{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:OR3C6H3XFNPK7ZPO6G7XRHJMEX","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":"ce7d756ac55e9f82f7da3bdccaecc80097858268d83476681057ac0cf875a211","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-02-13T00:13:53Z","title_canon_sha256":"e72363879d81a3fbc4a0403b71a0cb490d6c5e6508df597233b181ec0ba7a9e9"},"schema_version":"1.0","source":{"id":"0902.2236","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.2236","created_at":"2026-05-18T02:18:22Z"},{"alias_kind":"arxiv_version","alias_value":"0902.2236v2","created_at":"2026-05-18T02:18:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.2236","created_at":"2026-05-18T02:18:22Z"},{"alias_kind":"pith_short_12","alias_value":"OR3C6H3XFNPK","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"OR3C6H3XFNPK7ZPO","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"OR3C6H3X","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:a47aa1b2083cbbadd1a74406d4679f8782105ab5f09ffbd4e961ceaa16252180","target":"graph","created_at":"2026-05-18T02:18:22Z","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 study the $G/\\mathit{GI}/\\infty$ queue in heavy-traffic using tempered distribution-valued processes which track the age and residual service time of each customer in the system. In both cases, we use the continuous mapping theorem together with functional central limit theorem results in order to obtain fluid and diffusion limits for these processes in the space of tempered distribution-valued processes. We find that our diffusion limits are tempered distribution-valued Ornstein-Uhlenbeck processes.","authors_text":"Josh Reed, Rishi Talreja","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-02-13T00:13:53Z","title":"Distribution-valued heavy-traffic limits for the $G/\\mathit{GI}/\\infty$ queue"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.2236","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":"sha256:4756bf5b7da6b08cfe04370df5388a2cc35a7700343bee2a461fc30a5d76843c","target":"record","created_at":"2026-05-18T02:18:22Z","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":"ce7d756ac55e9f82f7da3bdccaecc80097858268d83476681057ac0cf875a211","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-02-13T00:13:53Z","title_canon_sha256":"e72363879d81a3fbc4a0403b71a0cb490d6c5e6508df597233b181ec0ba7a9e9"},"schema_version":"1.0","source":{"id":"0902.2236","kind":"arxiv","version":2}},"canonical_sha256":"74762f1f772b5eafe5eef1bf789d2c25cd5bf429a229fe56894315aeb84a1136","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"74762f1f772b5eafe5eef1bf789d2c25cd5bf429a229fe56894315aeb84a1136","first_computed_at":"2026-05-18T02:18:22.439837Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:18:22.439837Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1yUKLyGS2LXA1hVkYEEvGh5W5+jdN4n7hPs8j0pz1yR9CvPOIYzTsn/utV95veeD7abaXe6bhmODhTPeMXX7Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:18:22.440465Z","signed_message":"canonical_sha256_bytes"},"source_id":"0902.2236","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4756bf5b7da6b08cfe04370df5388a2cc35a7700343bee2a461fc30a5d76843c","sha256:a47aa1b2083cbbadd1a74406d4679f8782105ab5f09ffbd4e961ceaa16252180"],"state_sha256":"b2a9473c2bed81c29d3fde8a3021f855d0e7a2a3eb3b2db8e373c68010ef6327"}