{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:T4VUNJBTG6EXWD2WEHT73NZ7ET","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":"f3b81fc80f50d912c73ecf2b18e11fe35626d4b0b942628c35c3d01ff2dba617","cross_cats_sorted":["cs.NA","math.CV"],"license":"","primary_cat":"math.NA","submitted_at":"2006-06-12T13:02:22Z","title_canon_sha256":"32d883327e6c8eeac0b72a80d457821ec9c3d49fe32f316272167145e0bb06dd"},"schema_version":"1.0","source":{"id":"math/0606277","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0606277","created_at":"2026-06-03T22:06:19Z"},{"alias_kind":"arxiv_version","alias_value":"math/0606277v1","created_at":"2026-06-03T22:06:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0606277","created_at":"2026-06-03T22:06:19Z"},{"alias_kind":"pith_short_12","alias_value":"T4VUNJBTG6EX","created_at":"2026-06-03T22:06:19Z"},{"alias_kind":"pith_short_16","alias_value":"T4VUNJBTG6EXWD2W","created_at":"2026-06-03T22:06:19Z"},{"alias_kind":"pith_short_8","alias_value":"T4VUNJBT","created_at":"2026-06-03T22:06:19Z"}],"graph_snapshots":[{"event_id":"sha256:1fd0a7b462d9d06160f4b7e73d5812956473f0814fe6cb09887b3cbd9c03823e","target":"graph","created_at":"2026-06-03T22:06:19Z","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/math/0606277/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove an interesting fact describing the location of the roots of the generating polynomials of the numbers of derangements of length $n$, counted by their number of cycles. We then use this result to prove that if $k$ is the number of cycles of a randomly selected derangement of length $n$, then the probability that $k$ is congruent to a given $r$ modulo a given $q$ converges to $1/q$. Finally, we generalize our results to $a$-derangements, which are permutations in which each cycle is longer than $a$.","authors_text":"Miklos Bona","cross_cats":["cs.NA","math.CV"],"headline":"","license":"","primary_cat":"math.NA","submitted_at":"2006-06-12T13:02:22Z","title":"On a balanced property of derangements"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0606277","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":"sha256:6346b2464558c4b00806c63727e0d6b0733de244daa8ed591329487b0a560786","target":"record","created_at":"2026-06-03T22:06:19Z","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":"f3b81fc80f50d912c73ecf2b18e11fe35626d4b0b942628c35c3d01ff2dba617","cross_cats_sorted":["cs.NA","math.CV"],"license":"","primary_cat":"math.NA","submitted_at":"2006-06-12T13:02:22Z","title_canon_sha256":"32d883327e6c8eeac0b72a80d457821ec9c3d49fe32f316272167145e0bb06dd"},"schema_version":"1.0","source":{"id":"math/0606277","kind":"arxiv","version":1}},"canonical_sha256":"9f2b46a43337897b0f5621e7fdb73f24ebbe09ff039fa306544b3e9a9491e467","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f2b46a43337897b0f5621e7fdb73f24ebbe09ff039fa306544b3e9a9491e467","first_computed_at":"2026-06-03T22:06:19.864998Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T22:06:19.864998Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8lVaI677OEoOjr7VvITAEAl1w+3N4uxligksKQs6YUuQwNrDyfYqvAvelwdWGqtnXawelb2Rl03HHKUb+XAXAg==","signature_status":"signed_v1","signed_at":"2026-06-03T22:06:19.865419Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0606277","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6346b2464558c4b00806c63727e0d6b0733de244daa8ed591329487b0a560786","sha256:1fd0a7b462d9d06160f4b7e73d5812956473f0814fe6cb09887b3cbd9c03823e"],"state_sha256":"ba64248c80f0ac81b03e468a1da48c79f68743a640d7bfa75a9ffb5e80f0934b"}