{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:EQV4IAQXW6NDIX7QBCLTLUIIE3","short_pith_number":"pith:EQV4IAQX","canonical_record":{"source":{"id":"1801.04691","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-01-15T08:07:56Z","cross_cats_sorted":[],"title_canon_sha256":"499e2b157a29724ca4b8111d57ca9979548a91e980298ac87c1213b219ccbf4e","abstract_canon_sha256":"f5a1cb6c0f924f853f34f2eca7d2b1cee6626232549ab2545ae4f6480d8e7888"},"schema_version":"1.0"},"canonical_sha256":"242bc40217b79a345ff0089735d10826fba9a502137b049216e46ac3841c5d40","source":{"kind":"arxiv","id":"1801.04691","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.04691","created_at":"2026-05-17T23:58:54Z"},{"alias_kind":"arxiv_version","alias_value":"1801.04691v2","created_at":"2026-05-17T23:58:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.04691","created_at":"2026-05-17T23:58:54Z"},{"alias_kind":"pith_short_12","alias_value":"EQV4IAQXW6ND","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EQV4IAQXW6NDIX7Q","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EQV4IAQX","created_at":"2026-05-18T12:32:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:EQV4IAQXW6NDIX7QBCLTLUIIE3","target":"record","payload":{"canonical_record":{"source":{"id":"1801.04691","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-01-15T08:07:56Z","cross_cats_sorted":[],"title_canon_sha256":"499e2b157a29724ca4b8111d57ca9979548a91e980298ac87c1213b219ccbf4e","abstract_canon_sha256":"f5a1cb6c0f924f853f34f2eca7d2b1cee6626232549ab2545ae4f6480d8e7888"},"schema_version":"1.0"},"canonical_sha256":"242bc40217b79a345ff0089735d10826fba9a502137b049216e46ac3841c5d40","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:54.555622Z","signature_b64":"mUtfTzdwdmy+ToDjm9dmo+fdANXGLm3ehq9UfETq3FAjMyN3ZvxeTIrZ5CtPZrEO8agZc+b07gI8RxkuV7aHCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"242bc40217b79a345ff0089735d10826fba9a502137b049216e46ac3841c5d40","last_reissued_at":"2026-05-17T23:58:54.555102Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:54.555102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.04691","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:58:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XncVg4QBd0qsjHj35ZbbNTnndixNyTble/48bhm/4BbT2UAEJ+YK0lS4/y0sqmkwKqtInPD2amFFCAavi9BYBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T06:15:21.672101Z"},"content_sha256":"2d800828205c9ae6ecaab79f199af995f3b0f5d801766c1da0bc4ae585ebed3a","schema_version":"1.0","event_id":"sha256:2d800828205c9ae6ecaab79f199af995f3b0f5d801766c1da0bc4ae585ebed3a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:EQV4IAQXW6NDIX7QBCLTLUIIE3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic Correlation Structure of Discounted Incurred But Not Reported Claims under Fractional Poisson Arrival Process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Eric Cheung, Jae-Kyung Woo, Landy Rabehasaina (LMB), Ran Xu","submitted_at":"2018-01-15T08:07:56Z","abstract_excerpt":"This paper studies the joint moments of a compound discounted renewal process observed at different times with each arrival removed from the system after a random delay. This process can be used to describe the aggregate (discounted) Incurred But Not Reported claims in insurance and also the total number of customers in an infinite server queue. It is shown that the joint moments can be obtained recursively in terms of the renewal density, from which the covariance and correlation structures are derived. In particular, the fractional Poisson process defined via the renewal approach is also con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.04691","kind":"arxiv","version":2},"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":"2026-05-17T23:58:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xVWI3A5mxYk4sZXmtQq+JyMlbNMZMPsiuFM15IGQsCjO9Xx9/uwWLgk9thB4gXsLh4vbuPPQk0guRT2GtQ1bDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T06:15:21.672825Z"},"content_sha256":"0cb6a0f99b996e0425c535f89ba3db812576188b7d88d56a02c4b8d1ed5259ae","schema_version":"1.0","event_id":"sha256:0cb6a0f99b996e0425c535f89ba3db812576188b7d88d56a02c4b8d1ed5259ae"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EQV4IAQXW6NDIX7QBCLTLUIIE3/bundle.json","state_url":"https://pith.science