{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:MWARXIYPECY4VPC725K4PNRUNX","short_pith_number":"pith:MWARXIYP","canonical_record":{"source":{"id":"1606.03064","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-06-09T18:57:16Z","cross_cats_sorted":[],"title_canon_sha256":"fe8d81fe38709b4b88369c2ca8e374a5c4bbc78e0c39deb0ad007b27b961d519","abstract_canon_sha256":"747a1efaf1dc292b514e1f2df7bf97dfc32ae29723ec7303aa2af77aaa829be5"},"schema_version":"1.0"},"canonical_sha256":"65811ba30f20b1cabc5fd755c7b6346de7e1c6a4f87fa23bb26db771bb3115db","source":{"kind":"arxiv","id":"1606.03064","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.03064","created_at":"2026-05-18T01:12:38Z"},{"alias_kind":"arxiv_version","alias_value":"1606.03064v1","created_at":"2026-05-18T01:12:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.03064","created_at":"2026-05-18T01:12:38Z"},{"alias_kind":"pith_short_12","alias_value":"MWARXIYPECY4","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MWARXIYPECY4VPC7","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MWARXIYP","created_at":"2026-05-18T12:30:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:MWARXIYPECY4VPC725K4PNRUNX","target":"record","payload":{"canonical_record":{"source":{"id":"1606.03064","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-06-09T18:57:16Z","cross_cats_sorted":[],"title_canon_sha256":"fe8d81fe38709b4b88369c2ca8e374a5c4bbc78e0c39deb0ad007b27b961d519","abstract_canon_sha256":"747a1efaf1dc292b514e1f2df7bf97dfc32ae29723ec7303aa2af77aaa829be5"},"schema_version":"1.0"},"canonical_sha256":"65811ba30f20b1cabc5fd755c7b6346de7e1c6a4f87fa23bb26db771bb3115db","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:38.386929Z","signature_b64":"7/SNId4tKwiFtPGsTVKGT88x0eTsWKbTv3F+OwxozMHNiIWeebWsGODq+Y4oPWmUQ5QfirjwW9bGQr7lX7buDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65811ba30f20b1cabc5fd755c7b6346de7e1c6a4f87fa23bb26db771bb3115db","last_reissued_at":"2026-05-18T01:12:38.386561Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:38.386561Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.03064","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":"2026-05-18T01:12:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lo6T/O0nBqZ11PHIRyyXj6PJw28J/wwICu+DCqVzwZrCng6RPn1UhqqaP8qajXR07OpAPN09ErTj3mFBMrTlBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T07:44:30.063151Z"},"content_sha256":"2e46655cec0acaedc8ab3ef4aceba2fc017fd658b6b52dc718cae8269b0cd25b","schema_version":"1.0","event_id":"sha256:2e46655cec0acaedc8ab3ef4aceba2fc017fd658b6b52dc718cae8269b0cd25b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:MWARXIYPECY4VPC725K4PNRUNX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Finite subgroups of simple algebraic groups with irreducible centralizers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Adam R. Thomas, Martin W. Liebeck","submitted_at":"2016-06-09T18:57:16Z","abstract_excerpt":"We determine all finite subgroups of simple algebraic groups that have irreducible centralizers - that is, centralizers whose connected component does not lie in a parabolic subgroup."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03064","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":"2026-05-18T01:12:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UwYkjpBZv+njo/n8j5PnchOCP85B8qJxYpLQxbz7vx6WB4m9Waf3ucwcHjhErwmHLtO5JIXGut9Gi1S9aKpbBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T07:44:30.063573Z"},"content_sha256":"c70fa98f7c7de36b0a54e2ed3c537234708faa0faf5763ecb1e17221827e3a01","schema_version":"1.0","event_id":"sha256:c70fa98f7c7de36b0a54e2ed3c537234708faa0faf5763ecb1e17221827e3a01"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MWARXIYPECY4VPC725K4PNRUNX/bundle.json","state_url":"https://pith.science/pith/MWARXIYPECY4VPC725K4PNRUNX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MWARXIYPECY4VPC725K4PNRUNX/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":"2026-06-03T07:44:30Z","links":{"resolver":"https://pith.science/pith/MWARXIYPECY4VPC725K4PNRUNX","bundle":"https://pith.science/pith/MWARXIYPECY4VPC725K4PNRUNX/bundle.json","state":"https://pith.science/pith/MWARXIYPECY4VPC725K4PNRUNX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MWARXIYPECY4VPC725K4PNRUNX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:MWARXIYPECY4VPC725K4PNRUNX","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":"747a1efaf1dc292b514e1f2df7bf97dfc32ae29723ec7303aa2af77aaa829be5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-06-09T18:57:16Z","title_canon_sha256":"fe8d81fe38709b4b88369c2ca8e374a5c4bbc78e0c39deb0ad007b27b961d519"},"schema_version":"1.0","source":{"id":"1606.03064","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.03064","created_at":"2026-05-18T01:12:38Z"},{"alias_kind":"arxiv_version","alias_value":"1606.03064v1","created_at":"2026-05-18T01:12:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.03064","created_at":"2026-05-18T01:12:38Z"},{"alias_kind":"pith_short_12","alias_value":"MWARXIYPECY4","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MWARXIYPECY4VPC7","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MWARXIYP","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:c70fa98f7c7de36b0a54e2ed3c537234708faa0faf5763ecb1e17221827e3a01","target":"graph","created_at":"2026-05-18T01:12:38Z","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 determine all finite subgroups of simple algebraic groups that have irreducible centralizers - that is, centralizers whose connected component does not lie in a parabolic subgroup.","authors_text":"Adam R. Thomas, Martin W. Liebeck","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-06-09T18:57:16Z","title":"Finite subgroups of simple algebraic groups with irreducible centralizers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03064","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":"sha256:2e46655cec0acaedc8ab3ef4aceba2fc017fd658b6b52dc718cae8269b0cd25b","target":"record","created_at":"2026-05-18T01:12:38Z","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":"747a1efaf1dc292b514e1f2df7bf97dfc32ae29723ec7303aa2af77aaa829be5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-06-09T18:57:16Z","title_canon_sha256":"fe8d81fe38709b4b88369c2ca8e374a5c4bbc78e0c39deb0ad007b27b961d519"},"schema_version":"1.0","source":{"id":"1606.03064","kind":"arxiv","version":1}},"canonical_sha256":"65811ba30f20b1cabc5fd755c7b6346de7e1c6a4f87fa23bb26db771bb3115db","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"65811ba30f20b1cabc5fd755c7b6346de7e1c6a4f87fa23bb26db771bb3115db","first_computed_at":"2026-05-18T01:12:38.386561Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:38.386561Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7/SNId4tKwiFtPGsTVKGT88x0eTsWKbTv3F+OwxozMHNiIWeebWsGODq+Y4oPWmUQ5QfirjwW9bGQr7lX7buDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:38.386929Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.03064","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2e46655cec0acaedc8ab3ef4aceba2fc017fd658b6b52dc718cae8269b0cd25b","sha256:c70fa98f7c7de36b0a54e2ed3c537234708faa0faf5763ecb1e17221827e3a01"],"state_sha256":"178f0d65abd2cbec82a65c1f54ccfe82c1d24eb27ade0a407fb4203d5c1e54a5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YMbWt01FT+pXj1Vqr/BqnM8Nc8maTow+AiMtVhX2ZTgHw01P5pxGDQoOZ6LngdK77ajTzwg1obpyh2qYPB7XBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T07:44:30.065462Z","bundle_sha256":"073b47bd0d87adecef72883e8bdcfd5a4bfac112879ebe4cbcff4c4d99862028"}}