{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:FLIZ572ATRNSGI5DJWLYHVC2JN","short_pith_number":"pith:FLIZ572A","canonical_record":{"source":{"id":"2406.12745","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-06-18T16:06:18Z","cross_cats_sorted":[],"title_canon_sha256":"612fe3c451b88b59d94d8225e5da5d68f3d439bff875963d15a018c9b9118592","abstract_canon_sha256":"0e69c1fe549894677285b1065fe2f4c314fb4071a0b13feebdd86aa0384801f9"},"schema_version":"1.0"},"canonical_sha256":"2ad19eff409c5b2323a34d9783d45a4b6f823ea9578b4ae259319493f368a791","source":{"kind":"arxiv","id":"2406.12745","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.12745","created_at":"2026-07-05T10:32:27Z"},{"alias_kind":"arxiv_version","alias_value":"2406.12745v2","created_at":"2026-07-05T10:32:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.12745","created_at":"2026-07-05T10:32:27Z"},{"alias_kind":"pith_short_12","alias_value":"FLIZ572ATRNS","created_at":"2026-07-05T10:32:27Z"},{"alias_kind":"pith_short_16","alias_value":"FLIZ572ATRNSGI5D","created_at":"2026-07-05T10:32:27Z"},{"alias_kind":"pith_short_8","alias_value":"FLIZ572A","created_at":"2026-07-05T10:32:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:FLIZ572ATRNSGI5DJWLYHVC2JN","target":"record","payload":{"canonical_record":{"source":{"id":"2406.12745","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-06-18T16:06:18Z","cross_cats_sorted":[],"title_canon_sha256":"612fe3c451b88b59d94d8225e5da5d68f3d439bff875963d15a018c9b9118592","abstract_canon_sha256":"0e69c1fe549894677285b1065fe2f4c314fb4071a0b13feebdd86aa0384801f9"},"schema_version":"1.0"},"canonical_sha256":"2ad19eff409c5b2323a34d9783d45a4b6f823ea9578b4ae259319493f368a791","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:32:27.538640Z","signature_b64":"JQaGzbL8DwFCRK6SgI66ARBlAYNSpR7hq1WtMTnGpxAusIU8vyljRJsvSKXEvr2daCWiF4UU8KsSbFhayDPyAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2ad19eff409c5b2323a34d9783d45a4b6f823ea9578b4ae259319493f368a791","last_reissued_at":"2026-07-05T10:32:27.537500Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:32:27.537500Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2406.12745","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":"2026-07-05T10:32:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x7PRECaNqD8Mb6tW8z3m/mt6FCTCBu3kuGQCesBUaShz3JYLMHMvQFoly56w89krTCCEkeWg4+ThphoQiJg6Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T21:44:45.118753Z"},"content_sha256":"c6db71968da38be161380ddb8e8149d3384c83fb5be847f525ccc21ceb1a3699","schema_version":"1.0","event_id":"sha256:c6db71968da38be161380ddb8e8149d3384c83fb5be847f525ccc21ceb1a3699"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:FLIZ572ATRNSGI5DJWLYHVC2JN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Useful stochastic bounds in time-varying queues with service and patience times having general joint distribution","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Royi Jacobovic, Shreehari Anand Bodas","submitted_at":"2024-06-18T16:06:18Z","abstract_excerpt":"Consider a first-come, first-served single server queue with an initial workload $x>0$ and customers who arrive according to an inhomogeneous Poisson process with rate function $\\lambda:[0,\\infty)\\rightarrow[0,\\lambda_h ]$ for some $\\lambda_h>0$. For each $i\\in\\mathbb{N}$, let $S_i$ (resp., $Y_i$) be the service (resp., patience) time of the $i$'th customer and assume that $(S_1,Y_1),(S_2,Y_2),\\ldots$ is an iid sequence of bivariate random vectors with non-negative coordinates. A customer joins if and only if his patience time is not less than his prospective waiting time (i.e., the left-limit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.12745","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2406.12745/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":"2026-07-05T10:32:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iEK5ei7gFibYkJ7/vObJ+kkrReiD+NG1Nc5agYfN4PWfpXAW7/oXsJf4wJbupmRh90rEM72OxXEHdvE9qZkEDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T21:44:45.119792Z"},"content_sha256":"0ebda2d88748f02fdbe91987ee52e0b77327d04530df4b187194456b8a9d99e6","schema_version":"1.0","event_id":"sha256:0ebda2d88748f02fdbe91987ee52e0b77327d04530df4b187194456b8a9d99e6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FLIZ572ATRNSGI5DJWLYHVC2JN/bundle.json","state_url":"https://pith.science