{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:TRC7FTIDAX64TUUYDNYP63WSVX","short_pith_number":"pith:TRC7FTID","canonical_record":{"source":{"id":"1904.09565","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-04-21T08:22:12Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"6232b0445e9dc037b28d41c22185a3c5f6484d723d6fcda139412e9f58bb20ab","abstract_canon_sha256":"b161b6b0fdb1ed579eba2c2911b8d64d782ae9f51d112a8e0353b05a39686496"},"schema_version":"1.0"},"canonical_sha256":"9c45f2cd0305fdc9d2981b70ff6ed2ade4d24ed63dca796eb24f8d80b858def0","source":{"kind":"arxiv","id":"1904.09565","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.09565","created_at":"2026-05-17T23:48:03Z"},{"alias_kind":"arxiv_version","alias_value":"1904.09565v1","created_at":"2026-05-17T23:48:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.09565","created_at":"2026-05-17T23:48:03Z"},{"alias_kind":"pith_short_12","alias_value":"TRC7FTIDAX64","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"TRC7FTIDAX64TUUY","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"TRC7FTID","created_at":"2026-05-18T12:33:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:TRC7FTIDAX64TUUYDNYP63WSVX","target":"record","payload":{"canonical_record":{"source":{"id":"1904.09565","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-04-21T08:22:12Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"6232b0445e9dc037b28d41c22185a3c5f6484d723d6fcda139412e9f58bb20ab","abstract_canon_sha256":"b161b6b0fdb1ed579eba2c2911b8d64d782ae9f51d112a8e0353b05a39686496"},"schema_version":"1.0"},"canonical_sha256":"9c45f2cd0305fdc9d2981b70ff6ed2ade4d24ed63dca796eb24f8d80b858def0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:03.909837Z","signature_b64":"VdmPvcpAsRrKhF9NAqRoz690X1vHi9kK6+5S5Z658sjIBkWt7y4w6Goo1muDFkNMoyYdUqgKeCQjeHIg9JILBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9c45f2cd0305fdc9d2981b70ff6ed2ade4d24ed63dca796eb24f8d80b858def0","last_reissued_at":"2026-05-17T23:48:03.909384Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:03.909384Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.09565","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:48:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LZMAN9r5FK4saZDJbraLLwN734v20e4li5tBVQZppmGEOPJIc0si6lpOZYTyxO30zZIRjr6JxG8O2SlkE5w7CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T06:48:27.745605Z"},"content_sha256":"476005848983e3df4aa69b8816d0cbf801c7b3741f449f90625e87c7e9270cd2","schema_version":"1.0","event_id":"sha256:476005848983e3df4aa69b8816d0cbf801c7b3741f449f90625e87c7e9270cd2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:TRC7FTIDAX64TUUYDNYP63WSVX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantitative inequalities for the expected lifetime of Brownian motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Daesung Kim","submitted_at":"2019-04-21T08:22:12Z","abstract_excerpt":"The isoperimetric inequalities for the expected lifetime of Brownian motion state that the $L^p$-norms of the expected lifetime in a bounded domain for $1\\leq p\\leq \\infty$ are maximized when the region is a ball with the same volume. In this paper, we prove quantitative improvements of the inequalities. Since the isoperimetric properties hold for a wide class of L\\'evy processes, many questions arise from these improvements."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.09565","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:48:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V4C8TJynd8xMo327vPE8MUVOKfB5M5K7GNIxYWEo5CaQTi22+nNIj9ypPh0DHMa4yDVqpGSpQqqUPUtiy0IiAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T06:48:27.745937Z"},"content_sha256":"735f40f756b29cc645662e63bc46e6c5b1d7a2eb0b70d819c2db9fd31519c32a","schema_version":"1.0","event_id":"sha256:735f40f756b29cc645662e63bc46e6c5b1d7a2eb0b70d819c2db9fd31519c32a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TRC7FTIDAX64TUUYDNYP63WSVX/bundle.json","state_url":"https://pith.science