{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:MTE3W3O5L3H24ML6VOP3HHEKCX","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":"5ac1c480f0e8ab7248ffdd61fc1750509df04472f4dc99389665ac5ca00af4cb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-06T05:20:45Z","title_canon_sha256":"ec8aa2e5e30e38676d4fd9c46808d833780978a924c312517fb7316d2247a3ab"},"schema_version":"1.0","source":{"id":"1704.01709","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.01709","created_at":"2026-05-18T00:46:54Z"},{"alias_kind":"arxiv_version","alias_value":"1704.01709v1","created_at":"2026-05-18T00:46:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.01709","created_at":"2026-05-18T00:46:54Z"},{"alias_kind":"pith_short_12","alias_value":"MTE3W3O5L3H2","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MTE3W3O5L3H24ML6","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MTE3W3O5","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:13e4d6ce4dff446d2c038d5bf151dcb6c4c9e8e02657c5a7ef18ca305eff9ede","target":"graph","created_at":"2026-05-18T00:46:54Z","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 focuses on the problem of modeling the correspondence pattern for ordinary people. Suppose that letters arrive at a rate $\\lambda$ and are answered at a rate $\\mu$. Furthermore, we assume that, for a constant $T$, a letter is disregarded when its waiting time exceeds $T$, and the remains are answered in {\\it last in first out} order. Let $W_n$ be the waiting time of the $n$-th {\\it answered} letter. It is proved that $W_n$ converges weekly to $W_T$, a non-negative random variable which possesses a density with {\\it power-law} tail when $\\lambda=\\mu$ and with exponential tail otherwi","authors_text":"Feng Wang, Xian-Yuan Wu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-06T05:20:45Z","title":"On The Waiting Time for A M/M/1 Queue with Impatience"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.01709","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:d8a60d1359369e2ccc257ad0c37a1708412e8ef0c09058e36f702f56ac29cd5c","target":"record","created_at":"2026-05-18T00:46:54Z","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":"5ac1c480f0e8ab7248ffdd61fc1750509df04472f4dc99389665ac5ca00af4cb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-06T05:20:45Z","title_canon_sha256":"ec8aa2e5e30e38676d4fd9c46808d833780978a924c312517fb7316d2247a3ab"},"schema_version":"1.0","source":{"id":"1704.01709","kind":"arxiv","version":1}},"canonical_sha256":"64c9bb6ddd5ecfae317eab9fb39c8a15ce8a534b46c30e1d1527038e3c7a059f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"64c9bb6ddd5ecfae317eab9fb39c8a15ce8a534b46c30e1d1527038e3c7a059f","first_computed_at":"2026-05-18T00:46:54.510698Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:54.510698Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NPkmLBKWKUHBAXvJwE8Z+r2GIrX6x6Cl4O7RZFPbzK1jxyH/7TtQZbzpj5lHWqYZyeozZW0UHtxOUnbVzIUtCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:54.511169Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.01709","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d8a60d1359369e2ccc257ad0c37a1708412e8ef0c09058e36f702f56ac29cd5c","sha256:13e4d6ce4dff446d2c038d5bf151dcb6c4c9e8e02657c5a7ef18ca305eff9ede"],"state_sha256":"30c58c134f6067284b73593f89782bd6d8754e3c819feabec0067dcdc27159ec"}