{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:LNQR7D3D77QRVH2VSEKCFRYGNY","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":"5f3529d281569646d4929d54f9da2c1d05e7f51d46e791c49254f2bac405bb30","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2023-01-06T15:48:23Z","title_canon_sha256":"99648b71e7f54d285c6fde6a140ff910a6561fd3e008acfc76cf08df6efab47d"},"schema_version":"1.0","source":{"id":"2301.02570","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2301.02570","created_at":"2026-07-05T08:33:29Z"},{"alias_kind":"arxiv_version","alias_value":"2301.02570v1","created_at":"2026-07-05T08:33:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2301.02570","created_at":"2026-07-05T08:33:29Z"},{"alias_kind":"pith_short_12","alias_value":"LNQR7D3D77QR","created_at":"2026-07-05T08:33:29Z"},{"alias_kind":"pith_short_16","alias_value":"LNQR7D3D77QRVH2V","created_at":"2026-07-05T08:33:29Z"},{"alias_kind":"pith_short_8","alias_value":"LNQR7D3D","created_at":"2026-07-05T08:33:29Z"}],"graph_snapshots":[{"event_id":"sha256:1bb6b82bd757fc98f279e85ecbd7c48d3802c361921f0c99197800bf4f3ca70c","target":"graph","created_at":"2026-07-05T08:33:29Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2301.02570/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Given a finite group $G$ and a prime $p$, let $\\mathcal{A}_p(G)$ be the poset of nontrivial elementary abelian $p$-subgroups of $G$. The group $G$ satisfies the Quillen dimension property at $p$ if $\\mathcal{A}_p(G)$ has non-zero homology in the maximal possible degree, which is the $p$-rank of $G$ minus $1$. For example, D. Quillen showed that solvable groups with trivial $p$-core satisfy this property, and later, M. Aschbacher and S.D. Smith provided a list of all $p$-extensions of simple groups that may fail this property if $p$ is odd. In particular, a group $G$ with this property satisfie","authors_text":"Kevin Ivan Piterman","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2023-01-06T15:48:23Z","title":"Maximal subgroups of exceptional groups and Quillen's dimension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2301.02570","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":"sha256:605a1bca23a5169b06b5101f0c49f6352e10104a2ba32f9e9122aac950c2189d","target":"record","created_at":"2026-07-05T08:33:29Z","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":"5f3529d281569646d4929d54f9da2c1d05e7f51d46e791c49254f2bac405bb30","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2023-01-06T15:48:23Z","title_canon_sha256":"99648b71e7f54d285c6fde6a140ff910a6561fd3e008acfc76cf08df6efab47d"},"schema_version":"1.0","source":{"id":"2301.02570","kind":"arxiv","version":1}},"canonical_sha256":"5b611f8f63ffe11a9f55911422c7066e087c1934706ccffe27f4ec0ba5b8b3d3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5b611f8f63ffe11a9f55911422c7066e087c1934706ccffe27f4ec0ba5b8b3d3","first_computed_at":"2026-07-05T08:33:29.431838Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:33:29.431838Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"txNvfyo+081lLtpUz9akAH1SThnDwMItemLRcTcAUo34lQtpJagABFP4UkW1UyNeETdq4SGAV+hIU4XWSRq8Aw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:33:29.432253Z","signed_message":"canonical_sha256_bytes"},"source_id":"2301.02570","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:605a1bca23a5169b06b5101f0c49f6352e10104a2ba32f9e9122aac950c2189d","sha256:1bb6b82bd757fc98f279e85ecbd7c48d3802c361921f0c99197800bf4f3ca70c"],"state_sha256":"9c781b436fea48ce2c3a206a85369053770833e2b775587adea2addadfb9e3ce"}