{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:XZL3QIVZM5KPXRXHRRJES7HI4B","short_pith_number":"pith:XZL3QIVZ","canonical_record":{"source":{"id":"1506.04063","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-12T16:36:38Z","cross_cats_sorted":["math.OC","q-fin.MF"],"title_canon_sha256":"090b84ca7da244d9caf5280ea4f28e5185392a7b2500087a6f026c15f3bc1256","abstract_canon_sha256":"0398afbc2b105ecfe9a921e204237a7427d372ec14ade353a1c77a0f30fd6cd1"},"schema_version":"1.0"},"canonical_sha256":"be57b822b96754fbc6e78c52497ce8e065bf2cc7816ce18fcd8fa3408a9d8f13","source":{"kind":"arxiv","id":"1506.04063","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.04063","created_at":"2026-05-18T01:09:58Z"},{"alias_kind":"arxiv_version","alias_value":"1506.04063v2","created_at":"2026-05-18T01:09:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.04063","created_at":"2026-05-18T01:09:58Z"},{"alias_kind":"pith_short_12","alias_value":"XZL3QIVZM5KP","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XZL3QIVZM5KPXRXH","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XZL3QIVZ","created_at":"2026-05-18T12:29:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:XZL3QIVZM5KPXRXHRRJES7HI4B","target":"record","payload":{"canonical_record":{"source":{"id":"1506.04063","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-12T16:36:38Z","cross_cats_sorted":["math.OC","q-fin.MF"],"title_canon_sha256":"090b84ca7da244d9caf5280ea4f28e5185392a7b2500087a6f026c15f3bc1256","abstract_canon_sha256":"0398afbc2b105ecfe9a921e204237a7427d372ec14ade353a1c77a0f30fd6cd1"},"schema_version":"1.0"},"canonical_sha256":"be57b822b96754fbc6e78c52497ce8e065bf2cc7816ce18fcd8fa3408a9d8f13","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:58.013121Z","signature_b64":"KUsLU/uDCxQ+Hxu74b7FGsnpAUkgLwdwD6m46mECe5cu6k7m7WKYkIQriJ24Beml/awr4zjVeaO6W2Blv1d2Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"be57b822b96754fbc6e78c52497ce8e065bf2cc7816ce18fcd8fa3408a9d8f13","last_reissued_at":"2026-05-18T01:09:58.012520Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:58.012520Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.04063","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:09:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5ps+2ntajg2x42VNJWuKL5WARr6ei+/PsO0YyrxOw1VI6TjIDyhpmi7Y5ygSxMlLh6kjMahQeRzgDaAaXPl9CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T13:05:49.694759Z"},"content_sha256":"b4db6f9333231f90c5c7d37567a0b214a2ac32ce98e641985b8d24a2aef60db6","schema_version":"1.0","event_id":"sha256:b4db6f9333231f90c5c7d37567a0b214a2ac32ce98e641985b8d24a2aef60db6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:XZL3QIVZM5KPXRXHRRJES7HI4B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal Skorokhod embedding under finitely-many marginal constraints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","q-fin.MF"],"primary_cat":"math.PR","authors_text":"Gaoyue Guo, Nizar Touzi, Xiaolu Tan","submitted_at":"2015-06-12T16:36:38Z","abstract_excerpt":"The Skorokhod embedding problem aims to represent a given probability measure on the real line as the distribution of Brownian motion stopped at a chosen stopping time. In this paper, we consider an extension of the optimal Skorokhod embedding problem to the case of finitely-many marginal constraints. Using the classical convex duality approach together with the optimal stopping theory, we obtain the duality results which are formulated by means of probability measures on an enlarged space. We also relate these results to the problem of martingale optimal transport under multiple marginal cons"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.04063","kind":"arxiv","version":2},"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":"2026-05-18T01:09:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x4LHMar8eObJs0zPhHy2ex0gJIFiO7urNQrj2yD1gjiajVVLZFGBGzwQ2b4v5Nbq0vNMe50QgJYgG9STyqDiCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T13:05:49.695265Z"},"content_sha256":"daa72b7fb697fe4ad827df5e9a9e51a78b33f67a6a3a816fe19285e2a693c9f2","schema_version":"1.0","event_id":"sha256:daa72b7fb697fe4ad827df5e9a9e51a78b33f67a6a3a816fe19285e2a693c9f2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XZL3QIVZM5KPXRXHRRJES7HI4B/bundle.json","state_url":"https