{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:WQAV2PUOPEY36WHLOE6JN6GWI7","short_pith_number":"pith:WQAV2PUO","canonical_record":{"source":{"id":"1406.3234","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-06-12T13:26:36Z","cross_cats_sorted":[],"title_canon_sha256":"99e1f7ef2d4139e2e18ac18ce720ab64cbd93e0eb971f2320eaf1660c0512cda","abstract_canon_sha256":"8881c4772540acb428638d502c6e23055f81b61a10840146a030bb92cb81033a"},"schema_version":"1.0"},"canonical_sha256":"b4015d3e8e7931bf58eb713c96f8d647df7c7e0423c99434cc4883fa08896242","source":{"kind":"arxiv","id":"1406.3234","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.3234","created_at":"2026-05-18T01:20:47Z"},{"alias_kind":"arxiv_version","alias_value":"1406.3234v4","created_at":"2026-05-18T01:20:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.3234","created_at":"2026-05-18T01:20:47Z"},{"alias_kind":"pith_short_12","alias_value":"WQAV2PUOPEY3","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WQAV2PUOPEY36WHL","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WQAV2PUO","created_at":"2026-05-18T12:28:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:WQAV2PUOPEY36WHLOE6JN6GWI7","target":"record","payload":{"canonical_record":{"source":{"id":"1406.3234","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-06-12T13:26:36Z","cross_cats_sorted":[],"title_canon_sha256":"99e1f7ef2d4139e2e18ac18ce720ab64cbd93e0eb971f2320eaf1660c0512cda","abstract_canon_sha256":"8881c4772540acb428638d502c6e23055f81b61a10840146a030bb92cb81033a"},"schema_version":"1.0"},"canonical_sha256":"b4015d3e8e7931bf58eb713c96f8d647df7c7e0423c99434cc4883fa08896242","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:47.484153Z","signature_b64":"MrTWrk4fW5YFDKKDBNd7VQ6MrGe3VbCdQKFNCascEuEm11v/0d/VUqMwAeTsmdbeKkKrPlJS2NOcTsjB7JD3Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b4015d3e8e7931bf58eb713c96f8d647df7c7e0423c99434cc4883fa08896242","last_reissued_at":"2026-05-18T01:20:47.483634Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:47.483634Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.3234","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:20:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R+yBfT8itQb6/7lsQLgbDi/aYJVqQpA3aVBnt7bgn3VaTQu2o5uwZ/7EmCk8Fyrzo3oCHnHaS3bU4o+LA1DNDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T03:49:57.701523Z"},"content_sha256":"052ec01187f57ab00b25f0fbb49f7a9073278bbec5eebc04d9f8b458e750bea3","schema_version":"1.0","event_id":"sha256:052ec01187f57ab00b25f0fbb49f7a9073278bbec5eebc04d9f8b458e750bea3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:WQAV2PUOPEY36WHLOE6JN6GWI7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The local asymptotic estimation for the supremum of a random walk with generalized strong subexponential summands","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Changjun Yu, Dongya Cheng, Hui Xu, Yuebao Wang","submitted_at":"2014-06-12T13:26:36Z","abstract_excerpt":"In this paper, the local asymptotic estimation for the supremum of a random walk and its applications are presented. The summands of the random walk have common long-tailed and generalized strong subexponential distribution. This distribution class and the corresponding generalized local subexponential distribution class are two new distribution classes with some good properties. Further, some long-tailed distributions with intuitive and concrete forms are found, which show that the intersection of the two above-mentioned distribution classes with long-tailed distribution class properly contai"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3234","kind":"arxiv","version":4},"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":"2026-05-18T01:20:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pldUkSoDgWkCR8mzgluYF+n6hoV7U3yqWdgOCLDPvGW39WxAQUcg7CzaTvgflwJXDPDc3RS/wAdWMEwYRiZtDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T03:49:57.701871Z"},"content_sha256":"b65fc11b3ba7323a9815808bc75d5ab40f457316fe534773c351e34826e733a0","schema_version":"1.0","event_id":"sha256:b65fc11b3ba7323a9815808bc75d5ab40f457316fe534773c351e34826e733a0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WQAV2PUOPEY36WHLOE6JN6GWI7/bundle.json","state_url":"