{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:37REUUD54RFSUID5TD57FGCYC3","short_pith_number":"pith:37REUUD5","canonical_record":{"source":{"id":"1208.5804","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-08-28T22:36:25Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"ad9d634cc88cb5c90e0f640efc0c5ec24a5ae3a0d84a5d926dc454c26e62cf9d","abstract_canon_sha256":"83b9eebe917f3e04c31daa551e54f1d5dcc3636cfbcf27c1e511977a01c0c79a"},"schema_version":"1.0"},"canonical_sha256":"dfe24a507de44b2a207d98fbf2985816c690bdb06ec8a3de6eabe3668878900c","source":{"kind":"arxiv","id":"1208.5804","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.5804","created_at":"2026-05-18T01:54:50Z"},{"alias_kind":"arxiv_version","alias_value":"1208.5804v2","created_at":"2026-05-18T01:54:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.5804","created_at":"2026-05-18T01:54:50Z"},{"alias_kind":"pith_short_12","alias_value":"37REUUD54RFS","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"37REUUD54RFSUID5","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"37REUUD5","created_at":"2026-05-18T12:26:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:37REUUD54RFSUID5TD57FGCYC3","target":"record","payload":{"canonical_record":{"source":{"id":"1208.5804","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-08-28T22:36:25Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"ad9d634cc88cb5c90e0f640efc0c5ec24a5ae3a0d84a5d926dc454c26e62cf9d","abstract_canon_sha256":"83b9eebe917f3e04c31daa551e54f1d5dcc3636cfbcf27c1e511977a01c0c79a"},"schema_version":"1.0"},"canonical_sha256":"dfe24a507de44b2a207d98fbf2985816c690bdb06ec8a3de6eabe3668878900c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:54:50.550712Z","signature_b64":"njMxn4F5sHfhrwy3m/kOtW8f2vCFmwLgrG8kfhgRIBJOsLyGN0NhWoFpQA+tVqNhoqcHHhMhBqHpSWxZ6XDNDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dfe24a507de44b2a207d98fbf2985816c690bdb06ec8a3de6eabe3668878900c","last_reissued_at":"2026-05-18T01:54:50.550186Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:54:50.550186Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.5804","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:54:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y7n0phCrpyjsqS2XLhADJ16vkkPAW64QOejY8kyvgwhgRoBjh4RT2kQx/2RFKw8G+SQMYu85Ehz5PrsHE5kjBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T23:13:09.652881Z"},"content_sha256":"8ca60b5194459ec066746199f7fcf07b1dc9330cdaf50a9cada19cc53cb603fb","schema_version":"1.0","event_id":"sha256:8ca60b5194459ec066746199f7fcf07b1dc9330cdaf50a9cada19cc53cb603fb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:37REUUD54RFSUID5TD57FGCYC3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exponential Ergodicity of stochastic Burgers equations driven by $\\alpha$-stable processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Lihu Xu, Xicheng Zhang, Zhao Dong","submitted_at":"2012-08-28T22:36:25Z","abstract_excerpt":"In this work, we prove the strong Feller property and the exponential ergodicity of stochastic Burgers equations driven by $\\alpha/2$-subordinated cylindrical Brownian motions with $\\alpha\\in(1,2)$. To prove the results, we truncate the nonlinearity and use the derivative formula for SDEs driven by $\\alpha$-stable noises established in Zhang (arXiv:1204.2630v2)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.5804","kind":"arxiv","version":2},"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":"2026-05-18T01:54:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bOCtzNnS7uPhb0z4ef8kwY2gFy5E2T8K19xKiKleAlazg2EjHJh1WecDryo3vDptWmiWmSX6O7vpvWZEcZhdCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T23:13:09.653513Z"},"content_sha256":"ee2749b88bca1c341075e02509509b2c853b4c053e3684d8be93976121404088","schema_version":"1.0","event_id":"sha256:ee2749b88bca1c341075e02509509b2c853b4c053e3684d8be93976121404088"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/37REUUD54RFSUID5TD57FGCYC3/bundle.json","state_url":"https://pith.science/pith/