{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:2ANUN3I4UVBS7GGUZBSBZBPUO4","short_pith_number":"pith:2ANUN3I4","canonical_record":{"source":{"id":"1402.5290","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-02-21T13:19:10Z","cross_cats_sorted":[],"title_canon_sha256":"b4fe78b2292668f98462ac2bcae38942e163c3c2e3e4195317e5010dfd83a3ba","abstract_canon_sha256":"85c7fdc22bbd0d1aef79c8330c12272e9af7d33007f8feff5d24fb1f291f9895"},"schema_version":"1.0"},"canonical_sha256":"d01b46ed1ca5432f98d4c8641c85f477139f480e06900109eac32912482f06a8","source":{"kind":"arxiv","id":"1402.5290","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.5290","created_at":"2026-05-18T01:46:22Z"},{"alias_kind":"arxiv_version","alias_value":"1402.5290v2","created_at":"2026-05-18T01:46:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.5290","created_at":"2026-05-18T01:46:22Z"},{"alias_kind":"pith_short_12","alias_value":"2ANUN3I4UVBS","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"2ANUN3I4UVBS7GGU","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"2ANUN3I4","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:2ANUN3I4UVBS7GGUZBSBZBPUO4","target":"record","payload":{"canonical_record":{"source":{"id":"1402.5290","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-02-21T13:19:10Z","cross_cats_sorted":[],"title_canon_sha256":"b4fe78b2292668f98462ac2bcae38942e163c3c2e3e4195317e5010dfd83a3ba","abstract_canon_sha256":"85c7fdc22bbd0d1aef79c8330c12272e9af7d33007f8feff5d24fb1f291f9895"},"schema_version":"1.0"},"canonical_sha256":"d01b46ed1ca5432f98d4c8641c85f477139f480e06900109eac32912482f06a8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:46:22.569617Z","signature_b64":"Ovht49C1Mr6qL33RSxeWUIhCdxBSU+xlKslt8WQ7ZChFyU7+0mBJAnFlacCflnx5+rnAlmxZHsop02Nw4AagDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d01b46ed1ca5432f98d4c8641c85f477139f480e06900109eac32912482f06a8","last_reissued_at":"2026-05-18T01:46:22.568939Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:46:22.568939Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1402.5290","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":"2026-05-18T01:46:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TAyiuqvnVVm8g8s45QGhoqCUOqwDs9vGyw1MjVpZnm5mFZ7jJOOdX/Ss/Ngy7LsAH6kLuvEJg/YaZaVFebwfDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T01:08:14.058902Z"},"content_sha256":"e43c638de51a4f9e5988d11f662d17c0fd6cc6d61bf21a0d0a132bed0466f2da","schema_version":"1.0","event_id":"sha256:e43c638de51a4f9e5988d11f662d17c0fd6cc6d61bf21a0d0a132bed0466f2da"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:2ANUN3I4UVBS7GGUZBSBZBPUO4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analysis of Markov-modulated infinite-server queues in the central-limit regime","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Joke Blom, Koen De Turck, Michel Mandjes","submitted_at":"2014-02-21T13:19:10Z","abstract_excerpt":"This paper focuses on an infinite-server queue modulated by an independently evolving finite-state Markovian background process, with transition rate matrix $Q\\equiv(q_{ij})_{i,j=1}^d$. Both arrival rates and service rates are depending on the state of the background process. The main contribution concerns the derivation of central limit theorems for the number of customers in the system at time $t\\ge 0$, in the asymptotic regime in which the arrival rates $\\lambda_i$ are scaled by a factor $N$, and the transition rates $q_{ij}$ by a factor $N^\\alpha$, with $\\alpha \\in \\mathbb R^+$. The specif"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.5290","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":""},"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":"2026-05-18T01:46:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JRRMRnCXWNpGT5BprJXBr6IwK8J//bASrrwbKrsduQbc/AIDe/70akg2FN/TChtVgM2h1JOyNp/pqQcuINiFCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T01:08:14.059685Z"},"content_sha256":"c5344358f5dc7c6b81416437a2f00e487792088324b91288a450a879210f5b1b","schema_version":"1.0","event_id":"sha256:c5344358f5dc7c6b81416437a2f00e487792088324b91288a450a879210f5b1b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2ANUN3I4UVBS7GGUZBSBZBPUO4/bundle.json