{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:FMONAG5ZJ5QLVRTV7GUW5SJMSR","short_pith_number":"pith:FMONAG5Z","canonical_record":{"source":{"id":"1308.1044","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-08-05T17:05:11Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"6984fb1fafbe9abc97e0e5aebdefd3eba7a9e8f8405f0af80a79fc726e851d99","abstract_canon_sha256":"1fca9b71aa8d581d100bcb9f45231c144003a27887778c07374d49d653464e64"},"schema_version":"1.0"},"canonical_sha256":"2b1cd01bb94f60bac675f9a96ec92c9468b9bd64d12b3b59a0e4844f3429ffc4","source":{"kind":"arxiv","id":"1308.1044","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.1044","created_at":"2026-05-18T03:16:40Z"},{"alias_kind":"arxiv_version","alias_value":"1308.1044v1","created_at":"2026-05-18T03:16:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.1044","created_at":"2026-05-18T03:16:40Z"},{"alias_kind":"pith_short_12","alias_value":"FMONAG5ZJ5QL","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"FMONAG5ZJ5QLVRTV","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"FMONAG5Z","created_at":"2026-05-18T12:27:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:FMONAG5ZJ5QLVRTV7GUW5SJMSR","target":"record","payload":{"canonical_record":{"source":{"id":"1308.1044","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-08-05T17:05:11Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"6984fb1fafbe9abc97e0e5aebdefd3eba7a9e8f8405f0af80a79fc726e851d99","abstract_canon_sha256":"1fca9b71aa8d581d100bcb9f45231c144003a27887778c07374d49d653464e64"},"schema_version":"1.0"},"canonical_sha256":"2b1cd01bb94f60bac675f9a96ec92c9468b9bd64d12b3b59a0e4844f3429ffc4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:16:40.859342Z","signature_b64":"3w7/27q4BSsUmLfviFdzQtP31c/t7RFbUAepXwPPUvlBsJ3qKmRYwh5TkNxDXXF47o4QE4vnbTiKY+VArpxyCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b1cd01bb94f60bac675f9a96ec92c9468b9bd64d12b3b59a0e4844f3429ffc4","last_reissued_at":"2026-05-18T03:16:40.858711Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:16:40.858711Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.1044","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":"2026-05-18T03:16:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9rL2S+/LFFjYhJSk/wB7Tz4sHkI/BhkDDElHw9usnS/DoXUnoietAx3AaX23vw4sVB9x9I0ySmmF81G+goTFBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T02:46:14.035797Z"},"content_sha256":"a9682818ee4c06d9d66da3153988f9250ad722cc54b6d4a271ce0439a9e02f75","schema_version":"1.0","event_id":"sha256:a9682818ee4c06d9d66da3153988f9250ad722cc54b6d4a271ce0439a9e02f75"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:FMONAG5ZJ5QLVRTV7GUW5SJMSR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Controlling composition factors of a finite group by its character degree ratio","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.GR","authors_text":"Hung Ngoc Nguyen, James P. Cossey","submitted_at":"2013-08-05T17:05:11Z","abstract_excerpt":"For a finite nonabelian group $G$ let $\\rat(G)$ be the largest ratio of degrees of two nonlinear irreducible characters of $G$. We show that nonabelian composition factors of $G$ are controlled by $\\rat(G)$ in some sense. Specifically, if $S$ different from the simple linear groups $\\PSL_2(q)$ is a nonabelian composition factor of $G$, then the order of $S$ and the number of composition factors of $G$ isomorphic to $S$ are both bounded in terms of $\\rat(G)$. Furthermore, when the groups $\\PSL_2(q)$ are not composition factors of $G$, we prove that $|G:\\Oinfty(G)|\\leq \\rat(G)^{21}$ where $\\Oinf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.1044","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":"2026-05-18T03:16:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mwd9nrrj0RxaFwZdTbTcAokcA23H46F2gxhiBnH9ryqeFGmxY5MQfsxGaJxoEbieOIS4thXBdM4QoC+TXKgfBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T02:46:14.036167Z"},"content_sha256":"f4d15011ad7c356b549cdf25c9f335b329f65b0d42ac9fc236230fd8c231725b","schema_version":"1.0","event_id":"sha256:f4d15011ad7c356b549cdf25c9f335b329f65b0d42ac9fc236230fd8c231725b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FMONAG5ZJ5QLVRTV7GUW5SJMSR/bundle.json