{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:TQ4EPIYRD4CITWOMC4RFSVYBOF","short_pith_number":"pith:TQ4EPIYR","canonical_record":{"source":{"id":"1307.6296","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-07-24T04:58:13Z","cross_cats_sorted":[],"title_canon_sha256":"cb5c40f4d836e266926336f5e17372383dc9f11754e09d63f935128ad2ae03a6","abstract_canon_sha256":"cb2af382cfde75b5fba9ae445534e00d632c81e9374f293324a76e15c85b0be8"},"schema_version":"1.0"},"canonical_sha256":"9c3847a3111f0489d9cc1722595701716fdf5fa867a93a6e5d67bbcd5a342174","source":{"kind":"arxiv","id":"1307.6296","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.6296","created_at":"2026-05-18T02:45:04Z"},{"alias_kind":"arxiv_version","alias_value":"1307.6296v1","created_at":"2026-05-18T02:45:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.6296","created_at":"2026-05-18T02:45:04Z"},{"alias_kind":"pith_short_12","alias_value":"TQ4EPIYRD4CI","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"TQ4EPIYRD4CITWOM","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"TQ4EPIYR","created_at":"2026-05-18T12:28:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:TQ4EPIYRD4CITWOMC4RFSVYBOF","target":"record","payload":{"canonical_record":{"source":{"id":"1307.6296","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-07-24T04:58:13Z","cross_cats_sorted":[],"title_canon_sha256":"cb5c40f4d836e266926336f5e17372383dc9f11754e09d63f935128ad2ae03a6","abstract_canon_sha256":"cb2af382cfde75b5fba9ae445534e00d632c81e9374f293324a76e15c85b0be8"},"schema_version":"1.0"},"canonical_sha256":"9c3847a3111f0489d9cc1722595701716fdf5fa867a93a6e5d67bbcd5a342174","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:04.897767Z","signature_b64":"Qb6+Bh2PBqaQevSqePAL8R7NqkGOWrB6PFmpzJA0e/oma/pvHW85GtwqtbDghNuxO+wE7NPHYyguLHf3yLP0BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9c3847a3111f0489d9cc1722595701716fdf5fa867a93a6e5d67bbcd5a342174","last_reissued_at":"2026-05-18T02:45:04.896926Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:04.896926Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.6296","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":"2026-05-18T02:45:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RJv4K7hFdVAfcGrhyuwaGJ1sIP2Lee1EHS9tqKYfqYzgQv1rScVC7upLQKZ4giuN2Se4+qXmdcymrFbdLULgAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T02:48:46.612100Z"},"content_sha256":"9e0dd54fd1edfbf770a96452a8f42ad8afa291f95f823437fe43cf5cded42304","schema_version":"1.0","event_id":"sha256:9e0dd54fd1edfbf770a96452a8f42ad8afa291f95f823437fe43cf5cded42304"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:TQ4EPIYRD4CITWOMC4RFSVYBOF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-uniform approximations for sums of discrete m-dependent random variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"P. Vellaisamy, V. Cekanavicius","submitted_at":"2013-07-24T04:58:13Z","abstract_excerpt":"Non-uniform estimates are obtained for Poisson, compound Poisson, translated Poisson, negative binomial and binomial approximations to sums of of m-dependent integer-valued random variables. Estimates for Wasserstein metric also follow easily from our results. The results are then exemplified by the approximation of Poisson binomial distribution, 2-runs and $m$-dependent $(k_1,k_2)$-events."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.6296","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":"2026-05-18T02:45:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HHXa0l8/PR3s7J/dqu6vkF8RE2VyzHzNeiYG8+NaTWNDrokoqojFPTqnR9j0Z3EFy2AOhcbU7TxzEuab2KroDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T02:48:46.612455Z"},"content_sha256":"4d8beabcc7389e44eb5445c51d09ff15c8bc2d130615161ad087e311e9765a88","schema_version":"1.0","event_id":"sha256:4d8beabcc7389e44eb5445c51d09ff15c8bc2d130615161ad087e311e9765a88"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TQ4EPIYRD4CITWOMC4RFSVYBOF/bundle.json","state_url":"https://