{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:DK4XFPGUDPCLCQ2J7EX4472V5I","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":"a86eb21971fd8b2c65250a15cf111a23d0253be94d8ef186a437f8de464be2bd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-12-07T15:06:35Z","title_canon_sha256":"cc9c0161b645be4a3c76c0b10ff5d89873c0d8aa2a9ea27cd2476083e98e09b4"},"schema_version":"1.0","source":{"id":"1812.03059","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.03059","created_at":"2026-05-17T23:58:51Z"},{"alias_kind":"arxiv_version","alias_value":"1812.03059v1","created_at":"2026-05-17T23:58:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.03059","created_at":"2026-05-17T23:58:51Z"},{"alias_kind":"pith_short_12","alias_value":"DK4XFPGUDPCL","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DK4XFPGUDPCLCQ2J","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DK4XFPGU","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:9a7818d62e616c8e02ccd5beb35117a462d67103475e556eeb2af610d3467346","target":"graph","created_at":"2026-05-17T23:58:51Z","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 authors propose a new variation of random walks called ladder chains $L(r,s,p)$. We extend concepts such as ruin probability, hitting time, transience and recurrence of random walks to ladder chain. Take $L(2,2,p)$ for instance, we find the linear difference equations that the ruin probability and the hitting time satisfy. We also prove the recurrence of a critical case $(p=\\sqrt{2}-1)$. All approaches of these results can be generalized to solve similar problems for other ladder chains.","authors_text":"Chenhe Zhang, Xiang Fang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-12-07T15:06:35Z","title":"Ladder Chains: A Variation of Random Walks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.03059","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:c28fda7973033fd7a85ba7493d47f31245bee51f65eac097645ee42fd7044387","target":"record","created_at":"2026-05-17T23:58:51Z","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":"a86eb21971fd8b2c65250a15cf111a23d0253be94d8ef186a437f8de464be2bd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-12-07T15:06:35Z","title_canon_sha256":"cc9c0161b645be4a3c76c0b10ff5d89873c0d8aa2a9ea27cd2476083e98e09b4"},"schema_version":"1.0","source":{"id":"1812.03059","kind":"arxiv","version":1}},"canonical_sha256":"1ab972bcd41bc4b14349f92fce7f55ea05324b66b550795aa6b9892e246cd3f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ab972bcd41bc4b14349f92fce7f55ea05324b66b550795aa6b9892e246cd3f4","first_computed_at":"2026-05-17T23:58:51.058667Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:51.058667Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v5PNaMpHDDX4yu72nYGH+mx22NwdbgIpyvWw0pcUqSd/h10488vZCM6WVMSAxeIvuN+sQtmfTQOllC5Qx+UIAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:51.059188Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.03059","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c28fda7973033fd7a85ba7493d47f31245bee51f65eac097645ee42fd7044387","sha256:9a7818d62e616c8e02ccd5beb35117a462d67103475e556eeb2af610d3467346"],"state_sha256":"7a31fc676cc7aa168422bc2ecf9557091bf5aee69477e92c977e3f4578390d9b"}