{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:4BQYIQATN56AZIAHJPDLY3Q2WC","short_pith_number":"pith:4BQYIQAT","canonical_record":{"source":{"id":"2312.11284","kind":"arxiv","version":9},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2023-12-18T15:23:39Z","cross_cats_sorted":[],"title_canon_sha256":"728e965957b3e63f3e015ebff890f68fef657e1a22d2e27fb7f6a59402eaa984","abstract_canon_sha256":"5469b8bf92bb5a5c4c0b1f34db511314cb2430c85acca48ea35835e92a2e6f60"},"schema_version":"1.0"},"canonical_sha256":"e0618440136f7c0ca0074bc6bc6e1ab0a8650fd6cbe7df5838f6c65fdca8c8c3","source":{"kind":"arxiv","id":"2312.11284","version":9},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.11284","created_at":"2026-07-05T11:10:30Z"},{"alias_kind":"arxiv_version","alias_value":"2312.11284v9","created_at":"2026-07-05T11:10:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.11284","created_at":"2026-07-05T11:10:30Z"},{"alias_kind":"pith_short_12","alias_value":"4BQYIQATN56A","created_at":"2026-07-05T11:10:30Z"},{"alias_kind":"pith_short_16","alias_value":"4BQYIQATN56AZIAH","created_at":"2026-07-05T11:10:30Z"},{"alias_kind":"pith_short_8","alias_value":"4BQYIQAT","created_at":"2026-07-05T11:10:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:4BQYIQATN56AZIAHJPDLY3Q2WC","target":"record","payload":{"canonical_record":{"source":{"id":"2312.11284","kind":"arxiv","version":9},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2023-12-18T15:23:39Z","cross_cats_sorted":[],"title_canon_sha256":"728e965957b3e63f3e015ebff890f68fef657e1a22d2e27fb7f6a59402eaa984","abstract_canon_sha256":"5469b8bf92bb5a5c4c0b1f34db511314cb2430c85acca48ea35835e92a2e6f60"},"schema_version":"1.0"},"canonical_sha256":"e0618440136f7c0ca0074bc6bc6e1ab0a8650fd6cbe7df5838f6c65fdca8c8c3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:10:30.430205Z","signature_b64":"gEVyT6Ff62lppytzT5i7KQgycaMj291ja0LUYtYFQzx47n6Rm9kpKkHH9cgxiBa7+CWgH1wN3FRezTitG4VQDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e0618440136f7c0ca0074bc6bc6e1ab0a8650fd6cbe7df5838f6c65fdca8c8c3","last_reissued_at":"2026-07-05T11:10:30.429692Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:10:30.429692Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2312.11284","source_version":9,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:10:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oq2DZpo0xB03kUCJctbHaH/OCI+uuSJD8EQ7kwvc8YjiENn6A/G90T96huLH4bGsNuZu2oSQ8ebbS7XBt790DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T22:09:19.276263Z"},"content_sha256":"e6f9718e993ba3219d760b949895b1d699e854f368990788fd58156478f7438f","schema_version":"1.0","event_id":"sha256:e6f9718e993ba3219d760b949895b1d699e854f368990788fd58156478f7438f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:4BQYIQATN56AZIAHJPDLY3Q2WC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Diffusion approximation of the stationary distribution of a two-level single server queue","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Masakiyo Miyazawa","submitted_at":"2023-12-18T15:23:39Z","abstract_excerpt":"We consider a single server queue which has a threshold to change its arrival process and service speed by its queue length, which is referred to as a two-level single server queue. This model is motivated by an energy saving problem for a single server queue whose arrival process and service speed are controlled. To get its performance in tractable form, we study the limit of the stationary distribution of the queue length in this two-level queue under scaling in heavy traffic. Except for a special case, this limit corresponds to its diffusion approximation. It is shown that this limiting dis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.11284","kind":"arxiv","version":9},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2312.11284/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:10:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hDWYqn18ODwz+S0WTVmzI6M0IExCv5QTiecveRHvXHbFztCwkU5A3sJP8Vnh4J3hlHx6WkaOwnYySg6m/gJiAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T22:09:19.276806Z"},"content_sha256":"eff40692a974ec97c3dfc851ef793762311df71be9ccee0d3ccf97f37f0d23d3","schema_version":"1.0","event_id":"sha256:eff40692a974ec97c3dfc851ef793762311df71be9ccee0d3ccf97f37f0d23d3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4BQYIQATN56AZIAHJPDLY3Q2WC/bundle.json","state_url":"https://pith.science