{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:2KCIWF322MTXCR6QHZZBZQSTA2","short_pith_number":"pith:2KCIWF32","schema_version":"1.0","canonical_sha256":"d2848b177ad3277147d03e721cc25306b8fabc0e5a137b98bb86d4c62b7ac923","source":{"kind":"arxiv","id":"1508.04193","version":3},"attestation_state":"computed","paper":{"title":"Periods of Iterated Rational Functions over a Finite Field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Charles Burnette, Eric Schmutz","submitted_at":"2015-08-18T02:10:12Z","abstract_excerpt":"Choose a random degree d poly f with coefficients in a finite field F. We estimate the ultimate period of f under compositional iteration. We also determine the joint distribution of the small cycle lengths in the graph with edges (x,f(x)), x in F. The proofs use Lagrange interpolation and the method of factorial moments."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1508.04193","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-08-18T02:10:12Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"7d8ad3832328f3b35660b68ffe46dd4ebe28a03876eacce2343f7f76ac4db063","abstract_canon_sha256":"a0649f9f0347c3cb28fbb51e213e4ba0492c074f90e5f8afd0b293463a03fb09"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:15.930328Z","signature_b64":"LU42xy2tDlFl4/q9MzMi/vyI5RupWCvH8OXMSBkeire07RMA0CjnwyV6MqfJwOdumO7gcdA6LarQcMhGhdSUBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d2848b177ad3277147d03e721cc25306b8fabc0e5a137b98bb86d4c62b7ac923","last_reissued_at":"2026-05-18T00:53:15.929662Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:15.929662Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Periods of Iterated Rational Functions over a Finite Field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Charles Burnette, Eric Schmutz","submitted_at":"2015-08-18T02:10:12Z","abstract_excerpt":"Choose a random degree d poly f with coefficients in a finite field F. We estimate the ultimate period of f under compositional iteration. We also determine the joint distribution of the small cycle lengths in the graph with edges (x,f(x)), x in F. The proofs use Lagrange interpolation and the method of factorial moments."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.04193","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1508.04193","created_at":"2026-05-18T00:53:15.929746+00:00"},{"alias_kind":"arxiv_version","alias_value":"1508.04193v3","created_at":"2026-05-18T00:53:15.929746+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.04193","created_at":"2026-05-18T00:53:15.929746+00:00"},{"alias_kind":"pith_short_12","alias_value":"2KCIWF322MTX","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_16","alias_value":"2KCIWF322MTXCR6Q","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_8","alias_value":"2KCIWF32","created_at":"2026-05-18T12:28:59.999130+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2KCIWF322MTXCR6QHZZBZQSTA2","json":"https://pith.science/pith/2KCIWF322MTXCR6QHZZBZQSTA2.json","graph_json":"https://pith.science/api/pith-number/2KCIWF322MTXCR6QHZZBZQSTA2/graph.json","events_json":"https://pith.science/api/pith-number/2KCIWF322MTXCR6QHZZBZQSTA2/events.json","paper":"https://pith.science/paper/2KCIWF32"},"agent_actions":{"view_html":"https://pith.science/pith/2KCIWF322MTXCR6QHZZBZQSTA2","download_json":"https://pith.science/pith/2KCIWF322MTXCR6QHZZBZQSTA2.json","view_paper":"https://pith.science/paper/2KCIWF32","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1508.04193&json=true","fetch_graph":"https://pith.science/api/pith-number/2KCIWF322MTXCR6QHZZBZQSTA2/graph.json","fetch_events":"https://pith.science/api/pith-number/2KCIWF322MTXCR6QHZZBZQSTA2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2KCIWF322MTXCR6QHZZBZQSTA2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2KCIWF322MTXCR6QHZZBZQSTA2/action/storage_attestation","attest_author":"https://pith.science/pith/2KCIWF322MTXCR6QHZZBZQSTA2/action/author_attestation","sign_citation":"https://pith.science/pith/2KCIWF322MTXCR6QHZZBZQSTA2/action/citation_signature","submit_replication":"https://pith.science/pith/2KCIWF322MTXCR6QHZZBZQSTA2/action/replication_record"}},"created_at":"2026-05-18T00:53:15.929746+00:00","updated_at":"2026-05-18T00:53:15.929746+00:00"}