{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:OLHWKDDUCVGH5IJ6MSTUGIVUR7","short_pith_number":"pith:OLHWKDDU","canonical_record":{"source":{"id":"1705.06223","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-05-17T15:54:55Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"e54a53825f2a160f9c94c1d8123b774d8115851c18d59cb7ed7f406f3cd0059f","abstract_canon_sha256":"b6d04c992dd3ef094c25c15f04716d144b661bd3c2a674856ce457824f48606d"},"schema_version":"1.0"},"canonical_sha256":"72cf650c74154c7ea13e64a74322b48fe8bee4eff86cc85025376dbe45652596","source":{"kind":"arxiv","id":"1705.06223","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.06223","created_at":"2026-05-18T00:31:23Z"},{"alias_kind":"arxiv_version","alias_value":"1705.06223v2","created_at":"2026-05-18T00:31:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.06223","created_at":"2026-05-18T00:31:23Z"},{"alias_kind":"pith_short_12","alias_value":"OLHWKDDUCVGH","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"OLHWKDDUCVGH5IJ6","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"OLHWKDDU","created_at":"2026-05-18T12:31:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:OLHWKDDUCVGH5IJ6MSTUGIVUR7","target":"record","payload":{"canonical_record":{"source":{"id":"1705.06223","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-05-17T15:54:55Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"e54a53825f2a160f9c94c1d8123b774d8115851c18d59cb7ed7f406f3cd0059f","abstract_canon_sha256":"b6d04c992dd3ef094c25c15f04716d144b661bd3c2a674856ce457824f48606d"},"schema_version":"1.0"},"canonical_sha256":"72cf650c74154c7ea13e64a74322b48fe8bee4eff86cc85025376dbe45652596","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:23.755518Z","signature_b64":"HpLQUYmayoBanjtitSdz6x5msJ6OUuR3hr5WepnSVmeJTjFVG80NNPeMtmTnZjcT72mN57zKtjm4gwLcrzJ9BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"72cf650c74154c7ea13e64a74322b48fe8bee4eff86cc85025376dbe45652596","last_reissued_at":"2026-05-18T00:31:23.755056Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:23.755056Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.06223","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:31:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/fq+WExgcdNZVjonAZWm05eidy9I30bp1IY6nH86P715y7Etcy8cLd2snuw38uplW4tdHXwJ1ZDM9xUoiiDsBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T12:38:48.701416Z"},"content_sha256":"20ebe63f29e1d81bbcea108021d00580fbed34a38c24027b22f87b35cbcba3ed","schema_version":"1.0","event_id":"sha256:20ebe63f29e1d81bbcea108021d00580fbed34a38c24027b22f87b35cbcba3ed"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:OLHWKDDUCVGH5IJ6MSTUGIVUR7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Modular finite $W$-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Lewis W. Topley, Simon M. Goodwin","submitted_at":"2017-05-17T15:54:55Z","abstract_excerpt":"Let $k$ be an algebraically closed field of characteristic $p > 0$ and let $G$ be a connected reductive algebraic group over $k$. Under some standard hypothesis on $G$, we give a direct approach to the finite $W$-algebra $U(\\mathfrak g,e)$ associated to a nilpotent element $e \\in \\mathfrak g = \\operatorname{Lie} G$. We prove a PBW theorem and deduce a number of consequences, then move on to define and study the $p$-centre of $U(\\mathfrak g,e)$, which allows us to define reduced finite $W$-algebras $U_\\eta(\\mathfrak g,e)$ and we verify that they coincide with those previously appearing in the w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.06223","kind":"arxiv","version":2},"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":"2026-05-18T00:31:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HYck12xC7cWJfc63sOlllve8StpvOluMBzKMiGFDrs4jv0ZEYPea726MrjzLnzf5wVRrfOJaG2DusjVATT+ZAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T12:38:48.701778Z"},"content_sha256":"886d941a3f023ff8dbb6d26642fbc2c06341b91f37901c40409fa6a749f0627a","schema_version":"1.0","event_id":"sha256:886d941a3f023ff8dbb6d26642fbc2c06341b91f37901c40409fa6a749f0627a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OLHWKDDUCVGH5IJ6MSTUGIVUR7/bundle.json","state_url":"https://pith