/pith/4BQYIQATN56AZIAHJPDLY3Q2WC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4BQYIQATN56AZIAHJPDLY3Q2WC/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":"2026-08-11T22:09:19Z","links":{"resolver":"https://pith.science/pith/4BQYIQATN56AZIAHJPDLY3Q2WC","bundle":"https://pith.science/pith/4BQYIQATN56AZIAHJPDLY3Q2WC/bundle.json","state":"https://pith.science/pith/4BQYIQATN56AZIAHJPDLY3Q2WC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4BQYIQATN56AZIAHJPDLY3Q2WC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:4BQYIQATN56AZIAHJPDLY3Q2WC","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":"5469b8bf92bb5a5c4c0b1f34db511314cb2430c85acca48ea35835e92a2e6f60","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2023-12-18T15:23:39Z","title_canon_sha256":"728e965957b3e63f3e015ebff890f68fef657e1a22d2e27fb7f6a59402eaa984"},"schema_version":"1.0","source":{"id":"2312.11284","kind":"arxiv","version":9}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.11284","created_at":"2026-07-05T11:10:30Z"},{"alias_kind":"arxiv_version","alias_value":"2312.11284v9","created_at":"2026-07-05T11:10:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.11284","created_at":"2026-07-05T11:10:30Z"},{"alias_kind":"pith_short_12","alias_value":"4BQYIQATN56A","created_at":"2026-07-05T11:10:30Z"},{"alias_kind":"pith_short_16","alias_value":"4BQYIQATN56AZIAH","created_at":"2026-07-05T11:10:30Z"},{"alias_kind":"pith_short_8","alias_value":"4BQYIQAT","created_at":"2026-07-05T11:10:30Z"}],"graph_snapshots":[{"event_id":"sha256:eff40692a974ec97c3dfc851ef793762311df71be9ccee0d3ccf97f37f0d23d3","target":"graph","created_at":"2026-07-05T11:10:30Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2312.11284/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider a single server queue which has a threshold to change its arrival process and service speed by its queue length, which is referred to as a two-level single server queue. This model is motivated by an energy saving problem for a single server queue whose arrival process and service speed are controlled. To get its performance in tractable form, we study the limit of the stationary distribution of the queue length in this two-level queue under scaling in heavy traffic. Except for a special case, this limit corresponds to its diffusion approximation. It is shown that this limiting dis","authors_text":"Masakiyo Miyazawa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2023-12-18T15:23:39Z","title":"Diffusion approximation of the stationary distribution of a two-level single server queue"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.11284","kind":"arxiv","version":9},"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:e6f9718e993ba3219d760b949895b1d699e854f368990788fd58156478f7438f","target":"record","created_at":"2026-07-05T11:10:30Z","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":"5469b8bf92bb5a5c4c0b1f34db511314cb2430c85acca48ea35835e92a2e6f60","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2023-12-18T15:23:39Z","title_canon_sha256":"728e965957b3e63f3e015ebff890f68fef657e1a22d2e27fb7f6a59402eaa984"},"schema_version":"1.0","source":{"id":"2312.11284","kind":"arxiv","version":9}},"canonical_sha256":"e0618440136f7c0ca0074bc6bc6e1ab0a8650fd6cbe7df5838f6c65fdca8c8c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e0618440136f7c0ca0074bc6bc6e1ab0a8650fd6cbe7df5838f6c65fdca8c8c3","first_computed_at":"2026-07-05T11:10:30.429692Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:10:30.429692Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gEVyT6Ff62lppytzT5i7KQgycaMj291ja0LUYtYFQzx47n6Rm9kpKkHH9cgxiBa7+CWgH1wN3FRezTitG4VQDw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:10:30.430205Z","signed_message":"canonical_sha256_bytes"},"source_id":"2312.11284","source_kind":"arxiv","source_version":9}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e6f9718e993ba3219d760b949895b1d699e854f368990788fd58156478f7438f","sha256:eff40692a974ec97c3dfc851ef793762311df71be9ccee0d3ccf97f37f0d23d3"],"state_sha256":"e9d031e1a86f5232b55e9c32aa5f427973ab99c39e3cc3cfa6e58077139b9956"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AOnEokCnMdyQZTkFlLbDQ4RppurbgMl1c7HkxcrXgc90gnRj5nW4yM7uFpmlWhf5fqSq2IkOCizUkV4Fy6k4BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T22:09:19.279407Z","bundle_sha256":"44ec460ee7541df2b93bf096dce3ac36d27439060a87cb00eb174bb36d7bf007"}}