{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:77WSFIZ2DBDZPT6CLLZMOTBW5U","short_pith_number":"pith:77WSFIZ2","canonical_record":{"source":{"id":"1803.03306","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-03-08T21:07:17Z","cross_cats_sorted":[],"title_canon_sha256":"a47f347eec0d659a1e008cef5317497e9d482372b5264c99533070818a9c76c0","abstract_canon_sha256":"3d2970c1c9843ad9617f3632e250d7ad488058a2d14b9302c9ffe3ec2a1132df"},"schema_version":"1.0"},"canonical_sha256":"ffed22a33a184797cfc25af2c74c36ed1df36b1323e170868b6c333d62e8ef1f","source":{"kind":"arxiv","id":"1803.03306","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.03306","created_at":"2026-05-17T23:55:38Z"},{"alias_kind":"arxiv_version","alias_value":"1803.03306v2","created_at":"2026-05-17T23:55:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.03306","created_at":"2026-05-17T23:55:38Z"},{"alias_kind":"pith_short_12","alias_value":"77WSFIZ2DBDZ","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"77WSFIZ2DBDZPT6C","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"77WSFIZ2","created_at":"2026-05-18T12:32:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:77WSFIZ2DBDZPT6CLLZMOTBW5U","target":"record","payload":{"canonical_record":{"source":{"id":"1803.03306","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-03-08T21:07:17Z","cross_cats_sorted":[],"title_canon_sha256":"a47f347eec0d659a1e008cef5317497e9d482372b5264c99533070818a9c76c0","abstract_canon_sha256":"3d2970c1c9843ad9617f3632e250d7ad488058a2d14b9302c9ffe3ec2a1132df"},"schema_version":"1.0"},"canonical_sha256":"ffed22a33a184797cfc25af2c74c36ed1df36b1323e170868b6c333d62e8ef1f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:38.791267Z","signature_b64":"yXvY05wri5VwPdEuCOtNqdqxxUwVTdOy4FLscNdpxr+EVUojoOUtOWt7hclmqUaHpmV/59TiA/+wFZrn0yoyBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ffed22a33a184797cfc25af2c74c36ed1df36b1323e170868b6c333d62e8ef1f","last_reissued_at":"2026-05-17T23:55:38.790676Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:38.790676Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.03306","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":"2026-05-17T23:55:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KKIZj/Qaa+/p2Qr+kQT1Yl9RkGxNJMNCvDqRl+t0nvVwt89EN9z+odqbFyzrA0pfwSuuQBrpxsm7X6u/F09TAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T00:37:17.694083Z"},"content_sha256":"8067e8ddb128e5d787021073e71a1d0622b9e3e42ef8e4841dd743f15bd1dbfd","schema_version":"1.0","event_id":"sha256:8067e8ddb128e5d787021073e71a1d0622b9e3e42ef8e4841dd743f15bd1dbfd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:77WSFIZ2DBDZPT6CLLZMOTBW5U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Join-the-Shortest Queue Diffusion Limit in Halfin-Whitt Regime: Tail Asymptotics and Scaling of Extrema","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Debankur Mukherjee, Sayan Banerjee","submitted_at":"2018-03-08T21:07:17Z","abstract_excerpt":"Consider a system of $N$ parallel single-server queues with unit-exponential service time distribution and a single dispatcher where tasks arrive as a Poisson process of rate $\\lambda(N)$. When a task arrives, the dispatcher assigns it to one of the servers according to the Join-the-Shortest Queue (JSQ) policy. Eschenfeldt and Gamarnik (2015) established that in the Halfin-Whitt regime where $(N-\\lambda(N))/\\sqrt{N}\\to\\beta>0$ as $N\\to\\infty$, appropriately scaled occupancy measure of the system under the JSQ policy converges weakly on any finite time interval to a certain diffusion process as"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.03306","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":"2026-05-17T23:55:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CbMljokqAPCVn1nVQok5xKc1ZiQRkHQS92x/AZIO+5HleaN1QOPstOrKRHsmTMjo2EpR6FcuY3eN7QhKr+y3AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T00:37:17.694708Z"},"content_sha256":"3a96cd09a19eabf68c2dee343ee73fcdd46977b8293d66dbe433a9fe9cf68dbe","schema_version":"1.0","event_id":"sha256:3a96cd09a19eabf68c2dee343ee73fcdd46977b8293d66dbe433a9fe9cf68dbe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/77WSFIZ2DBDZPT6CLLZMOTBW5U/bundle.json","state_url":"https://