{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:UCFJW3KOAACHV75INMTG3RHZ5Q","short_pith_number":"pith:UCFJW3KO","canonical_record":{"source":{"id":"1511.05192","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-11-16T21:47:24Z","cross_cats_sorted":[],"title_canon_sha256":"ab7449fdbbf61cdea6e21cb823ea65a5e149bf1be3983d90fef9dd0c939cf8a9","abstract_canon_sha256":"2cb7d328eaf69355731a47262f2b4a94066c3a04f5c0eb563b441c275d173f9f"},"schema_version":"1.0"},"canonical_sha256":"a08a9b6d4e00047affa86b266dc4f9ec05598afe2dff264e2e3a3c6b14c91eaa","source":{"kind":"arxiv","id":"1511.05192","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.05192","created_at":"2026-05-18T01:26:49Z"},{"alias_kind":"arxiv_version","alias_value":"1511.05192v1","created_at":"2026-05-18T01:26:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.05192","created_at":"2026-05-18T01:26:49Z"},{"alias_kind":"pith_short_12","alias_value":"UCFJW3KOAACH","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UCFJW3KOAACHV75I","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UCFJW3KO","created_at":"2026-05-18T12:29:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:UCFJW3KOAACHV75INMTG3RHZ5Q","target":"record","payload":{"canonical_record":{"source":{"id":"1511.05192","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-11-16T21:47:24Z","cross_cats_sorted":[],"title_canon_sha256":"ab7449fdbbf61cdea6e21cb823ea65a5e149bf1be3983d90fef9dd0c939cf8a9","abstract_canon_sha256":"2cb7d328eaf69355731a47262f2b4a94066c3a04f5c0eb563b441c275d173f9f"},"schema_version":"1.0"},"canonical_sha256":"a08a9b6d4e00047affa86b266dc4f9ec05598afe2dff264e2e3a3c6b14c91eaa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:26:49.810559Z","signature_b64":"qpfrhcQiCcgo/z+ao57/4bUL7lxX23hraaT5cTfAhipS3DXyhVL4rFGFMqz2hojVo9i/lWOz5CVb1soSzjY6BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a08a9b6d4e00047affa86b266dc4f9ec05598afe2dff264e2e3a3c6b14c91eaa","last_reissued_at":"2026-05-18T01:26:49.809699Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:26:49.809699Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.05192","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":"2026-05-18T01:26:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U5ICYX5qFC8zUldb06v9/X7+HqO0yRV0YNTaezojv/7+AbCmV17GL9PCqm/ycLfGH+NnC+XomAQ1EP9bDpgXBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T10:39:42.214977Z"},"content_sha256":"bebd51d2ae7eb3e3825c6cc3e0a817e215029716f31a3ac466c106458399cb6c","schema_version":"1.0","event_id":"sha256:bebd51d2ae7eb3e3825c6cc3e0a817e215029716f31a3ac466c106458399cb6c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:UCFJW3KOAACHV75INMTG3RHZ5Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Compound Poisson process with a Poisson subordinator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Antonio Di Crescenzo, Barbara Martinucci, Shelemyahu Zacks","submitted_at":"2015-11-16T21:47:24Z","abstract_excerpt":"A compound Poisson process whose randomized time is an independent Poisson process is called compound Poisson process with Poisson subordinator. We provide its probability distribution, which is expressed in terms of the Bell polynomials, and investigate in detail both the special cases in which the compound Poisson process has exponential jumps and normal jumps. Then for the iterated Poisson process we discuss some properties and provide convergence results to a Poisson process. The first-crossing-time problem for the iterated Poisson process is finally tackled in the cases of (i) a decreasin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.05192","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":"2026-05-18T01:26:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z/krlSZibns32S2km8CveEzzyhCkGI8D9pfPd3iu7zDL3YRP2YtgbpGOCWu3i4t0i9hWa40zE06yzKRouYAJDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T10:39:42.215340Z"},"content_sha256":"06c92f7cca4a0b2227a85ee00b944265c1b0bcbdcf3038596207b417348dc569","schema_version":"1.0","event_id":"sha256:06c92f7cca4a0b2227a85ee00b944265c1b0bcbdcf3038596207b417348dc569"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UCFJW3KOAACHV75INMTG3RHZ5Q/bundle.json","state_url":