{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:HHGU3NM2L57UZWFCDCD5UJ4XT6","short_pith_number":"pith:HHGU3NM2","canonical_record":{"source":{"id":"1601.04637","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-01-18T18:13:17Z","cross_cats_sorted":[],"title_canon_sha256":"b975bb0b3b6017da14de6953f117ff2db387e5d9a897c125696871199b9c3e34","abstract_canon_sha256":"eddd98adf1985bb79f8223e169e7407578317a58fee846fb162368f060008fd1"},"schema_version":"1.0"},"canonical_sha256":"39cd4db59a5f7f4cd8a21887da27979fa74012781ff878993d6a8d4da628b56a","source":{"kind":"arxiv","id":"1601.04637","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.04637","created_at":"2026-05-18T00:36:09Z"},{"alias_kind":"arxiv_version","alias_value":"1601.04637v3","created_at":"2026-05-18T00:36:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.04637","created_at":"2026-05-18T00:36:09Z"},{"alias_kind":"pith_short_12","alias_value":"HHGU3NM2L57U","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"HHGU3NM2L57UZWFC","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"HHGU3NM2","created_at":"2026-05-18T12:30:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:HHGU3NM2L57UZWFCDCD5UJ4XT6","target":"record","payload":{"canonical_record":{"source":{"id":"1601.04637","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-01-18T18:13:17Z","cross_cats_sorted":[],"title_canon_sha256":"b975bb0b3b6017da14de6953f117ff2db387e5d9a897c125696871199b9c3e34","abstract_canon_sha256":"eddd98adf1985bb79f8223e169e7407578317a58fee846fb162368f060008fd1"},"schema_version":"1.0"},"canonical_sha256":"39cd4db59a5f7f4cd8a21887da27979fa74012781ff878993d6a8d4da628b56a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:09.985911Z","signature_b64":"c2RsgWcW3h0JqgF66csMuBtLtjjYFQWEuQGTvGji9KwbrC5jLc7bp4x29DE2vSGu3bXnsUtt5ADEQzfYTxOZBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"39cd4db59a5f7f4cd8a21887da27979fa74012781ff878993d6a8d4da628b56a","last_reissued_at":"2026-05-18T00:36:09.985341Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:09.985341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.04637","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:36:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s62W1ZZZOpgR6DHQfi0ZsPjlVz4fgJet8mYVvf1CUvxfg/uS/x6FCYDkq0BV6oIOvZ530yyZG5mum1WdGHExDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T23:44:13.288616Z"},"content_sha256":"76e0d1ac935efaf76555b8057766539d7e1b9465917ab985aa1a0df4472f1219","schema_version":"1.0","event_id":"sha256:76e0d1ac935efaf76555b8057766539d7e1b9465917ab985aa1a0df4472f1219"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:HHGU3NM2L57UZWFCDCD5UJ4XT6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ruin probabilities under Sarmanov dependence structure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Krishanu Maulik, Moumanti Podder","submitted_at":"2016-01-18T18:13:17Z","abstract_excerpt":"Our work aims to study the tail behaviour of weighted sums of the form $\\sum_{i=1}^{\\infty} X_{i} \\prod_{j=1}^{i}Y_{j}$, where $(X_{i}, Y_{i})$ are independent and identically distributed, with common joint distribution bivariate Sarmanov. Such quantities naturally arise in financial risk models. Each $X_{i}$ has a regularly varying tail. With sufficient conditions similar to those used by Denisov and Zwart (2007) imposed on these two sequences, and with certain suitably summable bounds similar to those proposed by Hazra and Maulik (2012), we explore the tail distribution of the random variabl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.04637","kind":"arxiv","version":3},"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":"2026-05-18T00:36:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y+6dy+jMjGgoBm1Q2svlUo8FplqQLrIpFZCd06z0DZX1YLhYfrr4QO6zPZ+P6uS8KGGlxXzKQ35gzA97D/+ICg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T23:44:13.289227Z"},"content_sha256":"493d3094b4901709ef3f8df2ff3e60fe76f918de90cae4b309413cec627c7647","schema_version":"1.0","event_id":"sha256:493d3094b4901709ef3f8df2ff3e60fe76f918de90cae4b309413cec627c7647"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HHGU3NM2L57UZWFCDCD5UJ4XT6/bundle.json","state_url":"https://pith