{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:3RVVWLNPAWPJN2MZXCTUYADSTL","short_pith_number":"pith:3RVVWLNP","canonical_record":{"source":{"id":"1105.4748","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-05-24T12:31:52Z","cross_cats_sorted":[],"title_canon_sha256":"19f4dddf470f562e0f19b337479445b5107438825aff5f7d5068fa4f632dcb23","abstract_canon_sha256":"5a217e49bff7c8985064c05508160b8f1692fc033f17e1c786e6742a064e0c35"},"schema_version":"1.0"},"canonical_sha256":"dc6b5b2daf059e96e999b8a74c00729aebd77afcca5659d5acb38eb8d6808010","source":{"kind":"arxiv","id":"1105.4748","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.4748","created_at":"2026-05-18T04:21:21Z"},{"alias_kind":"arxiv_version","alias_value":"1105.4748v1","created_at":"2026-05-18T04:21:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.4748","created_at":"2026-05-18T04:21:21Z"},{"alias_kind":"pith_short_12","alias_value":"3RVVWLNPAWPJ","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"3RVVWLNPAWPJN2MZ","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"3RVVWLNP","created_at":"2026-05-18T12:26:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:3RVVWLNPAWPJN2MZXCTUYADSTL","target":"record","payload":{"canonical_record":{"source":{"id":"1105.4748","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-05-24T12:31:52Z","cross_cats_sorted":[],"title_canon_sha256":"19f4dddf470f562e0f19b337479445b5107438825aff5f7d5068fa4f632dcb23","abstract_canon_sha256":"5a217e49bff7c8985064c05508160b8f1692fc033f17e1c786e6742a064e0c35"},"schema_version":"1.0"},"canonical_sha256":"dc6b5b2daf059e96e999b8a74c00729aebd77afcca5659d5acb38eb8d6808010","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:21:21.858307Z","signature_b64":"XYNCEfG7sM8+BHpgtvQlnlIPkfZSk+RrJQjiBLBDOLnwC5KlsBPosemwNULigm2N0omGPsMunTYjPOdSHeusDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dc6b5b2daf059e96e999b8a74c00729aebd77afcca5659d5acb38eb8d6808010","last_reissued_at":"2026-05-18T04:21:21.857884Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:21:21.857884Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.4748","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":"2026-05-18T04:21:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6gwqgQWVwZZpuLhiIl76+d/7H6l90canqimJJFaFNQXWFdAIv+fjmHLyNLT5i/B+3yzVBSf3Gwn//iCivJjQDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T21:21:51.706382Z"},"content_sha256":"cdd89bc9e5465390a42e67c6009333cca1996803d6ca52e39fcaba42bceec148","schema_version":"1.0","event_id":"sha256:cdd89bc9e5465390a42e67c6009333cca1996803d6ca52e39fcaba42bceec148"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:3RVVWLNPAWPJN2MZXCTUYADSTL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On noncommutative bases of the free module $W_n(\\mathbb K)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Ievgen Makedonskyi","submitted_at":"2011-05-24T12:31:52Z","abstract_excerpt":"Let $\\mathbb{K}$ be an algebraically closed field of characteristic zero and $R=\\mathbb{K}[x_1,x_2,...x_n]$ the polynomial ring in $n$ variables over $\\mathbb K.$ We study bases of the free $R$-module $W_n(\\mathbb{K})$ of all $\\mathbb{K}$-derivations of the ring $R$, such that their linear span over $\\mathbb K$ is a subalgebra of the Lie algebra $W_n(\\mathbb{K})$. We proved that for any Lie algebra $L$ of dimension $n$ over $\\mathbb{K}$ there exists a subalgebra $\\bar{L}$ of $W_n(\\mathbb{K})$ which is isomorphic to $L$ and such that every $\\mathbb{K}$-basis of $\\bar L$ is an $R$-basis of the $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4748","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":"2026-05-18T04:21:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mjuh3CvQQptg7UpXE3YB9ArV+YvwlMVD/A2kd8b1HpNQ74RNVbu1B+bHJHBG8+w9lhLWgWmyyn5fR3E32TQvDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T21:21:51.707069Z"},"content_sha256":"e863b9948e189432df5d30ff05a78c0e0a6301e742c00ac31f3051b4ce88c922","schema_version":"1.0","event_id":"sha256:e863b9948e189432df5d30ff05a78c0e0a6301e742c00ac31f3051b4ce88c922"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3RVVWLNPAWPJN2MZXCTUYADSTL/bundle.json","state_url":"https