{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:KOPZZWBB4EYNAHFYQHLZSS7JY6","short_pith_number":"pith:KOPZZWBB","canonical_record":{"source":{"id":"1902.04071","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-02-11T12:35:34Z","cross_cats_sorted":[],"title_canon_sha256":"917482cea30feeb87a55014ebbfc86cc46d91bd5cce09432161e38400af14510","abstract_canon_sha256":"213a1ad9c53ece57e0e816990227c6f6f4b29c1909f91774216f3b0c7a84fade"},"schema_version":"1.0"},"canonical_sha256":"539f9cd821e130d01cb881d7994be9c7af10f1312c3313b57863029ae1cf10a4","source":{"kind":"arxiv","id":"1902.04071","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.04071","created_at":"2026-05-17T23:54:13Z"},{"alias_kind":"arxiv_version","alias_value":"1902.04071v1","created_at":"2026-05-17T23:54:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.04071","created_at":"2026-05-17T23:54:13Z"},{"alias_kind":"pith_short_12","alias_value":"KOPZZWBB4EYN","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"KOPZZWBB4EYNAHFY","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"KOPZZWBB","created_at":"2026-05-18T12:33:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:KOPZZWBB4EYNAHFYQHLZSS7JY6","target":"record","payload":{"canonical_record":{"source":{"id":"1902.04071","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-02-11T12:35:34Z","cross_cats_sorted":[],"title_canon_sha256":"917482cea30feeb87a55014ebbfc86cc46d91bd5cce09432161e38400af14510","abstract_canon_sha256":"213a1ad9c53ece57e0e816990227c6f6f4b29c1909f91774216f3b0c7a84fade"},"schema_version":"1.0"},"canonical_sha256":"539f9cd821e130d01cb881d7994be9c7af10f1312c3313b57863029ae1cf10a4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:13.097705Z","signature_b64":"HxclGaAUA9pq8Bhsjjj48Gj00D751GUjOklnjyxny79Orga4xqc7zYY4jmKppoH/fT7mz8AQfkuAXq0ZD/YwBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"539f9cd821e130d01cb881d7994be9c7af10f1312c3313b57863029ae1cf10a4","last_reissued_at":"2026-05-17T23:54:13.097077Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:13.097077Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.04071","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":"2026-05-17T23:54:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jyKZB3AeCdPrG6QEeu8ll63JzdxGsfTCoq4qsCOo9q2Y84/FGe1psCVIqrf6shmFWQHRpiIcc7XQ9h7P2jlbAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T20:09:00.059745Z"},"content_sha256":"109d54c3242c148ba871c2e120fa5a856a82b6445b61b288e765101628942de0","schema_version":"1.0","event_id":"sha256:109d54c3242c148ba871c2e120fa5a856a82b6445b61b288e765101628942de0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:KOPZZWBB4EYNAHFYQHLZSS7JY6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Solvable Leibniz algebras with naturally graded non-Lie $p$-filiform nilradicals and maximal complemented space of its nilradical","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"B.A.Omirov, J.Q.Adashev, L.M.Camacho","submitted_at":"2019-02-11T12:35:34Z","abstract_excerpt":"The present article is a part of the study of solvable Leibniz algebras with a given nilradical. In this paper solvable Leibniz algebras, whose nilradicals is naturally graded $p$-filiform non-Lie Leibniz algebra $(n-p\\geq4)$ and the complemented space to nilradical has maximal dimension, are described up to isomorphism. Moreover, among obtained algebras we indicate the rigid and complete algebras"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.04071","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":"2026-05-17T23:54:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5r/dOVpCIK6kondNVR5wyvxMjXpjmnoY7yAxQglvWu2XonMHlmg3F/fJCKWWiLKkEuyUP3iBdgBZu4d9XwR0BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T20:09:00.060447Z"},"content_sha256":"8bdedf1d832631184a94ab1a0458e4299a56b8f74987fef8078ee4fc59176826","schema_version":"1.0","event_id":"sha256:8bdedf1d832631184a94ab1a0458e4299a56b8f74987fef8078ee4fc59176826"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KOPZZWBB4EYNAHFYQHLZSS7JY6/bundle.json","state_url":"https