{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:Q3IBDKWD7QYBEKENVKTA3BZXQA","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":"35c65be4fbdbcb377e2288dd850e85077e5f42fbda5e874ffe4b998713f7bad6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-02-16T09:14:44Z","title_canon_sha256":"31176f7329af0532f615126d2d2d36cd623fd39b2e8803c2825a7ccf8568d9eb"},"schema_version":"1.0","source":{"id":"1702.04898","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.04898","created_at":"2026-05-18T00:50:36Z"},{"alias_kind":"arxiv_version","alias_value":"1702.04898v1","created_at":"2026-05-18T00:50:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.04898","created_at":"2026-05-18T00:50:36Z"},{"alias_kind":"pith_short_12","alias_value":"Q3IBDKWD7QYB","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"Q3IBDKWD7QYBEKEN","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"Q3IBDKWD","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:7aa77699959c06c54639b73c4fe6ddfa44b638f0cf2a7435f5b528ba23238144","target":"graph","created_at":"2026-05-18T00:50:36Z","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":"We give a complete list of the class two groups with exponent $p$ and order dividing $p^8$. For each group in the list we compute the number of immediate descendants of order $p^9$ with exponent $p$. In each case the number of descendants is PORC, and so the total number of class three groups of order $p^9$ with exponent $p$ is PORC. Nevertheless, there are groups of order $p^8$ with exponent $p$ which have a non-PORC number of class three descendants of order $p^9$ with exponent $p$.","authors_text":"Michael Vaughan-Lee","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-02-16T09:14:44Z","title":"The class three groups of order $p^9$ with exponent $p$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.04898","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":"sha256:7de918c2dde93fa6578998242840e96610dfcf696f6db10ddd3566c22c5d5c13","target":"record","created_at":"2026-05-18T00:50:36Z","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":"35c65be4fbdbcb377e2288dd850e85077e5f42fbda5e874ffe4b998713f7bad6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-02-16T09:14:44Z","title_canon_sha256":"31176f7329af0532f615126d2d2d36cd623fd39b2e8803c2825a7ccf8568d9eb"},"schema_version":"1.0","source":{"id":"1702.04898","kind":"arxiv","version":1}},"canonical_sha256":"86d011aac3fc3012288daaa60d87378005dcf81731d9acad562904f6e13c1b30","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"86d011aac3fc3012288daaa60d87378005dcf81731d9acad562904f6e13c1b30","first_computed_at":"2026-05-18T00:50:36.839297Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:36.839297Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Uwh22F4Rmz/tUKxBvSRWtZmiDDGuNYsLeYj0ajMR9maMCodd+SxYIdAbhGV3up2xW8+eMlaqRuCXEO6eIqf2DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:36.840042Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.04898","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7de918c2dde93fa6578998242840e96610dfcf696f6db10ddd3566c22c5d5c13","sha256:7aa77699959c06c54639b73c4fe6ddfa44b638f0cf2a7435f5b528ba23238144"],"state_sha256":"b1253509d8f32ddda6696a78b08c87a23b17a5b330e461a986af888b12995195"}