{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:WWS2OYEWDNEGP3RBOGPBFLCTJY","short_pith_number":"pith:WWS2OYEW","canonical_record":{"source":{"id":"1501.04534","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-01-19T16:16:35Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"c2107abb5b355bf0f485f639528913d73cf81b1d81652ed65cb069e73e4efc8a","abstract_canon_sha256":"a64975bfe7edea7d549f8d9cb5792f1b5b8468629f9df0164dfd2020a5a9a968"},"schema_version":"1.0"},"canonical_sha256":"b5a5a760961b4867ee21719e12ac534e0a008602c4490493ba5c2dfb493b4b5f","source":{"kind":"arxiv","id":"1501.04534","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.04534","created_at":"2026-05-18T02:29:08Z"},{"alias_kind":"arxiv_version","alias_value":"1501.04534v1","created_at":"2026-05-18T02:29:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.04534","created_at":"2026-05-18T02:29:08Z"},{"alias_kind":"pith_short_12","alias_value":"WWS2OYEWDNEG","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WWS2OYEWDNEGP3RB","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WWS2OYEW","created_at":"2026-05-18T12:29:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:WWS2OYEWDNEGP3RBOGPBFLCTJY","target":"record","payload":{"canonical_record":{"source":{"id":"1501.04534","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-01-19T16:16:35Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"c2107abb5b355bf0f485f639528913d73cf81b1d81652ed65cb069e73e4efc8a","abstract_canon_sha256":"a64975bfe7edea7d549f8d9cb5792f1b5b8468629f9df0164dfd2020a5a9a968"},"schema_version":"1.0"},"canonical_sha256":"b5a5a760961b4867ee21719e12ac534e0a008602c4490493ba5c2dfb493b4b5f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:08.791223Z","signature_b64":"HauqdO2P8LUnuz4rLu3QS+G2DQx5z76n5ebrbRGmPGf0IYqxz63GENB8Zn9jc3Uf8v8tB+hKud7DKnGUWaTMDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b5a5a760961b4867ee21719e12ac534e0a008602c4490493ba5c2dfb493b4b5f","last_reissued_at":"2026-05-18T02:29:08.790604Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:08.790604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.04534","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":"2026-05-18T02:29:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6ZGpAuK7taAUbewMF5o32IZLEX0KcWSCjUU/T8RG+cAWEIDnv/CTX2mCPNHhZauA1YD+1yffK1U9UKnLUwhNDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T21:54:01.290852Z"},"content_sha256":"4cd605077227f4738c511d67b433b183065daf31d24481c2917f1025ede8db37","schema_version":"1.0","event_id":"sha256:4cd605077227f4738c511d67b433b183065daf31d24481c2917f1025ede8db37"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:WWS2OYEWDNEGP3RBOGPBFLCTJY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Katsylo theorem for sheets of spherical conjugacy classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RT","authors_text":"Francesco Esposito, Giovanna Carnovale","submitted_at":"2015-01-19T16:16:35Z","abstract_excerpt":"We show that, for a sheet or a Lusztig stratum S containing spherical conjugacy classes in a connected reductive algebraic group G over an algebraically closed field in good characteristic, the orbit space S/G is isomorphic to the quotient of an affine subvariety of G modulo the action of a finite abelian 2-group. The affine subvariety is a closed subset of a Bruhat double coset and the abelian group is a finite subgroup of a maximal torus of G. We show that sheets of spherical conjugacy classes in a simple group are always smooth and we list which strata containing spherical classes are smoot"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04534","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":"2026-05-18T02:29:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4nPRnvReDuB3Xt2FSanibP8avgofDXOlHJzxXqpJ6V7UHNseDRP9/I+pIWfs+9PmNnU5cG0A9LrlfoYeSjpUCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T21:54:01.291519Z"},"content_sha256":"eaf84a16ab0abea1e19faa0d40fc5c7bacd5daf9efc091d86db16fd7b5e4c280","schema_version":"1.0","event_id":"sha256:eaf84a16ab0abea1e19faa0d40fc5c7bacd5daf9efc091d86db16fd7b5e4c280"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WWS2OYEWDNEGP3RBOGPBFLCTJY/bundle.json","state