{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:OS3HGCFIOGYMJIOQFJYBUJGBGG","short_pith_number":"pith:OS3HGCFI","canonical_record":{"source":{"id":"1606.00038","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-05-31T20:43:49Z","cross_cats_sorted":[],"title_canon_sha256":"b03e3f32046a16c49258bc9966b917ac294a2ac0668435f054187723da4774e2","abstract_canon_sha256":"a8819a00df5e2038307a0ecb4d034f3618c6cb96b668c54b7e2e7a31f0f25f96"},"schema_version":"1.0"},"canonical_sha256":"74b67308a871b0c4a1d02a701a24c1319049748e8949ec0965296853355c860a","source":{"kind":"arxiv","id":"1606.00038","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.00038","created_at":"2026-05-18T01:13:09Z"},{"alias_kind":"arxiv_version","alias_value":"1606.00038v1","created_at":"2026-05-18T01:13:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.00038","created_at":"2026-05-18T01:13:09Z"},{"alias_kind":"pith_short_12","alias_value":"OS3HGCFIOGYM","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"OS3HGCFIOGYMJIOQ","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"OS3HGCFI","created_at":"2026-05-18T12:30:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:OS3HGCFIOGYMJIOQFJYBUJGBGG","target":"record","payload":{"canonical_record":{"source":{"id":"1606.00038","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-05-31T20:43:49Z","cross_cats_sorted":[],"title_canon_sha256":"b03e3f32046a16c49258bc9966b917ac294a2ac0668435f054187723da4774e2","abstract_canon_sha256":"a8819a00df5e2038307a0ecb4d034f3618c6cb96b668c54b7e2e7a31f0f25f96"},"schema_version":"1.0"},"canonical_sha256":"74b67308a871b0c4a1d02a701a24c1319049748e8949ec0965296853355c860a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:13:09.184698Z","signature_b64":"1uCOW4aehgobDCuLzTM9duuoSod6UVig2T814E79wZheAmpA055ZE4idkT5+YIX8fIogtpg4oRTZAvW+o/oIAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"74b67308a871b0c4a1d02a701a24c1319049748e8949ec0965296853355c860a","last_reissued_at":"2026-05-18T01:13:09.184362Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:13:09.184362Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.00038","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":"2026-05-18T01:13:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PiFOOW5OHJhEkpVpS88A52/iEboXYTglAG0JYjTO2tAmNcusnBku3t00NfwuYSQiETqPgn2ENzMkDazh4slsBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T16:52:56.347271Z"},"content_sha256":"a59572cdce43cafbe9370765122b50db7babca1bd908f642d38fa147a367cf25","schema_version":"1.0","event_id":"sha256:a59572cdce43cafbe9370765122b50db7babca1bd908f642d38fa147a367cf25"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:OS3HGCFIOGYMJIOQFJYBUJGBGG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A characterization of some projective special linear groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Ashraf Daneshkhah, Younes Jalilian","submitted_at":"2016-05-31T20:43:49Z","abstract_excerpt":"In this paper, we show that projective special linear groups $S:=L_3(q)$ with $q$ less than $100$ are uniquely determined by their orders and degree patterns of their prime graphs. Indeed, we prove that if $G$ is a finite group whose order and degree pattern of its prime graph is the same as the order and the degree pattern of $S$, then $G$ is isomorphic to $S$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.00038","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":"2026-05-18T01:13:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UT24LkqnPgJhYXJj3BSvH4+jYyoBWtb1+LwHJoSt5hfJEHO9vifN0jP1W1AXrx6A/WC8p7tb0Ethma1X2vupDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T16:52:56.348090Z"},"content_sha256":"891cb756d82fea6b75f80f766212361d8b15cb6cea0ee6e1d71e03ff9936cd49","schema_version":"1.0","event_id":"sha256:891cb756d82fea6b75f80f766212361d8b15cb6cea0ee6e1d71e03ff9936cd49"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OS3HGCFIOGYMJIOQFJYBUJGBGG/bundle.json","state_url":"https