{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:MXHFB5U6DHNZVMGULFK54AD43D","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":"cc782c16dce76e0f34eceb906ea2b239a18f5eabcf6279db8d42044dc6c1496c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-10T14:36:13Z","title_canon_sha256":"549e1dc9ad2803247dcc2c04e4ef3a98f32ec60301600f16151e7d7205dad3c0"},"schema_version":"1.0","source":{"id":"1609.03060","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.03060","created_at":"2026-05-18T01:04:49Z"},{"alias_kind":"arxiv_version","alias_value":"1609.03060v1","created_at":"2026-05-18T01:04:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.03060","created_at":"2026-05-18T01:04:49Z"},{"alias_kind":"pith_short_12","alias_value":"MXHFB5U6DHNZ","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MXHFB5U6DHNZVMGU","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MXHFB5U6","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:e1aad0663af59441aa0c697ab60a32d0d04bf51ab4efbd65c2ca230a81232c5e","target":"graph","created_at":"2026-05-18T01:04:49Z","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":"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 ${\\lambda} = 0$.","authors_text":"Grzegorz A. Rempa{\\l}a, Jacek Weso{\\l}owski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-10T14:36:13Z","title":"Double asymptotics for the chi-square statistic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03060","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":"sha256:4b3096de189c5c5bd37b3d9787a844318c05105fe213a3f550df6ff50d1af20f","target":"record","created_at":"2026-05-18T01:04:49Z","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":"cc782c16dce76e0f34eceb906ea2b239a18f5eabcf6279db8d42044dc6c1496c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-10T14:36:13Z","title_canon_sha256":"549e1dc9ad2803247dcc2c04e4ef3a98f32ec60301600f16151e7d7205dad3c0"},"schema_version":"1.0","source":{"id":"1609.03060","kind":"arxiv","version":1}},"canonical_sha256":"65ce50f69e19db9ab0d45955de007cd8d88439b5bf3a63969304033a7c16ef9e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"65ce50f69e19db9ab0d45955de007cd8d88439b5bf3a63969304033a7c16ef9e","first_computed_at":"2026-05-18T01:04:49.042287Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:49.042287Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pbVp2u87vpPjMmXJIZh08rJv9pId6ntIIHkRKZiDwMX9/5aoaTp/zTHgLZKm+AczzcX7kUcoPxtAwa42/PXYAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:49.042650Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.03060","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4b3096de189c5c5bd37b3d9787a844318c05105fe213a3f550df6ff50d1af20f","sha256:e1aad0663af59441aa0c697ab60a32d0d04bf51ab4efbd65c2ca230a81232c5e"],"state_sha256":"937460390e27b9fbe07779c9dbd3a30f7a54adde0305cf9ac516417437713a67"}