{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:4KFRKDWRTSJ6IXBFEWCXELF4MV","short_pith_number":"pith:4KFRKDWR","canonical_record":{"source":{"id":"1705.05900","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-05-16T20:12:59Z","cross_cats_sorted":[],"title_canon_sha256":"f3b95fd3ec90dbb556fca52608992abee50c5c135553e25cdbe66fa9b9348a59","abstract_canon_sha256":"7489d8d48b2c6e52ea32c3f4c82805e81348b005de91f4fba571dd991576572c"},"schema_version":"1.0"},"canonical_sha256":"e28b150ed19c93e45c252585722cbc657db0ffc53fe8c4822b0f26b66032976a","source":{"kind":"arxiv","id":"1705.05900","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.05900","created_at":"2026-05-18T00:29:46Z"},{"alias_kind":"arxiv_version","alias_value":"1705.05900v3","created_at":"2026-05-18T00:29:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.05900","created_at":"2026-05-18T00:29:46Z"},{"alias_kind":"pith_short_12","alias_value":"4KFRKDWRTSJ6","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"4KFRKDWRTSJ6IXBF","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"4KFRKDWR","created_at":"2026-05-18T12:31:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:4KFRKDWRTSJ6IXBFEWCXELF4MV","target":"record","payload":{"canonical_record":{"source":{"id":"1705.05900","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-05-16T20:12:59Z","cross_cats_sorted":[],"title_canon_sha256":"f3b95fd3ec90dbb556fca52608992abee50c5c135553e25cdbe66fa9b9348a59","abstract_canon_sha256":"7489d8d48b2c6e52ea32c3f4c82805e81348b005de91f4fba571dd991576572c"},"schema_version":"1.0"},"canonical_sha256":"e28b150ed19c93e45c252585722cbc657db0ffc53fe8c4822b0f26b66032976a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:46.050200Z","signature_b64":"B3y5/A+Ytbf/NvoU11YRu+qPkk31GAJcvDa4CkSdloTZ5ApcVfznPqWb6AMcCNT1xfxUhvVfYOEWZxVHIl8tAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e28b150ed19c93e45c252585722cbc657db0ffc53fe8c4822b0f26b66032976a","last_reissued_at":"2026-05-18T00:29:46.049574Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:46.049574Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.05900","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:29:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FY8jJ35wcw+N7gi/2xs+Eot2hyjOnVfHva2k1ZuOb9g5NHGdKItHoEmmzNpKO9MgOGUAJUMu3xuPHhKdaFBfBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T05:39:43.652197Z"},"content_sha256":"427e168b9f6a1636fbed9077c942b50f38836273d10e91cf118dfd505694faf6","schema_version":"1.0","event_id":"sha256:427e168b9f6a1636fbed9077c942b50f38836273d10e91cf118dfd505694faf6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:4KFRKDWRTSJ6IXBFEWCXELF4MV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lie algebras of vector fields on smooth affine varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Vyacheslav Futorny, Yuly Billig","submitted_at":"2017-05-16T20:12:59Z","abstract_excerpt":"We reprove the results of Jordan [18] and Siebert [31] and show that the Lie algebra of polynomial vector fields on an irreducible affine variety X is simple if and only if X is a smooth variety. Given proof is self-contained and does not depend on papers mentioned above. Besides, the structure of the module of polynomial functions on an irreducible smooth affine variety over the Lie algebra of vector fields is studied. Examples of Lie algebras of polynomial vector fields on an N-dimensional sphere, non-singular hyperelliptic curves and linear algebraic groups are considered."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.05900","kind":"arxiv","version":3},"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":"2026-05-18T00:29:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QiDn4tcIOCudn6yIrKCBn6DtM9fYbigLq30pTWa2BR+yHH7OS5yYUlRg+XVVNJMwkAlB0d6U3Fq44fcvr6sKDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T05:39:43.652849Z"},"content_sha256":"290c78c99b7a99fe604ca5be86e032378d4e5c4a8e2b454e30fb3c4dd2eb2dbc","schema_version":"1.0","event_id":"sha256:290c78c99b7a99fe604ca5be86e032378d4e5c4a8e2b454e30fb3c4dd2eb2dbc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4KFRKDWRTSJ6IXBFEWCXELF4MV/bundle.json","state_url":"https://pith