{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:D5RZCSR6YXNSOEKYWYMULGLKEJ","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":"273aa0a1d8b755e9af524b091736969e630d0fe83458b1a3267ebfcb217ca4ef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-05-16T08:08:33Z","title_canon_sha256":"99fc3643d1567d6d847ffa9c0f5d963dee3dc990550fc175a56138cdf4ca6ebb"},"schema_version":"1.0","source":{"id":"2605.16868","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.16868","created_at":"2026-05-20T00:03:27Z"},{"alias_kind":"arxiv_version","alias_value":"2605.16868v1","created_at":"2026-05-20T00:03:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.16868","created_at":"2026-05-20T00:03:27Z"},{"alias_kind":"pith_short_12","alias_value":"D5RZCSR6YXNS","created_at":"2026-05-20T00:03:27Z"},{"alias_kind":"pith_short_16","alias_value":"D5RZCSR6YXNSOEKY","created_at":"2026-05-20T00:03:27Z"},{"alias_kind":"pith_short_8","alias_value":"D5RZCSR6","created_at":"2026-05-20T00:03:27Z"}],"graph_snapshots":[{"event_id":"sha256:bf33dae3858f82475e624920edabad851333976411346e7ac565610a35667835","target":"graph","created_at":"2026-05-20T00:03:27Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"Under certain conditions the queueing system can be approximated by an infinite-dimensional fluid limit with a kernel function in place of the transition matrix. This limiting process can be characterized by an infinite-dimensional Skorokhod problem, for which we develop a new theory... We establish existence and uniqueness of a solution along with Lipschitz continuity provided the reflecting operator has a spectral radius less than 1."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The network growth and rate conditions allow the reflection operator to satisfy a spectral radius strictly less than 1, which is required for the Lipschitz property of the infinite-dimensional Skorokhod mapping and for the convergence arguments via the intermediate process and martingale estimates."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Proves fluid limits for growing open Markovian Jackson networks via a new theory of infinite-dimensional Skorokhod problems with existence, uniqueness, and Lipschitz continuity under a spectral radius condition."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Under suitable growth conditions, open Jackson networks converge in the fluid scale to the unique solution of an infinite-dimensional Skorokhod problem with a kernel reflection operator."}],"snapshot_sha256":"2e077b81c222fe1c52153b82fdd826bec3fb7150a19b3558d87fd4a11d64bd0c"},"formal_canon":{"evidence_count":2,"snapshot_sha256":"cd54bb079dc703530295a4d217452e27732e89b62797019be4d465d1402efc73"},"integrity":{"available":true,"clean":true,"detectors_run":[{"findings_count":0,"name":"doi_title_agreement","ran_at":"2026-05-19T20:01:18.978305Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"doi_compliance","ran_at":"2026-05-19T19:50:42.580855Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"claim_evidence","ran_at":"2026-05-19T18:41:56.300202Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"ai_meta_artifact","ran_at":"2026-05-19T18:33:26.376347Z","status":"skipped","version":"1.0.0"}],"endpoint":"/pith/2605.16868/integrity.json","findings":[],"snapshot_sha256":"9fafc548ee3178aaae8d10597cd7f8381dcf9a98b0a1dfa46545e8550f976b77","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study growing open Jackson networks where each station is a single-server queue that follows the first-come first-served discipline with Poisson arrivals and exponentially distributed service times, characterized by node-specific rates. In applying a fluid scaling to the queue-length process, we show that under certain conditions the queueing system can be approximated by an infinite-dimensional fluid limit with a kernel function in place of the transition matrix. This limiting process can be characterized by an infinite-dimensional Skorokhod problem, for which we develop a new theory by co","authors_text":"Guodong Pang, Louis T. Clarke, Ruoyu Wu","cross_cats":[],"headline":"Under suitable growth conditions, open Jackson networks converge in the fluid scale to the unique solution of an infinite-dimensional Skorokhod problem with a kernel reflection operator.