{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:B4LOINIQPPNLBL7KF2VVANSYS5","short_pith_number":"pith:B4LOINIQ","canonical_record":{"source":{"id":"1701.05490","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-01-19T16:02:50Z","cross_cats_sorted":[],"title_canon_sha256":"af5cd8bab719009b8987980292cadd38b9ddb5af5b49a7515df7e926f19f7638","abstract_canon_sha256":"b9d12b910102e82a1e7009851e0a1fa408f8ad43f323d310910d04226d237039"},"schema_version":"1.0"},"canonical_sha256":"0f16e435107bdab0afea2eab5036589755954f2ea6b53cc631319118f0cc1248","source":{"kind":"arxiv","id":"1701.05490","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.05490","created_at":"2026-05-18T00:52:29Z"},{"alias_kind":"arxiv_version","alias_value":"1701.05490v1","created_at":"2026-05-18T00:52:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.05490","created_at":"2026-05-18T00:52:29Z"},{"alias_kind":"pith_short_12","alias_value":"B4LOINIQPPNL","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"B4LOINIQPPNLBL7K","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"B4LOINIQ","created_at":"2026-05-18T12:31:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:B4LOINIQPPNLBL7KF2VVANSYS5","target":"record","payload":{"canonical_record":{"source":{"id":"1701.05490","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-01-19T16:02:50Z","cross_cats_sorted":[],"title_canon_sha256":"af5cd8bab719009b8987980292cadd38b9ddb5af5b49a7515df7e926f19f7638","abstract_canon_sha256":"b9d12b910102e82a1e7009851e0a1fa408f8ad43f323d310910d04226d237039"},"schema_version":"1.0"},"canonical_sha256":"0f16e435107bdab0afea2eab5036589755954f2ea6b53cc631319118f0cc1248","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:29.714398Z","signature_b64":"wFsN2Qo/yDI9FV0AlNDG1bDi27lMM6w+RQdkdTKnJB+D2COua8SBmhuFSPDh7O42X3Yo3IZSAVGqViemEQDaAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0f16e435107bdab0afea2eab5036589755954f2ea6b53cc631319118f0cc1248","last_reissued_at":"2026-05-18T00:52:29.713897Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:29.713897Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.05490","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":"2026-05-18T00:52:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M5/cYVfdomW6GS7EGWH9n85A7qt7WNXGwAKjy6Ytv2eZeMCFw4341SJ9UMzWL6d6I1QL/hrs+arPSdur6tQxBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T18:48:16.030419Z"},"content_sha256":"8d32273da498d52f5b43c6174a00ebdb11a4b2dc781eee09d9f3e5b97c777c00","schema_version":"1.0","event_id":"sha256:8d32273da498d52f5b43c6174a00ebdb11a4b2dc781eee09d9f3e5b97c777c00"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:B4LOINIQPPNLBL7KF2VVANSYS5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Groups satisfying the two-prime hypothesis with a composition factor isomorphic to ${\\rm PSL}_2(q)$ for $q\\geq 7$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Hung P. Tong-Viet, Mark L. Lewis, Yanjun Liu","submitted_at":"2017-01-19T16:02:50Z","abstract_excerpt":"Let $G$ be a finite group, and write ${\\rm cd}(G)$ for the degree set of the complex irreducible characters of $G$. The group $G$ is said to satisfy the {\\it two-prime hypothesis} if, for any distinct degrees $a, b \\in {\\rm cd}(G)$, the total number of (not necessarily different) primes of the greatest common divisor ${\\rm gcd}(a, b)$ is at most $2$. In this paper, we prove an upper bound on the number of irreducible character degrees of a nonsolvable group that has a composition factor isomorphic to ${\\rm PSL}_2 (q)$ for $q \\geq 7$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.05490","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":"2026-05-18T00:52:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"75GUOZeVi4ZqJxUGPyROOOzH0FiYbQAkmV+jjOivkdsaPLUtq24leJqDens2lTUT5xw6oLhtCc1cUaU6y1L1Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T18:48:16.030774Z"},"content_sha256":"d02f03252278c6a448783ea100135999a849c311eb1a798ed708571696d401a7","schema_version":"1.0","event_id":"sha256:d02f03252278c6a448783ea100135999a849c311eb1a798ed708571696d401a7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B4LOINIQPPNLBL7KF2VVANSYS5/bundle.json","state