{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:OIBHYAPS3OMLBOEZHSIYXDD245","short_pith_number":"pith:OIBHYAPS","canonical_record":{"source":{"id":"1701.07967","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-27T08:22:50Z","cross_cats_sorted":[],"title_canon_sha256":"76b347af2a5c143679d1d404e2e4c9479081edb2036e1f9cef63723bc20fb712","abstract_canon_sha256":"53d1584596d329c5787c22436eb8c29d67772316ac5234e9771e2bf786f793f7"},"schema_version":"1.0"},"canonical_sha256":"72027c01f2db98b0b8993c918b8c7ae740ccf480f988b06f98c384cfccaa9a4e","source":{"kind":"arxiv","id":"1701.07967","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.07967","created_at":"2026-05-18T00:51:59Z"},{"alias_kind":"arxiv_version","alias_value":"1701.07967v1","created_at":"2026-05-18T00:51:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.07967","created_at":"2026-05-18T00:51:59Z"},{"alias_kind":"pith_short_12","alias_value":"OIBHYAPS3OML","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"OIBHYAPS3OMLBOEZ","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"OIBHYAPS","created_at":"2026-05-18T12:31:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:OIBHYAPS3OMLBOEZHSIYXDD245","target":"record","payload":{"canonical_record":{"source":{"id":"1701.07967","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-27T08:22:50Z","cross_cats_sorted":[],"title_canon_sha256":"76b347af2a5c143679d1d404e2e4c9479081edb2036e1f9cef63723bc20fb712","abstract_canon_sha256":"53d1584596d329c5787c22436eb8c29d67772316ac5234e9771e2bf786f793f7"},"schema_version":"1.0"},"canonical_sha256":"72027c01f2db98b0b8993c918b8c7ae740ccf480f988b06f98c384cfccaa9a4e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:59.273670Z","signature_b64":"NTS5fz5NwZKoCF7xIT4ltDjmPNkYDX08t9g6kIi37zO29d+0Hlx05Sm/OAwab4x9Gacgj3DJ8YXPkbVkqMX+Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"72027c01f2db98b0b8993c918b8c7ae740ccf480f988b06f98c384cfccaa9a4e","last_reissued_at":"2026-05-18T00:51:59.273134Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:59.273134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.07967","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":"2026-05-18T00:51:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J0vvuOcUIrHcQaCcYGq4uenCQkdIl+FQtL07s5c8xmf1Z9Ze8CP0drI6/sZWeFc4WLewwtAAN+IGP3456FD8Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T10:21:54.842917Z"},"content_sha256":"90acfd12c9683393577e5a56fbb05f4ba97f6b62bfacade1981c8f842de6a2a9","schema_version":"1.0","event_id":"sha256:90acfd12c9683393577e5a56fbb05f4ba97f6b62bfacade1981c8f842de6a2a9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:OIBHYAPS3OMLBOEZHSIYXDD245","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Heavy-tailed random walks, buffered queues and hidden large deviations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Bikramjit Das, Harald Bernhard","submitted_at":"2017-01-27T08:22:50Z","abstract_excerpt":"It is well-known that large deviations of random walks driven by independent and identically distributed heavy-tailed random variables are governed by the so-called principle of one large jump. We note that further subtleties hold for such random walks in the large deviation scale which we call hidden large deviation. We apply this idea in the context of queueing processes with heavy-tailed service times and study approximations of severe congestion times for (buffered) queues. We conclude with simulated examples to verify our results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.07967","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":"2026-05-18T00:51:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8I1Fq/SdhnNUa0anWMFUYYysEJJT/RC9IDFUQe1l1XJM7qWcJuFrvxa9c65i9yM4fAV30WpG289XKlBha1Q6DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T10:21:54.843257Z"},"content_sha256":"8c29ab86a9d90fec410827e9f1877820fb9b78b8c6d11dcc0b2e0a5889b0adc9","schema_version":"1.0","event_id":"sha256:8c29ab86a9d90fec410827e9f1877820fb9b78b8c6d11dcc0b2e0a5889b0adc9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OIBHYAPS3OMLBOEZHSIYXDD245/bundle.json","state_url":"https