{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:IHAAHFWOW7XODWM5KMB5AGBY3K","short_pith_number":"pith:IHAAHFWO","canonical_record":{"source":{"id":"1106.4582","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-06-22T21:11:49Z","cross_cats_sorted":["cs.DC","cs.PF"],"title_canon_sha256":"2fb9ce175212c0ba9f048fb8bdb1765eca9be913608a40db457fb0adb17c499d","abstract_canon_sha256":"999eb55e26aaf2fd2f1eb816302f10270cc00764ab43a15b80f894deed4bd0ef"},"schema_version":"1.0"},"canonical_sha256":"41c00396ceb7eee1d99d5303d01838dabd1a2238d4d29bbd07991e703d68f771","source":{"kind":"arxiv","id":"1106.4582","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.4582","created_at":"2026-05-18T03:13:56Z"},{"alias_kind":"arxiv_version","alias_value":"1106.4582v2","created_at":"2026-05-18T03:13:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.4582","created_at":"2026-05-18T03:13:56Z"},{"alias_kind":"pith_short_12","alias_value":"IHAAHFWOW7XO","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"IHAAHFWOW7XODWM5","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"IHAAHFWO","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:IHAAHFWOW7XODWM5KMB5AGBY3K","target":"record","payload":{"canonical_record":{"source":{"id":"1106.4582","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-06-22T21:11:49Z","cross_cats_sorted":["cs.DC","cs.PF"],"title_canon_sha256":"2fb9ce175212c0ba9f048fb8bdb1765eca9be913608a40db457fb0adb17c499d","abstract_canon_sha256":"999eb55e26aaf2fd2f1eb816302f10270cc00764ab43a15b80f894deed4bd0ef"},"schema_version":"1.0"},"canonical_sha256":"41c00396ceb7eee1d99d5303d01838dabd1a2238d4d29bbd07991e703d68f771","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:13:56.483079Z","signature_b64":"1DTRhMTYhETjer4xRUOnjh/iW+N6K+k6Dz6o5vTV0D7WDaaoZ7itID2/mlGGqsRSi5g6KDLVz/QxrekwvGahDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"41c00396ceb7eee1d99d5303d01838dabd1a2238d4d29bbd07991e703d68f771","last_reissued_at":"2026-05-18T03:13:56.482388Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:13:56.482388Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1106.4582","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":"2026-05-18T03:13:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nbr2iArAi4A96vBRifUsJnWxfg4NIF1yivuz9tQJOfcSD5+mLA3aJgbTExdAInVXAeK+3/0Wvr4OO4bmHI6yBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T11:02:13.194812Z"},"content_sha256":"a4ed2e25d0937a7ae3b76bc0b1318016a624ea146bc81724ba4d02d11dfcd463","schema_version":"1.0","event_id":"sha256:a4ed2e25d0937a7ae3b76bc0b1318016a624ea146bc81724ba4d02d11dfcd463"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:IHAAHFWOW7XODWM5KMB5AGBY3K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Decay of tails at equilibrium for FIFO join the shortest queue networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DC","cs.PF"],"primary_cat":"math.PR","authors_text":"Balaji Prabhakar, Maury Bramson, Yi Lu","submitted_at":"2011-06-22T21:11:49Z","abstract_excerpt":"In join the shortest queue networks, incoming jobs are assigned to the shortest queue from among a randomly chosen subset of $D$ queues, in a system of $N$ queues; after completion of service at its queue, a job leaves the network. We also assume that jobs arrive into the system according to a rate-$\\alpha N$ Poisson process, $\\alpha<1$, with rate-1 service at each queue. When the service at queues is exponentially distributed, it was shown in Vvedenskaya et al. [Probl. Inf. Transm. 32 (1996) 15-29] that the tail of the equilibrium queue size decays doubly exponentially in the limit as $N\\righ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.4582","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":"2026-05-18T03:13:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"krpqvj6rnii2tDeAMfpgjztFdoj6yNr8Ty1B2KPhmAYwncu7QOtGUI9sbHBdDhS7NeF8CsWXSr19mZbcyZHZCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T11:02:13.195458Z"},"content_sha256":"0e15cf23436cfee321687b8aec372be7663435f046d640fdd055731421056b67","schema_version":"1.0","event_id":"sha256:0e15cf23436cfee321687b8aec372be7663435f046d640fdd055731421056b67"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IHAAHFWOW7XODWM5KMB5AGBY3K/bundle.json","state_url":"https://pith.science