{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:GSYPDOUJ2GACT37O5EQNAVHW55","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":"820ad7af441e00c3666dba0c3b343264eab11cf47afffe87349d2d96dca2ab25","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-02-20T14:39:20Z","title_canon_sha256":"1191865491614969a541b6099f348cd10292144bcbf5eebbe67c8f56f04f3d0d"},"schema_version":"1.0","source":{"id":"1802.07131","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.07131","created_at":"2026-05-18T00:22:53Z"},{"alias_kind":"arxiv_version","alias_value":"1802.07131v1","created_at":"2026-05-18T00:22:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.07131","created_at":"2026-05-18T00:22:53Z"},{"alias_kind":"pith_short_12","alias_value":"GSYPDOUJ2GAC","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"GSYPDOUJ2GACT37O","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"GSYPDOUJ","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:fc0bffc13dbc628a2777c5da4dd62289c351a2b87126e1ad63a66901dfbbb05b","target":"graph","created_at":"2026-05-18T00:22:53Z","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":"This is a part of an ongoing project, the goal of which is to classify all semi-direct products $\\mathfrak s=\\mathfrak g{\\ltimes} V$ such that $\\mathfrak g$ is a simple Lie algebra, $V$ is a $\\mathfrak g$-module, and $\\mathfrak s$ has a free algebra of symmetric invariants. In this paper, we obtain such a classification for the representations of the orthogonal and symplectic algebras.","authors_text":"Dmitri I. Panyushev, Oksana S. Yakimova","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-02-20T14:39:20Z","title":"Semi-direct products involving $Sp_{2n}$ or $Spin_n$ with free algebras of symmetric invariants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.07131","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":"sha256:202024899be20951880638e51c62bdc388c7b0810e618af5142f790611e2ab9e","target":"record","created_at":"2026-05-18T00:22:53Z","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":"820ad7af441e00c3666dba0c3b343264eab11cf47afffe87349d2d96dca2ab25","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-02-20T14:39:20Z","title_canon_sha256":"1191865491614969a541b6099f348cd10292144bcbf5eebbe67c8f56f04f3d0d"},"schema_version":"1.0","source":{"id":"1802.07131","kind":"arxiv","version":1}},"canonical_sha256":"34b0f1ba89d18029efeee920d054f6ef442bb92f2d6db4731049e96de10fbf5f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"34b0f1ba89d18029efeee920d054f6ef442bb92f2d6db4731049e96de10fbf5f","first_computed_at":"2026-05-18T00:22:53.483150Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:53.483150Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hrvi1KSO+k8L3jpDxSjR7oLBf1lPBAiIdvtU8O4eLzgMBe12DuWPavBxkpmflRDgH7tsRC5p+bl2dAP6CEDUDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:53.483512Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.07131","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:202024899be20951880638e51c62bdc388c7b0810e618af5142f790611e2ab9e","sha256:fc0bffc13dbc628a2777c5da4dd62289c351a2b87126e1ad63a66901dfbbb05b"],"state_sha256":"3112529dd1dd7f7c1ef3948e9ed80872a6e4def78340afe4efcd3a253df882b3"}