{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:64UUZBJSFY3V2TGIHDDEO7O6GC","short_pith_number":"pith:64UUZBJS","canonical_record":{"source":{"id":"1112.1041","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.PF","submitted_at":"2011-12-05T19:57:44Z","cross_cats_sorted":[],"title_canon_sha256":"1647ddddc03776723e96a9636dd6895ee2817d57af97a07791a04af2d8fb7871","abstract_canon_sha256":"a63e4c2fa50187709d4353b21172bc74420aabb22db8082d843668d49d3aefda"},"schema_version":"1.0"},"canonical_sha256":"f7294c85322e375d4cc838c6477dde30be311c000d41a1b1cf2dcbf072d7e9d9","source":{"kind":"arxiv","id":"1112.1041","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.1041","created_at":"2026-05-18T04:06:57Z"},{"alias_kind":"arxiv_version","alias_value":"1112.1041v1","created_at":"2026-05-18T04:06:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.1041","created_at":"2026-05-18T04:06:57Z"},{"alias_kind":"pith_short_12","alias_value":"64UUZBJSFY3V","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"64UUZBJSFY3V2TGI","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"64UUZBJS","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:64UUZBJSFY3V2TGIHDDEO7O6GC","target":"record","payload":{"canonical_record":{"source":{"id":"1112.1041","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.PF","submitted_at":"2011-12-05T19:57:44Z","cross_cats_sorted":[],"title_canon_sha256":"1647ddddc03776723e96a9636dd6895ee2817d57af97a07791a04af2d8fb7871","abstract_canon_sha256":"a63e4c2fa50187709d4353b21172bc74420aabb22db8082d843668d49d3aefda"},"schema_version":"1.0"},"canonical_sha256":"f7294c85322e375d4cc838c6477dde30be311c000d41a1b1cf2dcbf072d7e9d9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:06:57.142281Z","signature_b64":"IqsNSP+Eas55QVV8hlwamuRPz2uj8O62x5MwfWyFLYbKtk2h8/Tk9cDkHMjmV/jSWKSOv4d6ESTqUezQcTUWBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f7294c85322e375d4cc838c6477dde30be311c000d41a1b1cf2dcbf072d7e9d9","last_reissued_at":"2026-05-18T04:06:57.141689Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:06:57.141689Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.1041","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":"2026-05-18T04:06:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jPoqHOEIBcgKuTEZyTZeHDTPev419kpunbrlM/D0NPHY/jVzf6MjLFWmFZHXU9mNBRQQ/GDFAvtMbNmnp8A7Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T00:45:33.505531Z"},"content_sha256":"66fba566a7ad0dcbfcdaa00b521292809210fb9469f59b2b2ef75db374670d18","schema_version":"1.0","event_id":"sha256:66fba566a7ad0dcbfcdaa00b521292809210fb9469f59b2b2ef75db374670d18"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:64UUZBJSFY3V2TGIHDDEO7O6GC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stabilization of Branching Queueing Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.PF","authors_text":"Stefan Kiefer, Tom\\'a\\v{s} Br\\'azdil","submitted_at":"2011-12-05T19:57:44Z","abstract_excerpt":"Queueing networks are gaining attraction for the performance analysis of parallel computer systems. A Jackson network is a set of interconnected servers, where the completion of a job at server i may result in the creation of a new job for server j. We propose to extend Jackson networks by \"branching\" and by \"control\" features. Both extensions are new and substantially expand the modelling power of Jackson networks. On the other hand, the extensions raise computational questions, particularly concerning the stability of the networks, i.e, the ergodicity of the underlying Markov chain. We show "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1041","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":"2026-05-18T04:06:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jJ/HasymkE9XzaP5BmfZi8FNUoOkTF6cD+MLseLkNv9TOlrBtj5zZhCsXd2q8UcZCtRAz9RTur01qnVKrw90Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T00:45:33.506080Z"},"content_sha256":"418709f572ec11b690f9f1b5e2ae7591dba65a072566eaac267c83e9b413fd95","schema_version":"1.0","event_id":"sha256:418709f572ec11b690f9f1b5e2ae7591dba65a072566eaac267c83e9b413fd95"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/64UUZBJSFY3V2TGIHDDEO7O6GC/bundle.json","state_url":"https://pith.science/pith/64