/pith/IHAAHFWOW7XODWM5KMB5AGBY3K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IHAAHFWOW7XODWM5KMB5AGBY3K/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":"2026-05-30T11:02:13Z","links":{"resolver":"https://pith.science/pith/IHAAHFWOW7XODWM5KMB5AGBY3K","bundle":"https://pith.science/pith/IHAAHFWOW7XODWM5KMB5AGBY3K/bundle.json","state":"https://pith.science/pith/IHAAHFWOW7XODWM5KMB5AGBY3K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IHAAHFWOW7XODWM5KMB5AGBY3K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:IHAAHFWOW7XODWM5KMB5AGBY3K","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":"999eb55e26aaf2fd2f1eb816302f10270cc00764ab43a15b80f894deed4bd0ef","cross_cats_sorted":["cs.DC","cs.PF"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-06-22T21:11:49Z","title_canon_sha256":"2fb9ce175212c0ba9f048fb8bdb1765eca9be913608a40db457fb0adb17c499d"},"schema_version":"1.0","source":{"id":"1106.4582","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.4582","created_at":"2026-05-18T03:13:56Z"},{"alias_kind":"arxiv_version","alias_value":"1106.4582v2","created_at":"2026-05-18T03:13:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.4582","created_at":"2026-05-18T03:13:56Z"},{"alias_kind":"pith_short_12","alias_value":"IHAAHFWOW7XO","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"IHAAHFWOW7XODWM5","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"IHAAHFWO","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:0e15cf23436cfee321687b8aec372be7663435f046d640fdd055731421056b67","target":"graph","created_at":"2026-05-18T03:13:56Z","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 join the shortest queue networks, incoming jobs are assigned to the shortest queue from among a randomly chosen subset of $D$ queues, in a system of $N$ queues; after completion of service at its queue, a job leaves the network. We also assume that jobs arrive into the system according to a rate-$\\alpha N$ Poisson process, $\\alpha<1$, with rate-1 service at each queue. When the service at queues is exponentially distributed, it was shown in Vvedenskaya et al. [Probl. Inf. Transm. 32 (1996) 15-29] that the tail of the equilibrium queue size decays doubly exponentially in the limit as $N\\righ","authors_text":"Balaji Prabhakar, Maury Bramson, Yi Lu","cross_cats":["cs.DC","cs.PF"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-06-22T21:11:49Z","title":"Decay of tails at equilibrium for FIFO join the shortest queue networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.4582","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:a4ed2e25d0937a7ae3b76bc0b1318016a624ea146bc81724ba4d02d11dfcd463","target":"record","created_at":"2026-05-18T03:13:56Z","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":"999eb55e26aaf2fd2f1eb816302f10270cc00764ab43a15b80f894deed4bd0ef","cross_cats_sorted":["cs.DC","cs.PF"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-06-22T21:11:49Z","title_canon_sha256":"2fb9ce175212c0ba9f048fb8bdb1765eca9be913608a40db457fb0adb17c499d"},"schema_version":"1.0","source":{"id":"1106.4582","kind":"arxiv","version":2}},"canonical_sha256":"41c00396ceb7eee1d99d5303d01838dabd1a2238d4d29bbd07991e703d68f771","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"41c00396ceb7eee1d99d5303d01838dabd1a2238d4d29bbd07991e703d68f771","first_computed_at":"2026-05-18T03:13:56.482388Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:13:56.482388Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1DTRhMTYhETjer4xRUOnjh/iW+N6K+k6Dz6o5vTV0D7WDaaoZ7itID2/mlGGqsRSi5g6KDLVz/QxrekwvGahDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:13:56.483079Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.4582","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a4ed2e25d0937a7ae3b76bc0b1318016a624ea146bc81724ba4d02d11dfcd463","sha256:0e15cf23436cfee321687b8aec372be7663435f046d640fdd055731421056b67"],"state_sha256":"bba828f358880ff8a6b21a7b62d9f731328006d008d827a4128c4d030ce5ff0e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J6tENaXDBZRsAx/m1wq/hrlwKrbVd3dga03xN6bNsABclfjUYMufYhKs+naAxpqtvkFRJuj1n1c22OOEsyfNAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T11:02:13.199504Z","bundle_sha256":"4598d16c4d15c029aa0efa995940b52f3eca9fc18ef69fe41aa8ac99c947172e"}}