{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:TZHAM2WD6P25DOVI2JZGWNTCFE","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":"7418e689035f202e4540373b62ad853733ade6ac0423451e0cac46a14adb03f9","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-03-11T05:02:21Z","title_canon_sha256":"512bf9fa85151925c601955f1fac496478fa264af9ab123818d4b9daf69fb6f7"},"schema_version":"1.0","source":{"id":"2503.08047","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.08047","created_at":"2026-07-05T10:28:50Z"},{"alias_kind":"arxiv_version","alias_value":"2503.08047v1","created_at":"2026-07-05T10:28:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.08047","created_at":"2026-07-05T10:28:50Z"},{"alias_kind":"pith_short_12","alias_value":"TZHAM2WD6P25","created_at":"2026-07-05T10:28:50Z"},{"alias_kind":"pith_short_16","alias_value":"TZHAM2WD6P25DOVI","created_at":"2026-07-05T10:28:50Z"},{"alias_kind":"pith_short_8","alias_value":"TZHAM2WD","created_at":"2026-07-05T10:28:50Z"}],"graph_snapshots":[{"event_id":"sha256:ed4e098e1a6defd9c7eb0ff388f1ad2f1d4cce2b00d58bcf7ec339f4e9414de0","target":"graph","created_at":"2026-07-05T10:28:50Z","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/2503.08047/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we study the diffusion approximation for slow-fast stochastic differential equations with state-dependent switching, where the slow component $X^{\\varepsilon}$ is the solution of a stochastic differential equation with additional homogenization term, while the fast component $\\alpha^{\\varepsilon}$ is a switching process. We first prove the weak convergence of $\\{X^\\varepsilon\\}_{0<\\varepsilon\\leq 1}$ to $\\bar{X}$ in the space of continuous functions, as $\\varepsilon\\rightarrow 0$. Using the martingale problem approach and Poisson equation associated with a Markov chain, we ident","authors_text":"Jue Wang, Xiaobin Sun, Yingchao Xie","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-03-11T05:02:21Z","title":"Diffusion Approximation for Slow-Fast SDEs with State-Dependent Switching"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.08047","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":"sha256:52bf27a85bfcb28f6ddf1d0a3c654e4cf0b9f87db5ea98867de8ceac41e21d8d","target":"record","created_at":"2026-07-05T10:28:50Z","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":"7418e689035f202e4540373b62ad853733ade6ac0423451e0cac46a14adb03f9","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-03-11T05:02:21Z","title_canon_sha256":"512bf9fa85151925c601955f1fac496478fa264af9ab123818d4b9daf69fb6f7"},"schema_version":"1.0","source":{"id":"2503.08047","kind":"arxiv","version":1}},"canonical_sha256":"9e4e066ac3f3f5d1baa8d2726b3662292ea8ad04c9b96ab28c9abf6b8b6147ad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9e4e066ac3f3f5d1baa8d2726b3662292ea8ad04c9b96ab28c9abf6b8b6147ad","first_computed_at":"2026-07-05T10:28:50.080142Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:28:50.080142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mmiTqkp7M2nHMmcPuEKmXtS3f6s8A37C40vkZd8p09Cq+kKt8bwZd9DXfdWVkHOAlk+CDmX6N5gDwdzFOR5cBA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:28:50.080834Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.08047","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:52bf27a85bfcb28f6ddf1d0a3c654e4cf0b9f87db5ea98867de8ceac41e21d8d","sha256:ed4e098e1a6defd9c7eb0ff388f1ad2f1d4cce2b00d58bcf7ec339f4e9414de0"],"state_sha256":"cd6f81f2cff53c4f43edbc4e1bd62095d3b2f9e373c6f2661f95600a73a33264"}