{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:GEX2J3ZOVEFQC4SOXFDJLLJ36M","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":"b390125c901693da8f78e5b264b636a43355019463e23f3aa4c417a940130243","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2022-06-05T19:05:11Z","title_canon_sha256":"41814c604a60cdb295d4dca50b3c5a7176c1ec7839050f8fc60b60a23581109a"},"schema_version":"1.0","source":{"id":"2206.02240","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2206.02240","created_at":"2026-07-05T04:29:15Z"},{"alias_kind":"arxiv_version","alias_value":"2206.02240v1","created_at":"2026-07-05T04:29:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.02240","created_at":"2026-07-05T04:29:15Z"},{"alias_kind":"pith_short_12","alias_value":"GEX2J3ZOVEFQ","created_at":"2026-07-05T04:29:15Z"},{"alias_kind":"pith_short_16","alias_value":"GEX2J3ZOVEFQC4SO","created_at":"2026-07-05T04:29:15Z"},{"alias_kind":"pith_short_8","alias_value":"GEX2J3ZO","created_at":"2026-07-05T04:29:15Z"}],"graph_snapshots":[{"event_id":"sha256:e1f96bc87fb46d26d56d448c49b4ef7db8dd161310cc482127588586b1a561b1","target":"graph","created_at":"2026-07-05T04:29:15Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2206.02240/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A variety of physical phenomena involve the nonlinear transfer of energy from weakly damped modes subjected to external forcing to other modes which are more heavily damped. In this work we explore this in (finite-dimensional) stochastic differential equations in $\\mathbb R^n$ with a quadratic, conservative nonlinearity $B(x,x)$ and a linear damping term $-Ax$ which is degenerate in the sense that $\\mathrm{ker} A \\neq \\emptyset$. We investigate sufficient conditions to deduce the existence of a stationary measure for the associated Markov semigroups. Existence of such measures is straightforwa","authors_text":"Jacob Bedrossian, Kyle Liss","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2022-06-05T19:05:11Z","title":"Stationary measures for stochastic differential equations with degenerate damping"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.02240","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":"sha256:581824df301cbafd96486e9ae19f462f20fdc60b40160b7c4eaa97c3b3add868","target":"record","created_at":"2026-07-05T04:29:15Z","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":"b390125c901693da8f78e5b264b636a43355019463e23f3aa4c417a940130243","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2022-06-05T19:05:11Z","title_canon_sha256":"41814c604a60cdb295d4dca50b3c5a7176c1ec7839050f8fc60b60a23581109a"},"schema_version":"1.0","source":{"id":"2206.02240","kind":"arxiv","version":1}},"canonical_sha256":"312fa4ef2ea90b01724eb94695ad3bf300508e26497fbad039e6f3f6e6ff0a60","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"312fa4ef2ea90b01724eb94695ad3bf300508e26497fbad039e6f3f6e6ff0a60","first_computed_at":"2026-07-05T04:29:15.722325Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:29:15.722325Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VUyuxYit9EjH4YMXbp2LE60/L0sb3WmXzPuBrjXjCZSYYKYXChKzShh0Ws9NbEC5+Cw8phpPvOTH4Hks5UuyBw==","signature_status":"signed_v1","signed_at":"2026-07-05T04:29:15.722767Z","signed_message":"canonical_sha256_bytes"},"source_id":"2206.02240","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:581824df301cbafd96486e9ae19f462f20fdc60b40160b7c4eaa97c3b3add868","sha256:e1f96bc87fb46d26d56d448c49b4ef7db8dd161310cc482127588586b1a561b1"],"state_sha256":"6164c5d756cde8828e7d8496a02d17535052b8dad91f0d1ee0cce02f127cebb2"}