://pith.science/pith/3RVVWLNPAWPJN2MZXCTUYADSTL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3RVVWLNPAWPJN2MZXCTUYADSTL/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":"2026-05-27T21:21:51Z","links":{"resolver":"https://pith.science/pith/3RVVWLNPAWPJN2MZXCTUYADSTL","bundle":"https://pith.science/pith/3RVVWLNPAWPJN2MZXCTUYADSTL/bundle.json","state":"https://pith.science/pith/3RVVWLNPAWPJN2MZXCTUYADSTL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3RVVWLNPAWPJN2MZXCTUYADSTL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:3RVVWLNPAWPJN2MZXCTUYADSTL","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":"5a217e49bff7c8985064c05508160b8f1692fc033f17e1c786e6742a064e0c35","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-05-24T12:31:52Z","title_canon_sha256":"19f4dddf470f562e0f19b337479445b5107438825aff5f7d5068fa4f632dcb23"},"schema_version":"1.0","source":{"id":"1105.4748","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.4748","created_at":"2026-05-18T04:21:21Z"},{"alias_kind":"arxiv_version","alias_value":"1105.4748v1","created_at":"2026-05-18T04:21:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.4748","created_at":"2026-05-18T04:21:21Z"},{"alias_kind":"pith_short_12","alias_value":"3RVVWLNPAWPJ","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"3RVVWLNPAWPJN2MZ","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"3RVVWLNP","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:e863b9948e189432df5d30ff05a78c0e0a6301e742c00ac31f3051b4ce88c922","target":"graph","created_at":"2026-05-18T04:21:21Z","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":"Let $\\mathbb{K}$ be an algebraically closed field of characteristic zero and $R=\\mathbb{K}[x_1,x_2,...x_n]$ the polynomial ring in $n$ variables over $\\mathbb K.$ We study bases of the free $R$-module $W_n(\\mathbb{K})$ of all $\\mathbb{K}$-derivations of the ring $R$, such that their linear span over $\\mathbb K$ is a subalgebra of the Lie algebra $W_n(\\mathbb{K})$. We proved that for any Lie algebra $L$ of dimension $n$ over $\\mathbb{K}$ there exists a subalgebra $\\bar{L}$ of $W_n(\\mathbb{K})$ which is isomorphic to $L$ and such that every $\\mathbb{K}$-basis of $\\bar L$ is an $R$-basis of the $","authors_text":"Ievgen Makedonskyi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-05-24T12:31:52Z","title":"On noncommutative bases of the free module $W_n(\\mathbb K)$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4748","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:cdd89bc9e5465390a42e67c6009333cca1996803d6ca52e39fcaba42bceec148","target":"record","created_at":"2026-05-18T04:21:21Z","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":"5a217e49bff7c8985064c05508160b8f1692fc033f17e1c786e6742a064e0c35","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-05-24T12:31:52Z","title_canon_sha256":"19f4dddf470f562e0f19b337479445b5107438825aff5f7d5068fa4f632dcb23"},"schema_version":"1.0","source":{"id":"1105.4748","kind":"arxiv","version":1}},"canonical_sha256":"dc6b5b2daf059e96e999b8a74c00729aebd77afcca5659d5acb38eb8d6808010","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc6b5b2daf059e96e999b8a74c00729aebd77afcca5659d5acb38eb8d6808010","first_computed_at":"2026-05-18T04:21:21.857884Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:21:21.857884Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XYNCEfG7sM8+BHpgtvQlnlIPkfZSk+RrJQjiBLBDOLnwC5KlsBPosemwNULigm2N0omGPsMunTYjPOdSHeusDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:21:21.858307Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.4748","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cdd89bc9e5465390a42e67c6009333cca1996803d6ca52e39fcaba42bceec148","sha256:e863b9948e189432df5d30ff05a78c0e0a6301e742c00ac31f3051b4ce88c922"],"state_sha256":"13b054edae53bd13c03f7c17ed654e3f9ce99f098be36f3ec1f62c7bfcb18e8b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z2Ge3pQ/om7xiVx6Qzl2zB2fFXvzVg/iyg8TAOpk3GHIE+4PQgzUv13xpzJSgcaOZVdsM6IPMJBaPwzWqNLBAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T21:21:51.710705Z","bundle_sha256":"479ea7327a60dec342fec393f3487450ecef595f2ab094f48f5107368f5d3e64"}}