{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:4XB5S6FQ22QGWEKY3XATB46MRN","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":"08b7cd487879aaf34050ba8e899a283eed55208443f88713bf239555e74be834","cross_cats_sorted":["math.PR"],"license":"","primary_cat":"math.CO","submitted_at":"2002-07-29T16:52:07Z","title_canon_sha256":"a926aec21dc6fea7e64de50fe179ba80315d05da0eb13bdcbea49b630e1e05b7"},"schema_version":"1.0","source":{"id":"math/0207276","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0207276","created_at":"2026-07-04T14:36:21Z"},{"alias_kind":"arxiv_version","alias_value":"math/0207276v2","created_at":"2026-07-04T14:36:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0207276","created_at":"2026-07-04T14:36:21Z"},{"alias_kind":"pith_short_12","alias_value":"4XB5S6FQ22QG","created_at":"2026-07-04T14:36:21Z"},{"alias_kind":"pith_short_16","alias_value":"4XB5S6FQ22QGWEKY","created_at":"2026-07-04T14:36:21Z"},{"alias_kind":"pith_short_8","alias_value":"4XB5S6FQ","created_at":"2026-07-04T14:36:21Z"}],"graph_snapshots":[{"event_id":"sha256:d5212d83ccb7469728949b853cba877c2b0c87d67c8c3453ff75615aacdaa041","target":"graph","created_at":"2026-07-04T14:36:21Z","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/0207276/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let f_1,f_2,..., be functions chosen independently and uniformly from the set of all functions from a set of cardinality n into itself. Let g_t be the composition of the first t functions, and let T be the smallest t for which g_t is constant. We find the limiting distribution of T/n, as n --> infinity.","authors_text":"E. Schmutz, P. Hitczenko, W.M.Y. Goh","cross_cats":["math.PR"],"headline":"","license":"","primary_cat":"math.CO","submitted_at":"2002-07-29T16:52:07Z","title":"Iterating random functions on a finite set"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0207276","kind":"arxiv","version":2},"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":"sha256:623a35bfef19b1f29d884a19187154fb5769bdf95b2db0ec9ad839c256f49ed5","target":"record","created_at":"2026-07-04T14:36:21Z","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":"08b7cd487879aaf34050ba8e899a283eed55208443f88713bf239555e74be834","cross_cats_sorted":["math.PR"],"license":"","primary_cat":"math.CO","submitted_at":"2002-07-29T16:52:07Z","title_canon_sha256":"a926aec21dc6fea7e64de50fe179ba80315d05da0eb13bdcbea49b630e1e05b7"},"schema_version":"1.0","source":{"id":"math/0207276","kind":"arxiv","version":2}},"canonical_sha256":"e5c3d978b0d6a06b1158ddc130f3cc8b4674939904c54b1b1535d59cbba8dcf4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e5c3d978b0d6a06b1158ddc130f3cc8b4674939904c54b1b1535d59cbba8dcf4","first_computed_at":"2026-07-04T14:36:21.013365Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:36:21.013365Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"X26rwlM8A6UHIT4n1/IMgAAXG0Ob0pKxvOm90VMNOOuDxHldpBQFkYXc7yGCcZlZJqQHOzYb8rKfMZpbXgZZCQ==","signature_status":"signed_v1","signed_at":"2026-07-04T14:36:21.013746Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0207276","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:623a35bfef19b1f29d884a19187154fb5769bdf95b2db0ec9ad839c256f49ed5","sha256:d5212d83ccb7469728949b853cba877c2b0c87d67c8c3453ff75615aacdaa041"],"state_sha256":"c8fa175720d11fecff41b57840f67256062513d95c2e46b99c46488a76fa5f0b"}