.science/pith/4KFRKDWRTSJ6IXBFEWCXELF4MV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4KFRKDWRTSJ6IXBFEWCXELF4MV/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":"2026-05-31T05:39:43Z","links":{"resolver":"https://pith.science/pith/4KFRKDWRTSJ6IXBFEWCXELF4MV","bundle":"https://pith.science/pith/4KFRKDWRTSJ6IXBFEWCXELF4MV/bundle.json","state":"https://pith.science/pith/4KFRKDWRTSJ6IXBFEWCXELF4MV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4KFRKDWRTSJ6IXBFEWCXELF4MV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:4KFRKDWRTSJ6IXBFEWCXELF4MV","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":"7489d8d48b2c6e52ea32c3f4c82805e81348b005de91f4fba571dd991576572c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-05-16T20:12:59Z","title_canon_sha256":"f3b95fd3ec90dbb556fca52608992abee50c5c135553e25cdbe66fa9b9348a59"},"schema_version":"1.0","source":{"id":"1705.05900","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.05900","created_at":"2026-05-18T00:29:46Z"},{"alias_kind":"arxiv_version","alias_value":"1705.05900v3","created_at":"2026-05-18T00:29:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.05900","created_at":"2026-05-18T00:29:46Z"},{"alias_kind":"pith_short_12","alias_value":"4KFRKDWRTSJ6","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"4KFRKDWRTSJ6IXBF","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"4KFRKDWR","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:290c78c99b7a99fe604ca5be86e032378d4e5c4a8e2b454e30fb3c4dd2eb2dbc","target":"graph","created_at":"2026-05-18T00:29:46Z","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 reprove the results of Jordan [18] and Siebert [31] and show that the Lie algebra of polynomial vector fields on an irreducible affine variety X is simple if and only if X is a smooth variety. Given proof is self-contained and does not depend on papers mentioned above. Besides, the structure of the module of polynomial functions on an irreducible smooth affine variety over the Lie algebra of vector fields is studied. Examples of Lie algebras of polynomial vector fields on an N-dimensional sphere, non-singular hyperelliptic curves and linear algebraic groups are considered.","authors_text":"Vyacheslav Futorny, Yuly Billig","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-05-16T20:12:59Z","title":"Lie algebras of vector fields on smooth affine varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.05900","kind":"arxiv","version":3},"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":"sha256:427e168b9f6a1636fbed9077c942b50f38836273d10e91cf118dfd505694faf6","target":"record","created_at":"2026-05-18T00:29:46Z","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":"7489d8d48b2c6e52ea32c3f4c82805e81348b005de91f4fba571dd991576572c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-05-16T20:12:59Z","title_canon_sha256":"f3b95fd3ec90dbb556fca52608992abee50c5c135553e25cdbe66fa9b9348a59"},"schema_version":"1.0","source":{"id":"1705.05900","kind":"arxiv","version":3}},"canonical_sha256":"e28b150ed19c93e45c252585722cbc657db0ffc53fe8c4822b0f26b66032976a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e28b150ed19c93e45c252585722cbc657db0ffc53fe8c4822b0f26b66032976a","first_computed_at":"2026-05-18T00:29:46.049574Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:46.049574Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B3y5/A+Ytbf/NvoU11YRu+qPkk31GAJcvDa4CkSdloTZ5ApcVfznPqWb6AMcCNT1xfxUhvVfYOEWZxVHIl8tAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:46.050200Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.05900","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:427e168b9f6a1636fbed9077c942b50f38836273d10e91cf118dfd505694faf6","sha256:290c78c99b7a99fe604ca5be86e032378d4e5c4a8e2b454e30fb3c4dd2eb2dbc"],"state_sha256":"86e20ef6dcfbfa2546e892cd4e08f55518b640ee228f4faddcfe5dd99b026d8d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5Fw5ms+XVqIZDc3OXYonkwrxtIS63fXau7qGN9CdPbLS0v1E2xjd0NvBQLNQaTIkdt157S2x8qz7G7Y/JxeHBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T05:39:43.655831Z","bundle_sha256":"fed1fc2e7909453cb0b4f59d00a3d1449e332be6b6529760ecd8a76b2e6f810e"}}