{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:NJ62DFP2JVZ5MJ35FMZIHH6VHF","short_pith_number":"pith:NJ62DFP2","canonical_record":{"source":{"id":"1402.0183","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2014-02-02T12:24:46Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"540d5d8ec6d906d74a476851536bb7d134bf3c35a1de9619d99875140cf2da5e","abstract_canon_sha256":"e9afe92df01f5d3a6bc0a08ccfe080881e20858dbc9b929ede5762531d4b927d"},"schema_version":"1.0"},"canonical_sha256":"6a7da195fa4d73d6277d2b32839fd53963a406781d5c065f943aca5f776de02f","source":{"kind":"arxiv","id":"1402.0183","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.0183","created_at":"2026-05-18T03:00:24Z"},{"alias_kind":"arxiv_version","alias_value":"1402.0183v1","created_at":"2026-05-18T03:00:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.0183","created_at":"2026-05-18T03:00:24Z"},{"alias_kind":"pith_short_12","alias_value":"NJ62DFP2JVZ5","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NJ62DFP2JVZ5MJ35","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NJ62DFP2","created_at":"2026-05-18T12:28:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:NJ62DFP2JVZ5MJ35FMZIHH6VHF","target":"record","payload":{"canonical_record":{"source":{"id":"1402.0183","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2014-02-02T12:24:46Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"540d5d8ec6d906d74a476851536bb7d134bf3c35a1de9619d99875140cf2da5e","abstract_canon_sha256":"e9afe92df01f5d3a6bc0a08ccfe080881e20858dbc9b929ede5762531d4b927d"},"schema_version":"1.0"},"canonical_sha256":"6a7da195fa4d73d6277d2b32839fd53963a406781d5c065f943aca5f776de02f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:00:24.443792Z","signature_b64":"seQQ5YQHlHr9aeEZma1SATQNHN45Fx4NMih1NaIMUUXdnP4UNUoqrVK96ym57gakEOLJ8560BY2oOx5gQEZPAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a7da195fa4d73d6277d2b32839fd53963a406781d5c065f943aca5f776de02f","last_reissued_at":"2026-05-18T03:00:24.443091Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:00:24.443091Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1402.0183","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:00:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8DNaMCrWeMb6kCV2M7iQ1c6qxXvYMp4IPNSDuVCVP28oZL+VI1GpfIiS2dnLSMDy7+Is1CQ1EuJzQwopXyVgAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T09:27:22.549885Z"},"content_sha256":"f8c4e9555621de89492da19d9924eb37183ad4d8ac1deabdbbb567a9c9a4e7e5","schema_version":"1.0","event_id":"sha256:f8c4e9555621de89492da19d9924eb37183ad4d8ac1deabdbbb567a9c9a4e7e5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:NJ62DFP2JVZ5MJ35FMZIHH6VHF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Compound Poisson Convergence Theorem for Sums of $m$-Dependent Variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"P. Vellaisamy, V. Cekanavicius","submitted_at":"2014-02-02T12:24:46Z","abstract_excerpt":"We prove the Simons-Johnson theorem for the sums $S_n$ of $m$-dependent random variables, with exponential weights and limiting compound Poisson distribution $\\CP(s,\\lambda)$. More precisely, we give sufficient conditions for $\\sum_{k=0}^\\infty\\ee^{hk}\\ab{P(S_n=k)-\\CP(s,\\lambda)\\{k\\}}\\to 0$ and provide an estimate on the rate of convergence. It is shown that the Simons-Johnson theorem holds for weighted Wasserstein norm as well. %limiting sum of two Poisson variables defined on %different lattices. The results are then illustrated for $N(n;k_1,k_2)$ and $k$-runs statistics."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0183","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:00:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ipfWN4dq6G7GiHALIethyTCRNl2N64R75gHYoq8TuFSAHezqgse5+qTMbO52U06gkyEKdbIxJudTP0t59GPzBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T09:27:22.550237Z"},"content_sha256":"cca38d2bee06f8ab863af409895c8f99e2f17450640b61a2167d85e5b34a7f28","schema_version":"1.0","event_id":"sha256:cca38d2bee06f8ab863af409895c8f99e2f17450640b61a2167d85e5b34a7f28"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NJ62DFP2JVZ5MJ35FMZIHH6VHF/bundle.json","state_url":"https://pith.science/pith/NJ62DFP2JVZ5MJ35FMZIHH6VHF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NJ62DFP2JVZ5MJ35FMZIHH6VHF/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-01T09:27:22Z","links":{"resolver":"https://pith.science/pith/NJ62DFP2JVZ5MJ35FMZIHH6VHF","bundle":"https://pith.science/pith/NJ62DFP2JVZ5MJ35FMZIHH6VHF/bundle.json","state":"https://pith.science/pith/NJ62DFP2JVZ5MJ35FMZIHH6VHF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NJ62DFP2JVZ5MJ35FMZIHH6VHF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:NJ62DFP2JVZ5MJ35FMZIHH6VHF","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":"e9afe92df01f5d3a6bc0a08ccfe080881e20858dbc9b929ede5762531d4b927d","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2014-02-02T12:24:46Z","title_canon_sha256":"540d5d8ec6d906d74a476851536bb7d134bf3c35a1de9619d99875140cf2da5e"},"schema_version":"1.0","source":{"id":"1402.0183","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.0183","created_at":"2026-05-18T03:00:24Z"},{"alias_kind":"arxiv_version","alias_value":"1402.0183v1","created_at":"2026-05-18T03:00:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.0183","created_at":"2026-05-18T03:00:24Z"},{"alias_kind":"pith_short_12","alias_value":"NJ62DFP2JVZ5","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NJ62DFP2JVZ5MJ35","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NJ62DFP2","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:cca38d2bee06f8ab863af409895c8f99e2f17450640b61a2167d85e5b34a7f28","target":"graph","created_at":"2026-05-18T03:00:24Z","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 prove the Simons-Johnson theorem for the sums $S_n$ of $m$-dependent random variables, with exponential weights and limiting compound Poisson distribution $\\CP(s,\\lambda)$. More precisely, we give sufficient conditions for $\\sum_{k=0}^\\infty\\ee^{hk}\\ab{P(S_n=k)-\\CP(s,\\lambda)\\{k\\}}\\to 0$ and provide an estimate on the rate of convergence. It is shown that the Simons-Johnson theorem holds for weighted Wasserstein norm as well. %limiting sum of two Poisson variables defined on %different lattices. The results are then illustrated for $N(n;k_1,k_2)$ and $k$-runs statistics.","authors_text":"P. Vellaisamy, V. Cekanavicius","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2014-02-02T12:24:46Z","title":"A Compound Poisson Convergence Theorem for Sums of $m$-Dependent Variables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0183","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:f8c4e9555621de89492da19d9924eb37183ad4d8ac1deabdbbb567a9c9a4e7e5","target":"record","created_at":"2026-05-18T03:00:24Z","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":"e9afe92df01f5d3a6bc0a08ccfe080881e20858dbc9b929ede5762531d4b927d","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2014-02-02T12:24:46Z","title_canon_sha256":"540d5d8ec6d906d74a476851536bb7d134bf3c35a1de9619d99875140cf2da5e"},"schema_version":"1.0","source":{"id":"1402.0183","kind":"arxiv","version":1}},"canonical_sha256":"6a7da195fa4d73d6277d2b32839fd53963a406781d5c065f943aca5f776de02f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a7da195fa4d73d6277d2b32839fd53963a406781d5c065f943aca5f776de02f","first_computed_at":"2026-05-18T03:00:24.443091Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:00:24.443091Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"seQQ5YQHlHr9aeEZma1SATQNHN45Fx4NMih1NaIMUUXdnP4UNUoqrVK96ym57gakEOLJ8560BY2oOx5gQEZPAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:00:24.443792Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.0183","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f8c4e9555621de89492da19d9924eb37183ad4d8ac1deabdbbb567a9c9a4e7e5","sha256:cca38d2bee06f8ab863af409895c8f99e2f17450640b61a2167d85e5b34a7f28"],"state_sha256":"399adb6f1a52c174ecf5fd7efa5931db5b5e41757860dff525d86ed76bacd861"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DFnD3d1qXcRhQu/kemoYfNQ9U6tgPpcq0ZDoZxrXSY9zQZu0xi84VOQNuM65BsnCP3pjAXJ1Qz3i6vx5qHmPCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T09:27:22.552206Z","bundle_sha256":"345cf3a1a3b45bf27f4db80a8bdd0e667188b33a5e8aa16313d7423c0234ec15"}}