{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:PR63QM4K7Y5DQSSJFWMOKV2LSR","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":"08cf8aa4a5737481e710746b0be28c50284997d32425cece52c43c88d5c8a971","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-06-06T10:44:22Z","title_canon_sha256":"42d8c4f51a0c4b1d4c493b0098271c3b199c5c4e0c2dc930ac266622bd557db2"},"schema_version":"1.0","source":{"id":"1306.1368","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.1368","created_at":"2026-05-18T03:21:34Z"},{"alias_kind":"arxiv_version","alias_value":"1306.1368v1","created_at":"2026-05-18T03:21:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.1368","created_at":"2026-05-18T03:21:34Z"},{"alias_kind":"pith_short_12","alias_value":"PR63QM4K7Y5D","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"PR63QM4K7Y5DQSSJ","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"PR63QM4K","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:9f7dfb76eca41b65624784ed44a031d4721d38527f79e792a782db8e456c3ef7","target":"graph","created_at":"2026-05-18T03:21:34Z","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 V be a d-dimensional vector space over a field of prime order p. We classify the affine transformations of V of order at least p^d/4, and apply this classification to determine the finite primitive permutation groups of affine type, and of degree n, that contain a permutation of order at least n/4. Using this result we obtain a classification of finite primitive permutation groups of affine type containing a permutation with at most four cycles.","authors_text":"Cheryl Praeger, Joy Morris, Pablo Spiga, Simon Guest","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-06-06T10:44:22Z","title":"Affine transformations of finite vector spaces with large orders or few cycles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1368","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":"sha256:1cdd72e279d092b405636e8153720a9b97afae95fdea7029b408884b2f538cd9","target":"record","created_at":"2026-05-18T03:21:34Z","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":"08cf8aa4a5737481e710746b0be28c50284997d32425cece52c43c88d5c8a971","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-06-06T10:44:22Z","title_canon_sha256":"42d8c4f51a0c4b1d4c493b0098271c3b199c5c4e0c2dc930ac266622bd557db2"},"schema_version":"1.0","source":{"id":"1306.1368","kind":"arxiv","version":1}},"canonical_sha256":"7c7db8338afe3a384a492d98e5574b9458dfbb378417eb4e00d7153c120c7a54","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7c7db8338afe3a384a492d98e5574b9458dfbb378417eb4e00d7153c120c7a54","first_computed_at":"2026-05-18T03:21:34.444255Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:21:34.444255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6/tS+RI6hwLhJVNe6uffXDHWq6WkiQbVdkTdSzYpo3Oc7FaTo5ldKNvKniJjBUOQtRa7Vrha4wTpQCVDCTswCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:21:34.444799Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.1368","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1cdd72e279d092b405636e8153720a9b97afae95fdea7029b408884b2f538cd9","sha256:9f7dfb76eca41b65624784ed44a031d4721d38527f79e792a782db8e456c3ef7"],"state_sha256":"2294fc0452b2feab257fac344828f053cfb65eca7aa692f20fbec8ceda1e3c5b"}