{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:LA67DOLRPGB742JOIHC7QJJMZ6","short_pith_number":"pith:LA67DOLR","canonical_record":{"source":{"id":"1611.00493","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-11-02T07:46:35Z","cross_cats_sorted":[],"title_canon_sha256":"b0aad33874cee79ed8c32fbdfa5c5472ea8cf5e22426c3afd3b187a374f7e4a0","abstract_canon_sha256":"69c40a61e33546208a482b573c5296200e01eb14940c5672651492636def4568"},"schema_version":"1.0"},"canonical_sha256":"583df1b9717983fe692e41c5f8252ccfb2d39d392e4f97574907b611057cc8dc","source":{"kind":"arxiv","id":"1611.00493","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.00493","created_at":"2026-05-18T01:00:32Z"},{"alias_kind":"arxiv_version","alias_value":"1611.00493v1","created_at":"2026-05-18T01:00:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.00493","created_at":"2026-05-18T01:00:32Z"},{"alias_kind":"pith_short_12","alias_value":"LA67DOLRPGB7","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LA67DOLRPGB742JO","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LA67DOLR","created_at":"2026-05-18T12:30:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:LA67DOLRPGB742JOIHC7QJJMZ6","target":"record","payload":{"canonical_record":{"source":{"id":"1611.00493","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-11-02T07:46:35Z","cross_cats_sorted":[],"title_canon_sha256":"b0aad33874cee79ed8c32fbdfa5c5472ea8cf5e22426c3afd3b187a374f7e4a0","abstract_canon_sha256":"69c40a61e33546208a482b573c5296200e01eb14940c5672651492636def4568"},"schema_version":"1.0"},"canonical_sha256":"583df1b9717983fe692e41c5f8252ccfb2d39d392e4f97574907b611057cc8dc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:32.651808Z","signature_b64":"8sn+9Tv1aXDIp68bQ7ZfH6kkMnnOWkWWzOXoKKYKSOZp92yVrdrxXA60onmrLpvE1uyEy3LHq7Axu5YjW9WmAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"583df1b9717983fe692e41c5f8252ccfb2d39d392e4f97574907b611057cc8dc","last_reissued_at":"2026-05-18T01:00:32.651161Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:32.651161Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.00493","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":"2026-05-18T01:00:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GzUQImcdNIF+tATe16vTfpYl5U/PAI3DV/Xk0CDLQAEN8QpoIrWuIUDUGb6bB3Tlgxj8WHO2EGScGqaFK75FCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T09:58:51.534588Z"},"content_sha256":"cdb936790280c66dcfd9d85493920a53151239ea2be4afc4a9385adf99879550","schema_version":"1.0","event_id":"sha256:cdb936790280c66dcfd9d85493920a53151239ea2be4afc4a9385adf99879550"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:LA67DOLRPGB742JOIHC7QJJMZ6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"First-passage times for random walks with non-identically distributed increments","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexander Sakhanenko, Denis Denisov, Vitali Wachtel","submitted_at":"2016-11-02T07:46:35Z","abstract_excerpt":"We consider random walks with independent but not necessarily identical distributed increments. Assuming that the increments satisfy the well-known Lindeberg condition, we investigate the asymptotic behaviour of first-passage times over moving boundaries. Furthermore, we prove that a properly rescaled random walk conditioned to stay above the boundary up to time $n$ converges, as $n\\to\\infty$, towards the Brownian meander."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.00493","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":"2026-05-18T01:00:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4mEVS/R0pQ7xH34wYwQZTX+QldGUo91aLIMvbbqMpkzjh2J/Mz+GfLRCj9v+2NbdhX45ZCWe9CQL5UjweRBuBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T09:58:51.534928Z"},"content_sha256":"ba4854b1a7bb898c10e1335344d1a48b34d92aa618aeb9c24bff385ec510e38c","schema_version":"1.0","event_id":"sha256:ba4854b1a7bb898c10e1335344d1a48b34d92aa618aeb9c24bff385ec510e38c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LA67DOLRPGB742JOIHC7QJJMZ6/bundle.json","state_url":"