{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:6ZHWZBKCKBQ7WONIMN427DVERL","short_pith_number":"pith:6ZHWZBKC","canonical_record":{"source":{"id":"1308.5318","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-08-24T11:34:29Z","cross_cats_sorted":[],"title_canon_sha256":"8d647fb84663b093213fd698646e0a8a7d3bc45bc6e9a0d27e531358abfcec80","abstract_canon_sha256":"959c21ed2928da63cac4ca20b94861ace9d5cfb5ec1338c8ebf0a91a71c52d10"},"schema_version":"1.0"},"canonical_sha256":"f64f6c85425061fb39a86379af8ea48af719bff12fa9fb326196bceef42169bb","source":{"kind":"arxiv","id":"1308.5318","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.5318","created_at":"2026-05-18T03:15:05Z"},{"alias_kind":"arxiv_version","alias_value":"1308.5318v1","created_at":"2026-05-18T03:15:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.5318","created_at":"2026-05-18T03:15:05Z"},{"alias_kind":"pith_short_12","alias_value":"6ZHWZBKCKBQ7","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6ZHWZBKCKBQ7WONI","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6ZHWZBKC","created_at":"2026-05-18T12:27:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:6ZHWZBKCKBQ7WONIMN427DVERL","target":"record","payload":{"canonical_record":{"source":{"id":"1308.5318","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-08-24T11:34:29Z","cross_cats_sorted":[],"title_canon_sha256":"8d647fb84663b093213fd698646e0a8a7d3bc45bc6e9a0d27e531358abfcec80","abstract_canon_sha256":"959c21ed2928da63cac4ca20b94861ace9d5cfb5ec1338c8ebf0a91a71c52d10"},"schema_version":"1.0"},"canonical_sha256":"f64f6c85425061fb39a86379af8ea48af719bff12fa9fb326196bceef42169bb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:15:05.213546Z","signature_b64":"Q9o9W1la4hZJp+OeI+02uKsDp2T72GTkx+WVaJ94OxbzA5xFlYOiqiJzCFk50WV+3YfAHS8yZvBE4cny0bMIDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f64f6c85425061fb39a86379af8ea48af719bff12fa9fb326196bceef42169bb","last_reissued_at":"2026-05-18T03:15:05.212618Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:15:05.212618Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.5318","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:15:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"13ts4nTwribvCP22wMSTettpYgGMpvksq7hqq9lGACMSOc0FgnMixXSH18pFK0CeU4/gpZ8bVrkCYV2DpxRRDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T16:07:07.688575Z"},"content_sha256":"26a3c3c3fdf2d0dc0a919a83a5fff0b300287a1f374fae35c98367d78acbb751","schema_version":"1.0","event_id":"sha256:26a3c3c3fdf2d0dc0a919a83a5fff0b300287a1f374fae35c98367d78acbb751"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:6ZHWZBKCKBQ7WONIMN427DVERL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convergence to Equilibrium States for Fluid Models of Many-server Queues with Abandonment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jiheng Zhang, Zhenghua Long","submitted_at":"2013-08-24T11:34:29Z","abstract_excerpt":"Fluid models have become an important tool for the study of many-server queues with general service and patience time distributions. The equilibrium state of a fluid model has been revealed by Whitt (2006) and shown to yield reasonable approximations to the steady state of the original stochastic systems. However, it remains an open question whether the solution to a fluid model converges to the equilibrium state and under what condition. We show in this paper that the convergence holds under a mild condition. Our method builds on the framework of measure-valued processes developed in Zhang (2"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.5318","kind":"arxiv","version":1},"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":"2026-05-18T03:15:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UZE15vZudzL9ppjWDaX50RwfK53koTx6Myi28cQOieYX62y4U+WUrunmK/1AFLIyHBTPN64/Q8N3pKdj8ghPBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T16:07:07.688909Z"},"content_sha256":"8c6fb75be671ad7f6a9421da8a925e7771ef2d311c984bae4ebdfb7049e38785","schema_version":"1.0","event_id":"sha256:8c6fb75be671ad7f6a9421da8a925e7771ef2d311c984bae4ebdfb7049e38785"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6ZHWZBKCKBQ7WONIMN427DVERL/bundle.json","state_url":"https