{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:CQ3HT4RRXEEQKMMWHH6BQATE7X","short_pith_number":"pith:CQ3HT4RR","canonical_record":{"source":{"id":"1806.08427","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-06-21T21:13:03Z","cross_cats_sorted":[],"title_canon_sha256":"b49bb4eb3c7c388c986b662fb31439e38a095e203f9a02541a380d8e8f4c0978","abstract_canon_sha256":"ffc7cb38e7f92f6fc80fa07a3a729669d4aede6a4c359a1f1f0528c4ede09534"},"schema_version":"1.0"},"canonical_sha256":"143679f231b90905319639fc180264fdf2bc95fd672a4a06e811edaaf9e0a8c7","source":{"kind":"arxiv","id":"1806.08427","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.08427","created_at":"2026-05-18T00:12:37Z"},{"alias_kind":"arxiv_version","alias_value":"1806.08427v1","created_at":"2026-05-18T00:12:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.08427","created_at":"2026-05-18T00:12:37Z"},{"alias_kind":"pith_short_12","alias_value":"CQ3HT4RRXEEQ","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"CQ3HT4RRXEEQKMMW","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"CQ3HT4RR","created_at":"2026-05-18T12:32:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:CQ3HT4RRXEEQKMMWHH6BQATE7X","target":"record","payload":{"canonical_record":{"source":{"id":"1806.08427","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-06-21T21:13:03Z","cross_cats_sorted":[],"title_canon_sha256":"b49bb4eb3c7c388c986b662fb31439e38a095e203f9a02541a380d8e8f4c0978","abstract_canon_sha256":"ffc7cb38e7f92f6fc80fa07a3a729669d4aede6a4c359a1f1f0528c4ede09534"},"schema_version":"1.0"},"canonical_sha256":"143679f231b90905319639fc180264fdf2bc95fd672a4a06e811edaaf9e0a8c7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:37.380252Z","signature_b64":"vWXIUxX7+OJOpvyoG1DtGI/HTS98teXQjLXP3dQGnJbp7OEaDf6GdZs0urGAL3kKJNIZPHUWgB4HG2AhZc/5Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"143679f231b90905319639fc180264fdf2bc95fd672a4a06e811edaaf9e0a8c7","last_reissued_at":"2026-05-18T00:12:37.379551Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:37.379551Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.08427","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":"2026-05-18T00:12:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zov/x/NGIS+6SFCawzbGS7YT4S7y1kpUjttrJRTRFfmdgNzMadW8QgZFrUHkbiSxNcpkRDoicPvmvQIvikoPBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T17:21:03.970831Z"},"content_sha256":"3f19c7fd8687b715a922679108c4491a7c484420581ff58713b60818296cfb3e","schema_version":"1.0","event_id":"sha256:3f19c7fd8687b715a922679108c4491a7c484420581ff58713b60818296cfb3e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:CQ3HT4RRXEEQKMMWHH6BQATE7X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Thompson's conjecture for finite simple groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Ilya Gorshkov","submitted_at":"2018-06-21T21:13:03Z","abstract_excerpt":"Let $G$ be a finite group, $N(G)$ be the set of conjugacy classes of the group $G$. In the present paper it is proved $G\\simeq L$ if $N(G)=N(L)$, where $G$ is a finite group with trivial center and $L$ is a finite simple group."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.08427","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":"2026-05-18T00:12:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/8NGHoc+WaMVhf4EjgHOkl0iWlj+aZedunSVh9bXnoNX/rOQgpMFV6OnqPlZ5F0Cs/DONjlZeXNbWsNJhIbOAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T17:21:03.971176Z"},"content_sha256":"632233e5e76dac5da0a76775cb939baef3e8fb3a1b0ca34ff51d986869fa9420","schema_version":"1.0","event_id":"sha256:632233e5e76dac5da0a76775cb939baef3e8fb3a1b0ca34ff51d986869fa9420"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CQ3HT4RRXEEQKMMWHH6BQATE7X/bundle.json","state_url":"https