https://pith.science/pith/LA67DOLRPGB742JOIHC7QJJMZ6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LA67DOLRPGB742JOIHC7QJJMZ6/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":"2026-05-28T09:58:51Z","links":{"resolver":"https://pith.science/pith/LA67DOLRPGB742JOIHC7QJJMZ6","bundle":"https://pith.science/pith/LA67DOLRPGB742JOIHC7QJJMZ6/bundle.json","state":"https://pith.science/pith/LA67DOLRPGB742JOIHC7QJJMZ6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LA67DOLRPGB742JOIHC7QJJMZ6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:LA67DOLRPGB742JOIHC7QJJMZ6","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":"69c40a61e33546208a482b573c5296200e01eb14940c5672651492636def4568","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-11-02T07:46:35Z","title_canon_sha256":"b0aad33874cee79ed8c32fbdfa5c5472ea8cf5e22426c3afd3b187a374f7e4a0"},"schema_version":"1.0","source":{"id":"1611.00493","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.00493","created_at":"2026-05-18T01:00:32Z"},{"alias_kind":"arxiv_version","alias_value":"1611.00493v1","created_at":"2026-05-18T01:00:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.00493","created_at":"2026-05-18T01:00:32Z"},{"alias_kind":"pith_short_12","alias_value":"LA67DOLRPGB7","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LA67DOLRPGB742JO","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LA67DOLR","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:ba4854b1a7bb898c10e1335344d1a48b34d92aa618aeb9c24bff385ec510e38c","target":"graph","created_at":"2026-05-18T01:00:32Z","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 consider random walks with independent but not necessarily identical distributed increments. Assuming that the increments satisfy the well-known Lindeberg condition, we investigate the asymptotic behaviour of first-passage times over moving boundaries. Furthermore, we prove that a properly rescaled random walk conditioned to stay above the boundary up to time $n$ converges, as $n\\to\\infty$, towards the Brownian meander.","authors_text":"Alexander Sakhanenko, Denis Denisov, Vitali Wachtel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-11-02T07:46:35Z","title":"First-passage times for random walks with non-identically distributed increments"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.00493","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:cdb936790280c66dcfd9d85493920a53151239ea2be4afc4a9385adf99879550","target":"record","created_at":"2026-05-18T01:00:32Z","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":"69c40a61e33546208a482b573c5296200e01eb14940c5672651492636def4568","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-11-02T07:46:35Z","title_canon_sha256":"b0aad33874cee79ed8c32fbdfa5c5472ea8cf5e22426c3afd3b187a374f7e4a0"},"schema_version":"1.0","source":{"id":"1611.00493","kind":"arxiv","version":1}},"canonical_sha256":"583df1b9717983fe692e41c5f8252ccfb2d39d392e4f97574907b611057cc8dc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"583df1b9717983fe692e41c5f8252ccfb2d39d392e4f97574907b611057cc8dc","first_computed_at":"2026-05-18T01:00:32.651161Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:00:32.651161Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8sn+9Tv1aXDIp68bQ7ZfH6kkMnnOWkWWzOXoKKYKSOZp92yVrdrxXA60onmrLpvE1uyEy3LHq7Axu5YjW9WmAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:00:32.651808Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.00493","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cdb936790280c66dcfd9d85493920a53151239ea2be4afc4a9385adf99879550","sha256:ba4854b1a7bb898c10e1335344d1a48b34d92aa618aeb9c24bff385ec510e38c"],"state_sha256":"90d06bc37daf9bfab0f74c556daaab775504ec2332115a50b887b7118d820a4a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J3NaAcP4iqxBVgHKZ6ddM3Taxodqw1U3xcTvBpjtI5bSJf08Kc7GnKpZSW/LHfujajStZtK31oSXqHhp58CwAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T09:58:51.536868Z","bundle_sha256":"cc209692ac55c971953f052d9d5d2b63022e1dac133ab48f1ddbb58bd36dbe38"}}