37REUUD54RFSUID5TD57FGCYC3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/37REUUD54RFSUID5TD57FGCYC3/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":"2026-06-04T23:13:09Z","links":{"resolver":"https://pith.science/pith/37REUUD54RFSUID5TD57FGCYC3","bundle":"https://pith.science/pith/37REUUD54RFSUID5TD57FGCYC3/bundle.json","state":"https://pith.science/pith/37REUUD54RFSUID5TD57FGCYC3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/37REUUD54RFSUID5TD57FGCYC3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:37REUUD54RFSUID5TD57FGCYC3","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":"83b9eebe917f3e04c31daa551e54f1d5dcc3636cfbcf27c1e511977a01c0c79a","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-08-28T22:36:25Z","title_canon_sha256":"ad9d634cc88cb5c90e0f640efc0c5ec24a5ae3a0d84a5d926dc454c26e62cf9d"},"schema_version":"1.0","source":{"id":"1208.5804","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.5804","created_at":"2026-05-18T01:54:50Z"},{"alias_kind":"arxiv_version","alias_value":"1208.5804v2","created_at":"2026-05-18T01:54:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.5804","created_at":"2026-05-18T01:54:50Z"},{"alias_kind":"pith_short_12","alias_value":"37REUUD54RFS","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"37REUUD54RFSUID5","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"37REUUD5","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:ee2749b88bca1c341075e02509509b2c853b4c053e3684d8be93976121404088","target":"graph","created_at":"2026-05-18T01:54:50Z","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"},"paper":{"abstract_excerpt":"In this work, we prove the strong Feller property and the exponential ergodicity of stochastic Burgers equations driven by $\\alpha/2$-subordinated cylindrical Brownian motions with $\\alpha\\in(1,2)$. To prove the results, we truncate the nonlinearity and use the derivative formula for SDEs driven by $\\alpha$-stable noises established in Zhang (arXiv:1204.2630v2).","authors_text":"Lihu Xu, Xicheng Zhang, Zhao Dong","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-08-28T22:36:25Z","title":"Exponential Ergodicity of stochastic Burgers equations driven by $\\alpha$-stable processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.5804","kind":"arxiv","version":2},"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":"sha256:8ca60b5194459ec066746199f7fcf07b1dc9330cdaf50a9cada19cc53cb603fb","target":"record","created_at":"2026-05-18T01:54:50Z","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":"83b9eebe917f3e04c31daa551e54f1d5dcc3636cfbcf27c1e511977a01c0c79a","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-08-28T22:36:25Z","title_canon_sha256":"ad9d634cc88cb5c90e0f640efc0c5ec24a5ae3a0d84a5d926dc454c26e62cf9d"},"schema_version":"1.0","source":{"id":"1208.5804","kind":"arxiv","version":2}},"canonical_sha256":"dfe24a507de44b2a207d98fbf2985816c690bdb06ec8a3de6eabe3668878900c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dfe24a507de44b2a207d98fbf2985816c690bdb06ec8a3de6eabe3668878900c","first_computed_at":"2026-05-18T01:54:50.550186Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:54:50.550186Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"njMxn4F5sHfhrwy3m/kOtW8f2vCFmwLgrG8kfhgRIBJOsLyGN0NhWoFpQA+tVqNhoqcHHhMhBqHpSWxZ6XDNDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:54:50.550712Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.5804","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8ca60b5194459ec066746199f7fcf07b1dc9330cdaf50a9cada19cc53cb603fb","sha256:ee2749b88bca1c341075e02509509b2c853b4c053e3684d8be93976121404088"],"state_sha256":"0713da529f243b26686473220334c81b07fa4bc993891464eb7555f9749c8f06"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ei4FpIRj3EBYAJ1A2ar6tkj8vdCz7ZZNJpWnv4xg/V5NlZZO7kul0eyvVothd3pSJ1Z41oF2Nu9/NZ6LkYktAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T23:13:09.656818Z","bundle_sha256":"046cb7e5e77300b5a744123f38c3d540467cf2a4d5fa0601c04bb1ae7a201e14"}}