these $n$-ary algebras by using twisting principles, tensor product and T*-extension. Also is discussed their connections with representation theory and centroids. Moreover we show that one may derive from quadratic $n$-ary Hom-Nambu algebra ones of increasingly higher arities and ","authors_text":"Abdenacer Makhlouf, Faouzi Ammar, Sami Mabrouk","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-10-10T15:36:41Z","title":"Quadratic $n$-ary Hom-Nambu algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.2078","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:f3a14972ff54fafbc26d2f272566ffb8a545b1e42111e695914fb1046c0f8ac3","target":"record","created_at":"2026-05-18T04:11:19Z","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":"c73a9f22f960dc384d8a790ada31680603185596090142c8317400b23c2a2087","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-10-10T15:36:41Z","title_canon_sha256":"11e7a386ccfea574b66ebdbf7d839fb80cd47aec96b0749e2099f0b864aa648b"},"schema_version":"1.0","source":{"id":"1110.2078","kind":"arxiv","version":1}},"canonical_sha256":"3528ce583cd439aebb1a5fd2c4fd7f20de6052f49faf2538b2468c8737c8d7b9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3528ce583cd439aebb1a5fd2c4fd7f20de6052f49faf2538b2468c8737c8d7b9","first_computed_at":"2026-05-18T04:11:19.005511Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:11:19.005511Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"69MbUEybOdtyamCTrqmcSQHOMQJPz80ZqNHYFiQXIqnZ+ewqpHA0ctdLWq7EqEJh8xuytE00/djG0XPs1Sv4Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:11:19.006041Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.2078","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f3a14972ff54fafbc26d2f272566ffb8a545b1e42111e695914fb1046c0f8ac3","sha256:faaf30a2194121802f0f5341611b1352e31116b90f45741bae2b3e9d8fa9daa3"],"state_sha256":"4b151ccdd89731cc280cb282450a4896a8cf2fd65584c80027def77805fc2c92"}