{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:T3S545VVHB45GBLDIWEZ4LSFEL","short_pith_number":"pith:T3S545VV","canonical_record":{"source":{"id":"1304.2597","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-04-09T14:02:20Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"5c88fde3ab8c49e4c9f3d4f907a0d56c71d26ddd843e4c777d88bee6a0a60993","abstract_canon_sha256":"97d0f5349ca2d2298cc07cd7695b20d06a04bb9bde75f9388d4fe9c985e9689e"},"schema_version":"1.0"},"canonical_sha256":"9ee5de76b53879d3056345899e2e4522df89bb09a11cf611ae7d7e3fb87a8215","source":{"kind":"arxiv","id":"1304.2597","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.2597","created_at":"2026-05-18T03:04:49Z"},{"alias_kind":"arxiv_version","alias_value":"1304.2597v2","created_at":"2026-05-18T03:04:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.2597","created_at":"2026-05-18T03:04:49Z"},{"alias_kind":"pith_short_12","alias_value":"T3S545VVHB45","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"T3S545VVHB45GBLD","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"T3S545VV","created_at":"2026-05-18T12:27:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:T3S545VVHB45GBLDIWEZ4LSFEL","target":"record","payload":{"canonical_record":{"source":{"id":"1304.2597","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-04-09T14:02:20Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"5c88fde3ab8c49e4c9f3d4f907a0d56c71d26ddd843e4c777d88bee6a0a60993","abstract_canon_sha256":"97d0f5349ca2d2298cc07cd7695b20d06a04bb9bde75f9388d4fe9c985e9689e"},"schema_version":"1.0"},"canonical_sha256":"9ee5de76b53879d3056345899e2e4522df89bb09a11cf611ae7d7e3fb87a8215","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:04:49.437036Z","signature_b64":"4hBCfrhJFFRc4RQIeqDxcKbBKqaXbOiluEah2yxPHCvtR3AFlQoln6KM+8F14HSBtJgIi7KVSfXFhYbgS6yvAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9ee5de76b53879d3056345899e2e4522df89bb09a11cf611ae7d7e3fb87a8215","last_reissued_at":"2026-05-18T03:04:49.436352Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:04:49.436352Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.2597","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":"2026-05-18T03:04:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jmhfQTxnQlnMfSoI9FPh9BICoMB19mom6V0KW2pVD0dQLujS8jGAbWIm7SFaI0hKcMh9wYMGl4Dxk7BErw7IDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T22:08:21.395590Z"},"content_sha256":"c6d1fb3187221d1681ece0626e5bb340e76d09c4adba1a73cf1ba987389eb244","schema_version":"1.0","event_id":"sha256:c6d1fb3187221d1681ece0626e5bb340e76d09c4adba1a73cf1ba987389eb244"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:T3S545VVHB45GBLDIWEZ4LSFEL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Maximal finite subgroups and minimal classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.NT","authors_text":"Gabriele Nebe, Renaud Coulangeon","submitted_at":"2013-04-09T14:02:20Z","abstract_excerpt":"We apply Voronoi's algorithm to compute representatives of the conjugacy classes of maximal finite subgroups of the unit group of a maximal order in some simple $\\QQ $-algebra. This may be used to show in small cases that non-conjugate orders have non-isomorphic unit groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.2597","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":"2026-05-18T03:04:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0oM3G2SgKpw22Ca9RZ2aZYjojT5JhCEdUGQgDNgj6YP8Qp855DIn0SuiOb2XI6i7cUf8DjgLq0G+NGAktaCaCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T22:08:21.396484Z"},"content_sha256":"37bd4b5f2c795965e9fa9263a35e2864094acced69168399e3beebb5f7a6002c","schema_version":"1.0","event_id":"sha256:37bd4b5f2c795965e9fa9263a35e2864094acced69168399e3beebb5f7a6002c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T3S545VVHB45GBLDIWEZ4LSFEL/bundle.json","