{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:BVCPMGZJPNYGY6TLOZLCA2CMTR","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":"38e5d4a1fda23db4516dce954b17b195115d590a2e13cd58819505cfc54a6ec1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-08-11T14:15:50Z","title_canon_sha256":"a3dee3305926247e040d4e214a20a23fffdcef4c912f69da23e1c35deaa9a753"},"schema_version":"1.0","source":{"id":"1708.03550","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.03550","created_at":"2026-05-18T00:38:12Z"},{"alias_kind":"arxiv_version","alias_value":"1708.03550v1","created_at":"2026-05-18T00:38:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.03550","created_at":"2026-05-18T00:38:12Z"},{"alias_kind":"pith_short_12","alias_value":"BVCPMGZJPNYG","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"BVCPMGZJPNYGY6TL","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"BVCPMGZJ","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:96eabb689b34cc28cc4d9d5c35abb10ad4e8370104a8d2eb7a937d440b2d3853","target":"graph","created_at":"2026-05-18T00:38:12Z","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.\n  If $M_n < M_{n-1} < \\ldots < M_1 < M_{0}=G $ where $M_i$ is a maximal subgroup of $M_{i-1}$ for all $i=1, \\ldots ,n$, then $M_n $ ($n > 0$) is an \\emph{$n$-maximal subgroup} of $G$.\n  A subgroup $M$ of $G$ is called \\emph{modular} if the following conditions are held: (i) $\\langle X, M \\cap Z \\rangle=\\langle X, M \\rangle \\cap Z$ for all $X \\leq G, Z \\leq G$ such that $X \\leq Z$, and (ii) $\\langle M, Y \\cap Z \\rangle=\\langle M, Y \\rangle \\cap Z$ for all $Y \\leq G, Z \\leq G$ such that $M \\leq Z$.\n  In this paper, we study finite groups whose $n$-maximal subgroups are","authors_text":"Bin Hu, Jianhong Huang, Xun Zheng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-08-11T14:15:50Z","title":"On one generalization of modular subgroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.03550","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":"sha256:9c3759cf1c80d0e1a1ff53e10448769341914fff50fdd71a39be9f853be95c28","target":"record","created_at":"2026-05-18T00:38:12Z","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":"38e5d4a1fda23db4516dce954b17b195115d590a2e13cd58819505cfc54a6ec1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-08-11T14:15:50Z","title_canon_sha256":"a3dee3305926247e040d4e214a20a23fffdcef4c912f69da23e1c35deaa9a753"},"schema_version":"1.0","source":{"id":"1708.03550","kind":"arxiv","version":1}},"canonical_sha256":"0d44f61b297b706c7a6b765620684c9c766d495d9f3e39720dd6f43cba6418a9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0d44f61b297b706c7a6b765620684c9c766d495d9f3e39720dd6f43cba6418a9","first_computed_at":"2026-05-18T00:38:12.357224Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:12.357224Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Srmz9aZTpjLHDly5dQAM75eQnjpy6l9xtfbfuYdr56Jb+mDkiDO3m2Y8Kw7r94uGh6DN0LwCd/LurebyKEIlDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:12.357787Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.03550","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9c3759cf1c80d0e1a1ff53e10448769341914fff50fdd71a39be9f853be95c28","sha256:96eabb689b34cc28cc4d9d5c35abb10ad4e8370104a8d2eb7a937d440b2d3853"],"state_sha256":"febb587b35adbd51ae04bab47e0e9b60a7cc5e112fe2e25587bc9f21a5dcd1ba"}