://pith.science/pith/OIBHYAPS3OMLBOEZHSIYXDD245/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OIBHYAPS3OMLBOEZHSIYXDD245/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":"2026-06-26T10:21:54Z","links":{"resolver":"https://pith.science/pith/OIBHYAPS3OMLBOEZHSIYXDD245","bundle":"https://pith.science/pith/OIBHYAPS3OMLBOEZHSIYXDD245/bundle.json","state":"https://pith.science/pith/OIBHYAPS3OMLBOEZHSIYXDD245/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OIBHYAPS3OMLBOEZHSIYXDD245/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:OIBHYAPS3OMLBOEZHSIYXDD245","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":"53d1584596d329c5787c22436eb8c29d67772316ac5234e9771e2bf786f793f7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-27T08:22:50Z","title_canon_sha256":"76b347af2a5c143679d1d404e2e4c9479081edb2036e1f9cef63723bc20fb712"},"schema_version":"1.0","source":{"id":"1701.07967","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.07967","created_at":"2026-05-18T00:51:59Z"},{"alias_kind":"arxiv_version","alias_value":"1701.07967v1","created_at":"2026-05-18T00:51:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.07967","created_at":"2026-05-18T00:51:59Z"},{"alias_kind":"pith_short_12","alias_value":"OIBHYAPS3OML","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"OIBHYAPS3OMLBOEZ","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"OIBHYAPS","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:8c29ab86a9d90fec410827e9f1877820fb9b78b8c6d11dcc0b2e0a5889b0adc9","target":"graph","created_at":"2026-05-18T00:51:59Z","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":"It is well-known that large deviations of random walks driven by independent and identically distributed heavy-tailed random variables are governed by the so-called principle of one large jump. We note that further subtleties hold for such random walks in the large deviation scale which we call hidden large deviation. We apply this idea in the context of queueing processes with heavy-tailed service times and study approximations of severe congestion times for (buffered) queues. We conclude with simulated examples to verify our results.","authors_text":"Bikramjit Das, Harald Bernhard","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-27T08:22:50Z","title":"Heavy-tailed random walks, buffered queues and hidden large deviations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.07967","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":"sha256:90acfd12c9683393577e5a56fbb05f4ba97f6b62bfacade1981c8f842de6a2a9","target":"record","created_at":"2026-05-18T00:51:59Z","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":"53d1584596d329c5787c22436eb8c29d67772316ac5234e9771e2bf786f793f7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-27T08:22:50Z","title_canon_sha256":"76b347af2a5c143679d1d404e2e4c9479081edb2036e1f9cef63723bc20fb712"},"schema_version":"1.0","source":{"id":"1701.07967","kind":"arxiv","version":1}},"canonical_sha256":"72027c01f2db98b0b8993c918b8c7ae740ccf480f988b06f98c384cfccaa9a4e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"72027c01f2db98b0b8993c918b8c7ae740ccf480f988b06f98c384cfccaa9a4e","first_computed_at":"2026-05-18T00:51:59.273134Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:59.273134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NTS5fz5NwZKoCF7xIT4ltDjmPNkYDX08t9g6kIi37zO29d+0Hlx05Sm/OAwab4x9Gacgj3DJ8YXPkbVkqMX+Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:59.273670Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.07967","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:90acfd12c9683393577e5a56fbb05f4ba97f6b62bfacade1981c8f842de6a2a9","sha256:8c29ab86a9d90fec410827e9f1877820fb9b78b8c6d11dcc0b2e0a5889b0adc9"],"state_sha256":"41ee487781ac53bccb889ae0963fcefde57287cd051fa1fa62c0e614787a8567"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZtZIn+m/K6/Vn8d+iWCqzptfFNpwmP6NkDqC2ggT/3yUzXtvp+UVOsyjhuC0Avt3L+5VuepW2iiE8wgpq5v/Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T10:21:54.845183Z","bundle_sha256":"58297de5e2b9c03b156c622749802cd72a26666254b902b88cf24230120b3b57"}}