UUZBJSFY3V2TGIHDDEO7O6GC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/64UUZBJSFY3V2TGIHDDEO7O6GC/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":"2026-05-24T00:45:33Z","links":{"resolver":"https://pith.science/pith/64UUZBJSFY3V2TGIHDDEO7O6GC","bundle":"https://pith.science/pith/64UUZBJSFY3V2TGIHDDEO7O6GC/bundle.json","state":"https://pith.science/pith/64UUZBJSFY3V2TGIHDDEO7O6GC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/64UUZBJSFY3V2TGIHDDEO7O6GC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:64UUZBJSFY3V2TGIHDDEO7O6GC","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":"a63e4c2fa50187709d4353b21172bc74420aabb22db8082d843668d49d3aefda","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.PF","submitted_at":"2011-12-05T19:57:44Z","title_canon_sha256":"1647ddddc03776723e96a9636dd6895ee2817d57af97a07791a04af2d8fb7871"},"schema_version":"1.0","source":{"id":"1112.1041","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.1041","created_at":"2026-05-18T04:06:57Z"},{"alias_kind":"arxiv_version","alias_value":"1112.1041v1","created_at":"2026-05-18T04:06:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.1041","created_at":"2026-05-18T04:06:57Z"},{"alias_kind":"pith_short_12","alias_value":"64UUZBJSFY3V","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"64UUZBJSFY3V2TGI","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"64UUZBJS","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:418709f572ec11b690f9f1b5e2ae7591dba65a072566eaac267c83e9b413fd95","target":"graph","created_at":"2026-05-18T04:06:57Z","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":"Queueing networks are gaining attraction for the performance analysis of parallel computer systems. A Jackson network is a set of interconnected servers, where the completion of a job at server i may result in the creation of a new job for server j. We propose to extend Jackson networks by \"branching\" and by \"control\" features. Both extensions are new and substantially expand the modelling power of Jackson networks. On the other hand, the extensions raise computational questions, particularly concerning the stability of the networks, i.e, the ergodicity of the underlying Markov chain. We show ","authors_text":"Stefan Kiefer, Tom\\'a\\v{s} Br\\'azdil","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.PF","submitted_at":"2011-12-05T19:57:44Z","title":"Stabilization of Branching Queueing Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1041","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":"sha256:66fba566a7ad0dcbfcdaa00b521292809210fb9469f59b2b2ef75db374670d18","target":"record","created_at":"2026-05-18T04:06:57Z","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":"a63e4c2fa50187709d4353b21172bc74420aabb22db8082d843668d49d3aefda","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.PF","submitted_at":"2011-12-05T19:57:44Z","title_canon_sha256":"1647ddddc03776723e96a9636dd6895ee2817d57af97a07791a04af2d8fb7871"},"schema_version":"1.0","source":{"id":"1112.1041","kind":"arxiv","version":1}},"canonical_sha256":"f7294c85322e375d4cc838c6477dde30be311c000d41a1b1cf2dcbf072d7e9d9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f7294c85322e375d4cc838c6477dde30be311c000d41a1b1cf2dcbf072d7e9d9","first_computed_at":"2026-05-18T04:06:57.141689Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:06:57.141689Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IqsNSP+Eas55QVV8hlwamuRPz2uj8O62x5MwfWyFLYbKtk2h8/Tk9cDkHMjmV/jSWKSOv4d6ESTqUezQcTUWBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:06:57.142281Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.1041","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:66fba566a7ad0dcbfcdaa00b521292809210fb9469f59b2b2ef75db374670d18","sha256:418709f572ec11b690f9f1b5e2ae7591dba65a072566eaac267c83e9b413fd95"],"state_sha256":"a7dddd40e38cb40d25f5b4510ae0b3e1b268ac09dd5b2fde91ab6f954ed4b686"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"82C/CNdWTUWmp3EG7NwOy/sAvNxTP84tg2AejtiPnGMoJ3RRH3zrlHTqBeeHXUdnb+jLK13aEI6h3x4aqbCICw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T00:45:33.509242Z","bundle_sha256":"da259975834916c8e16d04afe40dd195b83051a0021a5bb1c50db0500881f2f5"}}