{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:C62NN4GG4RUXWHWB3SP2Z6J3TO","short_pith_number":"pith:C62NN4GG","schema_version":"1.0","canonical_sha256":"17b4d6f0c6e4697b1ec1dc9facf93b9b98ce659c5d508ae6e0a7aa7fe6fa396d","source":{"kind":"arxiv","id":"0906.0690","version":1},"attestation_state":"computed","paper":{"title":"Thinning, Entropy and the Law of Thin Numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.PR"],"primary_cat":"cs.IT","authors_text":"Ioannis Kontoyiannis, Oliver Johnson, Peter Harremoes","submitted_at":"2009-06-03T11:45:43Z","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"},"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":"0906.0690","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-06-03T11:45:43Z","cross_cats_sorted":["math.IT","math.PR"],"title_canon_sha256":"dcd49ae8b571c7109920b69e2b43337133cf3741115e23608e257766c0d2e3cb","abstract_canon_sha256":"25c2ebf760d752ec24492a50dc857e14f74508f761dfb446f838d850de19850c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:42:13.858440Z","signature_b64":"PYAhA5Nkb387SrXJR2BfUxcjgKeUgYbtRiyYB15ThmokaLIk59pKXF4AuJC+9l2Kuce4OitkhCnQOJdsxEnIDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"17b4d6f0c6e4697b1ec1dc9facf93b9b98ce659c5d508ae6e0a7aa7fe6fa396d","last_reissued_at":"2026-05-18T04:42:13.857939Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:42:13.857939Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Thinning, Entropy and the Law of Thin Numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.PR"],"primary_cat":"cs.IT","authors_text":"Ioannis Kontoyiannis, Oliver Johnson, Peter Harremoes","submitted_at":"2009-06-03T11:45:43Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.0690","kind":"arxiv","version":1},"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":"0906.0690","created_at":"2026-05-18T04:42:13.858007+00:00"},{"alias_kind":"arxiv_version","alias_value":"0906.0690v1","created_at":"2026-05-18T04:42:13.858007+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.0690","created_at":"2026-05-18T04:42:13.858007+00:00"},{"alias_kind":"pith_short_12","alias_value":"C62NN4GG4RUX","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_16","alias_value":"C62NN4GG4RUXWHWB","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_8","alias_value":"C62NN4GG","created_at":"2026-05-18T12:25:58.837520+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/C62NN4GG4RUXWHWB3SP2Z6J3TO","json":"https://pith.science/pith/C62NN4GG4RUXWHWB3SP2Z6J3TO.json","graph_json":"https://pith.science/api/pith-number/C62NN4GG4RUXWHWB3SP2Z6J3TO/graph.json","events_json":"https://pith.science/api/pith-number/C62NN4GG4RUXWHWB3SP2Z6J3TO/events.json","paper":"https://pith.science/paper/C62NN4GG"},"agent_actions":{"view_html":"https://pith.science/pith/C62NN4GG4RUXWHWB3SP2Z6J3TO","download_json":"https://pith.science/pith/C62NN4GG4RUXWHWB3SP2Z6J3TO.json","view_paper":"https://pith.science/paper/C62NN4GG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0906.0690&json=true","fetch_graph":"https://pith.science/api/pith-number/C62NN4GG4RUXWHWB3SP2Z6J3TO/graph.json","fetch_events":"https://pith.science/api/pith-number/C62NN4GG4RUXWHWB3SP2Z6J3TO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/C62NN4GG4RUXWHWB3SP2Z6J3TO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/C62NN4GG4RUXWHWB3SP2Z6J3TO/action/storage_attestation","attest_author":"https://pith.science/pith/C62NN4GG4RUXWHWB3SP2Z6J3TO/action/author_attestation","sign_citation":"https://pith.science/pith/C62NN4GG4RUXWHWB3SP2Z6J3TO/action/citation_signature","submit_replication":"https://pith.science/pith/C62NN4GG4RUXWHWB3SP2Z6J3TO/action/replication_record"}},"created_at":"2026-05-18T04:42:13.858007+00:00","updated_at":"2026-05-18T04:42:13.858007+00:00"}