_url":"https://pith.science/pith/B4LOINIQPPNLBL7KF2VVANSYS5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B4LOINIQPPNLBL7KF2VVANSYS5/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":"2026-05-30T18:48:16Z","links":{"resolver":"https://pith.science/pith/B4LOINIQPPNLBL7KF2VVANSYS5","bundle":"https://pith.science/pith/B4LOINIQPPNLBL7KF2VVANSYS5/bundle.json","state":"https://pith.science/pith/B4LOINIQPPNLBL7KF2VVANSYS5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B4LOINIQPPNLBL7KF2VVANSYS5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:B4LOINIQPPNLBL7KF2VVANSYS5","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":"b9d12b910102e82a1e7009851e0a1fa408f8ad43f323d310910d04226d237039","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-01-19T16:02:50Z","title_canon_sha256":"af5cd8bab719009b8987980292cadd38b9ddb5af5b49a7515df7e926f19f7638"},"schema_version":"1.0","source":{"id":"1701.05490","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.05490","created_at":"2026-05-18T00:52:29Z"},{"alias_kind":"arxiv_version","alias_value":"1701.05490v1","created_at":"2026-05-18T00:52:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.05490","created_at":"2026-05-18T00:52:29Z"},{"alias_kind":"pith_short_12","alias_value":"B4LOINIQPPNL","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"B4LOINIQPPNLBL7K","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"B4LOINIQ","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:d02f03252278c6a448783ea100135999a849c311eb1a798ed708571696d401a7","target":"graph","created_at":"2026-05-18T00:52:29Z","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, and write ${\\rm cd}(G)$ for the degree set of the complex irreducible characters of $G$. The group $G$ is said to satisfy the {\\it two-prime hypothesis} if, for any distinct degrees $a, b \\in {\\rm cd}(G)$, the total number of (not necessarily different) primes of the greatest common divisor ${\\rm gcd}(a, b)$ is at most $2$. In this paper, we prove an upper bound on the number of irreducible character degrees of a nonsolvable group that has a composition factor isomorphic to ${\\rm PSL}_2 (q)$ for $q \\geq 7$.","authors_text":"Hung P. Tong-Viet, Mark L. Lewis, Yanjun Liu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-01-19T16:02:50Z","title":"Groups satisfying the two-prime hypothesis with a composition factor isomorphic to ${\\rm PSL}_2(q)$ for $q\\geq 7$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.05490","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":"sha256:8d32273da498d52f5b43c6174a00ebdb11a4b2dc781eee09d9f3e5b97c777c00","target":"record","created_at":"2026-05-18T00:52:29Z","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":"b9d12b910102e82a1e7009851e0a1fa408f8ad43f323d310910d04226d237039","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-01-19T16:02:50Z","title_canon_sha256":"af5cd8bab719009b8987980292cadd38b9ddb5af5b49a7515df7e926f19f7638"},"schema_version":"1.0","source":{"id":"1701.05490","kind":"arxiv","version":1}},"canonical_sha256":"0f16e435107bdab0afea2eab5036589755954f2ea6b53cc631319118f0cc1248","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0f16e435107bdab0afea2eab5036589755954f2ea6b53cc631319118f0cc1248","first_computed_at":"2026-05-18T00:52:29.713897Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:29.713897Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wFsN2Qo/yDI9FV0AlNDG1bDi27lMM6w+RQdkdTKnJB+D2COua8SBmhuFSPDh7O42X3Yo3IZSAVGqViemEQDaAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:29.714398Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.05490","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8d32273da498d52f5b43c6174a00ebdb11a4b2dc781eee09d9f3e5b97c777c00","sha256:d02f03252278c6a448783ea100135999a849c311eb1a798ed708571696d401a7"],"state_sha256":"961da1a3536cf80a632b8ace87ef9a4c6bffdb1678c956917b479ffe8d318c3c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+KIS1PpVAH3+eeZXBHwr+/FxWZsu3P1kWLSd5rgpOl0S+uHLi3lv4uUjYelpyDYrZW4xWmEc3NyXi1+vgbIcCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T18:48:16.032735Z","bundle_sha256":"a5b099282054d286913280be857d02814712de471209af5e83eb4a7b21ac502f"}}