{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:MM6DLQOTZDZ4VSCDAOISPBWH25","short_pith_number":"pith:MM6DLQOT","canonical_record":{"source":{"id":"2506.02885","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2025-06-03T13:51:03Z","cross_cats_sorted":[],"title_canon_sha256":"9505a106c64b175d24a2653457f86a8b494f95dee39234c618652b46c316a700","abstract_canon_sha256":"55113f85c1f868bb6f8224594e77a649c44805ef51de046b276ef56d701fc161"},"schema_version":"1.0"},"canonical_sha256":"633c35c1d3c8f3cac84303912786c7d7671dbb2227217aa3e7cf493ef381f452","source":{"kind":"arxiv","id":"2506.02885","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.02885","created_at":"2026-07-05T11:17:46Z"},{"alias_kind":"arxiv_version","alias_value":"2506.02885v2","created_at":"2026-07-05T11:17:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.02885","created_at":"2026-07-05T11:17:46Z"},{"alias_kind":"pith_short_12","alias_value":"MM6DLQOTZDZ4","created_at":"2026-07-05T11:17:46Z"},{"alias_kind":"pith_short_16","alias_value":"MM6DLQOTZDZ4VSCD","created_at":"2026-07-05T11:17:46Z"},{"alias_kind":"pith_short_8","alias_value":"MM6DLQOT","created_at":"2026-07-05T11:17:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:MM6DLQOTZDZ4VSCDAOISPBWH25","target":"record","payload":{"canonical_record":{"source":{"id":"2506.02885","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2025-06-03T13:51:03Z","cross_cats_sorted":[],"title_canon_sha256":"9505a106c64b175d24a2653457f86a8b494f95dee39234c618652b46c316a700","abstract_canon_sha256":"55113f85c1f868bb6f8224594e77a649c44805ef51de046b276ef56d701fc161"},"schema_version":"1.0"},"canonical_sha256":"633c35c1d3c8f3cac84303912786c7d7671dbb2227217aa3e7cf493ef381f452","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:17:46.938999Z","signature_b64":"+cAf2135HLq8TB8xN0l/PlzxsX34dTQkzm89g54479rMlPPsfeH3PsNF3/jgKOaXZVN3zCfBHpl98m/TQuaKBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"633c35c1d3c8f3cac84303912786c7d7671dbb2227217aa3e7cf493ef381f452","last_reissued_at":"2026-07-05T11:17:46.938512Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:17:46.938512Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.02885","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":"2026-07-05T11:17:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LgW9MKhZTVEnZHXsmeoXQwXBwBPYV4La86anDheJXH9HYm6OISS/GhbadFuQebSCg0Kcjm4icxHY8O47dcEsCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T21:50:09.132689Z"},"content_sha256":"2658115c48bfb48372f3e728c0e7bb4368b1694b40e6f19fe94c13eec857dbc3","schema_version":"1.0","event_id":"sha256:2658115c48bfb48372f3e728c0e7bb4368b1694b40e6f19fe94c13eec857dbc3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:MM6DLQOTZDZ4VSCDAOISPBWH25","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On an extension of Shlyk's theorem","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Fanjie Xu, Jiangtao Shi, Na Li","submitted_at":"2025-06-03T13:51:03Z","abstract_excerpt":"In this paper, we prove that the intersection of all non-nilpotent maximal subgroups of a non-solvable group containing the normalizer of some Sylow subgroup is nilpotent, which provides an extension of Shlyk's theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.02885","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.02885/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:17:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oAEDQUqTfQ+bzw4aU5E2aOpJfl2cRAEUMyy1faLRr6CzhvysJUfiHcUclFg1p0ZNoryHJUtnQlAku0O+S2dACg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T21:50:09.133176Z"},"content_sha256":"7901f8cd19d834ff4e855e44c7e01b835af78a4b57a68d4e3afdaed84073fe7b","schema_version":"1.0","event_id":"sha256:7901f8cd19d834ff4e855e44c7e01b835af78a4b57a68d4e3afdaed84073fe7b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MM6DLQOTZDZ4VSCDAOISPBWH25/bundle.json","state_url":"https://pith.science