{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:RUZVYK6K47LQDX4YEEULQYQIVI","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":"2a79cf77ffb36ad11f9ca050de76a892a321480ea817f023eb4a314d4a8875fd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-07-12T14:46:18Z","title_canon_sha256":"88ee2a5f4fbc27c211b3f199e508dd82518d24d50b20b69e9bcd0b6c8ff922d8"},"schema_version":"1.0","source":{"id":"2507.09304","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.09304","created_at":"2026-06-03T14:05:17Z"},{"alias_kind":"arxiv_version","alias_value":"2507.09304v4","created_at":"2026-06-03T14:05:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.09304","created_at":"2026-06-03T14:05:17Z"},{"alias_kind":"pith_short_12","alias_value":"RUZVYK6K47LQ","created_at":"2026-06-03T14:05:17Z"},{"alias_kind":"pith_short_16","alias_value":"RUZVYK6K47LQDX4Y","created_at":"2026-06-03T14:05:17Z"},{"alias_kind":"pith_short_8","alias_value":"RUZVYK6K","created_at":"2026-06-03T14:05:17Z"}],"graph_snapshots":[{"event_id":"sha256:a6457c0bfba0d4bd7d0c75be69dfc4ff1441acebcf0c4eca8a4c1dab9b10011a","target":"graph","created_at":"2026-06-03T14:05:17Z","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/2507.09304/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Two-sort species yield differential equations for functional digraphs of Cayley permutations. From these we obtain an explicit formula for fixed-point-free Cayley permutations and prove that their proportion tends to $1/e$, as for permutations and endofunctions. Our approach also yields counting formulas when the functional digraph is a tree, forest, or connected.","authors_text":"Anders Claesson, Giulio Cerbai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-07-12T14:46:18Z","title":"Counting fixed-point-free Cayley permutations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.09304","kind":"arxiv","version":4},"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":"sha256:8e57b691c4f48b478532b513fe7c4f1d7e044b2412c27b42fa44f515db8f00f1","target":"record","created_at":"2026-06-03T14:05:17Z","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":"2a79cf77ffb36ad11f9ca050de76a892a321480ea817f023eb4a314d4a8875fd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-07-12T14:46:18Z","title_canon_sha256":"88ee2a5f4fbc27c211b3f199e508dd82518d24d50b20b69e9bcd0b6c8ff922d8"},"schema_version":"1.0","source":{"id":"2507.09304","kind":"arxiv","version":4}},"canonical_sha256":"8d335c2bcae7d701df982128b86208aa0e4ae0e081c26422808a902d58a3da20","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d335c2bcae7d701df982128b86208aa0e4ae0e081c26422808a902d58a3da20","first_computed_at":"2026-06-03T14:05:17.279056Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T14:05:17.279056Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jfBwuknN0W/kek6ricOz7J28twJk8UXPgCZp7OOIhLvhpsepPoamD0qSV5OC3L5Dsm9OLk7MrSI/pJGXZf35CQ==","signature_status":"signed_v1","signed_at":"2026-06-03T14:05:17.279538Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.09304","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8e57b691c4f48b478532b513fe7c4f1d7e044b2412c27b42fa44f515db8f00f1","sha256:a6457c0bfba0d4bd7d0c75be69dfc4ff1441acebcf0c4eca8a4c1dab9b10011a"],"state_sha256":"4ba22e4c1767c46d0949e4fcd9e7f72f77842defdca94483a0e069167c8730b5"}