{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:VM6VDTCYVXNGIGEUX24H6UC4ER","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":"16c25a483f16130a3392996268f301c34e75ead8520ac6759dfd91e440ed6da5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-08-29T06:55:41Z","title_canon_sha256":"79dd81f3e1e98724f0fc190fc2c602562bcf841020ba5dee652e35873e77b478"},"schema_version":"1.0","source":{"id":"1708.08606","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.08606","created_at":"2026-05-18T00:17:47Z"},{"alias_kind":"arxiv_version","alias_value":"1708.08606v2","created_at":"2026-05-18T00:17:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.08606","created_at":"2026-05-18T00:17:47Z"},{"alias_kind":"pith_short_12","alias_value":"VM6VDTCYVXNG","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VM6VDTCYVXNGIGEU","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VM6VDTCY","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:74857ad49e68c288fae8829add8141d6f9ee992d91ebcf0ca837501d41e567d4","target":"graph","created_at":"2026-05-18T00:17:47Z","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 discuss estimates of transition densities of subordinate Brownian motions in open subsets of Euclidean space. When $D$ is a $C^{1,1}$ domain, we establish sharp two-sided estimates for the transition densities of a large class of subordinate Brownian motions in $D$ whose scaling order is not necessarily strictly below $2$. Our estimates are explicit and written in terms of the dimension, the Euclidean distance between two points, the distance to the boundary and Laplace exponent of the corresponding subordinator only.","authors_text":"Ante Mimica, Panki Kim","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-08-29T06:55:41Z","title":"Estimates of Dirichlet heat kernels for subordinate Brownian motions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.08606","kind":"arxiv","version":2},"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":"sha256:2406da476149152667cd2b0238fd8716773ace1d76c1582651282d158b33539f","target":"record","created_at":"2026-05-18T00:17:47Z","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":"16c25a483f16130a3392996268f301c34e75ead8520ac6759dfd91e440ed6da5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-08-29T06:55:41Z","title_canon_sha256":"79dd81f3e1e98724f0fc190fc2c602562bcf841020ba5dee652e35873e77b478"},"schema_version":"1.0","source":{"id":"1708.08606","kind":"arxiv","version":2}},"canonical_sha256":"ab3d51cc58adda641894beb87f505c247452a458a143bde22f3089957b9334c2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ab3d51cc58adda641894beb87f505c247452a458a143bde22f3089957b9334c2","first_computed_at":"2026-05-18T00:17:47.414309Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:47.414309Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"erb/grvqHEl6VZeKgoFwZPP6Dz4i5LvlrKGvdC25pZqNZbIWwge8cGV9DplH9GuszDAkcejHi7iBq5yZ0Gk0BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:47.415017Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.08606","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2406da476149152667cd2b0238fd8716773ace1d76c1582651282d158b33539f","sha256:74857ad49e68c288fae8829add8141d6f9ee992d91ebcf0ca837501d41e567d4"],"state_sha256":"4a1c9d3096fb9676e917551e9215287f41b33a673162fb4a6516e2cf343d3428"}