/pith/EQV4IAQXW6NDIX7QBCLTLUIIE3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EQV4IAQXW6NDIX7QBCLTLUIIE3/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":"2026-06-09T06:15:21Z","links":{"resolver":"https://pith.science/pith/EQV4IAQXW6NDIX7QBCLTLUIIE3","bundle":"https://pith.science/pith/EQV4IAQXW6NDIX7QBCLTLUIIE3/bundle.json","state":"https://pith.science/pith/EQV4IAQXW6NDIX7QBCLTLUIIE3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EQV4IAQXW6NDIX7QBCLTLUIIE3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:EQV4IAQXW6NDIX7QBCLTLUIIE3","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":"f5a1cb6c0f924f853f34f2eca7d2b1cee6626232549ab2545ae4f6480d8e7888","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-01-15T08:07:56Z","title_canon_sha256":"499e2b157a29724ca4b8111d57ca9979548a91e980298ac87c1213b219ccbf4e"},"schema_version":"1.0","source":{"id":"1801.04691","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.04691","created_at":"2026-05-17T23:58:54Z"},{"alias_kind":"arxiv_version","alias_value":"1801.04691v2","created_at":"2026-05-17T23:58:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.04691","created_at":"2026-05-17T23:58:54Z"},{"alias_kind":"pith_short_12","alias_value":"EQV4IAQXW6ND","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EQV4IAQXW6NDIX7Q","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EQV4IAQX","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:0cb6a0f99b996e0425c535f89ba3db812576188b7d88d56a02c4b8d1ed5259ae","target":"graph","created_at":"2026-05-17T23:58:54Z","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":"This paper studies the joint moments of a compound discounted renewal process observed at different times with each arrival removed from the system after a random delay. This process can be used to describe the aggregate (discounted) Incurred But Not Reported claims in insurance and also the total number of customers in an infinite server queue. It is shown that the joint moments can be obtained recursively in terms of the renewal density, from which the covariance and correlation structures are derived. In particular, the fractional Poisson process defined via the renewal approach is also con","authors_text":"Eric Cheung, Jae-Kyung Woo, Landy Rabehasaina (LMB), Ran Xu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-01-15T08:07:56Z","title":"Asymptotic Correlation Structure of Discounted Incurred But Not Reported Claims under Fractional Poisson Arrival Process"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.04691","kind":"arxiv","version":2},"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":"sha256:2d800828205c9ae6ecaab79f199af995f3b0f5d801766c1da0bc4ae585ebed3a","target":"record","created_at":"2026-05-17T23:58:54Z","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":"f5a1cb6c0f924f853f34f2eca7d2b1cee6626232549ab2545ae4f6480d8e7888","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-01-15T08:07:56Z","title_canon_sha256":"499e2b157a29724ca4b8111d57ca9979548a91e980298ac87c1213b219ccbf4e"},"schema_version":"1.0","source":{"id":"1801.04691","kind":"arxiv","version":2}},"canonical_sha256":"242bc40217b79a345ff0089735d10826fba9a502137b049216e46ac3841c5d40","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"242bc40217b79a345ff0089735d10826fba9a502137b049216e46ac3841c5d40","first_computed_at":"2026-05-17T23:58:54.555102Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:54.555102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mUtfTzdwdmy+ToDjm9dmo+fdANXGLm3ehq9UfETq3FAjMyN3ZvxeTIrZ5CtPZrEO8agZc+b07gI8RxkuV7aHCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:54.555622Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.04691","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d800828205c9ae6ecaab79f199af995f3b0f5d801766c1da0bc4ae585ebed3a","sha256:0cb6a0f99b996e0425c535f89ba3db812576188b7d88d56a02c4b8d1ed5259ae"],"state_sha256":"5207b5fc28be32e5f1c11d98843444f634ff9957d203761089324d836e837020"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iqjhAZNX8gm4ehgwvz0M4wyLUCjfjgyuykDujR/yhXoX/bUNNcsVrhl+bBun6I0sxAYtT0LElEF+VYq2N7AJCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T06:15:21.676123Z","bundle_sha256":"f96ce9a4ec01da2943a48db21512d127635e41fcdb5203858325c9f5c45759e6"}}