{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:W2ZVQWMW2D77VEYIUMXRVGU4UG","short_pith_number":"pith:W2ZVQWMW","canonical_record":{"source":{"id":"1412.5654","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-12-17T22:25:43Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"084a65a473cca199ee582cc901f782adba7c116f7336fcbddc921bba4d354c05","abstract_canon_sha256":"698b010007675aab972c32871ac0c59054dac9e39bab2d748a95b9557e701c70"},"schema_version":"1.0"},"canonical_sha256":"b6b3585996d0fffa9308a32f1a9a9ca1936ee90676d831883ca27b8e289a3659","source":{"kind":"arxiv","id":"1412.5654","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.5654","created_at":"2026-05-18T01:17:30Z"},{"alias_kind":"arxiv_version","alias_value":"1412.5654v2","created_at":"2026-05-18T01:17:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.5654","created_at":"2026-05-18T01:17:30Z"},{"alias_kind":"pith_short_12","alias_value":"W2ZVQWMW2D77","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"W2ZVQWMW2D77VEYI","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"W2ZVQWMW","created_at":"2026-05-18T12:28:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:W2ZVQWMW2D77VEYIUMXRVGU4UG","target":"record","payload":{"canonical_record":{"source":{"id":"1412.5654","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-12-17T22:25:43Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"084a65a473cca199ee582cc901f782adba7c116f7336fcbddc921bba4d354c05","abstract_canon_sha256":"698b010007675aab972c32871ac0c59054dac9e39bab2d748a95b9557e701c70"},"schema_version":"1.0"},"canonical_sha256":"b6b3585996d0fffa9308a32f1a9a9ca1936ee90676d831883ca27b8e289a3659","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:30.906203Z","signature_b64":"E1I+xtuZmBjggL/vX389IXQUvtgnR2uGNyZ4/HU6rn7DjaMlO0c4yjlSZswKYXCFh/GOGiCIYnNb7JTymY88DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b6b3585996d0fffa9308a32f1a9a9ca1936ee90676d831883ca27b8e289a3659","last_reissued_at":"2026-05-18T01:17:30.905436Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:30.905436Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.5654","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":"2026-05-18T01:17:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ve+RbcqTFg2ZayK3WqeZpor/jp8m+FYBEqHe7f9JjJq8390A5FMzuy0cMTdt93/yUnXCROngKl9aWdE91I70AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T13:10:19.127946Z"},"content_sha256":"6b8d6126f3a1e2ec75bcbe6dd01a80331d82dc2687eba3a326d1b2181c95434e","schema_version":"1.0","event_id":"sha256:6b8d6126f3a1e2ec75bcbe6dd01a80331d82dc2687eba3a326d1b2181c95434e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:W2ZVQWMW2D77VEYIUMXRVGU4UG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Singularities of closures of spherical $B$-conjugacy classes of nilpotent orbits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Martin Bender, Nicolas Perrin","submitted_at":"2014-12-17T22:25:43Z","abstract_excerpt":"We prove that for a simply laced group, the closure of the Borel conjugacy class of any nilpotent element of height $2$ in its conjugacy class is normal and admits a rational resolution. We extend this, using Frobenius splitting techniques, to the closure in the whole Lie algebra if either the group has type $A$ or the element has rank $2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5654","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":"2026-05-18T01:17:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZP0Bi8sQE+dPC9PxcnkhFimaX4L/t7X7tgRF8oDPRndwmdZKr74Ki6nmAFUpfUiNC8wSvKUTZ9tHF0wzISCyAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T13:10:19.128306Z"},"content_sha256":"da8a3c849ca6221bc61f485d35cca17232c225d2031141b8a773bf50f9d8d707","schema_version":"1.0","event_id":"sha256:da8a3c849ca6221bc61f485d35cca17232c225d2031141b8a773bf50f9d8d707"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W2ZVQWMW2D77VEYIUMXRVGU4UG/bundle.json","state_url":"https