https://pith.science/pith/WQAV2PUOPEY36WHLOE6JN6GWI7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WQAV2PUOPEY36WHLOE6JN6GWI7/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":"2026-06-03T03:49:57Z","links":{"resolver":"https://pith.science/pith/WQAV2PUOPEY36WHLOE6JN6GWI7","bundle":"https://pith.science/pith/WQAV2PUOPEY36WHLOE6JN6GWI7/bundle.json","state":"https://pith.science/pith/WQAV2PUOPEY36WHLOE6JN6GWI7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WQAV2PUOPEY36WHLOE6JN6GWI7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:WQAV2PUOPEY36WHLOE6JN6GWI7","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":"8881c4772540acb428638d502c6e23055f81b61a10840146a030bb92cb81033a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-06-12T13:26:36Z","title_canon_sha256":"99e1f7ef2d4139e2e18ac18ce720ab64cbd93e0eb971f2320eaf1660c0512cda"},"schema_version":"1.0","source":{"id":"1406.3234","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.3234","created_at":"2026-05-18T01:20:47Z"},{"alias_kind":"arxiv_version","alias_value":"1406.3234v4","created_at":"2026-05-18T01:20:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.3234","created_at":"2026-05-18T01:20:47Z"},{"alias_kind":"pith_short_12","alias_value":"WQAV2PUOPEY3","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WQAV2PUOPEY36WHL","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WQAV2PUO","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:b65fc11b3ba7323a9815808bc75d5ab40f457316fe534773c351e34826e733a0","target":"graph","created_at":"2026-05-18T01:20:47Z","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, the local asymptotic estimation for the supremum of a random walk and its applications are presented. The summands of the random walk have common long-tailed and generalized strong subexponential distribution. This distribution class and the corresponding generalized local subexponential distribution class are two new distribution classes with some good properties. Further, some long-tailed distributions with intuitive and concrete forms are found, which show that the intersection of the two above-mentioned distribution classes with long-tailed distribution class properly contai","authors_text":"Changjun Yu, Dongya Cheng, Hui Xu, Yuebao Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-06-12T13:26:36Z","title":"The local asymptotic estimation for the supremum of a random walk with generalized strong subexponential summands"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3234","kind":"arxiv","version":4},"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":"sha256:052ec01187f57ab00b25f0fbb49f7a9073278bbec5eebc04d9f8b458e750bea3","target":"record","created_at":"2026-05-18T01:20:47Z","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":"8881c4772540acb428638d502c6e23055f81b61a10840146a030bb92cb81033a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-06-12T13:26:36Z","title_canon_sha256":"99e1f7ef2d4139e2e18ac18ce720ab64cbd93e0eb971f2320eaf1660c0512cda"},"schema_version":"1.0","source":{"id":"1406.3234","kind":"arxiv","version":4}},"canonical_sha256":"b4015d3e8e7931bf58eb713c96f8d647df7c7e0423c99434cc4883fa08896242","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b4015d3e8e7931bf58eb713c96f8d647df7c7e0423c99434cc4883fa08896242","first_computed_at":"2026-05-18T01:20:47.483634Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:47.483634Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MrTWrk4fW5YFDKKDBNd7VQ6MrGe3VbCdQKFNCascEuEm11v/0d/VUqMwAeTsmdbeKkKrPlJS2NOcTsjB7JD3Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:47.484153Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.3234","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:052ec01187f57ab00b25f0fbb49f7a9073278bbec5eebc04d9f8b458e750bea3","sha256:b65fc11b3ba7323a9815808bc75d5ab40f457316fe534773c351e34826e733a0"],"state_sha256":"80245338d49a33501df4ef91a5a1867ac2c54f72f0191afb0c24a3fb94e1dc12"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TqJfBeM/72hBVcUigzBZTwvYbovq/8GfG7UdycvEfKPJG5OR29gQSpuDsROZcwrWfbaIuwsNN64BkPHf18RRAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T03:49:57.703841Z","bundle_sha256":"11865ae8b4bb7a7c89411db2776dd7859552724c9efee60942fb5d2f80ba61e8"}}