{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:IREE42FYQCBR3ICY6NBOT6IAJE","short_pith_number":"pith:IREE42FY","canonical_record":{"source":{"id":"1412.5329","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-17T10:52:26Z","cross_cats_sorted":[],"title_canon_sha256":"fb5ccbed38a658e0c0628cd9b4502e2e6307c55e7168ed54782e4ea381cdce7c","abstract_canon_sha256":"d870c29d41d3857d5a5eef2626ce14af967eab51ff1b8a6d69a151100b74af69"},"schema_version":"1.0"},"canonical_sha256":"44484e68b880831da058f342e9f900493a1162f8ea58bbdc4070e7385c110a8a","source":{"kind":"arxiv","id":"1412.5329","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.5329","created_at":"2026-05-18T01:25:47Z"},{"alias_kind":"arxiv_version","alias_value":"1412.5329v2","created_at":"2026-05-18T01:25:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.5329","created_at":"2026-05-18T01:25:47Z"},{"alias_kind":"pith_short_12","alias_value":"IREE42FYQCBR","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"IREE42FYQCBR3ICY","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"IREE42FY","created_at":"2026-05-18T12:28:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:IREE42FYQCBR3ICY6NBOT6IAJE","target":"record","payload":{"canonical_record":{"source":{"id":"1412.5329","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-17T10:52:26Z","cross_cats_sorted":[],"title_canon_sha256":"fb5ccbed38a658e0c0628cd9b4502e2e6307c55e7168ed54782e4ea381cdce7c","abstract_canon_sha256":"d870c29d41d3857d5a5eef2626ce14af967eab51ff1b8a6d69a151100b74af69"},"schema_version":"1.0"},"canonical_sha256":"44484e68b880831da058f342e9f900493a1162f8ea58bbdc4070e7385c110a8a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:47.384792Z","signature_b64":"UoabzNWZgY0Jxfo4QLCOVmUsf2Hipir74mzSfovCgOJxFEGRvpF5ATqjIwN9NeK5k8YWl7VevXkKTX5F15U4Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"44484e68b880831da058f342e9f900493a1162f8ea58bbdc4070e7385c110a8a","last_reissued_at":"2026-05-18T01:25:47.384279Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:47.384279Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.5329","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":"2026-05-18T01:25:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kdPOzf7AUMOBdWHltmOpXVdNYDgxyx1EVatvwxoDifmPFoYqu5tSvpXtL/c67dKPxZ1CeH9FUSSsUhK5ltmcDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T04:01:43.900432Z"},"content_sha256":"af4c8a543b8b3697a4df575cc02db380159a296a2aade5461787b65d0cf8a7a1","schema_version":"1.0","event_id":"sha256:af4c8a543b8b3697a4df575cc02db380159a296a2aade5461787b65d0cf8a7a1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:IREE42FYQCBR3ICY6NBOT6IAJE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Heavy-traffic analysis through uniform acceleration of queues with diminishing populations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Gianmarco Bet, Johan S.H. van Leeuwaarden, Remco van der Hofstad","submitted_at":"2014-12-17T10:52:26Z","abstract_excerpt":"We consider a single server queue that serves a finite population of $n$ customers that will enter the queue (require service) only once, also known as the $\\Delta_{(i)}/G/1$ queue. This paper presents a method for analyzing heavy-traffic behavior by using uniform acceleration, which simultaneously lets $n$ and the service rate grow large, while the initial resource utilization approaches one. A key feature of the model is that, as time progresses, more customers have joined the queue, and fewer customers can potentially join. This diminishing population gives rise to a class of reflected stoc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5329","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":"2026-05-18T01:25:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dfqmLl1aDTePBkMIFE8SnFMD07Jrq7riWTvldIkPjxojYHnW0JjYPW9IdwOcwZaqK9Yb5SG0sHDmgWfl5ZgFCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T04:01:43.900801Z"},"content_sha256":"9fde92bf2efc00589b1aafb144b853d79dfcbc429400d8e642198059f6337953","schema_version":"1.0","event_id":"sha256:9fde92bf2efc00589b1aafb144b853d79dfcbc429400d8e642198059f6337953"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IREE42FYQCBR3ICY6NBOT6IAJE/bundle.json","state_url":"https