{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:DAFNMWUCODMXJXGRBKQVD4XNIR","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":"2102e5c66be3936a897f8bf0610fd786c1e8d06acaeabbe446f1cf482b1aedc1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-09-24T06:06:33Z","title_canon_sha256":"297a94ccb9b7b55786736b158a8de5b4478507cfc199e3d5e474fdf8d344c377"},"schema_version":"1.0","source":{"id":"1409.7335","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.7335","created_at":"2026-05-18T01:22:41Z"},{"alias_kind":"arxiv_version","alias_value":"1409.7335v2","created_at":"2026-05-18T01:22:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.7335","created_at":"2026-05-18T01:22:41Z"},{"alias_kind":"pith_short_12","alias_value":"DAFNMWUCODMX","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DAFNMWUCODMXJXGR","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DAFNMWUC","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:dea5471b96c9df65b0288ca1a8f7c05b3e3eff27c7d8ce0c5e5a0d7e2e2df7c4","target":"graph","created_at":"2026-05-18T01:22:41Z","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":"In this note, we investigate, under what circumstances, a warm standby system (formed by n active components and m warm standby components) has more number of surviving warm standby components than another similar system at the time of $k$th failure of the active component of the respective system. The number of such components being random, the comparison has been done with respect to different stochastic orders, viz. usual stochastic order, hazard rate and reversed hazard rate orders, and likelihood ratio order.","authors_text":"Asok K. Nanda, Nil Kamal Hazra","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-09-24T06:06:33Z","title":"A Note on Warm Standby System"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.7335","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:c3bbf06a6a5a2f9c24fb3071f04fa05eeedfea3a317b0656ce599982dcc19d72","target":"record","created_at":"2026-05-18T01:22:41Z","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":"2102e5c66be3936a897f8bf0610fd786c1e8d06acaeabbe446f1cf482b1aedc1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-09-24T06:06:33Z","title_canon_sha256":"297a94ccb9b7b55786736b158a8de5b4478507cfc199e3d5e474fdf8d344c377"},"schema_version":"1.0","source":{"id":"1409.7335","kind":"arxiv","version":2}},"canonical_sha256":"180ad65a8270d974dcd10aa151f2ed44694515232604f11d8c51f67ad3269c01","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"180ad65a8270d974dcd10aa151f2ed44694515232604f11d8c51f67ad3269c01","first_computed_at":"2026-05-18T01:22:41.836635Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:41.836635Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o3s2/wLefCwKPRW5ruAb13k2cNQR1ZTOEdYMe42Yk5yzWHFw4TT/y/8QgB2yEl3lIdVEhBMIcgQid7ZP9t5ACQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:41.837384Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.7335","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c3bbf06a6a5a2f9c24fb3071f04fa05eeedfea3a317b0656ce599982dcc19d72","sha256:dea5471b96c9df65b0288ca1a8f7c05b3e3eff27c7d8ce0c5e5a0d7e2e2df7c4"],"state_sha256":"cbf4a1182c8212c3400dfaa4742c7e3e477e13526ea4d1048da9431351401733"}