://pith.science/pith/W2ZVQWMW2D77VEYIUMXRVGU4UG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W2ZVQWMW2D77VEYIUMXRVGU4UG/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":"2026-06-11T13:10:19Z","links":{"resolver":"https://pith.science/pith/W2ZVQWMW2D77VEYIUMXRVGU4UG","bundle":"https://pith.science/pith/W2ZVQWMW2D77VEYIUMXRVGU4UG/bundle.json","state":"https://pith.science/pith/W2ZVQWMW2D77VEYIUMXRVGU4UG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W2ZVQWMW2D77VEYIUMXRVGU4UG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:W2ZVQWMW2D77VEYIUMXRVGU4UG","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":"698b010007675aab972c32871ac0c59054dac9e39bab2d748a95b9557e701c70","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-12-17T22:25:43Z","title_canon_sha256":"084a65a473cca199ee582cc901f782adba7c116f7336fcbddc921bba4d354c05"},"schema_version":"1.0","source":{"id":"1412.5654","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.5654","created_at":"2026-05-18T01:17:30Z"},{"alias_kind":"arxiv_version","alias_value":"1412.5654v2","created_at":"2026-05-18T01:17:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.5654","created_at":"2026-05-18T01:17:30Z"},{"alias_kind":"pith_short_12","alias_value":"W2ZVQWMW2D77","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"W2ZVQWMW2D77VEYI","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"W2ZVQWMW","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:da8a3c849ca6221bc61f485d35cca17232c225d2031141b8a773bf50f9d8d707","target":"graph","created_at":"2026-05-18T01:17:30Z","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 prove that for a simply laced group, the closure of the Borel conjugacy class of any nilpotent element of height $2$ in its conjugacy class is normal and admits a rational resolution. We extend this, using Frobenius splitting techniques, to the closure in the whole Lie algebra if either the group has type $A$ or the element has rank $2$.","authors_text":"Martin Bender, Nicolas Perrin","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-12-17T22:25:43Z","title":"Singularities of closures of spherical $B$-conjugacy classes of nilpotent orbits"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5654","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":"sha256:6b8d6126f3a1e2ec75bcbe6dd01a80331d82dc2687eba3a326d1b2181c95434e","target":"record","created_at":"2026-05-18T01:17:30Z","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":"698b010007675aab972c32871ac0c59054dac9e39bab2d748a95b9557e701c70","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-12-17T22:25:43Z","title_canon_sha256":"084a65a473cca199ee582cc901f782adba7c116f7336fcbddc921bba4d354c05"},"schema_version":"1.0","source":{"id":"1412.5654","kind":"arxiv","version":2}},"canonical_sha256":"b6b3585996d0fffa9308a32f1a9a9ca1936ee90676d831883ca27b8e289a3659","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b6b3585996d0fffa9308a32f1a9a9ca1936ee90676d831883ca27b8e289a3659","first_computed_at":"2026-05-18T01:17:30.905436Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:30.905436Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E1I+xtuZmBjggL/vX389IXQUvtgnR2uGNyZ4/HU6rn7DjaMlO0c4yjlSZswKYXCFh/GOGiCIYnNb7JTymY88DA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:30.906203Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.5654","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6b8d6126f3a1e2ec75bcbe6dd01a80331d82dc2687eba3a326d1b2181c95434e","sha256:da8a3c849ca6221bc61f485d35cca17232c225d2031141b8a773bf50f9d8d707"],"state_sha256":"4cebf49cb3f969358eec7684f72a1ab02bf42635f6bdc5dcffa412f0b36f6474"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ERe18SgBzm9w4hNyXgwXmmgJ2j+ZvGeJ+qzFrkwhcykHIirrACCusDh1L+KM1d92PmcSdf1OPIq20NIvamtaCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T13:10:19.130480Z","bundle_sha256":"ad47ab160219a61bec35337a5bcf9ee29d1001444a81475d6dbe1eda65efb6c2"}}