_url":"https://pith.science/pith/WWS2OYEWDNEGP3RBOGPBFLCTJY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WWS2OYEWDNEGP3RBOGPBFLCTJY/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":"2026-05-27T21:54:01Z","links":{"resolver":"https://pith.science/pith/WWS2OYEWDNEGP3RBOGPBFLCTJY","bundle":"https://pith.science/pith/WWS2OYEWDNEGP3RBOGPBFLCTJY/bundle.json","state":"https://pith.science/pith/WWS2OYEWDNEGP3RBOGPBFLCTJY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WWS2OYEWDNEGP3RBOGPBFLCTJY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:WWS2OYEWDNEGP3RBOGPBFLCTJY","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":"a64975bfe7edea7d549f8d9cb5792f1b5b8468629f9df0164dfd2020a5a9a968","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-01-19T16:16:35Z","title_canon_sha256":"c2107abb5b355bf0f485f639528913d73cf81b1d81652ed65cb069e73e4efc8a"},"schema_version":"1.0","source":{"id":"1501.04534","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.04534","created_at":"2026-05-18T02:29:08Z"},{"alias_kind":"arxiv_version","alias_value":"1501.04534v1","created_at":"2026-05-18T02:29:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.04534","created_at":"2026-05-18T02:29:08Z"},{"alias_kind":"pith_short_12","alias_value":"WWS2OYEWDNEG","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WWS2OYEWDNEGP3RB","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WWS2OYEW","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:eaf84a16ab0abea1e19faa0d40fc5c7bacd5daf9efc091d86db16fd7b5e4c280","target":"graph","created_at":"2026-05-18T02:29:08Z","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 show that, for a sheet or a Lusztig stratum S containing spherical conjugacy classes in a connected reductive algebraic group G over an algebraically closed field in good characteristic, the orbit space S/G is isomorphic to the quotient of an affine subvariety of G modulo the action of a finite abelian 2-group. The affine subvariety is a closed subset of a Bruhat double coset and the abelian group is a finite subgroup of a maximal torus of G. We show that sheets of spherical conjugacy classes in a simple group are always smooth and we list which strata containing spherical classes are smoot","authors_text":"Francesco Esposito, Giovanna Carnovale","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-01-19T16:16:35Z","title":"A Katsylo theorem for sheets of spherical conjugacy classes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04534","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":"sha256:4cd605077227f4738c511d67b433b183065daf31d24481c2917f1025ede8db37","target":"record","created_at":"2026-05-18T02:29:08Z","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":"a64975bfe7edea7d549f8d9cb5792f1b5b8468629f9df0164dfd2020a5a9a968","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-01-19T16:16:35Z","title_canon_sha256":"c2107abb5b355bf0f485f639528913d73cf81b1d81652ed65cb069e73e4efc8a"},"schema_version":"1.0","source":{"id":"1501.04534","kind":"arxiv","version":1}},"canonical_sha256":"b5a5a760961b4867ee21719e12ac534e0a008602c4490493ba5c2dfb493b4b5f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b5a5a760961b4867ee21719e12ac534e0a008602c4490493ba5c2dfb493b4b5f","first_computed_at":"2026-05-18T02:29:08.790604Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:08.790604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HauqdO2P8LUnuz4rLu3QS+G2DQx5z76n5ebrbRGmPGf0IYqxz63GENB8Zn9jc3Uf8v8tB+hKud7DKnGUWaTMDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:08.791223Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.04534","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4cd605077227f4738c511d67b433b183065daf31d24481c2917f1025ede8db37","sha256:eaf84a16ab0abea1e19faa0d40fc5c7bacd5daf9efc091d86db16fd7b5e4c280"],"state_sha256":"2bad9c4acb157a40e861bbbe2d8e68611fbd19cd6088cbabffada1c560ce1c07"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jyC4PuhaesBMteu3AdbOZbF3e+5n3QchbZ1xTc8ub2hqvfkjP/pcF/+uxeDujFBxfP2VzFxCuyIR0Uvv+edjBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T21:54:01.294493Z","bundle_sha256":"de5e76938a929fa485196ea8afef26805d32dfb816fbda410c3e3f97aef2113b"}}