state_url":"https://pith.science/pith/T3S545VVHB45GBLDIWEZ4LSFEL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T3S545VVHB45GBLDIWEZ4LSFEL/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":"2026-06-05T22:08:21Z","links":{"resolver":"https://pith.science/pith/T3S545VVHB45GBLDIWEZ4LSFEL","bundle":"https://pith.science/pith/T3S545VVHB45GBLDIWEZ4LSFEL/bundle.json","state":"https://pith.science/pith/T3S545VVHB45GBLDIWEZ4LSFEL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T3S545VVHB45GBLDIWEZ4LSFEL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:T3S545VVHB45GBLDIWEZ4LSFEL","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":"97d0f5349ca2d2298cc07cd7695b20d06a04bb9bde75f9388d4fe9c985e9689e","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-04-09T14:02:20Z","title_canon_sha256":"5c88fde3ab8c49e4c9f3d4f907a0d56c71d26ddd843e4c777d88bee6a0a60993"},"schema_version":"1.0","source":{"id":"1304.2597","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.2597","created_at":"2026-05-18T03:04:49Z"},{"alias_kind":"arxiv_version","alias_value":"1304.2597v2","created_at":"2026-05-18T03:04:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.2597","created_at":"2026-05-18T03:04:49Z"},{"alias_kind":"pith_short_12","alias_value":"T3S545VVHB45","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"T3S545VVHB45GBLD","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"T3S545VV","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:37bd4b5f2c795965e9fa9263a35e2864094acced69168399e3beebb5f7a6002c","target":"graph","created_at":"2026-05-18T03:04:49Z","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 apply Voronoi's algorithm to compute representatives of the conjugacy classes of maximal finite subgroups of the unit group of a maximal order in some simple $\\QQ $-algebra. This may be used to show in small cases that non-conjugate orders have non-isomorphic unit groups.","authors_text":"Gabriele Nebe, Renaud Coulangeon","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-04-09T14:02:20Z","title":"Maximal finite subgroups and minimal classes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.2597","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:c6d1fb3187221d1681ece0626e5bb340e76d09c4adba1a73cf1ba987389eb244","target":"record","created_at":"2026-05-18T03:04:49Z","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":"97d0f5349ca2d2298cc07cd7695b20d06a04bb9bde75f9388d4fe9c985e9689e","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-04-09T14:02:20Z","title_canon_sha256":"5c88fde3ab8c49e4c9f3d4f907a0d56c71d26ddd843e4c777d88bee6a0a60993"},"schema_version":"1.0","source":{"id":"1304.2597","kind":"arxiv","version":2}},"canonical_sha256":"9ee5de76b53879d3056345899e2e4522df89bb09a11cf611ae7d7e3fb87a8215","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9ee5de76b53879d3056345899e2e4522df89bb09a11cf611ae7d7e3fb87a8215","first_computed_at":"2026-05-18T03:04:49.436352Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:04:49.436352Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4hBCfrhJFFRc4RQIeqDxcKbBKqaXbOiluEah2yxPHCvtR3AFlQoln6KM+8F14HSBtJgIi7KVSfXFhYbgS6yvAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:04:49.437036Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.2597","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c6d1fb3187221d1681ece0626e5bb340e76d09c4adba1a73cf1ba987389eb244","sha256:37bd4b5f2c795965e9fa9263a35e2864094acced69168399e3beebb5f7a6002c"],"state_sha256":"fb1aa22dd6e6a737582cd52b81b30b4065ac0044fbff661e26ed5fbdb772293d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ek7BqEuClWUtZ8B6O/LVHlzuz2f32Ub9C0hdT38LyXR4JEA61DQo4KagQWroUOw2ADSTcATkyCZToP6TG/NyCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T22:08:21.400662Z","bundle_sha256":"f6de327f4156675e20f56bf4680d462fc18caf34f3c67451969cfd796216c922"}}