{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:MXJP5YGMXJ4EAFIADQCGX24DHN","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":"30989ca8033ea08469e873479c38cd5dd7c64058e96e8dcafcbb774e1d32020a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-03-26T12:05:23Z","title_canon_sha256":"cd77588d9c7b8ec434df081eed5c72127c4419b289e6c494a9bd8d9a2e94a0fd"},"schema_version":"1.0","source":{"id":"1303.6449","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.6449","created_at":"2026-05-18T00:44:29Z"},{"alias_kind":"arxiv_version","alias_value":"1303.6449v1","created_at":"2026-05-18T00:44:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.6449","created_at":"2026-05-18T00:44:29Z"},{"alias_kind":"pith_short_12","alias_value":"MXJP5YGMXJ4E","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MXJP5YGMXJ4EAFIA","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MXJP5YGM","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:e8506b26d845507904efb06a3885198adf1f9af8b9b8dbcfc013d56c808e2c6e","target":"graph","created_at":"2026-05-18T00:44:29Z","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 paper, we consider a large class of purely discontinuous rotationally symmetric Levy processes. We establish sharp two-sided estimates for the transition densities of such processes killed upon leaving an open set D. When D is a \\kappa-fat open set, the sharp two-sided estimates are given in terms of surviving probabilities and the global transition density of the Levy process. When D is a C^{1, 1} open set and the Levy exponent of the process is given by \\Psi(\\xi)= \\phi(|\\xi|^2) with \\phi being a complete Bernstein function satisfying a mild growth condition at infinity, our two-sided","authors_text":"Panki Kim, Renming Song, Zhen-Qing Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-03-26T12:05:23Z","title":"Dirichlet Heat Kernel Estimates for Rotationally Symmetric L\\'evy processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.6449","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":"sha256:1205325b0fa0ca53f770e11123f74df28368a178e93c7e45b1d8c67363ae04da","target":"record","created_at":"2026-05-18T00:44:29Z","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":"30989ca8033ea08469e873479c38cd5dd7c64058e96e8dcafcbb774e1d32020a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-03-26T12:05:23Z","title_canon_sha256":"cd77588d9c7b8ec434df081eed5c72127c4419b289e6c494a9bd8d9a2e94a0fd"},"schema_version":"1.0","source":{"id":"1303.6449","kind":"arxiv","version":1}},"canonical_sha256":"65d2fee0ccba784015001c046beb833b55dcc3612d76491ae1a1a9805dc3d490","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"65d2fee0ccba784015001c046beb833b55dcc3612d76491ae1a1a9805dc3d490","first_computed_at":"2026-05-18T00:44:29.915137Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:29.915137Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2LRf5q19RGXZK8tebrmogBvcRwIg6o2bjgw8FnsjFRIMElPK5PIwNczQjviDi73ahzXmndk1o7QYue3OH3ZxAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:29.915719Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.6449","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1205325b0fa0ca53f770e11123f74df28368a178e93c7e45b1d8c67363ae04da","sha256:e8506b26d845507904efb06a3885198adf1f9af8b9b8dbcfc013d56c808e2c6e"],"state_sha256":"b5ae257202b2c2464b010218388c6e7a1fa2e9e3147aa25d016470ec9973f8bd"}