/pith/FLIZ572ATRNSGI5DJWLYHVC2JN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FLIZ572ATRNSGI5DJWLYHVC2JN/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":"2026-08-03T21:44:45Z","links":{"resolver":"https://pith.science/pith/FLIZ572ATRNSGI5DJWLYHVC2JN","bundle":"https://pith.science/pith/FLIZ572ATRNSGI5DJWLYHVC2JN/bundle.json","state":"https://pith.science/pith/FLIZ572ATRNSGI5DJWLYHVC2JN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FLIZ572ATRNSGI5DJWLYHVC2JN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:FLIZ572ATRNSGI5DJWLYHVC2JN","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":"0e69c1fe549894677285b1065fe2f4c314fb4071a0b13feebdd86aa0384801f9","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-06-18T16:06:18Z","title_canon_sha256":"612fe3c451b88b59d94d8225e5da5d68f3d439bff875963d15a018c9b9118592"},"schema_version":"1.0","source":{"id":"2406.12745","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.12745","created_at":"2026-07-05T10:32:27Z"},{"alias_kind":"arxiv_version","alias_value":"2406.12745v2","created_at":"2026-07-05T10:32:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.12745","created_at":"2026-07-05T10:32:27Z"},{"alias_kind":"pith_short_12","alias_value":"FLIZ572ATRNS","created_at":"2026-07-05T10:32:27Z"},{"alias_kind":"pith_short_16","alias_value":"FLIZ572ATRNSGI5D","created_at":"2026-07-05T10:32:27Z"},{"alias_kind":"pith_short_8","alias_value":"FLIZ572A","created_at":"2026-07-05T10:32:27Z"}],"graph_snapshots":[{"event_id":"sha256:0ebda2d88748f02fdbe91987ee52e0b77327d04530df4b187194456b8a9d99e6","target":"graph","created_at":"2026-07-05T10:32:27Z","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/2406.12745/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Consider a first-come, first-served single server queue with an initial workload $x>0$ and customers who arrive according to an inhomogeneous Poisson process with rate function $\\lambda:[0,\\infty)\\rightarrow[0,\\lambda_h ]$ for some $\\lambda_h>0$. For each $i\\in\\mathbb{N}$, let $S_i$ (resp., $Y_i$) be the service (resp., patience) time of the $i$'th customer and assume that $(S_1,Y_1),(S_2,Y_2),\\ldots$ is an iid sequence of bivariate random vectors with non-negative coordinates. A customer joins if and only if his patience time is not less than his prospective waiting time (i.e., the left-limit","authors_text":"Royi Jacobovic, Shreehari Anand Bodas","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-06-18T16:06:18Z","title":"Useful stochastic bounds in time-varying queues with service and patience times having general joint distribution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.12745","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:c6db71968da38be161380ddb8e8149d3384c83fb5be847f525ccc21ceb1a3699","target":"record","created_at":"2026-07-05T10:32:27Z","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":"0e69c1fe549894677285b1065fe2f4c314fb4071a0b13feebdd86aa0384801f9","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-06-18T16:06:18Z","title_canon_sha256":"612fe3c451b88b59d94d8225e5da5d68f3d439bff875963d15a018c9b9118592"},"schema_version":"1.0","source":{"id":"2406.12745","kind":"arxiv","version":2}},"canonical_sha256":"2ad19eff409c5b2323a34d9783d45a4b6f823ea9578b4ae259319493f368a791","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2ad19eff409c5b2323a34d9783d45a4b6f823ea9578b4ae259319493f368a791","first_computed_at":"2026-07-05T10:32:27.537500Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:32:27.537500Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JQaGzbL8DwFCRK6SgI66ARBlAYNSpR7hq1WtMTnGpxAusIU8vyljRJsvSKXEvr2daCWiF4UU8KsSbFhayDPyAw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:32:27.538640Z","signed_message":"canonical_sha256_bytes"},"source_id":"2406.12745","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c6db71968da38be161380ddb8e8149d3384c83fb5be847f525ccc21ceb1a3699","sha256:0ebda2d88748f02fdbe91987ee52e0b77327d04530df4b187194456b8a9d99e6"],"state_sha256":"3df459b59aca1e7eba5fbefdcd1d025dd50bf31a7d77a05eabe3ea60f61f0731"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lzRx707fbjaB6TNpzkg9UVMdmX6JWMRjd8HvXWcN8fAYAl1uIJe3p7+Yy4ieQ9A/1LVZ8ATAFN2O4gyx425+DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T21:44:45.128087Z","bundle_sha256":"bec06fc7aef8baf79af937ed3284da1b8f24fc25d5a20373c9ae90d23dd7a52a"}}