{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:Z3HO2ENTU5BPJZGMPYH7FXXFKR","short_pith_number":"pith:Z3HO2ENT","canonical_record":{"source":{"id":"1506.01468","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-04T05:04:09Z","cross_cats_sorted":[],"title_canon_sha256":"d4862c91b9e67184c6347823f6a0b7fde4646735dbe77951ffd49ff58e06c8e5","abstract_canon_sha256":"75505810ea106250f59a87b2763233242c27268ba45a3e7310b7f1203e670dd1"},"schema_version":"1.0"},"canonical_sha256":"ceceed11b3a742f4e4cc7e0ff2dee55473d9be251d6afb8048e446d56220fe64","source":{"kind":"arxiv","id":"1506.01468","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.01468","created_at":"2026-05-18T01:26:57Z"},{"alias_kind":"arxiv_version","alias_value":"1506.01468v3","created_at":"2026-05-18T01:26:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.01468","created_at":"2026-05-18T01:26:57Z"},{"alias_kind":"pith_short_12","alias_value":"Z3HO2ENTU5BP","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"Z3HO2ENTU5BPJZGM","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"Z3HO2ENT","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:Z3HO2ENTU5BPJZGMPYH7FXXFKR","target":"record","payload":{"canonical_record":{"source":{"id":"1506.01468","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-04T05:04:09Z","cross_cats_sorted":[],"title_canon_sha256":"d4862c91b9e67184c6347823f6a0b7fde4646735dbe77951ffd49ff58e06c8e5","abstract_canon_sha256":"75505810ea106250f59a87b2763233242c27268ba45a3e7310b7f1203e670dd1"},"schema_version":"1.0"},"canonical_sha256":"ceceed11b3a742f4e4cc7e0ff2dee55473d9be251d6afb8048e446d56220fe64","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:26:57.590769Z","signature_b64":"Gy209zNz9bNx8SHUEuhOkar5kQBX9C3djQ+r8QurAYQuZ4Ehsd3vs8eRGLteatroDh/HHL3ExgnvaoS2J7EQBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ceceed11b3a742f4e4cc7e0ff2dee55473d9be251d6afb8048e446d56220fe64","last_reissued_at":"2026-05-18T01:26:57.590003Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:26:57.590003Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.01468","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:26:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o94r4eBGKALLLjFnXf5c52c9aEy2D8tGIsm+Mtcn83OmS0KxV31IKRQcpAa8Ahxs8x674yhUYiPYhtu293kdAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T21:14:14.329570Z"},"content_sha256":"9e1a9376630b1b6be98a3de480c9bdaeaaf81743504daaf5fb518740393e044f","schema_version":"1.0","event_id":"sha256:9e1a9376630b1b6be98a3de480c9bdaeaaf81743504daaf5fb518740393e044f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:Z3HO2ENTU5BPJZGMPYH7FXXFKR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the ergodicity bounds for a constant retrial rate queueing model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexander Zeifman, Andrey Gorshenin, Evsey Morozov, Ruslana Nekrasova, Yacov Satin","submitted_at":"2015-06-04T05:04:09Z","abstract_excerpt":"We consider a Markovian single-server retrial queueing system with a constant retrial rate. Conditions of null ergodicity and exponential ergodicity for the correspondent process, as well as bounds on the rate of convergence are obtained."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.01468","kind":"arxiv","version":3},"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":"2026-05-18T01:26:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f0bonFVpNCdqXlH9s+GnS9f2raCBzQGPnmRRJgg62eQLAkts9hdab54gh+ifW62K6ScKjj90QxSfyYA8ZAHxBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T21:14:14.330178Z"},"content_sha256":"5a4dbc092f790d87cf21b925951a5b388049fce4f3c30a090c2427280ce455f2","schema_version":"1.0","event_id":"sha256:5a4dbc092f790d87cf21b925951a5b388049fce4f3c30a090c2427280ce455f2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z3HO2ENTU5BPJZGMPYH7FXXFKR/bundle.json","state_url":"https://pith.science/pith/