.science/pith/OLHWKDDUCVGH5IJ6MSTUGIVUR7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OLHWKDDUCVGH5IJ6MSTUGIVUR7/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":"2026-07-02T12:38:48Z","links":{"resolver":"https://pith.science/pith/OLHWKDDUCVGH5IJ6MSTUGIVUR7","bundle":"https://pith.science/pith/OLHWKDDUCVGH5IJ6MSTUGIVUR7/bundle.json","state":"https://pith.science/pith/OLHWKDDUCVGH5IJ6MSTUGIVUR7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OLHWKDDUCVGH5IJ6MSTUGIVUR7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:OLHWKDDUCVGH5IJ6MSTUGIVUR7","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":"b6d04c992dd3ef094c25c15f04716d144b661bd3c2a674856ce457824f48606d","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-05-17T15:54:55Z","title_canon_sha256":"e54a53825f2a160f9c94c1d8123b774d8115851c18d59cb7ed7f406f3cd0059f"},"schema_version":"1.0","source":{"id":"1705.06223","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.06223","created_at":"2026-05-18T00:31:23Z"},{"alias_kind":"arxiv_version","alias_value":"1705.06223v2","created_at":"2026-05-18T00:31:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.06223","created_at":"2026-05-18T00:31:23Z"},{"alias_kind":"pith_short_12","alias_value":"OLHWKDDUCVGH","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"OLHWKDDUCVGH5IJ6","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"OLHWKDDU","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:886d941a3f023ff8dbb6d26642fbc2c06341b91f37901c40409fa6a749f0627a","target":"graph","created_at":"2026-05-18T00:31:23Z","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":"Let $k$ be an algebraically closed field of characteristic $p > 0$ and let $G$ be a connected reductive algebraic group over $k$. Under some standard hypothesis on $G$, we give a direct approach to the finite $W$-algebra $U(\\mathfrak g,e)$ associated to a nilpotent element $e \\in \\mathfrak g = \\operatorname{Lie} G$. We prove a PBW theorem and deduce a number of consequences, then move on to define and study the $p$-centre of $U(\\mathfrak g,e)$, which allows us to define reduced finite $W$-algebras $U_\\eta(\\mathfrak g,e)$ and we verify that they coincide with those previously appearing in the w","authors_text":"Lewis W. Topley, Simon M. Goodwin","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-05-17T15:54:55Z","title":"Modular finite $W$-algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.06223","kind":"arxiv","version":2},"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":"sha256:20ebe63f29e1d81bbcea108021d00580fbed34a38c24027b22f87b35cbcba3ed","target":"record","created_at":"2026-05-18T00:31:23Z","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":"b6d04c992dd3ef094c25c15f04716d144b661bd3c2a674856ce457824f48606d","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-05-17T15:54:55Z","title_canon_sha256":"e54a53825f2a160f9c94c1d8123b774d8115851c18d59cb7ed7f406f3cd0059f"},"schema_version":"1.0","source":{"id":"1705.06223","kind":"arxiv","version":2}},"canonical_sha256":"72cf650c74154c7ea13e64a74322b48fe8bee4eff86cc85025376dbe45652596","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"72cf650c74154c7ea13e64a74322b48fe8bee4eff86cc85025376dbe45652596","first_computed_at":"2026-05-18T00:31:23.755056Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:23.755056Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HpLQUYmayoBanjtitSdz6x5msJ6OUuR3hr5WepnSVmeJTjFVG80NNPeMtmTnZjcT72mN57zKtjm4gwLcrzJ9BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:23.755518Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.06223","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:20ebe63f29e1d81bbcea108021d00580fbed34a38c24027b22f87b35cbcba3ed","sha256:886d941a3f023ff8dbb6d26642fbc2c06341b91f37901c40409fa6a749f0627a"],"state_sha256":"d1edeade5f8250de21e9f3a95a47daaa39a92f13549007f6b97d16f47e2cc758"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zTqyEnJQDj9NQLmr/uuVDw57jvyJ2fGyKa2bWFUjI3zg4UX3EGt7Rri7g7Fki9RuIgxWqqHC0Isf7iBaTUiMBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T12:38:48.703902Z","bundle_sha256":"09b20a30c306e54d5d8162c912f53aa0d6b20e62fd4bbb57a757ecd8a5715497"}}