","state_url":"https://pith.science/pith/2ANUN3I4UVBS7GGUZBSBZBPUO4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2ANUN3I4UVBS7GGUZBSBZBPUO4/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":"2026-06-11T01:08:14Z","links":{"resolver":"https://pith.science/pith/2ANUN3I4UVBS7GGUZBSBZBPUO4","bundle":"https://pith.science/pith/2ANUN3I4UVBS7GGUZBSBZBPUO4/bundle.json","state":"https://pith.science/pith/2ANUN3I4UVBS7GGUZBSBZBPUO4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2ANUN3I4UVBS7GGUZBSBZBPUO4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:2ANUN3I4UVBS7GGUZBSBZBPUO4","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":"85c7fdc22bbd0d1aef79c8330c12272e9af7d33007f8feff5d24fb1f291f9895","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-02-21T13:19:10Z","title_canon_sha256":"b4fe78b2292668f98462ac2bcae38942e163c3c2e3e4195317e5010dfd83a3ba"},"schema_version":"1.0","source":{"id":"1402.5290","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.5290","created_at":"2026-05-18T01:46:22Z"},{"alias_kind":"arxiv_version","alias_value":"1402.5290v2","created_at":"2026-05-18T01:46:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.5290","created_at":"2026-05-18T01:46:22Z"},{"alias_kind":"pith_short_12","alias_value":"2ANUN3I4UVBS","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"2ANUN3I4UVBS7GGU","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"2ANUN3I4","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:c5344358f5dc7c6b81416437a2f00e487792088324b91288a450a879210f5b1b","target":"graph","created_at":"2026-05-18T01:46:22Z","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":"This paper focuses on an infinite-server queue modulated by an independently evolving finite-state Markovian background process, with transition rate matrix $Q\\equiv(q_{ij})_{i,j=1}^d$. Both arrival rates and service rates are depending on the state of the background process. The main contribution concerns the derivation of central limit theorems for the number of customers in the system at time $t\\ge 0$, in the asymptotic regime in which the arrival rates $\\lambda_i$ are scaled by a factor $N$, and the transition rates $q_{ij}$ by a factor $N^\\alpha$, with $\\alpha \\in \\mathbb R^+$. The specif","authors_text":"Joke Blom, Koen De Turck, Michel Mandjes","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-02-21T13:19:10Z","title":"Analysis of Markov-modulated infinite-server queues in the central-limit regime"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.5290","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:e43c638de51a4f9e5988d11f662d17c0fd6cc6d61bf21a0d0a132bed0466f2da","target":"record","created_at":"2026-05-18T01:46:22Z","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":"85c7fdc22bbd0d1aef79c8330c12272e9af7d33007f8feff5d24fb1f291f9895","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-02-21T13:19:10Z","title_canon_sha256":"b4fe78b2292668f98462ac2bcae38942e163c3c2e3e4195317e5010dfd83a3ba"},"schema_version":"1.0","source":{"id":"1402.5290","kind":"arxiv","version":2}},"canonical_sha256":"d01b46ed1ca5432f98d4c8641c85f477139f480e06900109eac32912482f06a8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d01b46ed1ca5432f98d4c8641c85f477139f480e06900109eac32912482f06a8","first_computed_at":"2026-05-18T01:46:22.568939Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:46:22.568939Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ovht49C1Mr6qL33RSxeWUIhCdxBSU+xlKslt8WQ7ZChFyU7+0mBJAnFlacCflnx5+rnAlmxZHsop02Nw4AagDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:46:22.569617Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.5290","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e43c638de51a4f9e5988d11f662d17c0fd6cc6d61bf21a0d0a132bed0466f2da","sha256:c5344358f5dc7c6b81416437a2f00e487792088324b91288a450a879210f5b1b"],"state_sha256":"aaf869aaf11b9aa59fc6034d16c1ba087b64fd07900352daaacda4f9abc070d9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mhSfp/VbW/GILi0wkIqq1l5K2oLg/Xr1+eLD7lFPVBq93TgkNJAtsvTT0JCcKHzrgNxs1Vcp889n72RYqWsPAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T01:08:14.063698Z","bundle_sha256":"603529aa6a27bdf9fe871b67de9f128c3c9b16c78886dd189d3eebfe11f554d3"}}