{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:PFZUF7J5WBWNFUYDQW3SEHYDUU","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":"fedb3a3586bc9833cd86f1357861075045012a28cd9325e3d3e074758ee3b982","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-05-13T20:22:49Z","title_canon_sha256":"7ef2f863b8dcc3a1293612b5fee19e4ce401e822564f7a548eb5bfe57f28de34"},"schema_version":"1.0","source":{"id":"1405.3298","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.3298","created_at":"2026-05-18T02:17:24Z"},{"alias_kind":"arxiv_version","alias_value":"1405.3298v3","created_at":"2026-05-18T02:17:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.3298","created_at":"2026-05-18T02:17:24Z"},{"alias_kind":"pith_short_12","alias_value":"PFZUF7J5WBWN","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"PFZUF7J5WBWNFUYD","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"PFZUF7J5","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:32eaa0d8f2981ac3b24ef7f17ade659b1f3fda3c30bb62a99e281ac0cec3d025","target":"graph","created_at":"2026-05-18T02:17:24Z","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 relative Fatou's theorem for nonnegative harmonic functions with respect to a large class of killed subordinate Brownian motions with Gaussian components in bounded $C^{1,1}$ open sets in $\\mathbb{R}^{d}$, $d\\geq 2$, which asserts the existence of nontangential limit of the ratio of two harmonic functions with respect to the killed processes. When $D=B(x_{0},r)$ is a ball we prove Fatou theorem. That is, we establish the existence of nontangential limit of a single nonnegative harmonic function. We also prove this is the best result possible by showing that there is a nonnegative harm","authors_text":"Hyunchul Park, Yunju Lee","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-05-13T20:22:49Z","title":"Fatou and relative Fatou theorem for subordinate Brownian motions with Gaussian components on smooth domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.3298","kind":"arxiv","version":3},"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:ef39e4acf4028106732955b241de5edd9a105052ca39e703ebe62cd5aba82221","target":"record","created_at":"2026-05-18T02:17:24Z","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":"fedb3a3586bc9833cd86f1357861075045012a28cd9325e3d3e074758ee3b982","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-05-13T20:22:49Z","title_canon_sha256":"7ef2f863b8dcc3a1293612b5fee19e4ce401e822564f7a548eb5bfe57f28de34"},"schema_version":"1.0","source":{"id":"1405.3298","kind":"arxiv","version":3}},"canonical_sha256":"797342fd3db06cd2d30385b7221f03a53e88aa994795c8a71cde681cd1280091","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"797342fd3db06cd2d30385b7221f03a53e88aa994795c8a71cde681cd1280091","first_computed_at":"2026-05-18T02:17:24.608263Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:17:24.608263Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rOh3Zp88UwVhJXKt5PYJ1V1/cJ8Be9inOlmeFgM+CApG1PsLFa60Plon3zx0TLc4gb5zmw8ndoB7w2wJR1sVDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:17:24.608894Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.3298","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ef39e4acf4028106732955b241de5edd9a105052ca39e703ebe62cd5aba82221","sha256:32eaa0d8f2981ac3b24ef7f17ade659b1f3fda3c30bb62a99e281ac0cec3d025"],"state_sha256":"7a3fcb7343423fd7257589deb4530a783c52346101d0fa7d36e1ca33a486ef51"}