{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:YCND4ETTZP2MHLSGCTWAPZME7H","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":"915289e43c1d314aac86696b2287c1080a1b153be973a08e9d398200cde59f2c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-05-02T16:55:44Z","title_canon_sha256":"86f47d4c4472d7bd67a73341b9aa7af5828f0f08e167e4822f51239dc4a1c94e"},"schema_version":"1.0","source":{"id":"1905.00852","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.00852","created_at":"2026-05-17T23:47:09Z"},{"alias_kind":"arxiv_version","alias_value":"1905.00852v1","created_at":"2026-05-17T23:47:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.00852","created_at":"2026-05-17T23:47:09Z"},{"alias_kind":"pith_short_12","alias_value":"YCND4ETTZP2M","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"YCND4ETTZP2MHLSG","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"YCND4ETT","created_at":"2026-05-18T12:33:33Z"}],"graph_snapshots":[{"event_id":"sha256:3209ef368e10a0493a54953f5698c39c142bf266126de1bf84a1f22daa5f5c5f","target":"graph","created_at":"2026-05-17T23:47:09Z","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":"Start a planar Brownian motion and let it run until it hits some given barrier. We show that the barrier may be crafted so that the x coordinate at the hitting time has any prescribed centered distribution with finite variance. This provides a new, complex-analytic proof of the Skorokhod embedding theorem. Our method is constructive and can give an explicit description of the barrier.","authors_text":"Renan Gross","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-05-02T16:55:44Z","title":"A conformal Skorokhod embedding"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.00852","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":"sha256:018f25d652fc9c807c0ad95779a422bff85ff10831434bbb05e4a08c05983274","target":"record","created_at":"2026-05-17T23:47:09Z","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":"915289e43c1d314aac86696b2287c1080a1b153be973a08e9d398200cde59f2c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-05-02T16:55:44Z","title_canon_sha256":"86f47d4c4472d7bd67a73341b9aa7af5828f0f08e167e4822f51239dc4a1c94e"},"schema_version":"1.0","source":{"id":"1905.00852","kind":"arxiv","version":1}},"canonical_sha256":"c09a3e1273cbf4c3ae4614ec07e584f9fff04447e2fa6d38bfdd77903656cc9d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c09a3e1273cbf4c3ae4614ec07e584f9fff04447e2fa6d38bfdd77903656cc9d","first_computed_at":"2026-05-17T23:47:09.082408Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:09.082408Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JUKfKV/ahKHnRasqI92KkyXSK2749jMPcL+8HYjcutokOZyEuwCEt5LZVGkoXhmFT/FH1oChICUIQ3SMXI9bDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:09.083094Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.00852","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:018f25d652fc9c807c0ad95779a422bff85ff10831434bbb05e4a08c05983274","sha256:3209ef368e10a0493a54953f5698c39c142bf266126de1bf84a1f22daa5f5c5f"],"state_sha256":"aa34e463b966e41c401f39d6616daba65adf3d267649655289e9fe3114700d24"}