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-05-16T08:08:33Z","title":"Growing open Markovian Jackson networks: Fluid limit and infinite-dimensional Skorokhod problem"},"references":{"count":47,"internal_anchors":0,"resolved_work":47,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"S. Banerjee and A. Sankararaman. Ergodicity and steady state analysis for interference queueing networks.arXiv preprint arXiv:2005.13051, 2020","work_id":"db0555ed-d461-4156-997c-d7a79e0a89d5","year":2005},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"E. Bayraktar, S. Chakraborty, and R. Wu. Graphon mean field systems.The Annals of Applied Probability, 33(5):3587–3619, 2023","work_id":"cec144c7-4150-4fe0-bb05-d970137a421c","year":2023},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"G. Bet, F. Coppini, and F. R. Nardi. Weakly interacting oscillators on dense random graphs.Journal of Applied Probability, 61(1):255–278, 2024","work_id":"cbe085ec-b92a-4672-9e64-f153014ea0ee","year":2024},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"K. A. Borovkov. Propagation of chaos for queueing networks.Theory of Probability & Its Applications, 42(3):385– 394, 1998","work_id":"1fd10356-5bfd-4a6c-9fe4-fb20631e243b","year":1998},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"A. Budhiraja, D. Mukherjee, and R. Wu. Supermarket model on graphs.The Annals of Applied Probability, 29(3):1740–1777, 2019","work_id":"e346c883-ef8f-4e48-abc0-f6a8680d2f5e","year":2019}],"snapshot_sha256":"325bebd3d343eaa06616cc6cc3e62c9096cd04ed463629a564f4a698bfe54424"},"source":{"id":"2605.16868","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-19T19:46:44.297971Z","id":"54599425-f5b2-4c07-bf64-c678ee3a6de5","model_set":{"reader":"grok-4.3"},"one_line_summary":"Proves fluid limits for growing open Markovian Jackson networks via a new theory of infinite-dimensional Skorokhod problems with existence, uniqueness, and Lipschitz continuity under a spectral radius condition.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Under suitable growth conditions, open Jackson networks converge in the fluid scale to the unique solution of an infinite-dimensional Skorokhod problem with a kernel reflection operator.","strongest_claim":"Under certain conditions the queueing system can be approximated by an infinite-dimensional fluid limit with a kernel function in place of the transition matrix. This limiting process can be characterized by an infinite-dimensional Skorokhod problem, for which we develop a new theory... We establish existence and uniqueness of a solution along with Lipschitz continuity provided the reflecting operator has a spectral radius less than 1.","weakest_assumption":"The network growth and rate conditions allow the reflection operator to satisfy a spectral radius strictly less than 1, which is required for the Lipschitz property of the infinite-dimensional Skorokhod mapping and for the convergence arguments via the intermediate process and martingale estimates."}},"verdict_id":"54599425-f5b2-4c07-bf64-c678ee3a6de5"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:47e2b6b2956816549e536b84a4d5bfe8a8a8ffe8ae48cf9c76257e7f11e8d92d","target":"record","created_at":"2026-05-20T00:03:27Z","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":"273aa0a1d8b755e9af524b091736969e630d0fe83458b1a3267ebfcb217ca4ef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-05-16T08:08:33Z","title_canon_sha256":"99fc3643d1567d6d847ffa9c0f5d963dee3dc990550fc175a56138cdf4ca6ebb"},"schema_version":"1.0","source":{"id":"2605.16868","kind":"arxiv","version":1}},"canonical_sha256":"1f63914a3ec5db271158b61945996a2264f565f7ddf64258d75f540e0e0d0c78","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f63914a3ec5db271158b61945996a2264f565f7ddf64258d75f540e0e0d0c78","first_computed_at":"2026-05-20T00:03:27.320367Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:03:27.320367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"otnsHhxyEL/Huz4vehRTcv0yLtxcS/5aYl1pSdt1cqpbphc2OpSxektVRbmhsE4gPFcaf/btsv2Te8eYYMGoBg==","signature_status":"signed_v1","signed_at":"2026-05-20T00:03:27.321053Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.16868","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47e2b6b2956816549e536b84a4d5bfe8a8a8ffe8ae48cf9c76257e7f11e8d92d","sha256:bf33dae3858f82475e624920edabad851333976411346e7ac565610a35667835"],"state_sha256":"3014c9d82f4c3a85eb2bd7ea5554600c0bc4c32dc9edc83344001d06270d90ef"}