{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:Q4W2HT3WWO42MQL6ZH3UOH2RE2","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":"99cf4d7e38ff570de33bc52b184ad796615e42e5ce1425625a5dd86a10239c1a","cross_cats_sorted":["math.FA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-31T08:57:37Z","title_canon_sha256":"4f3c2bc8a41f1df548264e65e44fbd171be2062892af6bfb41b015a827d9d1dd"},"schema_version":"1.0","source":{"id":"1705.10992","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.10992","created_at":"2026-05-18T00:43:19Z"},{"alias_kind":"arxiv_version","alias_value":"1705.10992v1","created_at":"2026-05-18T00:43:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.10992","created_at":"2026-05-18T00:43:19Z"},{"alias_kind":"pith_short_12","alias_value":"Q4W2HT3WWO42","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"Q4W2HT3WWO42MQL6","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"Q4W2HT3W","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:2cc34293a710993c4dfa0daffdca877116e259632e3a072a8d702b1985639761","target":"graph","created_at":"2026-05-18T00:43:19Z","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 study a spatial asymptotic behaviour at infinity of kernels $p_t(x)$ for convolution semigroups of nonlocal pseudo-differential operators. We give general and sharp sufficient conditions under which the limits $$\n  \\lim_{r \\to \\infty} \\frac{p_t(r\\theta-y)}{t \\, \\nu(r\\theta)}, \\quad t \\in T, \\ \\ \\theta \\in E, \\ \\ y \\in \\mathbb R^d, $$ exist and can be effectively computed. Here $\\nu$ is the corresponding L\\'evy density, $T \\subset (0,\\infty)$ is a bounded time-set and $E$ is a subset of the unit sphere in $\\mathbb R^d$, $d \\geq 1$. Our results are local on the unit sphere. They apply to a wi","authors_text":"Kamil Kaleta, Pawe{\\l} Sztonyk","cross_cats":["math.FA","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-31T08:57:37Z","title":"Spatial asymptotics at infinity for heat kernels of integro-differential operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.10992","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":"sha256:8501656b74d9e9e8faf0c65926b1f011db387011aee48c0613c008f5d9e835ad","target":"record","created_at":"2026-05-18T00:43:19Z","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":"99cf4d7e38ff570de33bc52b184ad796615e42e5ce1425625a5dd86a10239c1a","cross_cats_sorted":["math.FA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-31T08:57:37Z","title_canon_sha256":"4f3c2bc8a41f1df548264e65e44fbd171be2062892af6bfb41b015a827d9d1dd"},"schema_version":"1.0","source":{"id":"1705.10992","kind":"arxiv","version":1}},"canonical_sha256":"872da3cf76b3b9a6417ec9f7471f5126a749726e86ce073b3b5e4f54d35d47f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"872da3cf76b3b9a6417ec9f7471f5126a749726e86ce073b3b5e4f54d35d47f4","first_computed_at":"2026-05-18T00:43:19.592037Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:19.592037Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lfgZ1TFdKlW1S2I+EcFdBXh8O0WacOhpLoIf1r4RMNlwj1u/HoikqOrwCguE0f7FyCyPO4e9A01hLfLHwyTZDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:19.592675Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.10992","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8501656b74d9e9e8faf0c65926b1f011db387011aee48c0613c008f5d9e835ad","sha256:2cc34293a710993c4dfa0daffdca877116e259632e3a072a8d702b1985639761"],"state_sha256":"b463882b6607fa9149e4b9049c3ef4548afd88eaa85d7009f103ba71655affbb"}