{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:EUOAI4SSG3UIVKWA5UNROB2XC3","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":"c2ff76ac2466c3305ec667252fd1f3e3d338debeb4e907a70c462339c3578a3f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-07-12T23:22:54Z","title_canon_sha256":"202f082d15eef5dc5c81c9edd574cc51039ef389d54ee1c08b2521e5e64fdff8"},"schema_version":"1.0","source":{"id":"1707.03932","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.03932","created_at":"2026-05-18T00:40:23Z"},{"alias_kind":"arxiv_version","alias_value":"1707.03932v1","created_at":"2026-05-18T00:40:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.03932","created_at":"2026-05-18T00:40:23Z"},{"alias_kind":"pith_short_12","alias_value":"EUOAI4SSG3UI","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EUOAI4SSG3UIVKWA","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EUOAI4SS","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:2b1089c96544d21612062eadc2d9f1633d13f0b7215cf0b5e9d7cf11d346895c","target":"graph","created_at":"2026-05-18T00:40:23Z","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":"We classify gradings by arbitrary abelian groups on the classical simple Lie superalgebras $P(n)$, $n \\geq 2$, and on the simple associative superalgebras $M(m,n)$, $m, n \\geq 1$, over an algebraically closed field: fine gradings up to equivalence and $G$-gradings, for a fixed group $G$, up to isomorphism. As a corollary, we also classify up to isomorphism the $G$-gradings on the classical Lie superalgebra $A(m,n)$ that are induced from $G$-gradings on $M(m+1,n+1)$. In the case of Lie superalgebras, the characteristic is assumed to be $0$.","authors_text":"Caio De Naday Hornhardt, Helen Samara Dos Santos, Mikhail Kochetov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-07-12T23:22:54Z","title":"Group gradings on the superalgebras M(m,n), A(m,n) and P(n)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.03932","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":"sha256:3f6023e3aab8e218a99866286eeabcd943c008444658164990ab03f8c1802aa7","target":"record","created_at":"2026-05-18T00:40:23Z","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":"c2ff76ac2466c3305ec667252fd1f3e3d338debeb4e907a70c462339c3578a3f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-07-12T23:22:54Z","title_canon_sha256":"202f082d15eef5dc5c81c9edd574cc51039ef389d54ee1c08b2521e5e64fdff8"},"schema_version":"1.0","source":{"id":"1707.03932","kind":"arxiv","version":1}},"canonical_sha256":"251c04725236e88aaac0ed1b17075716d842a2ed317d93d1e02f11c641f6bfd9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"251c04725236e88aaac0ed1b17075716d842a2ed317d93d1e02f11c641f6bfd9","first_computed_at":"2026-05-18T00:40:23.070382Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:23.070382Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4JNM0oRLgjzoPa99+cfqcgY/7o20iYiu89HoUXj/yGL/pWfqBhtdt/FRshco9CDL5avSEVUjuS6ypqGStgIFBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:23.070892Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.03932","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3f6023e3aab8e218a99866286eeabcd943c008444658164990ab03f8c1802aa7","sha256:2b1089c96544d21612062eadc2d9f1633d13f0b7215cf0b5e9d7cf11d346895c"],"state_sha256":"3894d7903ea98a581a68631ff14f8e6992e259da33f811d8fe55b2bda694d3d4"}