{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:4EZZVWAJ72LC53OWK3OPX4LR3O","short_pith_number":"pith:4EZZVWAJ","canonical_record":{"source":{"id":"1404.6061","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.PR","submitted_at":"2014-04-24T09:11:59Z","cross_cats_sorted":[],"title_canon_sha256":"c81dd6faa756774dd4d03695965403c0964171fe2c47884e13a83ae8fa350cc5","abstract_canon_sha256":"ace07d72641ab48dbfec1cabadf942115182b208bc0a0363ad090723481c8007"},"schema_version":"1.0"},"canonical_sha256":"e1339ad809fe962eedd656dcfbf171db930300e789ae2a1f4863aaa75116ed05","source":{"kind":"arxiv","id":"1404.6061","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.6061","created_at":"2026-05-18T02:53:18Z"},{"alias_kind":"arxiv_version","alias_value":"1404.6061v1","created_at":"2026-05-18T02:53:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.6061","created_at":"2026-05-18T02:53:18Z"},{"alias_kind":"pith_short_12","alias_value":"4EZZVWAJ72LC","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"4EZZVWAJ72LC53OW","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"4EZZVWAJ","created_at":"2026-05-18T12:28:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:4EZZVWAJ72LC53OWK3OPX4LR3O","target":"record","payload":{"canonical_record":{"source":{"id":"1404.6061","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.PR","submitted_at":"2014-04-24T09:11:59Z","cross_cats_sorted":[],"title_canon_sha256":"c81dd6faa756774dd4d03695965403c0964171fe2c47884e13a83ae8fa350cc5","abstract_canon_sha256":"ace07d72641ab48dbfec1cabadf942115182b208bc0a0363ad090723481c8007"},"schema_version":"1.0"},"canonical_sha256":"e1339ad809fe962eedd656dcfbf171db930300e789ae2a1f4863aaa75116ed05","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:53:18.479342Z","signature_b64":"zvLNFlwWWhssTclhUQkHW9um2IOOk9M44DPzVn7t6IXAKhbkODt2cDSu9EwXrOyJPqW8yUWRk85FXTfwQ3AQDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e1339ad809fe962eedd656dcfbf171db930300e789ae2a1f4863aaa75116ed05","last_reissued_at":"2026-05-18T02:53:18.478638Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:53:18.478638Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.6061","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":"2026-05-18T02:53:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GSfU3q4Wg/wpfU6rw7aVkkHEs9hpbX19e5btzalLx6+RDpH5/w/8UvuI+AFTpYtAVPv5oSvYtJZ7z9oqcR15Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T20:58:15.326614Z"},"content_sha256":"35feefa1908669c0ccac614ddad993af5c597ecd2798e80672d09430366524cf","schema_version":"1.0","event_id":"sha256:35feefa1908669c0ccac614ddad993af5c597ecd2798e80672d09430366524cf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:4EZZVWAJ72LC53OWK3OPX4LR3O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the accuracy of phase-type approximations of heavy-tailed risk models","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Bert Zwart, Eleni Vatamidou, Ivo J.B.F. Adan, Maria Vlasiou","submitted_at":"2014-04-24T09:11:59Z","abstract_excerpt":"Numerical evaluation of ruin probabilities in the classical risk model is an important problem. If claim sizes are heavy-tailed, then such evaluations are challenging. To overcome this, an attractive way is to approximate the claim sizes with a phase-type distribution. What is not clear though is how many phases are enough in order to achieve a specific accuracy in the approximation of the ruin probability. The goals of this paper are to investigate the number of phases required so that we can achieve a pre-specified accuracy for the ruin probability and to provide error bounds. Also, in the s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.6061","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":"2026-05-18T02:53:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l3d8HOkTkhjua/HW+Ke7973DVGZ/F8a84dV2MA4invCTVe98Q1WO4soFca/OmsSqEiLug9yNaM57nVbm+glIBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T20:58:15.327749Z"},"content_sha256":"b62edba543cd2a285f17783d7b3587a271dae67886e1dcf37af32d10a70565c0","schema_version":"1.0","event_id":"sha256:b62edba543cd2a285f17783d7b3587a271dae67886e1dcf37af32d10a70565c0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4EZZVWAJ72LC53OWK3OPX4LR3O/bundle.json","state_url":"https://pith.science/