{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:2IHRC4K4BEL4QNBZKWEWYPTDNP","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":"8faf8eb8c25d7032a07b304872a6c727164c55178234a05036496c060bad9c92","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-03-21T16:07:54Z","title_canon_sha256":"d17d0afa39797a08f7e5dfb2e23e1e60acf5360a66b249327b67030fa3ad35d4"},"schema_version":"1.0","source":{"id":"1103.4064","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.4064","created_at":"2026-05-18T04:26:21Z"},{"alias_kind":"arxiv_version","alias_value":"1103.4064v1","created_at":"2026-05-18T04:26:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.4064","created_at":"2026-05-18T04:26:21Z"},{"alias_kind":"pith_short_12","alias_value":"2IHRC4K4BEL4","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"2IHRC4K4BEL4QNBZ","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"2IHRC4K4","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:8db9588be84917b7138dafdf586f80a5f23ff034ad7deb23ec2ed7c62bcd0ae4","target":"graph","created_at":"2026-05-18T04:26:21Z","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 two-sided exit problem is solved for a difference of a compound Poisson process and a compound renewal process. More precisely, the Laplace transforms of the joint distribution of the first exit time, the value of the overshoot and the value of a linear component at this instant are found. Further, we study the process reflected in its supremum. We determine the main two-boundary characteristics of the process reflected in its supremum. These results are then applied for studying the $ M^{\\varkappa}|G^{\\delta}|1|B$ system. We derive the distribution of a busy period and the numbers of custom","authors_text":"Noel Veraverbeke, Tetyana Kadankova, Victor Kadankov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-03-21T16:07:54Z","title":"Busy period, time of the first loss of a customer and the number of customers in $ M^{\\varkappa}|G^{\\delta}|1|B$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.4064","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:a38f92592e042065064c6ab6747d6e19f0297ca5fd2fa8428685574157d41461","target":"record","created_at":"2026-05-18T04:26:21Z","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":"8faf8eb8c25d7032a07b304872a6c727164c55178234a05036496c060bad9c92","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-03-21T16:07:54Z","title_canon_sha256":"d17d0afa39797a08f7e5dfb2e23e1e60acf5360a66b249327b67030fa3ad35d4"},"schema_version":"1.0","source":{"id":"1103.4064","kind":"arxiv","version":1}},"canonical_sha256":"d20f11715c0917c8343955896c3e636bceaac5355ef3edb0c3eacefb1e493edd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d20f11715c0917c8343955896c3e636bceaac5355ef3edb0c3eacefb1e493edd","first_computed_at":"2026-05-18T04:26:21.889900Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:26:21.889900Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CmmlbjuNqqU97NGtMISr8fUD3x2r8HkIbBSaeXOJuYgvqlsE81Tk1qr1VXsf3jGUlusx1TmsG8kHuHa7g24dDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:26:21.890446Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.4064","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a38f92592e042065064c6ab6747d6e19f0297ca5fd2fa8428685574157d41461","sha256:8db9588be84917b7138dafdf586f80a5f23ff034ad7deb23ec2ed7c62bcd0ae4"],"state_sha256":"c25a8d30020519b8def35230fdc42ae85361ceecb3be9ac00ae62864765c4b2c"}