","state_url":"https://pith.science/pith/FMONAG5ZJ5QLVRTV7GUW5SJMSR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FMONAG5ZJ5QLVRTV7GUW5SJMSR/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":"2026-06-20T02:46:14Z","links":{"resolver":"https://pith.science/pith/FMONAG5ZJ5QLVRTV7GUW5SJMSR","bundle":"https://pith.science/pith/FMONAG5ZJ5QLVRTV7GUW5SJMSR/bundle.json","state":"https://pith.science/pith/FMONAG5ZJ5QLVRTV7GUW5SJMSR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FMONAG5ZJ5QLVRTV7GUW5SJMSR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:FMONAG5ZJ5QLVRTV7GUW5SJMSR","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":"1fca9b71aa8d581d100bcb9f45231c144003a27887778c07374d49d653464e64","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-08-05T17:05:11Z","title_canon_sha256":"6984fb1fafbe9abc97e0e5aebdefd3eba7a9e8f8405f0af80a79fc726e851d99"},"schema_version":"1.0","source":{"id":"1308.1044","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.1044","created_at":"2026-05-18T03:16:40Z"},{"alias_kind":"arxiv_version","alias_value":"1308.1044v1","created_at":"2026-05-18T03:16:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.1044","created_at":"2026-05-18T03:16:40Z"},{"alias_kind":"pith_short_12","alias_value":"FMONAG5ZJ5QL","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"FMONAG5ZJ5QLVRTV","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"FMONAG5Z","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:f4d15011ad7c356b549cdf25c9f335b329f65b0d42ac9fc236230fd8c231725b","target":"graph","created_at":"2026-05-18T03:16:40Z","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":"For a finite nonabelian group $G$ let $\\rat(G)$ be the largest ratio of degrees of two nonlinear irreducible characters of $G$. We show that nonabelian composition factors of $G$ are controlled by $\\rat(G)$ in some sense. Specifically, if $S$ different from the simple linear groups $\\PSL_2(q)$ is a nonabelian composition factor of $G$, then the order of $S$ and the number of composition factors of $G$ isomorphic to $S$ are both bounded in terms of $\\rat(G)$. Furthermore, when the groups $\\PSL_2(q)$ are not composition factors of $G$, we prove that $|G:\\Oinfty(G)|\\leq \\rat(G)^{21}$ where $\\Oinf","authors_text":"Hung Ngoc Nguyen, James P. Cossey","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-08-05T17:05:11Z","title":"Controlling composition factors of a finite group by its character degree ratio"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.1044","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:a9682818ee4c06d9d66da3153988f9250ad722cc54b6d4a271ce0439a9e02f75","target":"record","created_at":"2026-05-18T03:16:40Z","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":"1fca9b71aa8d581d100bcb9f45231c144003a27887778c07374d49d653464e64","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-08-05T17:05:11Z","title_canon_sha256":"6984fb1fafbe9abc97e0e5aebdefd3eba7a9e8f8405f0af80a79fc726e851d99"},"schema_version":"1.0","source":{"id":"1308.1044","kind":"arxiv","version":1}},"canonical_sha256":"2b1cd01bb94f60bac675f9a96ec92c9468b9bd64d12b3b59a0e4844f3429ffc4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b1cd01bb94f60bac675f9a96ec92c9468b9bd64d12b3b59a0e4844f3429ffc4","first_computed_at":"2026-05-18T03:16:40.858711Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:16:40.858711Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3w7/27q4BSsUmLfviFdzQtP31c/t7RFbUAepXwPPUvlBsJ3qKmRYwh5TkNxDXXF47o4QE4vnbTiKY+VArpxyCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:16:40.859342Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.1044","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a9682818ee4c06d9d66da3153988f9250ad722cc54b6d4a271ce0439a9e02f75","sha256:f4d15011ad7c356b549cdf25c9f335b329f65b0d42ac9fc236230fd8c231725b"],"state_sha256":"9c1e6c53bf55218c736cadecbf721ee9dc21d78af2304461810279baad4a6c19"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OFG3WpgnaqI9VMbFCn8dbaokWwqs/1ujUgm6fAXx3sf/CHBFpxQuF0/xkbFBpOFxW0ZvqoFePU2a1Ku1fHN6Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T02:46:14.038103Z","bundle_sha256":"e16aeb2361bdf632af96634196a058c2ca5f05c67bb02c92d1fe6d3501a0efee"}}