{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:WGHN4L6REXAKBE2CPGFPBTSPPW","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":"386b897203bb95fd0772cf5358ddec6f53772369262498f0a1d6e7a3872be236","cross_cats_sorted":["math.DS","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-09-01T13:07:48Z","title_canon_sha256":"95e179b2b97b49e506d699abc0f8378ae37ea7c2fbdd324c0d919d8ae104b2b8"},"schema_version":"1.0","source":{"id":"1209.0090","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.0090","created_at":"2026-05-18T03:46:30Z"},{"alias_kind":"arxiv_version","alias_value":"1209.0090v1","created_at":"2026-05-18T03:46:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.0090","created_at":"2026-05-18T03:46:30Z"},{"alias_kind":"pith_short_12","alias_value":"WGHN4L6REXAK","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"WGHN4L6REXAKBE2C","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"WGHN4L6R","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:89891334651d98938688d1e826de0b7e5056025782fea8e10ba6d25c29974855","target":"graph","created_at":"2026-05-18T03:46:30Z","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":"By applying Rohlin's result on the classification of homomorphisms of Lebesgue space, the random inertial manifold of a stochastic damped nonlinear wave equations with singular perturbation is proved to be approximated almost surely by that of a stochastic nonlinear heat equation which is driven by a new Wiener process depending on the singular perturbation parameter. This approximation can be seen as the Smolukowski--Kramers approximation as time goes to infinity. However, as time goes infinity, the approximation changes with the small parameter, which is different from the approximation on a","authors_text":"Anthony Roberts, Wei Wang, Yan Lv","cross_cats":["math.DS","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-09-01T13:07:48Z","title":"Approximation of the random inertial manifold of singularly perturbed stochastic wave equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.0090","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":"sha256:2b1dc8a1dd1707ed5e70c0f231c52442a74ab3db37b125a53b4b34bce940eb22","target":"record","created_at":"2026-05-18T03:46:30Z","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":"386b897203bb95fd0772cf5358ddec6f53772369262498f0a1d6e7a3872be236","cross_cats_sorted":["math.DS","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-09-01T13:07:48Z","title_canon_sha256":"95e179b2b97b49e506d699abc0f8378ae37ea7c2fbdd324c0d919d8ae104b2b8"},"schema_version":"1.0","source":{"id":"1209.0090","kind":"arxiv","version":1}},"canonical_sha256":"b18ede2fd125c0a09342798af0ce4f7d9129d1e25fcc38538b95e0b45931dea3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b18ede2fd125c0a09342798af0ce4f7d9129d1e25fcc38538b95e0b45931dea3","first_computed_at":"2026-05-18T03:46:30.018268Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:46:30.018268Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2gXakuA4HaS6pDEpoQ5h7DN/W0VdFpGwALZt2JRUUgzYlkDGWN1UMWfh76Gwid8jC851l3zTnOdRPqvFIV8xCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:46:30.019272Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.0090","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2b1dc8a1dd1707ed5e70c0f231c52442a74ab3db37b125a53b4b34bce940eb22","sha256:89891334651d98938688d1e826de0b7e5056025782fea8e10ba6d25c29974855"],"state_sha256":"1cc418d59af3c7fd70ce008268c3692097cd545f192161037fb8920070fcb0ba"}