{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:WZ47HSMX7JU7E3OXRTCDFKTKNN","short_pith_number":"pith:WZ47HSMX","canonical_record":{"source":{"id":"1412.2540","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-08T12:33:43Z","cross_cats_sorted":[],"title_canon_sha256":"a98571630d9022ecb29f5b5cfa07547b9b9ebefd44d904cddd333e9d64e6b2de","abstract_canon_sha256":"0d6612b1e06463a883477201a390d959910431144ffea2123255ffde30833296"},"schema_version":"1.0"},"canonical_sha256":"b679f3c997fa69f26dd78cc432aa6a6b67ed94d7a3eeb1f12f588b10aae878d8","source":{"kind":"arxiv","id":"1412.2540","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.2540","created_at":"2026-05-18T02:31:57Z"},{"alias_kind":"arxiv_version","alias_value":"1412.2540v1","created_at":"2026-05-18T02:31:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.2540","created_at":"2026-05-18T02:31:57Z"},{"alias_kind":"pith_short_12","alias_value":"WZ47HSMX7JU7","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WZ47HSMX7JU7E3OX","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WZ47HSMX","created_at":"2026-05-18T12:28:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:WZ47HSMX7JU7E3OXRTCDFKTKNN","target":"record","payload":{"canonical_record":{"source":{"id":"1412.2540","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-08T12:33:43Z","cross_cats_sorted":[],"title_canon_sha256":"a98571630d9022ecb29f5b5cfa07547b9b9ebefd44d904cddd333e9d64e6b2de","abstract_canon_sha256":"0d6612b1e06463a883477201a390d959910431144ffea2123255ffde30833296"},"schema_version":"1.0"},"canonical_sha256":"b679f3c997fa69f26dd78cc432aa6a6b67ed94d7a3eeb1f12f588b10aae878d8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:31:57.643460Z","signature_b64":"bU7TBZZFBisUI4bH+JqcNiVTXVnvMx7eiskRum9S3cwOZ61fZdv0oFKP1Jkb/26ZB2xDDZLeDK5lUvGXP32dBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b679f3c997fa69f26dd78cc432aa6a6b67ed94d7a3eeb1f12f588b10aae878d8","last_reissued_at":"2026-05-18T02:31:57.642906Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:31:57.642906Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.2540","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":"2026-05-18T02:31:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+7EKkrURAXkpzT4V4kUf6nroTIzwNfFElkvVd69u2jKJl8NQ2760U+tca9blc5c5k0PHOq//1S0GoLOORzjRBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T09:55:46.316833Z"},"content_sha256":"bf828bcc1430445315d2661528fbb6d26ea8a400ae30bb653cce2e71f800af35","schema_version":"1.0","event_id":"sha256:bf828bcc1430445315d2661528fbb6d26ea8a400ae30bb653cce2e71f800af35"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:WZ47HSMX7JU7E3OXRTCDFKTKNN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Flow coupling and stochastic ordering of throughputs in linear networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Lasse Leskel\\\"a","submitted_at":"2014-12-08T12:33:43Z","abstract_excerpt":"Robust estimates for the performance of complicated queueing networks can be obtained by showing that the number of jobs in the network is stochastically comparable to a simpler, analytically tractable reference network. Classical coupling results on stochastic ordering of network populations require strong monotonicity assumptions which are often violated in practice. However, in most real-world applications we care more about what goes through a network than what sits inside it. This paper describes a new approach for ordering flows instead of populations by augmenting network states with th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2540","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":"2026-05-18T02:31:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"odTK5NtNZyjLjXWL55qsDPZl+0D6eUSbWZRVyr936aLqvei/xQvIwSX/CAMkid22/+Tc4NrcOyl2I8zQDCfxCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T09:55:46.317179Z"},"content_sha256":"7fef43753e759097dbfe1a7a738e5260ca3a706c901f09f268a9b645428363aa","schema_version":"1.0","event_id":"sha256:7fef43753e759097dbfe1a7a738e5260ca3a706c901f09f268a9b645428363aa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WZ47HSMX7JU7E3OXRTCDFKTKNN/bundle.json","state_url":"https