{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:MXHFB5U6DHNZVMGULFK54AD43D","short_pith_number":"pith:MXHFB5U6","schema_version":"1.0","canonical_sha256":"65ce50f69e19db9ab0d45955de007cd8d88439b5bf3a63969304033a7c16ef9e","source":{"kind":"arxiv","id":"1609.03060","version":1},"attestation_state":"computed","paper":{"title":"Double asymptotics for the chi-square statistic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Grzegorz A. Rempa{\\l}a, Jacek Weso{\\l}owski","submitted_at":"2016-09-10T14:36:13Z","abstract_excerpt":"We consider distributional limit of the Pearson chi-square statistic when the number of classes m increases with the sample size n in such way that $n/\\sqrt{m} \\to {\\lambda}$. Under mild moment conditions, the limit is Gaussian for ${\\lambda} = \\infty$, Poisson for finite ${\\lambda} > 0$, and degenerate for ${\\lambda} = 0$."},"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":"1609.03060","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-10T14:36:13Z","cross_cats_sorted":[],"title_canon_sha256":"549e1dc9ad2803247dcc2c04e4ef3a98f32ec60301600f16151e7d7205dad3c0","abstract_canon_sha256":"cc782c16dce76e0f34eceb906ea2b239a18f5eabcf6279db8d42044dc6c1496c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:49.042650Z","signature_b64":"pbVp2u87vpPjMmXJIZh08rJv9pId6ntIIHkRKZiDwMX9/5aoaTp/zTHgLZKm+AczzcX7kUcoPxtAwa42/PXYAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65ce50f69e19db9ab0d45955de007cd8d88439b5bf3a63969304033a7c16ef9e","last_reissued_at":"2026-05-18T01:04:49.042287Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:49.042287Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Double asymptotics for the chi-square statistic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Grzegorz A. Rempa{\\l}a, Jacek Weso{\\l}owski","submitted_at":"2016-09-10T14:36:13Z","abstract_excerpt":"We consider distributional limit of the Pearson chi-square statistic when the number of classes m increases with the sample size n in such way that $n/\\sqrt{m} \\to {\\lambda}$. Under mild moment conditions, the limit is Gaussian for ${\\lambda} = \\infty$, Poisson for finite ${\\lambda} > 0$, and degenerate for ${\\lambda} = 0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03060","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":"1609.03060","created_at":"2026-05-18T01:04:49.042350+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.03060v1","created_at":"2026-05-18T01:04:49.042350+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.03060","created_at":"2026-05-18T01:04:49.042350+00:00"},{"alias_kind":"pith_short_12","alias_value":"MXHFB5U6DHNZ","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_16","alias_value":"MXHFB5U6DHNZVMGU","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_8","alias_value":"MXHFB5U6","created_at":"2026-05-18T12:30:32.724797+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/MXHFB5U6DHNZVMGULFK54AD43D","json":"https://pith.science/pith/MXHFB5U6DHNZVMGULFK54AD43D.json","graph_json":"https://pith.science/api/pith-number/MXHFB5U6DHNZVMGULFK54AD43D/graph.json","events_json":"https://pith.science/api/pith-number/MXHFB5U6DHNZVMGULFK54AD43D/events.json","paper":"https://pith.science/paper/MXHFB5U6"},"agent_actions":{"view_html":"https://pith.science/pith/MXHFB5U6DHNZVMGULFK54AD43D","download_json":"https://pith.science/pith/MXHFB5U6DHNZVMGULFK54AD43D.json","view_paper":"https://pith.science/paper/MXHFB5U6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.03060&json=true","fetch_graph":"https://pith.science/api/pith-number/MXHFB5U6DHNZVMGULFK54AD43D/graph.json","fetch_events":"https://pith.science/api/pith-number/MXHFB5U6DHNZVMGULFK54AD43D/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MXHFB5U6DHNZVMGULFK54AD43D/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MXHFB5U6DHNZVMGULFK54AD43D/action/storage_attestation","attest_author":"https://pith.science/pith/MXHFB5U6DHNZVMGULFK54AD43D/action/author_attestation","sign_citation":"https://pith.science/pith/MXHFB5U6DHNZVMGULFK54AD43D/action/citation_signature","submit_replication":"https://pith.science/pith/MXHFB5U6DHNZVMGULFK54AD43D/action/replication_record"}},"created_at":"2026-05-18T01:04:49.042350+00:00","updated_at":"2026-05-18T01:04:49.042350+00:00"}