{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:5QM4532DC2ZPJ2U7CFQF6XGC3O","short_pith_number":"pith:5QM4532D","canonical_record":{"source":{"id":"1602.05799","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-02-18T13:47:36Z","cross_cats_sorted":[],"title_canon_sha256":"0f3c86ba9c3ea1329ab8baa30039bc690123836eab12c528248264a939c2811f","abstract_canon_sha256":"38db6711fa93fee41336665310dd3181e57730a2ca87a85572909a8cc94ef4d8"},"schema_version":"1.0"},"canonical_sha256":"ec19ceef4316b2f4ea9f11605f5cc2db9e0119b4d71378aeb55b468a4d0d851f","source":{"kind":"arxiv","id":"1602.05799","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.05799","created_at":"2026-05-18T01:20:23Z"},{"alias_kind":"arxiv_version","alias_value":"1602.05799v1","created_at":"2026-05-18T01:20:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.05799","created_at":"2026-05-18T01:20:23Z"},{"alias_kind":"pith_short_12","alias_value":"5QM4532DC2ZP","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5QM4532DC2ZPJ2U7","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5QM4532D","created_at":"2026-05-18T12:30:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:5QM4532DC2ZPJ2U7CFQF6XGC3O","target":"record","payload":{"canonical_record":{"source":{"id":"1602.05799","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-02-18T13:47:36Z","cross_cats_sorted":[],"title_canon_sha256":"0f3c86ba9c3ea1329ab8baa30039bc690123836eab12c528248264a939c2811f","abstract_canon_sha256":"38db6711fa93fee41336665310dd3181e57730a2ca87a85572909a8cc94ef4d8"},"schema_version":"1.0"},"canonical_sha256":"ec19ceef4316b2f4ea9f11605f5cc2db9e0119b4d71378aeb55b468a4d0d851f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:23.189407Z","signature_b64":"AVbe+/7tED5p6XhSUFMoRsNidTy/pdDvRfxaW17VAq1wPZvJI2FFoRsZZOywXfJMaNhybV4CspHBclrd0i4vAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ec19ceef4316b2f4ea9f11605f5cc2db9e0119b4d71378aeb55b468a4d0d851f","last_reissued_at":"2026-05-18T01:20:23.188662Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:23.188662Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.05799","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":"2026-05-18T01:20:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"izN0YJwkY7xoWo5+li8frUcQ3WMc0UeAF6QXf84UKz2bcWDuRVfpxrmm8tdfK3XKs/mMooB/KnoiqtESeuQmBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T03:37:18.976937Z"},"content_sha256":"a0e19bce7d21d3e61c42e889ed9830a1c82e87a551a4bc209768b1dbf3f62e91","schema_version":"1.0","event_id":"sha256:a0e19bce7d21d3e61c42e889ed9830a1c82e87a551a4bc209768b1dbf3f62e91"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:5QM4532DC2ZPJ2U7CFQF6XGC3O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Group gradings on finite dimensional Lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Du\\v{s}an Pagon, Du\\v{s}an Repov\\v{s}, Mikhail Zaicev","submitted_at":"2016-02-18T13:47:36Z","abstract_excerpt":"We study gradings by noncommutative groups on finite dimensional Lie algebras over an algebraically closed field of characteristic zero. It is shown that if $L$ is gradeg by a non-abelian finite group $G$ then the solvable radical $R$ of $L$ is $G$-graded and there exists a Levi subalgebra $B=H_1\\oplus\\cdots\\oplus H_m$ homogeneous in $G$-grading with graded simple summands $H_1, \\ldots, H_m$. All supports $Supp~H_i, i=1\\ldots, m$, are commutative subsets of $G$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05799","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":""},"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":"2026-05-18T01:20:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LYyGNBIatZwmo7CKfPaPmb2/2X2nBuQS4qj24k6HUMF75xHLl05Fpz50Mw4USca8sbsjaCcevgmw1ZvOVXOSDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T03:37:18.977691Z"},"content_sha256":"2b27324eaa8b2892d511f0a983a93e494ae411498061f41e33f77fdc6a06ac17","schema_version":"1.0","event_id":"sha256:2b27324eaa8b2892d511f0a983a93e494ae411498061f41e33f77fdc6a06ac17"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5QM4532DC2ZPJ2U7CFQF6