.science/pith/HHGU3NM2L57UZWFCDCD5UJ4XT6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HHGU3NM2L57UZWFCDCD5UJ4XT6/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":"2026-05-26T23:44:13Z","links":{"resolver":"https://pith.science/pith/HHGU3NM2L57UZWFCDCD5UJ4XT6","bundle":"https://pith.science/pith/HHGU3NM2L57UZWFCDCD5UJ4XT6/bundle.json","state":"https://pith.science/pith/HHGU3NM2L57UZWFCDCD5UJ4XT6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HHGU3NM2L57UZWFCDCD5UJ4XT6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:HHGU3NM2L57UZWFCDCD5UJ4XT6","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":"eddd98adf1985bb79f8223e169e7407578317a58fee846fb162368f060008fd1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-01-18T18:13:17Z","title_canon_sha256":"b975bb0b3b6017da14de6953f117ff2db387e5d9a897c125696871199b9c3e34"},"schema_version":"1.0","source":{"id":"1601.04637","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.04637","created_at":"2026-05-18T00:36:09Z"},{"alias_kind":"arxiv_version","alias_value":"1601.04637v3","created_at":"2026-05-18T00:36:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.04637","created_at":"2026-05-18T00:36:09Z"},{"alias_kind":"pith_short_12","alias_value":"HHGU3NM2L57U","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"HHGU3NM2L57UZWFC","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"HHGU3NM2","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:493d3094b4901709ef3f8df2ff3e60fe76f918de90cae4b309413cec627c7647","target":"graph","created_at":"2026-05-18T00:36:09Z","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":"Our work aims to study the tail behaviour of weighted sums of the form $\\sum_{i=1}^{\\infty} X_{i} \\prod_{j=1}^{i}Y_{j}$, where $(X_{i}, Y_{i})$ are independent and identically distributed, with common joint distribution bivariate Sarmanov. Such quantities naturally arise in financial risk models. Each $X_{i}$ has a regularly varying tail. With sufficient conditions similar to those used by Denisov and Zwart (2007) imposed on these two sequences, and with certain suitably summable bounds similar to those proposed by Hazra and Maulik (2012), we explore the tail distribution of the random variabl","authors_text":"Krishanu Maulik, Moumanti Podder","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-01-18T18:13:17Z","title":"Ruin probabilities under Sarmanov dependence structure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.04637","kind":"arxiv","version":3},"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":"sha256:76e0d1ac935efaf76555b8057766539d7e1b9465917ab985aa1a0df4472f1219","target":"record","created_at":"2026-05-18T00:36:09Z","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":"eddd98adf1985bb79f8223e169e7407578317a58fee846fb162368f060008fd1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-01-18T18:13:17Z","title_canon_sha256":"b975bb0b3b6017da14de6953f117ff2db387e5d9a897c125696871199b9c3e34"},"schema_version":"1.0","source":{"id":"1601.04637","kind":"arxiv","version":3}},"canonical_sha256":"39cd4db59a5f7f4cd8a21887da27979fa74012781ff878993d6a8d4da628b56a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"39cd4db59a5f7f4cd8a21887da27979fa74012781ff878993d6a8d4da628b56a","first_computed_at":"2026-05-18T00:36:09.985341Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:09.985341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c2RsgWcW3h0JqgF66csMuBtLtjjYFQWEuQGTvGji9KwbrC5jLc7bp4x29DE2vSGu3bXnsUtt5ADEQzfYTxOZBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:09.985911Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.04637","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:76e0d1ac935efaf76555b8057766539d7e1b9465917ab985aa1a0df4472f1219","sha256:493d3094b4901709ef3f8df2ff3e60fe76f918de90cae4b309413cec627c7647"],"state_sha256":"deb40e608cf8e7369d096a1118698c6baa13347ada41457c59a79da8d7698f3d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"idymYpgY0H9hDKg3SgBbGnrQuuMaKUEmomHwrAVXvpQ+u/r0uybRjdEAXZ39Qn8tdhijeY//q3U/SZLzCdUwBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T23:44:13.294888Z","bundle_sha256":"21eb5c730205934e8cba446ddebc93dd94237679674f1fd19e12dbc2704c0e66"}}