{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:6GDHL7TQR3S2C5FWDQKNWQPIQN","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":"f536787e55456784d07f0bb6a75fa46e207ba42904a3db781618b9f49a2f526c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-06-11T07:45:20Z","title_canon_sha256":"a2e8a80f692171fd8469cadbfe870a4e59f3edf4dd2cd528bb7473ff221148de"},"schema_version":"1.0","source":{"id":"1806.03844","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.03844","created_at":"2026-05-18T00:13:41Z"},{"alias_kind":"arxiv_version","alias_value":"1806.03844v1","created_at":"2026-05-18T00:13:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.03844","created_at":"2026-05-18T00:13:41Z"},{"alias_kind":"pith_short_12","alias_value":"6GDHL7TQR3S2","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"6GDHL7TQR3S2C5FW","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"6GDHL7TQ","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:720d2ac9f9b64ed3b3bd8ebf511d6b89656212ba729e7f2b734f4d3a0611f919","target":"graph","created_at":"2026-05-18T00:13:41Z","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":"The effect that weighted summands have on each other in approximations of $S=w_1S_1+w_2S_2+\\cdots+w_NS_N$ is investigated. Here, $S_i$'s are sums of integer-valued random variables, and $w_i$ denote weights, $i=1,\\dots,N$. Two cases are considered: the general case of independent random variables when their closeness is ensured by the matching of factorial moments and the case when the $S_i$ has the Markov Binomial distribution. The Kolmogorov metric is used to estimate the accuracy of approximation.","authors_text":"Palaniappan Vellaisamy, Vydas \\v{C}ekanavi\\v{c}ius","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-06-11T07:45:20Z","title":"On closeness of two discrete weighted sums"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.03844","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:b0f6280b84e20a66d5b8df522e0d4e488d7c61bc9995fe3d8c7eccf8e21bbaf6","target":"record","created_at":"2026-05-18T00:13:41Z","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":"f536787e55456784d07f0bb6a75fa46e207ba42904a3db781618b9f49a2f526c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-06-11T07:45:20Z","title_canon_sha256":"a2e8a80f692171fd8469cadbfe870a4e59f3edf4dd2cd528bb7473ff221148de"},"schema_version":"1.0","source":{"id":"1806.03844","kind":"arxiv","version":1}},"canonical_sha256":"f18675fe708ee5a174b61c14db41e883470d715d8b2380619509df067b06ac6e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f18675fe708ee5a174b61c14db41e883470d715d8b2380619509df067b06ac6e","first_computed_at":"2026-05-18T00:13:41.870643Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:41.870643Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ys2GvDhLSiye6FU0dO+UzCgwYIgiZGAfjdf/2RgT+ZCf7/ysehvQGXUeH8Jfvlk3katkfuvDqgeROm8fucexAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:41.871296Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.03844","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b0f6280b84e20a66d5b8df522e0d4e488d7c61bc9995fe3d8c7eccf8e21bbaf6","sha256:720d2ac9f9b64ed3b3bd8ebf511d6b89656212ba729e7f2b734f4d3a0611f919"],"state_sha256":"8058e37d5a4eec250b2f94e1f0eb66de0cfd4db5bb1576a190c6f2f5cba13cb1"}