{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:JQ3GIQAV6JKIOB4J6HPSJUFAXH","short_pith_number":"pith:JQ3GIQAV","canonical_record":{"source":{"id":"1906.04879","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-06-12T01:41:49Z","cross_cats_sorted":[],"title_canon_sha256":"5f4d96309025a1a89a37bb89c0db28797323b6cc7c77525fa29889bbfc6b86d8","abstract_canon_sha256":"75c732029ad3038c9127b9673b61d125c3315cef3ee75b2101a9735ced793e5b"},"schema_version":"1.0"},"canonical_sha256":"4c36644015f254870789f1df24d0a0b9e6524adb32f4e28d7fa45c425a5fa9f1","source":{"kind":"arxiv","id":"1906.04879","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.04879","created_at":"2026-05-17T23:43:30Z"},{"alias_kind":"arxiv_version","alias_value":"1906.04879v1","created_at":"2026-05-17T23:43:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.04879","created_at":"2026-05-17T23:43:30Z"},{"alias_kind":"pith_short_12","alias_value":"JQ3GIQAV6JKI","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"JQ3GIQAV6JKIOB4J","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"JQ3GIQAV","created_at":"2026-05-18T12:33:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:JQ3GIQAV6JKIOB4J6HPSJUFAXH","target":"record","payload":{"canonical_record":{"source":{"id":"1906.04879","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-06-12T01:41:49Z","cross_cats_sorted":[],"title_canon_sha256":"5f4d96309025a1a89a37bb89c0db28797323b6cc7c77525fa29889bbfc6b86d8","abstract_canon_sha256":"75c732029ad3038c9127b9673b61d125c3315cef3ee75b2101a9735ced793e5b"},"schema_version":"1.0"},"canonical_sha256":"4c36644015f254870789f1df24d0a0b9e6524adb32f4e28d7fa45c425a5fa9f1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:30.269206Z","signature_b64":"dnaIfSxKUi8J5FAqDz8EztSBFlxBf3QSu+QkL12v7nfwWRqA6Bq0Mqexrz/4CQIOy5Y7S4qv81zD8S9BA4UNDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4c36644015f254870789f1df24d0a0b9e6524adb32f4e28d7fa45c425a5fa9f1","last_reissued_at":"2026-05-17T23:43:30.268620Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:30.268620Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1906.04879","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":"2026-05-17T23:43:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wyZOcwN753jcUbRZ5s2bG8oMp8bXZ1kycakYU59E1RbGO2duxq/lEvHcdbh5/SLXMXLR4kH8xzqbsnLK+YR/Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T09:23:27.174543Z"},"content_sha256":"43c8156c3e7b8ac67c47d0dc1b79226ba2b0c66535b6b5975472cf2c40ce696c","schema_version":"1.0","event_id":"sha256:43c8156c3e7b8ac67c47d0dc1b79226ba2b0c66535b6b5975472cf2c40ce696c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:JQ3GIQAV6JKIOB4J6HPSJUFAXH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gambler's ruin estimates on finite inner uniform domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Kelsey Houston-Edwards, Laurent Saloff-Coste, Persi Diaconis","submitted_at":"2019-06-12T01:41:49Z","abstract_excerpt":"Gambler's ruin estimates can be viewed as harmonic measure estimates for finite Markov chains which are absorbed (or killed) at boundary points. We relate such estimates to properties of the underlying chain and its Doob transform. Precisely, we show that gambler's ruin estimates reduce to a good understanding of the Perron-Frobenius eigenfunction and eigenvalue whenever the underlying chain and its Doob transform are Harnack Markov chains. Finite inner-uniform domains (say, in the square grid $\\mathbb Z^n$) provide a large class of examples where these ideas apply and lead to detailed estimat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.04879","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":"2026-05-17T23:43:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CHtYZe+PdLiHevmlBFEyKeUEo2N5C5UukNqVIveWwjVHUHplP1UZWgsuO0cLdjNfdnZY8e+kXTad6oyNkKKkBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T09:23:27.174905Z"},"content_sha256":"d5a9e747f2bdb2561edd88cde2b2b2fd6dea5d2094a4566d62452ba26be134b5","schema_version":"1.0","event_id":"sha256:d5a9e747f2bdb2561edd88cde2b2b2fd6dea5d2094a4566d62452ba26be134b5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JQ3GIQAV6JKIOB4J6HPSJUFAXH/bundle.json","state_url":"https