{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:IMHHSEJKM6HZX3D345JGZP3QNO","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":"2a1148a1b64a3a0bbf5cb1f21f67ac9c7c3168085d5afd542f08361c7036be50","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-06-01T12:46:01Z","title_canon_sha256":"e187cb401adc766e5cca709b18727d9d446da153e6060837d292efda4cf6fa26"},"schema_version":"1.0","source":{"id":"2506.00990","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.00990","created_at":"2026-07-05T11:13:44Z"},{"alias_kind":"arxiv_version","alias_value":"2506.00990v1","created_at":"2026-07-05T11:13:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.00990","created_at":"2026-07-05T11:13:44Z"},{"alias_kind":"pith_short_12","alias_value":"IMHHSEJKM6HZ","created_at":"2026-07-05T11:13:44Z"},{"alias_kind":"pith_short_16","alias_value":"IMHHSEJKM6HZX3D3","created_at":"2026-07-05T11:13:44Z"},{"alias_kind":"pith_short_8","alias_value":"IMHHSEJK","created_at":"2026-07-05T11:13:44Z"}],"graph_snapshots":[{"event_id":"sha256:f5fb95ffd2f8e89ec3e9c70c498a4b30a11a08d630ca621761822d5ac5c2c3b0","target":"graph","created_at":"2026-07-05T11:13:44Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.00990/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Assume that letters (from a finite alphabet) in a text form a Markov chain. We track two distinct words, $U$ and $D$. A gambler gains 1 point for each occurrence of $U$ (including overlapping occurrences) and loses 1 point for each occurrence of $D$ (also including overlapping occurrences). We determine the probability of gaining $A$ points before losing $B$ points, where $A$ and $B$ are integers. Additionally, we find the expected waiting time until one of the two events -- gaining $A$ points or losing $B$ points -- occurs.","authors_text":"Vladimir Pozdnyakov, Zhiyi Chi","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-06-01T12:46:01Z","title":"On a Variation of Gambler's Ruin Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.00990","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:daa459e8b1c5cc8e16e1483b70e5232a94ffc478566e8a6cf3209b48d43f2bff","target":"record","created_at":"2026-07-05T11:13:44Z","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":"2a1148a1b64a3a0bbf5cb1f21f67ac9c7c3168085d5afd542f08361c7036be50","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-06-01T12:46:01Z","title_canon_sha256":"e187cb401adc766e5cca709b18727d9d446da153e6060837d292efda4cf6fa26"},"schema_version":"1.0","source":{"id":"2506.00990","kind":"arxiv","version":1}},"canonical_sha256":"430e79112a678f9bec7be7526cbf706b99ee9971c5805130bbec2291817bc66c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"430e79112a678f9bec7be7526cbf706b99ee9971c5805130bbec2291817bc66c","first_computed_at":"2026-07-05T11:13:44.135283Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:13:44.135283Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DTzf/c6hnzwLbp5S4lY4N1eXmyYZLxidMeJluJ5wlz3lnDo6GMYZRzM9rHGtdYB7kOer3XiSnMrMRE4c/b0wCw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:13:44.135712Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.00990","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:daa459e8b1c5cc8e16e1483b70e5232a94ffc478566e8a6cf3209b48d43f2bff","sha256:f5fb95ffd2f8e89ec3e9c70c498a4b30a11a08d630ca621761822d5ac5c2c3b0"],"state_sha256":"c7c7f336ef9521129bb8b67bf6091681b962057ef0251880c8434bbda81c17db"}