{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:6ICGVMHXVYZEA7OOLBZ3FLVFLB","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":"f8668c4af4b3f7281296a04e5426798dbd1c5fa611537567a9036bd53b46f566","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-02-23T22:04:36Z","title_canon_sha256":"70838233ee7cd605479d41e6367b42b206c4a4584456910958baa35af77e3954"},"schema_version":"1.0","source":{"id":"1702.07406","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.07406","created_at":"2026-05-18T00:50:03Z"},{"alias_kind":"arxiv_version","alias_value":"1702.07406v1","created_at":"2026-05-18T00:50:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.07406","created_at":"2026-05-18T00:50:03Z"},{"alias_kind":"pith_short_12","alias_value":"6ICGVMHXVYZE","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6ICGVMHXVYZEA7OO","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6ICGVMHX","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:ef870825f6936520389ce5d7f447442b250198391e158ff96c7e839841cbfe50","target":"graph","created_at":"2026-05-18T00:50:03Z","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 detailed analysis of the proportion of elements in the symmetric group on $n$ points whose order divides $m$, for $n$ sufficiently large and $m \\ge n$ with $m = O(n)$.","authors_text":"Alice C. Niemeyer, Cheryl E. Praeger","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-02-23T22:04:36Z","title":"On permutations of order dividing a given integer"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.07406","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":"sha256:2b9fce5b0a506c4413d47f96196553324c127854b277a27a2e724cc6fb59b30f","target":"record","created_at":"2026-05-18T00:50:03Z","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":"f8668c4af4b3f7281296a04e5426798dbd1c5fa611537567a9036bd53b46f566","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-02-23T22:04:36Z","title_canon_sha256":"70838233ee7cd605479d41e6367b42b206c4a4584456910958baa35af77e3954"},"schema_version":"1.0","source":{"id":"1702.07406","kind":"arxiv","version":1}},"canonical_sha256":"f2046ab0f7ae32407dce5873b2aea558586e02ece95a9e38d7a637296081fdf2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2046ab0f7ae32407dce5873b2aea558586e02ece95a9e38d7a637296081fdf2","first_computed_at":"2026-05-18T00:50:03.471768Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:03.471768Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LmSWbib4bxTTsxk81JZ47A2hb0Sm60RXb6ay3AcxsGfLApWnevbouuV7SKyDf7EG8Ez7cjgktxykmjRERt/pAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:03.472515Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.07406","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2b9fce5b0a506c4413d47f96196553324c127854b277a27a2e724cc6fb59b30f","sha256:ef870825f6936520389ce5d7f447442b250198391e158ff96c7e839841cbfe50"],"state_sha256":"3e45f432b2147497290631faafa2b086fb276d26dbdac7872cd69b886326801a"}