://pith.science/pith/WZ47HSMX7JU7E3OXRTCDFKTKNN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WZ47HSMX7JU7E3OXRTCDFKTKNN/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":"2026-05-30T09:55:46Z","links":{"resolver":"https://pith.science/pith/WZ47HSMX7JU7E3OXRTCDFKTKNN","bundle":"https://pith.science/pith/WZ47HSMX7JU7E3OXRTCDFKTKNN/bundle.json","state":"https://pith.science/pith/WZ47HSMX7JU7E3OXRTCDFKTKNN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WZ47HSMX7JU7E3OXRTCDFKTKNN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:WZ47HSMX7JU7E3OXRTCDFKTKNN","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":"0d6612b1e06463a883477201a390d959910431144ffea2123255ffde30833296","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-08T12:33:43Z","title_canon_sha256":"a98571630d9022ecb29f5b5cfa07547b9b9ebefd44d904cddd333e9d64e6b2de"},"schema_version":"1.0","source":{"id":"1412.2540","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.2540","created_at":"2026-05-18T02:31:57Z"},{"alias_kind":"arxiv_version","alias_value":"1412.2540v1","created_at":"2026-05-18T02:31:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.2540","created_at":"2026-05-18T02:31:57Z"},{"alias_kind":"pith_short_12","alias_value":"WZ47HSMX7JU7","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WZ47HSMX7JU7E3OX","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WZ47HSMX","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:7fef43753e759097dbfe1a7a738e5260ca3a706c901f09f268a9b645428363aa","target":"graph","created_at":"2026-05-18T02:31:57Z","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":"Robust estimates for the performance of complicated queueing networks can be obtained by showing that the number of jobs in the network is stochastically comparable to a simpler, analytically tractable reference network. Classical coupling results on stochastic ordering of network populations require strong monotonicity assumptions which are often violated in practice. However, in most real-world applications we care more about what goes through a network than what sits inside it. This paper describes a new approach for ordering flows instead of populations by augmenting network states with th","authors_text":"Lasse Leskel\\\"a","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-08T12:33:43Z","title":"Flow coupling and stochastic ordering of throughputs in linear networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2540","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:bf828bcc1430445315d2661528fbb6d26ea8a400ae30bb653cce2e71f800af35","target":"record","created_at":"2026-05-18T02:31:57Z","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":"0d6612b1e06463a883477201a390d959910431144ffea2123255ffde30833296","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-08T12:33:43Z","title_canon_sha256":"a98571630d9022ecb29f5b5cfa07547b9b9ebefd44d904cddd333e9d64e6b2de"},"schema_version":"1.0","source":{"id":"1412.2540","kind":"arxiv","version":1}},"canonical_sha256":"b679f3c997fa69f26dd78cc432aa6a6b67ed94d7a3eeb1f12f588b10aae878d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b679f3c997fa69f26dd78cc432aa6a6b67ed94d7a3eeb1f12f588b10aae878d8","first_computed_at":"2026-05-18T02:31:57.642906Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:31:57.642906Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bU7TBZZFBisUI4bH+JqcNiVTXVnvMx7eiskRum9S3cwOZ61fZdv0oFKP1Jkb/26ZB2xDDZLeDK5lUvGXP32dBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:31:57.643460Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.2540","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bf828bcc1430445315d2661528fbb6d26ea8a400ae30bb653cce2e71f800af35","sha256:7fef43753e759097dbfe1a7a738e5260ca3a706c901f09f268a9b645428363aa"],"state_sha256":"4efe4015a20a831fe3a1ccfb7039278907260ff1c271b607151a9291087bdd08"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N3QOgSMhBrrtOeAcS3BzvNBY/pq+vFW/ndtZijLtBMfGJfNsCboh61f7DKZ4ySDfXHszZAoHxqwsCn/VdCOmDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T09:55:46.319179Z","bundle_sha256":"f52c61554a45ed576a48782afb827d19245204a4a7ec21851671f93e0d1b151f"}}