{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:TKYEVFZ4CWMZZ7XQBBPMRCB3LU","short_pith_number":"pith:TKYEVFZ4","canonical_record":{"source":{"id":"1305.1203","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-06T14:09:29Z","cross_cats_sorted":[],"title_canon_sha256":"730074aae1bd0fb74b48375313c4fc8e9cb8ce63dac7158f9c500afea4011024","abstract_canon_sha256":"00630e0e38d0422dbe3fbd8ccdfa077165853b7d6fc49014be2cfa1dd2dc8972"},"schema_version":"1.0"},"canonical_sha256":"9ab04a973c15999cfef0085ec8883b5d054c42ba7e31fc76f3881054c8cebe5a","source":{"kind":"arxiv","id":"1305.1203","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.1203","created_at":"2026-05-18T02:29:32Z"},{"alias_kind":"arxiv_version","alias_value":"1305.1203v2","created_at":"2026-05-18T02:29:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.1203","created_at":"2026-05-18T02:29:32Z"},{"alias_kind":"pith_short_12","alias_value":"TKYEVFZ4CWMZ","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"TKYEVFZ4CWMZZ7XQ","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"TKYEVFZ4","created_at":"2026-05-18T12:28:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:TKYEVFZ4CWMZZ7XQBBPMRCB3LU","target":"record","payload":{"canonical_record":{"source":{"id":"1305.1203","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-06T14:09:29Z","cross_cats_sorted":[],"title_canon_sha256":"730074aae1bd0fb74b48375313c4fc8e9cb8ce63dac7158f9c500afea4011024","abstract_canon_sha256":"00630e0e38d0422dbe3fbd8ccdfa077165853b7d6fc49014be2cfa1dd2dc8972"},"schema_version":"1.0"},"canonical_sha256":"9ab04a973c15999cfef0085ec8883b5d054c42ba7e31fc76f3881054c8cebe5a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:32.426508Z","signature_b64":"gc6MQ4cp5DIBzejet1cIlFoYFrRVnj1IeEl3uGox9twgGabB9voOiY/SNgschuCakAiXUwF73mMSS0/A+VprBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9ab04a973c15999cfef0085ec8883b5d054c42ba7e31fc76f3881054c8cebe5a","last_reissued_at":"2026-05-18T02:29:32.426067Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:32.426067Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.1203","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:29:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QZeQtnVQQ2bEzu82JDWF7ql2yN397XoVSy2oO6Uj0Rm3hMBTw18tmOj+MZt32rgaagxEQnypPy32vgAXi86ABA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T01:23:57.392219Z"},"content_sha256":"4134273a912908462f0d7c4d93802b881a9cc4cd51bc7941ad2e54c830eb57eb","schema_version":"1.0","event_id":"sha256:4134273a912908462f0d7c4d93802b881a9cc4cd51bc7941ad2e54c830eb57eb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:TKYEVFZ4CWMZZ7XQBBPMRCB3LU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The first passage time problem over a moving boundary for asymptotically stable L\\'evy processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Frank Aurzada, Tanja Kramm","submitted_at":"2013-05-06T14:09:29Z","abstract_excerpt":"We study the asymptotic tail behaviour of the first-passage time over a moving boundary for asymptotically $\\alpha$-stable L\\'evy processes with $\\alpha<1$.\n  Our main result states that if the left tail of the L\\'evy measure is regularly varying with index $- \\alpha$ and the moving boundary is equal to $1 - t^{\\gamma}$ for some $\\gamma<1/\\alpha$, then the probability that the process stays below the moving boundary has the same asymptotic polynomial order as in the case of a constant boundary. The same is true for the increasing boundary $1 + t^{\\gamma}$ with $\\gamma<1/\\alpha$ under the assum"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.1203","kind":"arxiv","version":2},"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":"2026-05-18T02:29:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e/4kO0HvVK8t3+1aEnWdIiGzdymmyYB4tnP7i3qO3cUo9i7YmYQmRsKt53bx8ttkL6Tai/44RgwEdxGNO32/DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T01:23:57.392880Z"},"content_sha256":"326a2dc705af38a935a06613a1d6a962694c1673788d17e932b228db5999a605","schema_version":"1.0","event_id":"sha256:326a2dc705af38a935a06613a1d6a962694c1673788d17e932b228db5999a605"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TKYEVFZ4CWMZZ7XQBBPMRCB3LU/bundle.json","state_