{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:SHR5XPFWTKLB3CJJQTXKK3WQY3","short_pith_number":"pith:SHR5XPFW","canonical_record":{"source":{"id":"1506.04013","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-12T13:19:12Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"4e32e427bdb8df900574cbfccb999406958d9e3b6e402b1db370db7afeae6506","abstract_canon_sha256":"8721522fbeb75aec08ce9f9cb9abf6abef36a44cfa4f6fcc4684f511bf328f51"},"schema_version":"1.0"},"canonical_sha256":"91e3dbbcb69a961d892984eea56ed0c6caedc7bb6f2532212d006da403490bf6","source":{"kind":"arxiv","id":"1506.04013","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.04013","created_at":"2026-05-18T01:08:21Z"},{"alias_kind":"arxiv_version","alias_value":"1506.04013v4","created_at":"2026-05-18T01:08:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.04013","created_at":"2026-05-18T01:08:21Z"},{"alias_kind":"pith_short_12","alias_value":"SHR5XPFWTKLB","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SHR5XPFWTKLB3CJJ","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SHR5XPFW","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:SHR5XPFWTKLB3CJJQTXKK3WQY3","target":"record","payload":{"canonical_record":{"source":{"id":"1506.04013","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-12T13:19:12Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"4e32e427bdb8df900574cbfccb999406958d9e3b6e402b1db370db7afeae6506","abstract_canon_sha256":"8721522fbeb75aec08ce9f9cb9abf6abef36a44cfa4f6fcc4684f511bf328f51"},"schema_version":"1.0"},"canonical_sha256":"91e3dbbcb69a961d892984eea56ed0c6caedc7bb6f2532212d006da403490bf6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:21.200560Z","signature_b64":"x7Lqbt2osCRfMRj/HnHKe8ct/bOBkkf6e3ipraM42AdWyqSviwekeyqYG9qDT/hhEVR1abuubap/p+sDotnYBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"91e3dbbcb69a961d892984eea56ed0c6caedc7bb6f2532212d006da403490bf6","last_reissued_at":"2026-05-18T01:08:21.200034Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:21.200034Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.04013","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:08:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xIv3NByz2EBmnWOQgB9JFnTr5zRX9NMXTOVRkEurej4ELKkB2YLHZ7hCuPJGOgymkGNXb++zzPUvfNc19ZQfCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T09:09:49.758211Z"},"content_sha256":"08b7939ea0b3272c3356c57f93f1cd8525e44af3004c703cdd959750f001667b","schema_version":"1.0","event_id":"sha256:08b7939ea0b3272c3356c57f93f1cd8525e44af3004c703cdd959750f001667b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:SHR5XPFWTKLB3CJJQTXKK3WQY3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stationary and Ergodic Properties of Stochastic Non-Linear Systems Controlled over Communication Channels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"math.PR","authors_text":"Serdar Y\\\"uksel","submitted_at":"2015-06-12T13:19:12Z","abstract_excerpt":"This paper is concerned with the following problem: Given a stochastic non-linear system controlled over a noisy channel, what is the largest class of channels for which there exist coding and control policies so that the closed loop system is stochastically stable? Stochastic stability notions considered are stationarity, ergodicity or asymptotic mean stationarity. We do not restrict the state space to be compact, for example systems considered can be driven by unbounded noise. Necessary and sufficient conditions are obtained for a large class of systems and channels. A generalization of Bode"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.04013","kind":"arxiv","version":4},"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":"2026-05-18T01:08:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5OmM+AHSlVX12hGKXh+5zRn1E2+DFqHk9MrCZHWWC1+sQSeQ1nOv4qtQfStwgoi+KLz7gsze1qP+DR1Vv50aCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T09:09:49.758575Z"},"content_sha256":"5ca697159aef9e5c289fe14d43cf2d621df37a9a82cdf0a3c0f544186ec09471","schema_version":"1.0","event_id":"sha256:5ca697159aef9e5c289fe14d43cf2d621df37a9a82cdf0a3c0f544186ec09471"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SHR5XPFWTKLB3CJJQTXKK3WQY3/bundle.json","state_url":"https://pith.science