pith.science/pith/77WSFIZ2DBDZPT6CLLZMOTBW5U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/77WSFIZ2DBDZPT6CLLZMOTBW5U/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":"2026-06-12T00:37:17Z","links":{"resolver":"https://pith.science/pith/77WSFIZ2DBDZPT6CLLZMOTBW5U","bundle":"https://pith.science/pith/77WSFIZ2DBDZPT6CLLZMOTBW5U/bundle.json","state":"https://pith.science/pith/77WSFIZ2DBDZPT6CLLZMOTBW5U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/77WSFIZ2DBDZPT6CLLZMOTBW5U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:77WSFIZ2DBDZPT6CLLZMOTBW5U","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":"3d2970c1c9843ad9617f3632e250d7ad488058a2d14b9302c9ffe3ec2a1132df","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-03-08T21:07:17Z","title_canon_sha256":"a47f347eec0d659a1e008cef5317497e9d482372b5264c99533070818a9c76c0"},"schema_version":"1.0","source":{"id":"1803.03306","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.03306","created_at":"2026-05-17T23:55:38Z"},{"alias_kind":"arxiv_version","alias_value":"1803.03306v2","created_at":"2026-05-17T23:55:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.03306","created_at":"2026-05-17T23:55:38Z"},{"alias_kind":"pith_short_12","alias_value":"77WSFIZ2DBDZ","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"77WSFIZ2DBDZPT6C","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"77WSFIZ2","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:3a96cd09a19eabf68c2dee343ee73fcdd46977b8293d66dbe433a9fe9cf68dbe","target":"graph","created_at":"2026-05-17T23:55:38Z","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":"Consider a system of $N$ parallel single-server queues with unit-exponential service time distribution and a single dispatcher where tasks arrive as a Poisson process of rate $\\lambda(N)$. When a task arrives, the dispatcher assigns it to one of the servers according to the Join-the-Shortest Queue (JSQ) policy. Eschenfeldt and Gamarnik (2015) established that in the Halfin-Whitt regime where $(N-\\lambda(N))/\\sqrt{N}\\to\\beta>0$ as $N\\to\\infty$, appropriately scaled occupancy measure of the system under the JSQ policy converges weakly on any finite time interval to a certain diffusion process as","authors_text":"Debankur Mukherjee, Sayan Banerjee","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-03-08T21:07:17Z","title":"Join-the-Shortest Queue Diffusion Limit in Halfin-Whitt Regime: Tail Asymptotics and Scaling of Extrema"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.03306","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":"sha256:8067e8ddb128e5d787021073e71a1d0622b9e3e42ef8e4841dd743f15bd1dbfd","target":"record","created_at":"2026-05-17T23:55:38Z","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":"3d2970c1c9843ad9617f3632e250d7ad488058a2d14b9302c9ffe3ec2a1132df","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-03-08T21:07:17Z","title_canon_sha256":"a47f347eec0d659a1e008cef5317497e9d482372b5264c99533070818a9c76c0"},"schema_version":"1.0","source":{"id":"1803.03306","kind":"arxiv","version":2}},"canonical_sha256":"ffed22a33a184797cfc25af2c74c36ed1df36b1323e170868b6c333d62e8ef1f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ffed22a33a184797cfc25af2c74c36ed1df36b1323e170868b6c333d62e8ef1f","first_computed_at":"2026-05-17T23:55:38.790676Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:38.790676Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yXvY05wri5VwPdEuCOtNqdqxxUwVTdOy4FLscNdpxr+EVUojoOUtOWt7hclmqUaHpmV/59TiA/+wFZrn0yoyBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:38.791267Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.03306","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8067e8ddb128e5d787021073e71a1d0622b9e3e42ef8e4841dd743f15bd1dbfd","sha256:3a96cd09a19eabf68c2dee343ee73fcdd46977b8293d66dbe433a9fe9cf68dbe"],"state_sha256":"505d6e3206e9065a2b26af869001ad820bc9529d2eb975194ed4d6659ad961a1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kxShByrj/+AKqyIoVFAX3OMqhqKjsibcUXER/jIRj8o54GPo/RM0js7l5vjO1a3agldcqj+33rHXteqmUiu7Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T00:37:17.697229Z","bundle_sha256":"aa862d29e5cd8bbc8ab048ecf1c6abe6f42398aea1672f95560c4a06bee6d104"}}