://pith.science/pith/KOPZZWBB4EYNAHFYQHLZSS7JY6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KOPZZWBB4EYNAHFYQHLZSS7JY6/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":"2026-06-11T20:09:00Z","links":{"resolver":"https://pith.science/pith/KOPZZWBB4EYNAHFYQHLZSS7JY6","bundle":"https://pith.science/pith/KOPZZWBB4EYNAHFYQHLZSS7JY6/bundle.json","state":"https://pith.science/pith/KOPZZWBB4EYNAHFYQHLZSS7JY6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KOPZZWBB4EYNAHFYQHLZSS7JY6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:KOPZZWBB4EYNAHFYQHLZSS7JY6","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":"213a1ad9c53ece57e0e816990227c6f6f4b29c1909f91774216f3b0c7a84fade","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-02-11T12:35:34Z","title_canon_sha256":"917482cea30feeb87a55014ebbfc86cc46d91bd5cce09432161e38400af14510"},"schema_version":"1.0","source":{"id":"1902.04071","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.04071","created_at":"2026-05-17T23:54:13Z"},{"alias_kind":"arxiv_version","alias_value":"1902.04071v1","created_at":"2026-05-17T23:54:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.04071","created_at":"2026-05-17T23:54:13Z"},{"alias_kind":"pith_short_12","alias_value":"KOPZZWBB4EYN","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"KOPZZWBB4EYNAHFY","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"KOPZZWBB","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:8bdedf1d832631184a94ab1a0458e4299a56b8f74987fef8078ee4fc59176826","target":"graph","created_at":"2026-05-17T23:54:13Z","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 present article is a part of the study of solvable Leibniz algebras with a given nilradical. In this paper solvable Leibniz algebras, whose nilradicals is naturally graded $p$-filiform non-Lie Leibniz algebra $(n-p\\geq4)$ and the complemented space to nilradical has maximal dimension, are described up to isomorphism. Moreover, among obtained algebras we indicate the rigid and complete algebras","authors_text":"B.A.Omirov, J.Q.Adashev, L.M.Camacho","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-02-11T12:35:34Z","title":"Solvable Leibniz algebras with naturally graded non-Lie $p$-filiform nilradicals and maximal complemented space of its nilradical"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.04071","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":"sha256:109d54c3242c148ba871c2e120fa5a856a82b6445b61b288e765101628942de0","target":"record","created_at":"2026-05-17T23:54:13Z","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":"213a1ad9c53ece57e0e816990227c6f6f4b29c1909f91774216f3b0c7a84fade","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-02-11T12:35:34Z","title_canon_sha256":"917482cea30feeb87a55014ebbfc86cc46d91bd5cce09432161e38400af14510"},"schema_version":"1.0","source":{"id":"1902.04071","kind":"arxiv","version":1}},"canonical_sha256":"539f9cd821e130d01cb881d7994be9c7af10f1312c3313b57863029ae1cf10a4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"539f9cd821e130d01cb881d7994be9c7af10f1312c3313b57863029ae1cf10a4","first_computed_at":"2026-05-17T23:54:13.097077Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:13.097077Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HxclGaAUA9pq8Bhsjjj48Gj00D751GUjOklnjyxny79Orga4xqc7zYY4jmKppoH/fT7mz8AQfkuAXq0ZD/YwBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:13.097705Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.04071","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:109d54c3242c148ba871c2e120fa5a856a82b6445b61b288e765101628942de0","sha256:8bdedf1d832631184a94ab1a0458e4299a56b8f74987fef8078ee4fc59176826"],"state_sha256":"da98a37d10a6b5a75c161b9257d78c61975898b3165b490c3e1e1326f7a4d292"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PZwm75kicWsffB4AlnJQiA1YEYEoUH1Oes6g62cIp5JYHObAzHKOjzwXZt0SydBNn+tXnfqeT/uLQhpxL23pCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T20:09:00.064889Z","bundle_sha256":"f9dbf4ab0037d9913379b0bec4804b7b3cbbf551012c04ab4d1ee8d152231286"}}