{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:XWWZETDMVOF2RTNSKJWMPXLP7G","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":"7f0c3f53fa2ca95ce3714f8eb1c3b96a14a41a82019cd3d237585b5e286d18ed","cross_cats_sorted":["cs.SY","math.DS","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-01T07:53:56Z","title_canon_sha256":"0b8074d0aaa08f5f2704e9ae0be883d6474ca6a69ada03c5fd16ff85b3463b77"},"schema_version":"1.0","source":{"id":"1107.0132","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.0132","created_at":"2026-05-18T03:14:39Z"},{"alias_kind":"arxiv_version","alias_value":"1107.0132v3","created_at":"2026-05-18T03:14:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.0132","created_at":"2026-05-18T03:14:39Z"},{"alias_kind":"pith_short_12","alias_value":"XWWZETDMVOF2","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"XWWZETDMVOF2RTNS","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"XWWZETDM","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:c791b91c504395b8b8dc6b52fef3fd53742d09923a06353df8ce0982607f7194","target":"graph","created_at":"2026-05-18T03:14:39Z","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 study the pointwise stabilizability of a discrete-time, time-homogeneous, and stationary Markovian jump linear system. By using measure theory, ergodic theory and a splitting theorem of state space we show in a relatively simple way that if the system is essentially product-bounded, then it is pointwise convergent if and only if it is pointwise exponentially convergent.","authors_text":"Mingqing Xiao, Xiongping Dai, Yu Huang","cross_cats":["cs.SY","math.DS","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-01T07:53:56Z","title":"Pointwise Stabilization of Discrete-time Stationary Matrix-valued Markovian Chains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0132","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":"sha256:830ad49b56ecf6fb040e06a31112ac86943d8633da805a9dd30baf12a72dd8ba","target":"record","created_at":"2026-05-18T03:14:39Z","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":"7f0c3f53fa2ca95ce3714f8eb1c3b96a14a41a82019cd3d237585b5e286d18ed","cross_cats_sorted":["cs.SY","math.DS","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-01T07:53:56Z","title_canon_sha256":"0b8074d0aaa08f5f2704e9ae0be883d6474ca6a69ada03c5fd16ff85b3463b77"},"schema_version":"1.0","source":{"id":"1107.0132","kind":"arxiv","version":3}},"canonical_sha256":"bdad924c6cab8ba8cdb2526cc7dd6ff9869b3b88d96427ac5fc11365439f454d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bdad924c6cab8ba8cdb2526cc7dd6ff9869b3b88d96427ac5fc11365439f454d","first_computed_at":"2026-05-18T03:14:39.463599Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:14:39.463599Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kEeVI/grnaiLgl9nBNCOrBLBJ/Ci+4pi7UaiImMBRfLeUkNZfHV9WJmDr2gHzRiWXuG5X52Hu2zLYrDqNCTZDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:14:39.464331Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.0132","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:830ad49b56ecf6fb040e06a31112ac86943d8633da805a9dd30baf12a72dd8ba","sha256:c791b91c504395b8b8dc6b52fef3fd53742d09923a06353df8ce0982607f7194"],"state_sha256":"4fc1b429284c6cadd116eeba52ccf60deed50dee576eefbefdf192eb2655d927"}