/pith/SHR5XPFWTKLB3CJJQTXKK3WQY3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SHR5XPFWTKLB3CJJQTXKK3WQY3/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":"2026-06-20T09:09:49Z","links":{"resolver":"https://pith.science/pith/SHR5XPFWTKLB3CJJQTXKK3WQY3","bundle":"https://pith.science/pith/SHR5XPFWTKLB3CJJQTXKK3WQY3/bundle.json","state":"https://pith.science/pith/SHR5XPFWTKLB3CJJQTXKK3WQY3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SHR5XPFWTKLB3CJJQTXKK3WQY3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:SHR5XPFWTKLB3CJJQTXKK3WQY3","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":"8721522fbeb75aec08ce9f9cb9abf6abef36a44cfa4f6fcc4684f511bf328f51","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-12T13:19:12Z","title_canon_sha256":"4e32e427bdb8df900574cbfccb999406958d9e3b6e402b1db370db7afeae6506"},"schema_version":"1.0","source":{"id":"1506.04013","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.04013","created_at":"2026-05-18T01:08:21Z"},{"alias_kind":"arxiv_version","alias_value":"1506.04013v4","created_at":"2026-05-18T01:08:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.04013","created_at":"2026-05-18T01:08:21Z"},{"alias_kind":"pith_short_12","alias_value":"SHR5XPFWTKLB","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SHR5XPFWTKLB3CJJ","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SHR5XPFW","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:5ca697159aef9e5c289fe14d43cf2d621df37a9a82cdf0a3c0f544186ec09471","target":"graph","created_at":"2026-05-18T01:08:21Z","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 is concerned with the following problem: Given a stochastic non-linear system controlled over a noisy channel, what is the largest class of channels for which there exist coding and control policies so that the closed loop system is stochastically stable? Stochastic stability notions considered are stationarity, ergodicity or asymptotic mean stationarity. We do not restrict the state space to be compact, for example systems considered can be driven by unbounded noise. Necessary and sufficient conditions are obtained for a large class of systems and channels. A generalization of Bode","authors_text":"Serdar Y\\\"uksel","cross_cats":["cs.IT","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-12T13:19:12Z","title":"Stationary and Ergodic Properties of Stochastic Non-Linear Systems Controlled over Communication Channels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.04013","kind":"arxiv","version":4},"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":"sha256:08b7939ea0b3272c3356c57f93f1cd8525e44af3004c703cdd959750f001667b","target":"record","created_at":"2026-05-18T01:08:21Z","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":"8721522fbeb75aec08ce9f9cb9abf6abef36a44cfa4f6fcc4684f511bf328f51","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-12T13:19:12Z","title_canon_sha256":"4e32e427bdb8df900574cbfccb999406958d9e3b6e402b1db370db7afeae6506"},"schema_version":"1.0","source":{"id":"1506.04013","kind":"arxiv","version":4}},"canonical_sha256":"91e3dbbcb69a961d892984eea56ed0c6caedc7bb6f2532212d006da403490bf6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"91e3dbbcb69a961d892984eea56ed0c6caedc7bb6f2532212d006da403490bf6","first_computed_at":"2026-05-18T01:08:21.200034Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:21.200034Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x7Lqbt2osCRfMRj/HnHKe8ct/bOBkkf6e3ipraM42AdWyqSviwekeyqYG9qDT/hhEVR1abuubap/p+sDotnYBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:21.200560Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.04013","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:08b7939ea0b3272c3356c57f93f1cd8525e44af3004c703cdd959750f001667b","sha256:5ca697159aef9e5c289fe14d43cf2d621df37a9a82cdf0a3c0f544186ec09471"],"state_sha256":"7cdd916bcf2bbe8295731d6dfd614f3b603ca9859ec5ffad37c358e816f54c82"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2d4dnV4+wMybdFFSj6dY1aA2YJ2nOAGJNnvU6XnAzrv4UZEMSIz7VO6Exoi5F4FLGR48yEKN/65jicT2ESr9AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T09:09:49.760548Z","bundle_sha256":"9c383c619551cc7ba0259f2ddd4d834500db53c80e8a195d14e512f14b4d6d73"}}