XGC3O/bundle.json","state_url":"https://pith.science/pith/5QM4532DC2ZPJ2U7CFQF6XGC3O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5QM4532DC2ZPJ2U7CFQF6XGC3O/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":"2026-06-12T03:37:18Z","links":{"resolver":"https://pith.science/pith/5QM4532DC2ZPJ2U7CFQF6XGC3O","bundle":"https://pith.science/pith/5QM4532DC2ZPJ2U7CFQF6XGC3O/bundle.json","state":"https://pith.science/pith/5QM4532DC2ZPJ2U7CFQF6XGC3O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5QM4532DC2ZPJ2U7CFQF6XGC3O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:5QM4532DC2ZPJ2U7CFQF6XGC3O","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":"38db6711fa93fee41336665310dd3181e57730a2ca87a85572909a8cc94ef4d8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-02-18T13:47:36Z","title_canon_sha256":"0f3c86ba9c3ea1329ab8baa30039bc690123836eab12c528248264a939c2811f"},"schema_version":"1.0","source":{"id":"1602.05799","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.05799","created_at":"2026-05-18T01:20:23Z"},{"alias_kind":"arxiv_version","alias_value":"1602.05799v1","created_at":"2026-05-18T01:20:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.05799","created_at":"2026-05-18T01:20:23Z"},{"alias_kind":"pith_short_12","alias_value":"5QM4532DC2ZP","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5QM4532DC2ZPJ2U7","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5QM4532D","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:2b27324eaa8b2892d511f0a983a93e494ae411498061f41e33f77fdc6a06ac17","target":"graph","created_at":"2026-05-18T01:20:23Z","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 study gradings by noncommutative groups on finite dimensional Lie algebras over an algebraically closed field of characteristic zero. It is shown that if $L$ is gradeg by a non-abelian finite group $G$ then the solvable radical $R$ of $L$ is $G$-graded and there exists a Levi subalgebra $B=H_1\\oplus\\cdots\\oplus H_m$ homogeneous in $G$-grading with graded simple summands $H_1, \\ldots, H_m$. All supports $Supp~H_i, i=1\\ldots, m$, are commutative subsets of $G$.","authors_text":"Du\\v{s}an Pagon, Du\\v{s}an Repov\\v{s}, Mikhail Zaicev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-02-18T13:47:36Z","title":"Group gradings on finite dimensional Lie algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05799","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:a0e19bce7d21d3e61c42e889ed9830a1c82e87a551a4bc209768b1dbf3f62e91","target":"record","created_at":"2026-05-18T01:20:23Z","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":"38db6711fa93fee41336665310dd3181e57730a2ca87a85572909a8cc94ef4d8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-02-18T13:47:36Z","title_canon_sha256":"0f3c86ba9c3ea1329ab8baa30039bc690123836eab12c528248264a939c2811f"},"schema_version":"1.0","source":{"id":"1602.05799","kind":"arxiv","version":1}},"canonical_sha256":"ec19ceef4316b2f4ea9f11605f5cc2db9e0119b4d71378aeb55b468a4d0d851f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ec19ceef4316b2f4ea9f11605f5cc2db9e0119b4d71378aeb55b468a4d0d851f","first_computed_at":"2026-05-18T01:20:23.188662Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:23.188662Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AVbe+/7tED5p6XhSUFMoRsNidTy/pdDvRfxaW17VAq1wPZvJI2FFoRsZZOywXfJMaNhybV4CspHBclrd0i4vAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:23.189407Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.05799","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a0e19bce7d21d3e61c42e889ed9830a1c82e87a551a4bc209768b1dbf3f62e91","sha256:2b27324eaa8b2892d511f0a983a93e494ae411498061f41e33f77fdc6a06ac17"],"state_sha256":"3c8ac351f58bb0ed59cc0bfebdfffab50307fbb751aaab028a33952a5d369393"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PbRUZCUEL+QeFuslRjGwH7ZoZwta6L/m+rXGS1OLSMQyeXsixFZQXyzLS3eKbME1ey5DZw36amxHTYPOUo1EDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T03:37:18.982132Z","bundle_sha256":"0a700892fd3b3824063fdf2eaf5f8e03991b5a0588765bd9ac8486df9bca9205"}}