{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:C62NN4GG4RUXWHWB3SP2Z6J3TO","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":"25c2ebf760d752ec24492a50dc857e14f74508f761dfb446f838d850de19850c","cross_cats_sorted":["math.IT","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-06-03T11:45:43Z","title_canon_sha256":"dcd49ae8b571c7109920b69e2b43337133cf3741115e23608e257766c0d2e3cb"},"schema_version":"1.0","source":{"id":"0906.0690","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0906.0690","created_at":"2026-05-18T04:42:13Z"},{"alias_kind":"arxiv_version","alias_value":"0906.0690v1","created_at":"2026-05-18T04:42:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.0690","created_at":"2026-05-18T04:42:13Z"},{"alias_kind":"pith_short_12","alias_value":"C62NN4GG4RUX","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"C62NN4GG4RUXWHWB","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"C62NN4GG","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:c7f5e0eb36b7dc46ec9fe5d32c6a915eb6db7ee9f659707e4cb88494ccf4c260","target":"graph","created_at":"2026-05-18T04:42:13Z","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":"Renyi's \"thinning\" operation on a discrete random variable is a natural discrete analog of the scaling operation for continuous random variables. The properties of thinning are investigated in an information-theoretic context, especially in connection with information-theoretic inequalities related to Poisson approximation results. The classical Binomial-to-Poisson convergence (sometimes referred to as the \"law of small numbers\" is seen to be a special case of a thinning limit theorem for convolutions of discrete distributions. A rate of convergence is provided for this limit, and nonasymptoti","authors_text":"Ioannis Kontoyiannis, Oliver Johnson, Peter Harremoes","cross_cats":["math.IT","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-06-03T11:45:43Z","title":"Thinning, Entropy and the Law of Thin Numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.0690","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:dad2fd1e85fd121ed366645143f3f55c73f2b1b57a1dc06e37d35a96e577b2e6","target":"record","created_at":"2026-05-18T04:42:13Z","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":"25c2ebf760d752ec24492a50dc857e14f74508f761dfb446f838d850de19850c","cross_cats_sorted":["math.IT","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-06-03T11:45:43Z","title_canon_sha256":"dcd49ae8b571c7109920b69e2b43337133cf3741115e23608e257766c0d2e3cb"},"schema_version":"1.0","source":{"id":"0906.0690","kind":"arxiv","version":1}},"canonical_sha256":"17b4d6f0c6e4697b1ec1dc9facf93b9b98ce659c5d508ae6e0a7aa7fe6fa396d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"17b4d6f0c6e4697b1ec1dc9facf93b9b98ce659c5d508ae6e0a7aa7fe6fa396d","first_computed_at":"2026-05-18T04:42:13.857939Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:13.857939Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PYAhA5Nkb387SrXJR2BfUxcjgKeUgYbtRiyYB15ThmokaLIk59pKXF4AuJC+9l2Kuce4OitkhCnQOJdsxEnIDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:13.858440Z","signed_message":"canonical_sha256_bytes"},"source_id":"0906.0690","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dad2fd1e85fd121ed366645143f3f55c73f2b1b57a1dc06e37d35a96e577b2e6","sha256:c7f5e0eb36b7dc46ec9fe5d32c6a915eb6db7ee9f659707e4cb88494ccf4c260"],"state_sha256":"38e9f8c8f0fd61b7fdafe3943cbf35a17ff323c2e23010113c6e9635a02868ba"}