{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:OKC4FXMHXX6BBJ3J6OCB73QFRH","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":"70a058faaed2e1159e140b475fbbedd7896c9d6d9824767a6276aac9ef590aff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-05-16T10:43:52Z","title_canon_sha256":"71e08c3693392677af4a549d434b3a2396093667f7ecad7de7f90d8dc83d9b86"},"schema_version":"1.0","source":{"id":"1705.05635","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.05635","created_at":"2026-05-18T00:04:40Z"},{"alias_kind":"arxiv_version","alias_value":"1705.05635v2","created_at":"2026-05-18T00:04:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.05635","created_at":"2026-05-18T00:04:40Z"},{"alias_kind":"pith_short_12","alias_value":"OKC4FXMHXX6B","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"OKC4FXMHXX6BBJ3J","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"OKC4FXMH","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:882a46d8ae6d791a0e02199c8aea91279e9c9426ba4fdb4cae5665f504328b10","target":"graph","created_at":"2026-05-18T00:04:40Z","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":"Motivated by problems in behavioural finance, we provide two explicit constructions of a randomized stopping time which embeds a given centered distribution $\\mu$ on integers into a simple symmetric random walk in a uniformly integrable manner. Our first construction has a simple Markovian structure: at each step, we stop if an independent coin with a state-dependent bias returns tails. Our second construction is a discrete analogue of the celebrated Az\\'ema-Yor solution and requires independent coin tosses only when excursions away from maximum breach predefined levels. Further, this construc","authors_text":"Jan Ob\\l\\'oj, Sang Hu, Xuedong He, Xunyu Zhou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-05-16T10:43:52Z","title":"Two explicit Skorokhod embeddings for simple symmetric random walk"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.05635","kind":"arxiv","version":2},"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:d303ed35a166f1030b2305fcdd44e741ca5b81bd006796061e0e5a77949a9822","target":"record","created_at":"2026-05-18T00:04:40Z","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":"70a058faaed2e1159e140b475fbbedd7896c9d6d9824767a6276aac9ef590aff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-05-16T10:43:52Z","title_canon_sha256":"71e08c3693392677af4a549d434b3a2396093667f7ecad7de7f90d8dc83d9b86"},"schema_version":"1.0","source":{"id":"1705.05635","kind":"arxiv","version":2}},"canonical_sha256":"7285c2dd87bdfc10a769f3841fee0589c3d1855b6a334d6c876660acd37de046","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7285c2dd87bdfc10a769f3841fee0589c3d1855b6a334d6c876660acd37de046","first_computed_at":"2026-05-18T00:04:40.047927Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:40.047927Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Nz+s6HmNEar+4SfjTpWqKfyHvnsPptR2p2+7ZLuhaj/wvgo6Duc9vw5VVPYyFYKl/ZRwr/SKSJQKW3biINdMAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:40.048529Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.05635","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d303ed35a166f1030b2305fcdd44e741ca5b81bd006796061e0e5a77949a9822","sha256:882a46d8ae6d791a0e02199c8aea91279e9c9426ba4fdb4cae5665f504328b10"],"state_sha256":"8918a9a5147463ab96baca04f96023f1e5a3a337102937c8756ac2f88d2c685f"}