pith.science/pith/TQ4EPIYRD4CITWOMC4RFSVYBOF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TQ4EPIYRD4CITWOMC4RFSVYBOF/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":"2026-06-02T02:48:46Z","links":{"resolver":"https://pith.science/pith/TQ4EPIYRD4CITWOMC4RFSVYBOF","bundle":"https://pith.science/pith/TQ4EPIYRD4CITWOMC4RFSVYBOF/bundle.json","state":"https://pith.science/pith/TQ4EPIYRD4CITWOMC4RFSVYBOF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TQ4EPIYRD4CITWOMC4RFSVYBOF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:TQ4EPIYRD4CITWOMC4RFSVYBOF","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":"cb2af382cfde75b5fba9ae445534e00d632c81e9374f293324a76e15c85b0be8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-07-24T04:58:13Z","title_canon_sha256":"cb5c40f4d836e266926336f5e17372383dc9f11754e09d63f935128ad2ae03a6"},"schema_version":"1.0","source":{"id":"1307.6296","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.6296","created_at":"2026-05-18T02:45:04Z"},{"alias_kind":"arxiv_version","alias_value":"1307.6296v1","created_at":"2026-05-18T02:45:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.6296","created_at":"2026-05-18T02:45:04Z"},{"alias_kind":"pith_short_12","alias_value":"TQ4EPIYRD4CI","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"TQ4EPIYRD4CITWOM","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"TQ4EPIYR","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:4d8beabcc7389e44eb5445c51d09ff15c8bc2d130615161ad087e311e9765a88","target":"graph","created_at":"2026-05-18T02:45:04Z","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":"Non-uniform estimates are obtained for Poisson, compound Poisson, translated Poisson, negative binomial and binomial approximations to sums of of m-dependent integer-valued random variables. Estimates for Wasserstein metric also follow easily from our results. The results are then exemplified by the approximation of Poisson binomial distribution, 2-runs and $m$-dependent $(k_1,k_2)$-events.","authors_text":"P. Vellaisamy, V. Cekanavicius","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-07-24T04:58:13Z","title":"Non-uniform approximations for sums of discrete m-dependent random variables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.6296","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":"sha256:9e0dd54fd1edfbf770a96452a8f42ad8afa291f95f823437fe43cf5cded42304","target":"record","created_at":"2026-05-18T02:45:04Z","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":"cb2af382cfde75b5fba9ae445534e00d632c81e9374f293324a76e15c85b0be8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-07-24T04:58:13Z","title_canon_sha256":"cb5c40f4d836e266926336f5e17372383dc9f11754e09d63f935128ad2ae03a6"},"schema_version":"1.0","source":{"id":"1307.6296","kind":"arxiv","version":1}},"canonical_sha256":"9c3847a3111f0489d9cc1722595701716fdf5fa867a93a6e5d67bbcd5a342174","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c3847a3111f0489d9cc1722595701716fdf5fa867a93a6e5d67bbcd5a342174","first_computed_at":"2026-05-18T02:45:04.896926Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:04.896926Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Qb6+Bh2PBqaQevSqePAL8R7NqkGOWrB6PFmpzJA0e/oma/pvHW85GtwqtbDghNuxO+wE7NPHYyguLHf3yLP0BA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:04.897767Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.6296","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e0dd54fd1edfbf770a96452a8f42ad8afa291f95f823437fe43cf5cded42304","sha256:4d8beabcc7389e44eb5445c51d09ff15c8bc2d130615161ad087e311e9765a88"],"state_sha256":"83d2efedf340329c155cf46f2850f78215da422c2085e020ad118e3195105cd6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fa3XaEa4VjP2bypp1iesnLkBOdUnI/3NLcpvTXyDdUW2zbFQO/IzQ7pBuEs5VgvMtv4ipyQbLKUwBgrDU43dBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T02:48:46.614434Z","bundle_sha256":"f4679b1968dd7363fe2c077ca7342eb7c4f212bb5b1eaa19cf6756c9dc090427"}}