://pith.science/pith/6ZHWZBKCKBQ7WONIMN427DVERL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6ZHWZBKCKBQ7WONIMN427DVERL/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":"2026-06-03T16:07:07Z","links":{"resolver":"https://pith.science/pith/6ZHWZBKCKBQ7WONIMN427DVERL","bundle":"https://pith.science/pith/6ZHWZBKCKBQ7WONIMN427DVERL/bundle.json","state":"https://pith.science/pith/6ZHWZBKCKBQ7WONIMN427DVERL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6ZHWZBKCKBQ7WONIMN427DVERL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:6ZHWZBKCKBQ7WONIMN427DVERL","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":"959c21ed2928da63cac4ca20b94861ace9d5cfb5ec1338c8ebf0a91a71c52d10","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-08-24T11:34:29Z","title_canon_sha256":"8d647fb84663b093213fd698646e0a8a7d3bc45bc6e9a0d27e531358abfcec80"},"schema_version":"1.0","source":{"id":"1308.5318","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.5318","created_at":"2026-05-18T03:15:05Z"},{"alias_kind":"arxiv_version","alias_value":"1308.5318v1","created_at":"2026-05-18T03:15:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.5318","created_at":"2026-05-18T03:15:05Z"},{"alias_kind":"pith_short_12","alias_value":"6ZHWZBKCKBQ7","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6ZHWZBKCKBQ7WONI","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6ZHWZBKC","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:8c6fb75be671ad7f6a9421da8a925e7771ef2d311c984bae4ebdfb7049e38785","target":"graph","created_at":"2026-05-18T03:15:05Z","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":"Fluid models have become an important tool for the study of many-server queues with general service and patience time distributions. The equilibrium state of a fluid model has been revealed by Whitt (2006) and shown to yield reasonable approximations to the steady state of the original stochastic systems. However, it remains an open question whether the solution to a fluid model converges to the equilibrium state and under what condition. We show in this paper that the convergence holds under a mild condition. Our method builds on the framework of measure-valued processes developed in Zhang (2","authors_text":"Jiheng Zhang, Zhenghua Long","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-08-24T11:34:29Z","title":"Convergence to Equilibrium States for Fluid Models of Many-server Queues with Abandonment"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.5318","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":"sha256:26a3c3c3fdf2d0dc0a919a83a5fff0b300287a1f374fae35c98367d78acbb751","target":"record","created_at":"2026-05-18T03:15:05Z","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":"959c21ed2928da63cac4ca20b94861ace9d5cfb5ec1338c8ebf0a91a71c52d10","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-08-24T11:34:29Z","title_canon_sha256":"8d647fb84663b093213fd698646e0a8a7d3bc45bc6e9a0d27e531358abfcec80"},"schema_version":"1.0","source":{"id":"1308.5318","kind":"arxiv","version":1}},"canonical_sha256":"f64f6c85425061fb39a86379af8ea48af719bff12fa9fb326196bceef42169bb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f64f6c85425061fb39a86379af8ea48af719bff12fa9fb326196bceef42169bb","first_computed_at":"2026-05-18T03:15:05.212618Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:15:05.212618Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Q9o9W1la4hZJp+OeI+02uKsDp2T72GTkx+WVaJ94OxbzA5xFlYOiqiJzCFk50WV+3YfAHS8yZvBE4cny0bMIDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:15:05.213546Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.5318","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:26a3c3c3fdf2d0dc0a919a83a5fff0b300287a1f374fae35c98367d78acbb751","sha256:8c6fb75be671ad7f6a9421da8a925e7771ef2d311c984bae4ebdfb7049e38785"],"state_sha256":"70b78cca300715f7262d12057f8959f4df4b93a7c4cf41786741d753621207f1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PNx6eHlOsiAVEVdAAOkyYBLFdmEcmXC/jopUd5GnizpFIWQ7RpfZgqQCr587o+BOuK8Wd1fXl2JGpb0+vLkDCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T16:07:07.690691Z","bundle_sha256":"2b2094f42f16dda3ed2ed5bdd23b1f5e4f70b7062abdee5a417f934bbb3b94eb"}}