://pith.science/pith/IREE42FYQCBR3ICY6NBOT6IAJE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IREE42FYQCBR3ICY6NBOT6IAJE/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":"2026-06-01T04:01:43Z","links":{"resolver":"https://pith.science/pith/IREE42FYQCBR3ICY6NBOT6IAJE","bundle":"https://pith.science/pith/IREE42FYQCBR3ICY6NBOT6IAJE/bundle.json","state":"https://pith.science/pith/IREE42FYQCBR3ICY6NBOT6IAJE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IREE42FYQCBR3ICY6NBOT6IAJE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:IREE42FYQCBR3ICY6NBOT6IAJE","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":"d870c29d41d3857d5a5eef2626ce14af967eab51ff1b8a6d69a151100b74af69","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-17T10:52:26Z","title_canon_sha256":"fb5ccbed38a658e0c0628cd9b4502e2e6307c55e7168ed54782e4ea381cdce7c"},"schema_version":"1.0","source":{"id":"1412.5329","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.5329","created_at":"2026-05-18T01:25:47Z"},{"alias_kind":"arxiv_version","alias_value":"1412.5329v2","created_at":"2026-05-18T01:25:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.5329","created_at":"2026-05-18T01:25:47Z"},{"alias_kind":"pith_short_12","alias_value":"IREE42FYQCBR","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"IREE42FYQCBR3ICY","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"IREE42FY","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:9fde92bf2efc00589b1aafb144b853d79dfcbc429400d8e642198059f6337953","target":"graph","created_at":"2026-05-18T01:25:47Z","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":"We consider a single server queue that serves a finite population of $n$ customers that will enter the queue (require service) only once, also known as the $\\Delta_{(i)}/G/1$ queue. This paper presents a method for analyzing heavy-traffic behavior by using uniform acceleration, which simultaneously lets $n$ and the service rate grow large, while the initial resource utilization approaches one. A key feature of the model is that, as time progresses, more customers have joined the queue, and fewer customers can potentially join. This diminishing population gives rise to a class of reflected stoc","authors_text":"Gianmarco Bet, Johan S.H. van Leeuwaarden, Remco van der Hofstad","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-17T10:52:26Z","title":"Heavy-traffic analysis through uniform acceleration of queues with diminishing populations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5329","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:af4c8a543b8b3697a4df575cc02db380159a296a2aade5461787b65d0cf8a7a1","target":"record","created_at":"2026-05-18T01:25:47Z","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":"d870c29d41d3857d5a5eef2626ce14af967eab51ff1b8a6d69a151100b74af69","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-17T10:52:26Z","title_canon_sha256":"fb5ccbed38a658e0c0628cd9b4502e2e6307c55e7168ed54782e4ea381cdce7c"},"schema_version":"1.0","source":{"id":"1412.5329","kind":"arxiv","version":2}},"canonical_sha256":"44484e68b880831da058f342e9f900493a1162f8ea58bbdc4070e7385c110a8a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"44484e68b880831da058f342e9f900493a1162f8ea58bbdc4070e7385c110a8a","first_computed_at":"2026-05-18T01:25:47.384279Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:25:47.384279Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UoabzNWZgY0Jxfo4QLCOVmUsf2Hipir74mzSfovCgOJxFEGRvpF5ATqjIwN9NeK5k8YWl7VevXkKTX5F15U4Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:25:47.384792Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.5329","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:af4c8a543b8b3697a4df575cc02db380159a296a2aade5461787b65d0cf8a7a1","sha256:9fde92bf2efc00589b1aafb144b853d79dfcbc429400d8e642198059f6337953"],"state_sha256":"2e3dc6061a4c31f5b4b26a5d47cd30de6c19322996c02b48698a6bab80890440"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bwx3NUovan69xjE1tBOIdOx6RKVdd65VpajSSRfX2IJpB+ysKlvSGsvA5PBL1pYF9+iXGwLlExH9/CjPP2rdBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T04:01:43.902942Z","bundle_sha256":"198a6729699a4fc6bfcc7e1104811e5a67aa77d7b30aceccaa34e7236dd16aa1"}}