url":"https://pith.science/pith/TKYEVFZ4CWMZZ7XQBBPMRCB3LU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TKYEVFZ4CWMZZ7XQBBPMRCB3LU/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":"2026-06-10T01:23:57Z","links":{"resolver":"https://pith.science/pith/TKYEVFZ4CWMZZ7XQBBPMRCB3LU","bundle":"https://pith.science/pith/TKYEVFZ4CWMZZ7XQBBPMRCB3LU/bundle.json","state":"https://pith.science/pith/TKYEVFZ4CWMZZ7XQBBPMRCB3LU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TKYEVFZ4CWMZZ7XQBBPMRCB3LU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:TKYEVFZ4CWMZZ7XQBBPMRCB3LU","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":"00630e0e38d0422dbe3fbd8ccdfa077165853b7d6fc49014be2cfa1dd2dc8972","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-06T14:09:29Z","title_canon_sha256":"730074aae1bd0fb74b48375313c4fc8e9cb8ce63dac7158f9c500afea4011024"},"schema_version":"1.0","source":{"id":"1305.1203","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.1203","created_at":"2026-05-18T02:29:32Z"},{"alias_kind":"arxiv_version","alias_value":"1305.1203v2","created_at":"2026-05-18T02:29:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.1203","created_at":"2026-05-18T02:29:32Z"},{"alias_kind":"pith_short_12","alias_value":"TKYEVFZ4CWMZ","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"TKYEVFZ4CWMZZ7XQ","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"TKYEVFZ4","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:326a2dc705af38a935a06613a1d6a962694c1673788d17e932b228db5999a605","target":"graph","created_at":"2026-05-18T02:29:32Z","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 the asymptotic tail behaviour of the first-passage time over a moving boundary for asymptotically $\\alpha$-stable L\\'evy processes with $\\alpha<1$.\n  Our main result states that if the left tail of the L\\'evy measure is regularly varying with index $- \\alpha$ and the moving boundary is equal to $1 - t^{\\gamma}$ for some $\\gamma<1/\\alpha$, then the probability that the process stays below the moving boundary has the same asymptotic polynomial order as in the case of a constant boundary. The same is true for the increasing boundary $1 + t^{\\gamma}$ with $\\gamma<1/\\alpha$ under the assum","authors_text":"Frank Aurzada, Tanja Kramm","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-06T14:09:29Z","title":"The first passage time problem over a moving boundary for asymptotically stable L\\'evy processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.1203","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":"sha256:4134273a912908462f0d7c4d93802b881a9cc4cd51bc7941ad2e54c830eb57eb","target":"record","created_at":"2026-05-18T02:29:32Z","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":"00630e0e38d0422dbe3fbd8ccdfa077165853b7d6fc49014be2cfa1dd2dc8972","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-06T14:09:29Z","title_canon_sha256":"730074aae1bd0fb74b48375313c4fc8e9cb8ce63dac7158f9c500afea4011024"},"schema_version":"1.0","source":{"id":"1305.1203","kind":"arxiv","version":2}},"canonical_sha256":"9ab04a973c15999cfef0085ec8883b5d054c42ba7e31fc76f3881054c8cebe5a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9ab04a973c15999cfef0085ec8883b5d054c42ba7e31fc76f3881054c8cebe5a","first_computed_at":"2026-05-18T02:29:32.426067Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:32.426067Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gc6MQ4cp5DIBzejet1cIlFoYFrRVnj1IeEl3uGox9twgGabB9voOiY/SNgschuCakAiXUwF73mMSS0/A+VprBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:32.426508Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.1203","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4134273a912908462f0d7c4d93802b881a9cc4cd51bc7941ad2e54c830eb57eb","sha256:326a2dc705af38a935a06613a1d6a962694c1673788d17e932b228db5999a605"],"state_sha256":"6a63ca2ba1af8eadb96fb025f5538705d212e9deb934e71c09c72557cdf869a9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AOUUE3wQgAVQ2L77PGpKmz4tKPV98Uw4rNViPWPyQBlN/st/8yl7CDahdamQvZbuuc/so6BxZStiTVSLeyzPAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T01:23:57.397008Z","bundle_sha256":"ec1ac812b1a59c47a14256b3432c72bed72ae301f6681ac138d668420181004d"}}