Z3HO2ENTU5BPJZGMPYH7FXXFKR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z3HO2ENTU5BPJZGMPYH7FXXFKR/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":"2026-05-30T21:14:14Z","links":{"resolver":"https://pith.science/pith/Z3HO2ENTU5BPJZGMPYH7FXXFKR","bundle":"https://pith.science/pith/Z3HO2ENTU5BPJZGMPYH7FXXFKR/bundle.json","state":"https://pith.science/pith/Z3HO2ENTU5BPJZGMPYH7FXXFKR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z3HO2ENTU5BPJZGMPYH7FXXFKR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:Z3HO2ENTU5BPJZGMPYH7FXXFKR","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":"75505810ea106250f59a87b2763233242c27268ba45a3e7310b7f1203e670dd1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-04T05:04:09Z","title_canon_sha256":"d4862c91b9e67184c6347823f6a0b7fde4646735dbe77951ffd49ff58e06c8e5"},"schema_version":"1.0","source":{"id":"1506.01468","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.01468","created_at":"2026-05-18T01:26:57Z"},{"alias_kind":"arxiv_version","alias_value":"1506.01468v3","created_at":"2026-05-18T01:26:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.01468","created_at":"2026-05-18T01:26:57Z"},{"alias_kind":"pith_short_12","alias_value":"Z3HO2ENTU5BP","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"Z3HO2ENTU5BPJZGM","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"Z3HO2ENT","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:5a4dbc092f790d87cf21b925951a5b388049fce4f3c30a090c2427280ce455f2","target":"graph","created_at":"2026-05-18T01:26:57Z","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":"We consider a Markovian single-server retrial queueing system with a constant retrial rate. Conditions of null ergodicity and exponential ergodicity for the correspondent process, as well as bounds on the rate of convergence are obtained.","authors_text":"Alexander Zeifman, Andrey Gorshenin, Evsey Morozov, Ruslana Nekrasova, Yacov Satin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-04T05:04:09Z","title":"On the ergodicity bounds for a constant retrial rate queueing model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.01468","kind":"arxiv","version":3},"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":"sha256:9e1a9376630b1b6be98a3de480c9bdaeaaf81743504daaf5fb518740393e044f","target":"record","created_at":"2026-05-18T01:26:57Z","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":"75505810ea106250f59a87b2763233242c27268ba45a3e7310b7f1203e670dd1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-04T05:04:09Z","title_canon_sha256":"d4862c91b9e67184c6347823f6a0b7fde4646735dbe77951ffd49ff58e06c8e5"},"schema_version":"1.0","source":{"id":"1506.01468","kind":"arxiv","version":3}},"canonical_sha256":"ceceed11b3a742f4e4cc7e0ff2dee55473d9be251d6afb8048e446d56220fe64","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ceceed11b3a742f4e4cc7e0ff2dee55473d9be251d6afb8048e446d56220fe64","first_computed_at":"2026-05-18T01:26:57.590003Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:26:57.590003Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Gy209zNz9bNx8SHUEuhOkar5kQBX9C3djQ+r8QurAYQuZ4Ehsd3vs8eRGLteatroDh/HHL3ExgnvaoS2J7EQBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:26:57.590769Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.01468","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e1a9376630b1b6be98a3de480c9bdaeaaf81743504daaf5fb518740393e044f","sha256:5a4dbc092f790d87cf21b925951a5b388049fce4f3c30a090c2427280ce455f2"],"state_sha256":"f2bb04ddd78482e40b96d455636fea5b0620c1abe068e8c05f0a5c48384de421"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a6jdfbpIjWPSPEAP2TrHvrxnPoiHcTHjA12Oqv2vbFwFwtBCIFzPw9JiyXUsggobhsu1WS8yhU6wA1SXuT8cAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T21:14:14.333508Z","bundle_sha256":"560619b799a249954b27cccc0625660777e9a7a0e0f64d76ff80d145a414a00a"}}