://pith.science/pith/JQ3GIQAV6JKIOB4J6HPSJUFAXH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JQ3GIQAV6JKIOB4J6HPSJUFAXH/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":"2026-06-03T09:23:27Z","links":{"resolver":"https://pith.science/pith/JQ3GIQAV6JKIOB4J6HPSJUFAXH","bundle":"https://pith.science/pith/JQ3GIQAV6JKIOB4J6HPSJUFAXH/bundle.json","state":"https://pith.science/pith/JQ3GIQAV6JKIOB4J6HPSJUFAXH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JQ3GIQAV6JKIOB4J6HPSJUFAXH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:JQ3GIQAV6JKIOB4J6HPSJUFAXH","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":"75c732029ad3038c9127b9673b61d125c3315cef3ee75b2101a9735ced793e5b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-06-12T01:41:49Z","title_canon_sha256":"5f4d96309025a1a89a37bb89c0db28797323b6cc7c77525fa29889bbfc6b86d8"},"schema_version":"1.0","source":{"id":"1906.04879","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.04879","created_at":"2026-05-17T23:43:30Z"},{"alias_kind":"arxiv_version","alias_value":"1906.04879v1","created_at":"2026-05-17T23:43:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.04879","created_at":"2026-05-17T23:43:30Z"},{"alias_kind":"pith_short_12","alias_value":"JQ3GIQAV6JKI","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"JQ3GIQAV6JKIOB4J","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"JQ3GIQAV","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:d5a9e747f2bdb2561edd88cde2b2b2fd6dea5d2094a4566d62452ba26be134b5","target":"graph","created_at":"2026-05-17T23:43:30Z","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":"Gambler's ruin estimates can be viewed as harmonic measure estimates for finite Markov chains which are absorbed (or killed) at boundary points. We relate such estimates to properties of the underlying chain and its Doob transform. Precisely, we show that gambler's ruin estimates reduce to a good understanding of the Perron-Frobenius eigenfunction and eigenvalue whenever the underlying chain and its Doob transform are Harnack Markov chains. Finite inner-uniform domains (say, in the square grid $\\mathbb Z^n$) provide a large class of examples where these ideas apply and lead to detailed estimat","authors_text":"Kelsey Houston-Edwards, Laurent Saloff-Coste, Persi Diaconis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-06-12T01:41:49Z","title":"Gambler's ruin estimates on finite inner uniform domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.04879","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":"sha256:43c8156c3e7b8ac67c47d0dc1b79226ba2b0c66535b6b5975472cf2c40ce696c","target":"record","created_at":"2026-05-17T23:43:30Z","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":"75c732029ad3038c9127b9673b61d125c3315cef3ee75b2101a9735ced793e5b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-06-12T01:41:49Z","title_canon_sha256":"5f4d96309025a1a89a37bb89c0db28797323b6cc7c77525fa29889bbfc6b86d8"},"schema_version":"1.0","source":{"id":"1906.04879","kind":"arxiv","version":1}},"canonical_sha256":"4c36644015f254870789f1df24d0a0b9e6524adb32f4e28d7fa45c425a5fa9f1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4c36644015f254870789f1df24d0a0b9e6524adb32f4e28d7fa45c425a5fa9f1","first_computed_at":"2026-05-17T23:43:30.268620Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:30.268620Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dnaIfSxKUi8J5FAqDz8EztSBFlxBf3QSu+QkL12v7nfwWRqA6Bq0Mqexrz/4CQIOy5Y7S4qv81zD8S9BA4UNDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:30.269206Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.04879","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:43c8156c3e7b8ac67c47d0dc1b79226ba2b0c66535b6b5975472cf2c40ce696c","sha256:d5a9e747f2bdb2561edd88cde2b2b2fd6dea5d2094a4566d62452ba26be134b5"],"state_sha256":"1322b3745a0ac72261457e4430b41ce258eeca0a4a76f3df4186177b9b6c823f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gzUnmGP7Vug690ezu2SOGgfWzZMR89p7DFbHT2vQ+RgduNu+4Gtlfz5LHfvDn+yEuImy5FJqvv59RYy2MzHpCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T09:23:27.176954Z","bundle_sha256":"76f697904842ce39b1d4122c73c2b7e487c51d348996efedba77ca329f850644"}}