{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:HIJ3RK6IQCYQ52DUBWHU7RW6GG","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":"e1d7c7e150f491f9127da2d97460ef3a405d8c1c90c6f7eb9469d7a707a193ef","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.PR","submitted_at":"2024-11-15T05:02:50Z","title_canon_sha256":"a8194939ae1e4a7bbcfa8730c2300d5edd3b37e4d9e0b8902277c7a0c8b8b48d"},"schema_version":"1.0","source":{"id":"2411.09949","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.09949","created_at":"2026-07-05T09:35:56Z"},{"alias_kind":"arxiv_version","alias_value":"2411.09949v1","created_at":"2026-07-05T09:35:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.09949","created_at":"2026-07-05T09:35:56Z"},{"alias_kind":"pith_short_12","alias_value":"HIJ3RK6IQCYQ","created_at":"2026-07-05T09:35:56Z"},{"alias_kind":"pith_short_16","alias_value":"HIJ3RK6IQCYQ52DU","created_at":"2026-07-05T09:35:56Z"},{"alias_kind":"pith_short_8","alias_value":"HIJ3RK6I","created_at":"2026-07-05T09:35:56Z"}],"graph_snapshots":[{"event_id":"sha256:b4db03ea0f0492214b37c3c2e1b3f3c5b683866c6f3e2c42973ff473ab7f7dd7","target":"graph","created_at":"2026-07-05T09:35:56Z","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/2411.09949/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"By establishing the regularity estimates for nonlocal Stein/Poisson equations under $\\gamma$-order H\\\"older and dissipative conditions on the coefficients, we derive the $W_{\\bf d}$-convergence rate for the Euler-Maruyama schemes applied to the invariant measure of SDEs driven by multiplicative $\\alpha$-stable noises with $\\alpha \\in (\\frac{1}{2}, 2)$, where $W_{\\bf d}$ denotes the Wasserstein metric with ${\\bf d}(x,y)=|x-y|^\\gamma\\wedge 1$ and $\\gamma \\in ((1-\\alpha)_+, 1]$.","authors_text":"Lihu Xu, Peng Chen, XiaoLong Zhang, Xicheng Zhang","cross_cats":[],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.PR","submitted_at":"2024-11-15T05:02:50Z","title":"$W_{\\bf d}$-convergence rate of EM schemes for invariant measures of supercritical stable SDEs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.09949","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":"sha256:4f4a21201b48510eb4395bfcf4ace96133c21519f65b3c6f891ed8d424c30ab2","target":"record","created_at":"2026-07-05T09:35:56Z","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":"e1d7c7e150f491f9127da2d97460ef3a405d8c1c90c6f7eb9469d7a707a193ef","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.PR","submitted_at":"2024-11-15T05:02:50Z","title_canon_sha256":"a8194939ae1e4a7bbcfa8730c2300d5edd3b37e4d9e0b8902277c7a0c8b8b48d"},"schema_version":"1.0","source":{"id":"2411.09949","kind":"arxiv","version":1}},"canonical_sha256":"3a13b8abc880b10ee8740d8f4fc6de318cc6e0f4e08e236313dfcc49e9972bb5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3a13b8abc880b10ee8740d8f4fc6de318cc6e0f4e08e236313dfcc49e9972bb5","first_computed_at":"2026-07-05T09:35:56.160237Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:35:56.160237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YP2MPTTzBzRPiKWvdtqHWZxdECyZB+8Q28AuhaQaWBIcf0sVO/57WSj0C7IKahiL34KjE+iltvt5Ro8zHDN9DQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:35:56.160751Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.09949","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4f4a21201b48510eb4395bfcf4ace96133c21519f65b3c6f891ed8d424c30ab2","sha256:b4db03ea0f0492214b37c3c2e1b3f3c5b683866c6f3e2c42973ff473ab7f7dd7"],"state_sha256":"f8d8c16659bc4aaa45ebfe304e007ed52f7313ddc58d8610b3261bbfe496b419"}