://pith.science/pith/XZL3QIVZM5KPXRXHRRJES7HI4B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XZL3QIVZM5KPXRXHRRJES7HI4B/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":"2026-05-30T13:05:49Z","links":{"resolver":"https://pith.science/pith/XZL3QIVZM5KPXRXHRRJES7HI4B","bundle":"https://pith.science/pith/XZL3QIVZM5KPXRXHRRJES7HI4B/bundle.json","state":"https://pith.science/pith/XZL3QIVZM5KPXRXHRRJES7HI4B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XZL3QIVZM5KPXRXHRRJES7HI4B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:XZL3QIVZM5KPXRXHRRJES7HI4B","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":"0398afbc2b105ecfe9a921e204237a7427d372ec14ade353a1c77a0f30fd6cd1","cross_cats_sorted":["math.OC","q-fin.MF"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-12T16:36:38Z","title_canon_sha256":"090b84ca7da244d9caf5280ea4f28e5185392a7b2500087a6f026c15f3bc1256"},"schema_version":"1.0","source":{"id":"1506.04063","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.04063","created_at":"2026-05-18T01:09:58Z"},{"alias_kind":"arxiv_version","alias_value":"1506.04063v2","created_at":"2026-05-18T01:09:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.04063","created_at":"2026-05-18T01:09:58Z"},{"alias_kind":"pith_short_12","alias_value":"XZL3QIVZM5KP","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XZL3QIVZM5KPXRXH","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XZL3QIVZ","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:daa72b7fb697fe4ad827df5e9a9e51a78b33f67a6a3a816fe19285e2a693c9f2","target":"graph","created_at":"2026-05-18T01:09:58Z","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 Skorokhod embedding problem aims to represent a given probability measure on the real line as the distribution of Brownian motion stopped at a chosen stopping time. In this paper, we consider an extension of the optimal Skorokhod embedding problem to the case of finitely-many marginal constraints. Using the classical convex duality approach together with the optimal stopping theory, we obtain the duality results which are formulated by means of probability measures on an enlarged space. We also relate these results to the problem of martingale optimal transport under multiple marginal cons","authors_text":"Gaoyue Guo, Nizar Touzi, Xiaolu Tan","cross_cats":["math.OC","q-fin.MF"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-12T16:36:38Z","title":"Optimal Skorokhod embedding under finitely-many marginal constraints"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.04063","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:b4db6f9333231f90c5c7d37567a0b214a2ac32ce98e641985b8d24a2aef60db6","target":"record","created_at":"2026-05-18T01:09:58Z","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":"0398afbc2b105ecfe9a921e204237a7427d372ec14ade353a1c77a0f30fd6cd1","cross_cats_sorted":["math.OC","q-fin.MF"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-12T16:36:38Z","title_canon_sha256":"090b84ca7da244d9caf5280ea4f28e5185392a7b2500087a6f026c15f3bc1256"},"schema_version":"1.0","source":{"id":"1506.04063","kind":"arxiv","version":2}},"canonical_sha256":"be57b822b96754fbc6e78c52497ce8e065bf2cc7816ce18fcd8fa3408a9d8f13","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"be57b822b96754fbc6e78c52497ce8e065bf2cc7816ce18fcd8fa3408a9d8f13","first_computed_at":"2026-05-18T01:09:58.012520Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:58.012520Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KUsLU/uDCxQ+Hxu74b7FGsnpAUkgLwdwD6m46mECe5cu6k7m7WKYkIQriJ24Beml/awr4zjVeaO6W2Blv1d2Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:58.013121Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.04063","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b4db6f9333231f90c5c7d37567a0b214a2ac32ce98e641985b8d24a2aef60db6","sha256:daa72b7fb697fe4ad827df5e9a9e51a78b33f67a6a3a816fe19285e2a693c9f2"],"state_sha256":"988dcdc67f101dd163583e4be0364b32ee2dfa574b36220816c4806b7600a0ea"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PlgoBsumyXQnVbmMPUqmVS2lJkJU5wbDT/Ufm0Dlc/rvJEq857DnHUZx8Phy5KWDN7r5Z7pjYNhdMsiYQSurDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T13:05:49.698148Z","bundle_sha256":"9e631efa1f4841c053311e957dd5850423fa1459bc5749fd7ed2875acb9fb4a6"}}