://pith.science/pith/OS3HGCFIOGYMJIOQFJYBUJGBGG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OS3HGCFIOGYMJIOQFJYBUJGBGG/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":"2026-06-11T16:52:56Z","links":{"resolver":"https://pith.science/pith/OS3HGCFIOGYMJIOQFJYBUJGBGG","bundle":"https://pith.science/pith/OS3HGCFIOGYMJIOQFJYBUJGBGG/bundle.json","state":"https://pith.science/pith/OS3HGCFIOGYMJIOQFJYBUJGBGG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OS3HGCFIOGYMJIOQFJYBUJGBGG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:OS3HGCFIOGYMJIOQFJYBUJGBGG","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":"a8819a00df5e2038307a0ecb4d034f3618c6cb96b668c54b7e2e7a31f0f25f96","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-05-31T20:43:49Z","title_canon_sha256":"b03e3f32046a16c49258bc9966b917ac294a2ac0668435f054187723da4774e2"},"schema_version":"1.0","source":{"id":"1606.00038","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.00038","created_at":"2026-05-18T01:13:09Z"},{"alias_kind":"arxiv_version","alias_value":"1606.00038v1","created_at":"2026-05-18T01:13:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.00038","created_at":"2026-05-18T01:13:09Z"},{"alias_kind":"pith_short_12","alias_value":"OS3HGCFIOGYM","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"OS3HGCFIOGYMJIOQ","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"OS3HGCFI","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:891cb756d82fea6b75f80f766212361d8b15cb6cea0ee6e1d71e03ff9936cd49","target":"graph","created_at":"2026-05-18T01:13:09Z","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":"In this paper, we show that projective special linear groups $S:=L_3(q)$ with $q$ less than $100$ are uniquely determined by their orders and degree patterns of their prime graphs. Indeed, we prove that if $G$ is a finite group whose order and degree pattern of its prime graph is the same as the order and the degree pattern of $S$, then $G$ is isomorphic to $S$.","authors_text":"Ashraf Daneshkhah, Younes Jalilian","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-05-31T20:43:49Z","title":"A characterization of some projective special linear groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.00038","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:a59572cdce43cafbe9370765122b50db7babca1bd908f642d38fa147a367cf25","target":"record","created_at":"2026-05-18T01:13:09Z","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":"a8819a00df5e2038307a0ecb4d034f3618c6cb96b668c54b7e2e7a31f0f25f96","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-05-31T20:43:49Z","title_canon_sha256":"b03e3f32046a16c49258bc9966b917ac294a2ac0668435f054187723da4774e2"},"schema_version":"1.0","source":{"id":"1606.00038","kind":"arxiv","version":1}},"canonical_sha256":"74b67308a871b0c4a1d02a701a24c1319049748e8949ec0965296853355c860a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"74b67308a871b0c4a1d02a701a24c1319049748e8949ec0965296853355c860a","first_computed_at":"2026-05-18T01:13:09.184362Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:13:09.184362Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1uCOW4aehgobDCuLzTM9duuoSod6UVig2T814E79wZheAmpA055ZE4idkT5+YIX8fIogtpg4oRTZAvW+o/oIAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:13:09.184698Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.00038","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a59572cdce43cafbe9370765122b50db7babca1bd908f642d38fa147a367cf25","sha256:891cb756d82fea6b75f80f766212361d8b15cb6cea0ee6e1d71e03ff9936cd49"],"state_sha256":"a6430f0738a3999f096fb13a822520247d3722fe972deae29d364bab91c3821b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qx5TrDdzgECTDNS+4nrak9PzviOAPw3NQhbV/NcYoYBxJjUGBa7TfxD0iTOLvkbF/aD5601q+TOpiNiqB403CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T16:52:56.353019Z","bundle_sha256":"a471e16534d30f63e1f0788fe449cb253c4a59774449a48374759052ed07ad27"}}