/pith/MM6DLQOTZDZ4VSCDAOISPBWH25/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MM6DLQOTZDZ4VSCDAOISPBWH25/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":"2026-08-07T21:50:09Z","links":{"resolver":"https://pith.science/pith/MM6DLQOTZDZ4VSCDAOISPBWH25","bundle":"https://pith.science/pith/MM6DLQOTZDZ4VSCDAOISPBWH25/bundle.json","state":"https://pith.science/pith/MM6DLQOTZDZ4VSCDAOISPBWH25/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MM6DLQOTZDZ4VSCDAOISPBWH25/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:MM6DLQOTZDZ4VSCDAOISPBWH25","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":"55113f85c1f868bb6f8224594e77a649c44805ef51de046b276ef56d701fc161","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2025-06-03T13:51:03Z","title_canon_sha256":"9505a106c64b175d24a2653457f86a8b494f95dee39234c618652b46c316a700"},"schema_version":"1.0","source":{"id":"2506.02885","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.02885","created_at":"2026-07-05T11:17:46Z"},{"alias_kind":"arxiv_version","alias_value":"2506.02885v2","created_at":"2026-07-05T11:17:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.02885","created_at":"2026-07-05T11:17:46Z"},{"alias_kind":"pith_short_12","alias_value":"MM6DLQOTZDZ4","created_at":"2026-07-05T11:17:46Z"},{"alias_kind":"pith_short_16","alias_value":"MM6DLQOTZDZ4VSCD","created_at":"2026-07-05T11:17:46Z"},{"alias_kind":"pith_short_8","alias_value":"MM6DLQOT","created_at":"2026-07-05T11:17:46Z"}],"graph_snapshots":[{"event_id":"sha256:7901f8cd19d834ff4e855e44c7e01b835af78a4b57a68d4e3afdaed84073fe7b","target":"graph","created_at":"2026-07-05T11:17:46Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.02885/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we prove that the intersection of all non-nilpotent maximal subgroups of a non-solvable group containing the normalizer of some Sylow subgroup is nilpotent, which provides an extension of Shlyk's theorem.","authors_text":"Fanjie Xu, Jiangtao Shi, Na Li","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2025-06-03T13:51:03Z","title":"On an extension of Shlyk's theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.02885","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":"sha256:2658115c48bfb48372f3e728c0e7bb4368b1694b40e6f19fe94c13eec857dbc3","target":"record","created_at":"2026-07-05T11:17:46Z","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":"55113f85c1f868bb6f8224594e77a649c44805ef51de046b276ef56d701fc161","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2025-06-03T13:51:03Z","title_canon_sha256":"9505a106c64b175d24a2653457f86a8b494f95dee39234c618652b46c316a700"},"schema_version":"1.0","source":{"id":"2506.02885","kind":"arxiv","version":2}},"canonical_sha256":"633c35c1d3c8f3cac84303912786c7d7671dbb2227217aa3e7cf493ef381f452","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"633c35c1d3c8f3cac84303912786c7d7671dbb2227217aa3e7cf493ef381f452","first_computed_at":"2026-07-05T11:17:46.938512Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:17:46.938512Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+cAf2135HLq8TB8xN0l/PlzxsX34dTQkzm89g54479rMlPPsfeH3PsNF3/jgKOaXZVN3zCfBHpl98m/TQuaKBw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:17:46.938999Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.02885","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2658115c48bfb48372f3e728c0e7bb4368b1694b40e6f19fe94c13eec857dbc3","sha256:7901f8cd19d834ff4e855e44c7e01b835af78a4b57a68d4e3afdaed84073fe7b"],"state_sha256":"b861ba94d90b1a38228c475583e7cfccb7828a9498230c95cdb3baea30582a1e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FnJ3jcZf/bO3d4guF2CknmxK/uHOEWgWlEjPuHF7fcCKsB/6iQve02zwwuWCrbooXw9As7jeSHDN6CEdqquYAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T21:50:09.137569Z","bundle_sha256":"7581f6af9822ab2ae6552b16dc2d08f5b8f6600dc558d8b8b2dbbd326d527d60"}}