/pith/TRC7FTIDAX64TUUYDNYP63WSVX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TRC7FTIDAX64TUUYDNYP63WSVX/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-20T06:48:27Z","links":{"resolver":"https://pith.science/pith/TRC7FTIDAX64TUUYDNYP63WSVX","bundle":"https://pith.science/pith/TRC7FTIDAX64TUUYDNYP63WSVX/bundle.json","state":"https://pith.science/pith/TRC7FTIDAX64TUUYDNYP63WSVX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TRC7FTIDAX64TUUYDNYP63WSVX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:TRC7FTIDAX64TUUYDNYP63WSVX","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":"b161b6b0fdb1ed579eba2c2911b8d64d782ae9f51d112a8e0353b05a39686496","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-04-21T08:22:12Z","title_canon_sha256":"6232b0445e9dc037b28d41c22185a3c5f6484d723d6fcda139412e9f58bb20ab"},"schema_version":"1.0","source":{"id":"1904.09565","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.09565","created_at":"2026-05-17T23:48:03Z"},{"alias_kind":"arxiv_version","alias_value":"1904.09565v1","created_at":"2026-05-17T23:48:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.09565","created_at":"2026-05-17T23:48:03Z"},{"alias_kind":"pith_short_12","alias_value":"TRC7FTIDAX64","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"TRC7FTIDAX64TUUY","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"TRC7FTID","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:735f40f756b29cc645662e63bc46e6c5b1d7a2eb0b70d819c2db9fd31519c32a","target":"graph","created_at":"2026-05-17T23:48:03Z","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":"The isoperimetric inequalities for the expected lifetime of Brownian motion state that the $L^p$-norms of the expected lifetime in a bounded domain for $1\\leq p\\leq \\infty$ are maximized when the region is a ball with the same volume. In this paper, we prove quantitative improvements of the inequalities. Since the isoperimetric properties hold for a wide class of L\\'evy processes, many questions arise from these improvements.","authors_text":"Daesung Kim","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-04-21T08:22:12Z","title":"Quantitative inequalities for the expected lifetime of Brownian motion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.09565","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":"sha256:476005848983e3df4aa69b8816d0cbf801c7b3741f449f90625e87c7e9270cd2","target":"record","created_at":"2026-05-17T23:48:03Z","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":"b161b6b0fdb1ed579eba2c2911b8d64d782ae9f51d112a8e0353b05a39686496","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-04-21T08:22:12Z","title_canon_sha256":"6232b0445e9dc037b28d41c22185a3c5f6484d723d6fcda139412e9f58bb20ab"},"schema_version":"1.0","source":{"id":"1904.09565","kind":"arxiv","version":1}},"canonical_sha256":"9c45f2cd0305fdc9d2981b70ff6ed2ade4d24ed63dca796eb24f8d80b858def0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c45f2cd0305fdc9d2981b70ff6ed2ade4d24ed63dca796eb24f8d80b858def0","first_computed_at":"2026-05-17T23:48:03.909384Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:03.909384Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VdmPvcpAsRrKhF9NAqRoz690X1vHi9kK6+5S5Z658sjIBkWt7y4w6Goo1muDFkNMoyYdUqgKeCQjeHIg9JILBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:03.909837Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.09565","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:476005848983e3df4aa69b8816d0cbf801c7b3741f449f90625e87c7e9270cd2","sha256:735f40f756b29cc645662e63bc46e6c5b1d7a2eb0b70d819c2db9fd31519c32a"],"state_sha256":"7e2c61e35e4da2770bbebb23566359b27b79e6bf20166f429e5862a4d0eb693f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f6Q46SYuRnCLjxWDSjmCR/6tRSfdCl514hx+xMIdO5JvA2l9GZ3bS2AQTtgjtkd74bJGbBGCuqYvfL/rrKblDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T06:48:27.747869Z","bundle_sha256":"4290c7570ca419f8e756e1d31c8454a99434e62fdba4620738448d2b25294c8a"}}