{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:PYO452G4QSR7YY7DEFEDPNDKRS","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":"60399b2ac323c1344a003b225d9f26308569581fc958cad44e8e47db2a287bce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-05-28T10:31:45Z","title_canon_sha256":"6f857906954f5c01643866daee55167bbff12b5fe1e1996a62fbf6d86a12fcf1"},"schema_version":"1.0","source":{"id":"1005.5260","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.5260","created_at":"2026-05-18T04:06:45Z"},{"alias_kind":"arxiv_version","alias_value":"1005.5260v1","created_at":"2026-05-18T04:06:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.5260","created_at":"2026-05-18T04:06:45Z"},{"alias_kind":"pith_short_12","alias_value":"PYO452G4QSR7","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"PYO452G4QSR7YY7D","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"PYO452G4","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:c818e8ed58235429a22f58baf9002908c7d1a1c657f19f9f0956427bcbafb39a","target":"graph","created_at":"2026-05-18T04:06:45Z","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":"For a zero-delayed random walk on the real line, let $\\tau(x)$, $N(x)$ and $\\rho(x)$ denote the first passage time into the interval $(x,\\infty)$, the number of visits to the interval $(-\\infty,x]$ and the last exit time from $(-\\infty,x]$, respectively. In the present paper, we provide ultimate criteria for the finiteness of exponential moments of these quantities. Moreover, whenever these moments are finite, we derive their asymptotic behaviour, as $x \\to \\infty$.","authors_text":"Alexander Iksanov, Matthias Meiners","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-05-28T10:31:45Z","title":"Exponential moments of first passage times and related quantities for random walks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.5260","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":"sha256:2a75a570772f0f852ac972e7f42cf710d07f92cbcb902d47ee4360f40148de18","target":"record","created_at":"2026-05-18T04:06:45Z","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":"60399b2ac323c1344a003b225d9f26308569581fc958cad44e8e47db2a287bce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-05-28T10:31:45Z","title_canon_sha256":"6f857906954f5c01643866daee55167bbff12b5fe1e1996a62fbf6d86a12fcf1"},"schema_version":"1.0","source":{"id":"1005.5260","kind":"arxiv","version":1}},"canonical_sha256":"7e1dcee8dc84a3fc63e3214837b46a8ca916aad637284f89c9588da414b50488","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e1dcee8dc84a3fc63e3214837b46a8ca916aad637284f89c9588da414b50488","first_computed_at":"2026-05-18T04:06:45.162882Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:06:45.162882Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xVJC9qD0hp+H2zH5EjAkpbw3TCV+gy1+dyD/7lVlPMDRzETcaxS9Ze9jmS1Gfrk77WKiymSPbMQS64WCbbG1Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:06:45.163333Z","signed_message":"canonical_sha256_bytes"},"source_id":"1005.5260","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a75a570772f0f852ac972e7f42cf710d07f92cbcb902d47ee4360f40148de18","sha256:c818e8ed58235429a22f58baf9002908c7d1a1c657f19f9f0956427bcbafb39a"],"state_sha256":"8893ec97dab1dc2b2727bf6203201c708f1dee85dd94bd9cdd1d676835904966"}