://pith.science/pith/CQ3HT4RRXEEQKMMWHH6BQATE7X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CQ3HT4RRXEEQKMMWHH6BQATE7X/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":"2026-06-30T17:21:03Z","links":{"resolver":"https://pith.science/pith/CQ3HT4RRXEEQKMMWHH6BQATE7X","bundle":"https://pith.science/pith/CQ3HT4RRXEEQKMMWHH6BQATE7X/bundle.json","state":"https://pith.science/pith/CQ3HT4RRXEEQKMMWHH6BQATE7X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CQ3HT4RRXEEQKMMWHH6BQATE7X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:CQ3HT4RRXEEQKMMWHH6BQATE7X","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":"ffc7cb38e7f92f6fc80fa07a3a729669d4aede6a4c359a1f1f0528c4ede09534","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-06-21T21:13:03Z","title_canon_sha256":"b49bb4eb3c7c388c986b662fb31439e38a095e203f9a02541a380d8e8f4c0978"},"schema_version":"1.0","source":{"id":"1806.08427","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.08427","created_at":"2026-05-18T00:12:37Z"},{"alias_kind":"arxiv_version","alias_value":"1806.08427v1","created_at":"2026-05-18T00:12:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.08427","created_at":"2026-05-18T00:12:37Z"},{"alias_kind":"pith_short_12","alias_value":"CQ3HT4RRXEEQ","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"CQ3HT4RRXEEQKMMW","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"CQ3HT4RR","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:632233e5e76dac5da0a76775cb939baef3e8fb3a1b0ca34ff51d986869fa9420","target":"graph","created_at":"2026-05-18T00:12:37Z","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 $G$ be a finite group, $N(G)$ be the set of conjugacy classes of the group $G$. In the present paper it is proved $G\\simeq L$ if $N(G)=N(L)$, where $G$ is a finite group with trivial center and $L$ is a finite simple group.","authors_text":"Ilya Gorshkov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-06-21T21:13:03Z","title":"On Thompson's conjecture for finite simple groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.08427","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":"sha256:3f19c7fd8687b715a922679108c4491a7c484420581ff58713b60818296cfb3e","target":"record","created_at":"2026-05-18T00:12:37Z","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":"ffc7cb38e7f92f6fc80fa07a3a729669d4aede6a4c359a1f1f0528c4ede09534","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-06-21T21:13:03Z","title_canon_sha256":"b49bb4eb3c7c388c986b662fb31439e38a095e203f9a02541a380d8e8f4c0978"},"schema_version":"1.0","source":{"id":"1806.08427","kind":"arxiv","version":1}},"canonical_sha256":"143679f231b90905319639fc180264fdf2bc95fd672a4a06e811edaaf9e0a8c7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"143679f231b90905319639fc180264fdf2bc95fd672a4a06e811edaaf9e0a8c7","first_computed_at":"2026-05-18T00:12:37.379551Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:37.379551Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vWXIUxX7+OJOpvyoG1DtGI/HTS98teXQjLXP3dQGnJbp7OEaDf6GdZs0urGAL3kKJNIZPHUWgB4HG2AhZc/5Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:37.380252Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.08427","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3f19c7fd8687b715a922679108c4491a7c484420581ff58713b60818296cfb3e","sha256:632233e5e76dac5da0a76775cb939baef3e8fb3a1b0ca34ff51d986869fa9420"],"state_sha256":"6b696edd30982226d44323ffed41285e7389a93a8c85c0bdf80e7bbd306751c8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yrFGcY5fmF+fQEKvKM2Pwcz6ICAnmJHeINMIiKsVZ538OTMb8EZOoUe8ObBKsMQPpdHdaiTC++4dLoqvSHdiBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T17:21:03.975528Z","bundle_sha256":"e65afdbd77d3404aa84c801240685894191796f68d176ba550762b8a0cc8b749"}}