{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:EBZANJUGOFCTG3DBTMLJVJWAHW","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":"7effba4b4ffdd40a3f5a579c3cb0e3631245f4e442edd6936a38d515a8ac7d54","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-26T14:10:51Z","title_canon_sha256":"433d9fabc9a80823259b325e5b4c84b67bfa74ff077433fab1589123cfb43a57"},"schema_version":"1.0","source":{"id":"1201.5523","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.5523","created_at":"2026-05-18T04:03:46Z"},{"alias_kind":"arxiv_version","alias_value":"1201.5523v1","created_at":"2026-05-18T04:03:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.5523","created_at":"2026-05-18T04:03:46Z"},{"alias_kind":"pith_short_12","alias_value":"EBZANJUGOFCT","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"EBZANJUGOFCTG3DB","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"EBZANJUG","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:68105c23a0732d4abb6fce0531cef6402cc6cf9db0924027a0114c180ae03eea","target":"graph","created_at":"2026-05-18T04:03:46Z","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":"In the supermarket model, there are $n$ queues, each with a single server. Customers arrive in a Poisson process with arrival rate $\\lambda n$, where $\\lambda = \\lambda (n) \\in (0,1)$. Upon arrival, a customer selects $d=d(n)$ servers uniformly at random, and joins the queue of a least-loaded server amongst those chosen. Service times are independent exponentially distributed random variables with mean~1. In this paper, we analyse the behaviour of the supermarket model in a regime where $\\lambda(n)$ tends to~1, and $d(n)$ tends to infinity, as $n \\to \\infty$. For suitable triples $(n,d,\\lambda","authors_text":"Graham Brightwell, Malwina Luczak","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-26T14:10:51Z","title":"The supermarket model with arrival rate tending to one"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.5523","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:e054137725de8ece2dc8a57a0e65d42fb74cec44202c14d4e3308fa7490fb9f1","target":"record","created_at":"2026-05-18T04:03:46Z","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":"7effba4b4ffdd40a3f5a579c3cb0e3631245f4e442edd6936a38d515a8ac7d54","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-26T14:10:51Z","title_canon_sha256":"433d9fabc9a80823259b325e5b4c84b67bfa74ff077433fab1589123cfb43a57"},"schema_version":"1.0","source":{"id":"1201.5523","kind":"arxiv","version":1}},"canonical_sha256":"207206a6867145336c619b169aa6c03d87e26a7b831fef946bbb35ba46d5d798","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"207206a6867145336c619b169aa6c03d87e26a7b831fef946bbb35ba46d5d798","first_computed_at":"2026-05-18T04:03:46.038218Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:03:46.038218Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QZu7UltOxsUGew6Cfk8zi8YTxKhRw6ZljShsP81NQBkLwpLwyFWZkXQVlW7q1sxqmlj+3klAx+DS5bTGpyKvDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:03:46.038725Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.5523","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e054137725de8ece2dc8a57a0e65d42fb74cec44202c14d4e3308fa7490fb9f1","sha256:68105c23a0732d4abb6fce0531cef6402cc6cf9db0924027a0114c180ae03eea"],"state_sha256":"1827f0cee4c8e8cf268e2651c86c9982c60f4554d35774821c3707129a2340dc"}