{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:AHFRFMHEU3Z2FQ6RDYO4AM4YZJ","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":"b00c640cfc79d88afffe0aee9b18357437eb41b441469a64e7b980d9538f99d4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-09-25T08:45:48Z","title_canon_sha256":"d1995836147042d9c1bd956bd6945a8fffe9aefefd7ccf80485bc09758163138"},"schema_version":"1.0","source":{"id":"1209.5541","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.5541","created_at":"2026-05-18T03:44:48Z"},{"alias_kind":"arxiv_version","alias_value":"1209.5541v1","created_at":"2026-05-18T03:44:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.5541","created_at":"2026-05-18T03:44:48Z"},{"alias_kind":"pith_short_12","alias_value":"AHFRFMHEU3Z2","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"AHFRFMHEU3Z2FQ6R","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"AHFRFMHE","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:846484f446339372e0784ed64f6a8b7ad41df93399292e2368fe6286bd422aec","target":"graph","created_at":"2026-05-18T03:44:48Z","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":"Any simple elliptic singularity of type $\\tilde{D}_5$ can be obtained by taking the intersection of the nilpotent variety and the 4-dimensional \"good slices\" in the semi-simple Lie algebra ${\\frak sl}(2, {\\mathbb C}) \\oplus {\\frak sl}(2, {\\mathbb C})$. We describe these new slices purely by the structure of the Lie algebra. We also construct the semi-universal deformation spaces of $\\tilde{D}_5$-singularities by using the 4-dimensional \"good slices\".","authors_text":"K.Nakamoto, M.Tosun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-09-25T08:45:48Z","title":"A new construction of $\\tilde{D}_5$-singularities and generalization of Slodowy slices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.5541","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":"sha256:7597e6d6814068fa94f63fc5775fd2fe1a7c4381a759e9681b7067a07569fe84","target":"record","created_at":"2026-05-18T03:44:48Z","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":"b00c640cfc79d88afffe0aee9b18357437eb41b441469a64e7b980d9538f99d4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-09-25T08:45:48Z","title_canon_sha256":"d1995836147042d9c1bd956bd6945a8fffe9aefefd7ccf80485bc09758163138"},"schema_version":"1.0","source":{"id":"1209.5541","kind":"arxiv","version":1}},"canonical_sha256":"01cb12b0e4a6f3a2c3d11e1dc03398ca677fadca317622efe3f3fab6e32e2a14","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"01cb12b0e4a6f3a2c3d11e1dc03398ca677fadca317622efe3f3fab6e32e2a14","first_computed_at":"2026-05-18T03:44:48.238467Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:44:48.238467Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7gQNZZEkPWrHftHRU2DW0qd/2Y3q0G+J+0/wUV6Q30HNrtT5PnWBKbRM+vqompd3nwOncZw5sQnyaREQppwlCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:44:48.239148Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.5541","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7597e6d6814068fa94f63fc5775fd2fe1a7c4381a759e9681b7067a07569fe84","sha256:846484f446339372e0784ed64f6a8b7ad41df93399292e2368fe6286bd422aec"],"state_sha256":"fed6c2725350da294f81d356da674ece542982dd0854b6e298f25d3de22d40d3"}