pith/4EZZVWAJ72LC53OWK3OPX4LR3O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4EZZVWAJ72LC53OWK3OPX4LR3O/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":"2026-05-24T20:58:15Z","links":{"resolver":"https://pith.science/pith/4EZZVWAJ72LC53OWK3OPX4LR3O","bundle":"https://pith.science/pith/4EZZVWAJ72LC53OWK3OPX4LR3O/bundle.json","state":"https://pith.science/pith/4EZZVWAJ72LC53OWK3OPX4LR3O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4EZZVWAJ72LC53OWK3OPX4LR3O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:4EZZVWAJ72LC53OWK3OPX4LR3O","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":"ace07d72641ab48dbfec1cabadf942115182b208bc0a0363ad090723481c8007","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.PR","submitted_at":"2014-04-24T09:11:59Z","title_canon_sha256":"c81dd6faa756774dd4d03695965403c0964171fe2c47884e13a83ae8fa350cc5"},"schema_version":"1.0","source":{"id":"1404.6061","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.6061","created_at":"2026-05-18T02:53:18Z"},{"alias_kind":"arxiv_version","alias_value":"1404.6061v1","created_at":"2026-05-18T02:53:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.6061","created_at":"2026-05-18T02:53:18Z"},{"alias_kind":"pith_short_12","alias_value":"4EZZVWAJ72LC","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"4EZZVWAJ72LC53OW","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"4EZZVWAJ","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:b62edba543cd2a285f17783d7b3587a271dae67886e1dcf37af32d10a70565c0","target":"graph","created_at":"2026-05-18T02:53:18Z","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":"Numerical evaluation of ruin probabilities in the classical risk model is an important problem. If claim sizes are heavy-tailed, then such evaluations are challenging. To overcome this, an attractive way is to approximate the claim sizes with a phase-type distribution. What is not clear though is how many phases are enough in order to achieve a specific accuracy in the approximation of the ruin probability. The goals of this paper are to investigate the number of phases required so that we can achieve a pre-specified accuracy for the ruin probability and to provide error bounds. Also, in the s","authors_text":"Bert Zwart, Eleni Vatamidou, Ivo J.B.F. Adan, Maria Vlasiou","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.PR","submitted_at":"2014-04-24T09:11:59Z","title":"On the accuracy of phase-type approximations of heavy-tailed risk models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.6061","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":"sha256:35feefa1908669c0ccac614ddad993af5c597ecd2798e80672d09430366524cf","target":"record","created_at":"2026-05-18T02:53:18Z","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":"ace07d72641ab48dbfec1cabadf942115182b208bc0a0363ad090723481c8007","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.PR","submitted_at":"2014-04-24T09:11:59Z","title_canon_sha256":"c81dd6faa756774dd4d03695965403c0964171fe2c47884e13a83ae8fa350cc5"},"schema_version":"1.0","source":{"id":"1404.6061","kind":"arxiv","version":1}},"canonical_sha256":"e1339ad809fe962eedd656dcfbf171db930300e789ae2a1f4863aaa75116ed05","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e1339ad809fe962eedd656dcfbf171db930300e789ae2a1f4863aaa75116ed05","first_computed_at":"2026-05-18T02:53:18.478638Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:53:18.478638Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zvLNFlwWWhssTclhUQkHW9um2IOOk9M44DPzVn7t6IXAKhbkODt2cDSu9EwXrOyJPqW8yUWRk85FXTfwQ3AQDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:53:18.479342Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.6061","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:35feefa1908669c0ccac614ddad993af5c597ecd2798e80672d09430366524cf","sha256:b62edba543cd2a285f17783d7b3587a271dae67886e1dcf37af32d10a70565c0"],"state_sha256":"19d301d17b8a77289e5b55160e27fc9fc8cc5ae2d74e55cf1a1b9c59e2182f0a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kdoEhLjTLw1lo6LyFS+0qRqy/QgFGl1BZO6fkHJxsTuivQW+7rDLhk8OS45WQlWxeSqEE4yKyzU9HuU4/4FvAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T20:58:15.331198Z","bundle_sha256":"28e1e6f52722446a643424fd96285a8bd7ada82b9533d0044a396f5c49e01c6d"}}