{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:MXHKA3CULNYIAOA77AER56G5NW","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":"9cde6cf3492efecb724eddd5a8e990c46f3e6393fa1c43e598943b83647c359b","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-05-10T00:48:21Z","title_canon_sha256":"59bea3534d9a1ad4ecd8c4a4cf93947b324005cdef16b25e67d171ff399df129"},"schema_version":"1.0","source":{"id":"1805.03764","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.03764","created_at":"2026-05-18T00:16:18Z"},{"alias_kind":"arxiv_version","alias_value":"1805.03764v1","created_at":"2026-05-18T00:16:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.03764","created_at":"2026-05-18T00:16:18Z"},{"alias_kind":"pith_short_12","alias_value":"MXHKA3CULNYI","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"MXHKA3CULNYIAOA7","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"MXHKA3CU","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:125536cca737bc5a2f9c9e4a9a2dc69ad175bf22a23273514da8959460df61b5","target":"graph","created_at":"2026-05-18T00:16:18Z","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":"We prove the equivalence of two different types of capacities in abstract Wiener spaces. This yields a criterion for the $L^p$-uniqueness of the Ornstein-Uhlenbeck operator and its integer powers defined on suitable algebras of functions vanishing in a neighborhood of a given closed set $\\Sigma$ of zero Gaussian measure. To prove the equivalence we show the $W^{r,p}(B,\\mu)$-boundedness of certain smooth nonlinear truncation operators acting on potentials of nonnegative functions. We also give connections to Gaussian Hausdorff measures. Roughly speaking, if $L^p$-uniqueness holds then the 'remo","authors_text":"Michael Hinz, Seunghyun Kang","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-05-10T00:48:21Z","title":"Capacities, removable sets and $L^p$-uniqueness on Wiener spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.03764","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:acb32e517ff69023538ae4b6bc888efdea95b8b98d89ff4acfdabe81a93328ae","target":"record","created_at":"2026-05-18T00:16:18Z","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":"9cde6cf3492efecb724eddd5a8e990c46f3e6393fa1c43e598943b83647c359b","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-05-10T00:48:21Z","title_canon_sha256":"59bea3534d9a1ad4ecd8c4a4cf93947b324005cdef16b25e67d171ff399df129"},"schema_version":"1.0","source":{"id":"1805.03764","kind":"arxiv","version":1}},"canonical_sha256":"65cea06c545b7080381ff8091ef8dd6d859fc80065cf9ea713c1b14237a0adc9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"65cea06c545b7080381ff8091ef8dd6d859fc80065cf9ea713c1b14237a0adc9","first_computed_at":"2026-05-18T00:16:18.834977Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:18.834977Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G1BtwrWH4DkUv8gvx7+E2aXeyMCrO5FSDfTsu8aG9Pez+NMTsw4NAw7yPJ23llCpOXZIMHJbjmNl8cu/gVT6DA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:18.835487Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.03764","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:acb32e517ff69023538ae4b6bc888efdea95b8b98d89ff4acfdabe81a93328ae","sha256:125536cca737bc5a2f9c9e4a9a2dc69ad175bf22a23273514da8959460df61b5"],"state_sha256":"773063cf56b2ee575cac1515eef91e8d3d8a0f37c9bf1099d7e5830f3c70017b"}