{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:PXHAKVNOWXPOMSOPMPTRJXTFV7","short_pith_number":"pith:PXHAKVNO","canonical_record":{"source":{"id":"2407.12716","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-07-17T16:37:48Z","cross_cats_sorted":[],"title_canon_sha256":"3b24e11cd24b17711c640d19afac44c98746e3feaedf794ff270367b33a06bb8","abstract_canon_sha256":"8d14a6da94835fb6f54fd32d67f7f5e269fbd040ef9c2c41e48fdc6987954e03"},"schema_version":"1.0"},"canonical_sha256":"7dce0555aeb5dee649cf63e714de65aff39c13938c178be651b76c981b85c6a9","source":{"kind":"arxiv","id":"2407.12716","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.12716","created_at":"2026-07-01T01:18:23Z"},{"alias_kind":"arxiv_version","alias_value":"2407.12716v4","created_at":"2026-07-01T01:18:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.12716","created_at":"2026-07-01T01:18:23Z"},{"alias_kind":"pith_short_12","alias_value":"PXHAKVNOWXPO","created_at":"2026-07-01T01:18:23Z"},{"alias_kind":"pith_short_16","alias_value":"PXHAKVNOWXPOMSOP","created_at":"2026-07-01T01:18:23Z"},{"alias_kind":"pith_short_8","alias_value":"PXHAKVNO","created_at":"2026-07-01T01:18:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:PXHAKVNOWXPOMSOPMPTRJXTFV7","target":"record","payload":{"canonical_record":{"source":{"id":"2407.12716","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-07-17T16:37:48Z","cross_cats_sorted":[],"title_canon_sha256":"3b24e11cd24b17711c640d19afac44c98746e3feaedf794ff270367b33a06bb8","abstract_canon_sha256":"8d14a6da94835fb6f54fd32d67f7f5e269fbd040ef9c2c41e48fdc6987954e03"},"schema_version":"1.0"},"canonical_sha256":"7dce0555aeb5dee649cf63e714de65aff39c13938c178be651b76c981b85c6a9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-01T01:18:23.615785Z","signature_b64":"3YQcPDwfdF64D2R/iIe62KgRRTbLEbeoBhe22M3ntY/b0KRK6cu/G8RPbPpEW2xg/+8CfajbPIyw/O/32XJmAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7dce0555aeb5dee649cf63e714de65aff39c13938c178be651b76c981b85c6a9","last_reissued_at":"2026-07-01T01:18:23.615035Z","signature_status":"signed_v1","first_computed_at":"2026-07-01T01:18:23.615035Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2407.12716","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-01T01:18:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KiC0wxdRoCSfo7ZtYr0kjFstjAkNUsIg2joRSvrLty2Mt247SazGp622POX3fWQxT6imir9VmhGWPH9WIiXpBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T09:48:27.993733Z"},"content_sha256":"72f6bf0360c8a9fe0770c997e9b6f3a4cb25ef76c8bb54e248ad9a58e78da60f","schema_version":"1.0","event_id":"sha256:72f6bf0360c8a9fe0770c997e9b6f3a4cb25ef76c8bb54e248ad9a58e78da60f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:PXHAKVNOWXPOMSOPMPTRJXTFV7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Diffusion approximation error for queueing systems with general primitives","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Anton Braverman, Ziv Scully","submitted_at":"2024-07-17T16:37:48Z","abstract_excerpt":"We investigate the steady-state diffusion-approximation error for continuous-time queueing systems with generally distributed primitives. A common picture emerges after analyzing a number of canonical systems: the error decomposes into interior and boundary terms. The former are simpler to handle and can be bounded using only low-order moments of the system's primitives -- when the approximation error is measured using the Wasserstein distance, three moments suffice. The boundary terms are inherently more delicate: while crude bounds are easy to obtain, sharper (e.g., order optimal) bounds req"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.12716","kind":"arxiv","version":4},"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/2407.12716/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":"2026-07-01T01:18:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wi2zDhli7eFxAq0wb7juzV6RjXypHzyaxwTznpHO0W9JK3Ty7gxihwnI2EPy7bVfM9Xgj1TytOHVNp9giFbqBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T09:48:27.994115Z"},"content_sha256":"684bb9a2a8f3854bc1f463b0f5ec6b5ea15ed1f57061663fd5d76fb13342cb85","schema_version":"1.0","event_id":"sha256:684bb9a2a8f3854bc1f463b0f5ec6b5ea15ed1f57061663fd5d76fb13342cb85"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PXHAKVNOWXPOMSOPMPTRJXTFV7/bundle.json","state_url":"https://pith.science/pith/PXHAKVNOWXPOMSOPMPTRJXTFV7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PXHAKVNOWXPOMSOPMPTRJXTFV7/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":"2026-07-04T09:48:27Z","links":{"resolver":"https://pith.science/pith/PXHAKVNOWXPOMSOPMPTRJXTFV7","bundle":"https://pith.science/pith/PXHAKVNOWXPOMSOPMPTRJXTFV7/bundle.json","state":"https://pith.science/pith/PXHAKVNOWXPOMSOPMPTRJXTFV7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PXHAKVNOWXPOMSOPMPTRJXTFV7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:PXHAKVNOWXPOMSOPMPTRJXTFV7","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":"8d14a6da94835fb6f54fd32d67f7f5e269fbd040ef9c2c41e48fdc6987954e03","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-07-17T16:37:48Z","title_canon_sha256":"3b24e11cd24b17711c640d19afac44c98746e3feaedf794ff270367b33a06bb8"},"schema_version":"1.0","source":{"id":"2407.12716","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.12716","created_at":"2026-07-01T01:18:23Z"},{"alias_kind":"arxiv_version","alias_value":"2407.12716v4","created_at":"2026-07-01T01:18:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.12716","created_at":"2026-07-01T01:18:23Z"},{"alias_kind":"pith_short_12","alias_value":"PXHAKVNOWXPO","created_at":"2026-07-01T01:18:23Z"},{"alias_kind":"pith_short_16","alias_value":"PXHAKVNOWXPOMSOP","created_at":"2026-07-01T01:18:23Z"},{"alias_kind":"pith_short_8","alias_value":"PXHAKVNO","created_at":"2026-07-01T01:18:23Z"}],"graph_snapshots":[{"event_id":"sha256:684bb9a2a8f3854bc1f463b0f5ec6b5ea15ed1f57061663fd5d76fb13342cb85","target":"graph","created_at":"2026-07-01T01:18:23Z","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/2407.12716/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate the steady-state diffusion-approximation error for continuous-time queueing systems with generally distributed primitives. A common picture emerges after analyzing a number of canonical systems: the error decomposes into interior and boundary terms. The former are simpler to handle and can be bounded using only low-order moments of the system's primitives -- when the approximation error is measured using the Wasserstein distance, three moments suffice. The boundary terms are inherently more delicate: while crude bounds are easy to obtain, sharper (e.g., order optimal) bounds req","authors_text":"Anton Braverman, Ziv Scully","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-07-17T16:37:48Z","title":"Diffusion approximation error for queueing systems with general primitives"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.12716","kind":"arxiv","version":4},"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":"sha256:72f6bf0360c8a9fe0770c997e9b6f3a4cb25ef76c8bb54e248ad9a58e78da60f","target":"record","created_at":"2026-07-01T01:18:23Z","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":"8d14a6da94835fb6f54fd32d67f7f5e269fbd040ef9c2c41e48fdc6987954e03","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-07-17T16:37:48Z","title_canon_sha256":"3b24e11cd24b17711c640d19afac44c98746e3feaedf794ff270367b33a06bb8"},"schema_version":"1.0","source":{"id":"2407.12716","kind":"arxiv","version":4}},"canonical_sha256":"7dce0555aeb5dee649cf63e714de65aff39c13938c178be651b76c981b85c6a9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7dce0555aeb5dee649cf63e714de65aff39c13938c178be651b76c981b85c6a9","first_computed_at":"2026-07-01T01:18:23.615035Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-01T01:18:23.615035Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3YQcPDwfdF64D2R/iIe62KgRRTbLEbeoBhe22M3ntY/b0KRK6cu/G8RPbPpEW2xg/+8CfajbPIyw/O/32XJmAg==","signature_status":"signed_v1","signed_at":"2026-07-01T01:18:23.615785Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.12716","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:72f6bf0360c8a9fe0770c997e9b6f3a4cb25ef76c8bb54e248ad9a58e78da60f","sha256:684bb9a2a8f3854bc1f463b0f5ec6b5ea15ed1f57061663fd5d76fb13342cb85"],"state_sha256":"985ea1321561f29b87ed583139563211c1ab33dd1d2aa318e76c8e6f090de51d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u/BQENXzSjAKBf9DNGm/CKginnffs8K0Ohi3ge7lD0sHWrQ98Vn/uOfl+cpaGpQ4K7cZ0O8u58dR63o3BhU6Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T09:48:27.996155Z","bundle_sha256":"48dc46c0f75fc53588684d7c9eab9b0bc60d088986ab77f40367f0e7f77d461c"}}