"https://pith.science/pith/UCFJW3KOAACHV75INMTG3RHZ5Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UCFJW3KOAACHV75INMTG3RHZ5Q/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":"2026-06-03T10:39:42Z","links":{"resolver":"https://pith.science/pith/UCFJW3KOAACHV75INMTG3RHZ5Q","bundle":"https://pith.science/pith/UCFJW3KOAACHV75INMTG3RHZ5Q/bundle.json","state":"https://pith.science/pith/UCFJW3KOAACHV75INMTG3RHZ5Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UCFJW3KOAACHV75INMTG3RHZ5Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:UCFJW3KOAACHV75INMTG3RHZ5Q","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":"2cb7d328eaf69355731a47262f2b4a94066c3a04f5c0eb563b441c275d173f9f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-11-16T21:47:24Z","title_canon_sha256":"ab7449fdbbf61cdea6e21cb823ea65a5e149bf1be3983d90fef9dd0c939cf8a9"},"schema_version":"1.0","source":{"id":"1511.05192","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.05192","created_at":"2026-05-18T01:26:49Z"},{"alias_kind":"arxiv_version","alias_value":"1511.05192v1","created_at":"2026-05-18T01:26:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.05192","created_at":"2026-05-18T01:26:49Z"},{"alias_kind":"pith_short_12","alias_value":"UCFJW3KOAACH","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UCFJW3KOAACHV75I","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UCFJW3KO","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:06c92f7cca4a0b2227a85ee00b944265c1b0bcbdcf3038596207b417348dc569","target":"graph","created_at":"2026-05-18T01:26:49Z","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":"A compound Poisson process whose randomized time is an independent Poisson process is called compound Poisson process with Poisson subordinator. We provide its probability distribution, which is expressed in terms of the Bell polynomials, and investigate in detail both the special cases in which the compound Poisson process has exponential jumps and normal jumps. Then for the iterated Poisson process we discuss some properties and provide convergence results to a Poisson process. The first-crossing-time problem for the iterated Poisson process is finally tackled in the cases of (i) a decreasin","authors_text":"Antonio Di Crescenzo, Barbara Martinucci, Shelemyahu Zacks","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-11-16T21:47:24Z","title":"Compound Poisson process with a Poisson subordinator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.05192","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:bebd51d2ae7eb3e3825c6cc3e0a817e215029716f31a3ac466c106458399cb6c","target":"record","created_at":"2026-05-18T01:26:49Z","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":"2cb7d328eaf69355731a47262f2b4a94066c3a04f5c0eb563b441c275d173f9f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-11-16T21:47:24Z","title_canon_sha256":"ab7449fdbbf61cdea6e21cb823ea65a5e149bf1be3983d90fef9dd0c939cf8a9"},"schema_version":"1.0","source":{"id":"1511.05192","kind":"arxiv","version":1}},"canonical_sha256":"a08a9b6d4e00047affa86b266dc4f9ec05598afe2dff264e2e3a3c6b14c91eaa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a08a9b6d4e00047affa86b266dc4f9ec05598afe2dff264e2e3a3c6b14c91eaa","first_computed_at":"2026-05-18T01:26:49.809699Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:26:49.809699Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qpfrhcQiCcgo/z+ao57/4bUL7lxX23hraaT5cTfAhipS3DXyhVL4rFGFMqz2hojVo9i/lWOz5CVb1soSzjY6BA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:26:49.810559Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.05192","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bebd51d2ae7eb3e3825c6cc3e0a817e215029716f31a3ac466c106458399cb6c","sha256:06c92f7cca4a0b2227a85ee00b944265c1b0bcbdcf3038596207b417348dc569"],"state_sha256":"70bd78b5194044d2b212e28954a3d9a755569895e63673b670ad55eb915c27c8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MEeKEdgI+/EF5GZvuRBPcQhq1YyfbHBI8RgGGVgudvcTlzXQO229QlIGeec4d1/NxBJ0mwl9yci+vbARpJgpCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T10:39:42.217288Z","bundle_sha256":"8de5440c6692575f5f0eb3cfbf0e7bd1af3523d31aee3052ed0affec5f77c79a"}}