{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:CORN4USEGBCN6XAHY4XAAHBNV6","short_pith_number":"pith:CORN4USE","canonical_record":{"source":{"id":"1701.06779","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-24T09:21:36Z","cross_cats_sorted":["q-fin.MF"],"title_canon_sha256":"87bfa9c686f25ea7910e581228495d4c0d28cba7a31e4720ba5da0a88249b853","abstract_canon_sha256":"3ad198da8cf1ffb93c7d824ec05908b682afc5bc7b4a3b3c0d0888eb1552bd47"},"schema_version":"1.0"},"canonical_sha256":"13a2de52443044df5c07c72e001c2daf8941deda979f6ae53509c5e92873821a","source":{"kind":"arxiv","id":"1701.06779","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.06779","created_at":"2026-05-18T00:52:12Z"},{"alias_kind":"arxiv_version","alias_value":"1701.06779v1","created_at":"2026-05-18T00:52:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.06779","created_at":"2026-05-18T00:52:12Z"},{"alias_kind":"pith_short_12","alias_value":"CORN4USEGBCN","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CORN4USEGBCN6XAH","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CORN4USE","created_at":"2026-05-18T12:31:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:CORN4USEGBCN6XAHY4XAAHBNV6","target":"record","payload":{"canonical_record":{"source":{"id":"1701.06779","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-24T09:21:36Z","cross_cats_sorted":["q-fin.MF"],"title_canon_sha256":"87bfa9c686f25ea7910e581228495d4c0d28cba7a31e4720ba5da0a88249b853","abstract_canon_sha256":"3ad198da8cf1ffb93c7d824ec05908b682afc5bc7b4a3b3c0d0888eb1552bd47"},"schema_version":"1.0"},"canonical_sha256":"13a2de52443044df5c07c72e001c2daf8941deda979f6ae53509c5e92873821a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:12.198565Z","signature_b64":"uDGKFdZcCSF1/CAkCiV+H3I/yqDv8vPnFXbGQzwpP+Nb0z9tmbGfWwd7VlQozuvWwHi9riVgV87UQqo+ApifCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"13a2de52443044df5c07c72e001c2daf8941deda979f6ae53509c5e92873821a","last_reissued_at":"2026-05-18T00:52:12.198081Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:12.198081Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.06779","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":"2026-05-18T00:52:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B72TIDR/RIqTZsZ9WQf2EkhUk5V8+lMSjn3fscOeUqupqSWjMSUAwOUwXm+5VAC0+/6aMlRw4PdDlYN3hhYuDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T20:24:23.168538Z"},"content_sha256":"b315a2d58b35e78f78cb6ebc1d7217eb257bf1c293326855a444411eb3264a61","schema_version":"1.0","event_id":"sha256:b315a2d58b35e78f78cb6ebc1d7217eb257bf1c293326855a444411eb3264a61"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:CORN4USEGBCN6XAHY4XAAHBNV6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Monotone Martingale Transport Plans and Skorohod Embedding","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-fin.MF"],"primary_cat":"math.PR","authors_text":"Mathias Beiglboeck, Nizar Touzi, Pierre Henry-Labordere","submitted_at":"2017-01-24T09:21:36Z","abstract_excerpt":"We show that the left-monotone martingale coupling is optimal for any given performance function satisfying the martingale version of the Spence-Mirrlees condition, without assuming additional structural conditions on the marginals. We also give a new interpretation of the left monotone coupling in terms of Skorokhod embedding which allows us to give a short proof of uniqueness."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06779","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":"2026-05-18T00:52:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CX9+fcT7CxNRqJOITm3MzJpKrdwZPImGanviNX9IAcopUCfLd+6qkWqKOTr3YeOEtVghCRT/F6urFgoiXkwaDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T20:24:23.168884Z"},"content_sha256":"810d1453ba9d1a8675d58b509725d8efa06467fb1f49626081b95f74921c7ce4","schema_version":"1.0","event_id":"sha256:810d1453ba9d1a8675d58b509725d8efa06467fb1f49626081b95f74921c7ce4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CORN4USEGBCN6XAHY4XAAHBNV6/bundle.json","state_url":"https://pith.science/pith/CORN4USEGBCN6XAHY4XAAHBNV6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CORN4USEGBCN6XAHY4XAAHBNV6/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":"2026-07-01T20:24:23Z","links":{"resolver":"https://pith.science/pith/CORN4USEGBCN6XAHY4XAAHBNV6","bundle":"https://pith.science/pith/CORN4USEGBCN6XAHY4XAAHBNV6/bundle.json","state":"https://pith.science/pith/CORN4USEGBCN6XAHY4XAAHBNV6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CORN4USEGBCN6XAHY4XAAHBNV6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:CORN4USEGBCN6XAHY4XAAHBNV6","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":"3ad198da8cf1ffb93c7d824ec05908b682afc5bc7b4a3b3c0d0888eb1552bd47","cross_cats_sorted":["q-fin.MF"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-24T09:21:36Z","title_canon_sha256":"87bfa9c686f25ea7910e581228495d4c0d28cba7a31e4720ba5da0a88249b853"},"schema_version":"1.0","source":{"id":"1701.06779","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.06779","created_at":"2026-05-18T00:52:12Z"},{"alias_kind":"arxiv_version","alias_value":"1701.06779v1","created_at":"2026-05-18T00:52:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.06779","created_at":"2026-05-18T00:52:12Z"},{"alias_kind":"pith_short_12","alias_value":"CORN4USEGBCN","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CORN4USEGBCN6XAH","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CORN4USE","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:810d1453ba9d1a8675d58b509725d8efa06467fb1f49626081b95f74921c7ce4","target":"graph","created_at":"2026-05-18T00:52:12Z","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":"We show that the left-monotone martingale coupling is optimal for any given performance function satisfying the martingale version of the Spence-Mirrlees condition, without assuming additional structural conditions on the marginals. We also give a new interpretation of the left monotone coupling in terms of Skorokhod embedding which allows us to give a short proof of uniqueness.","authors_text":"Mathias Beiglboeck, Nizar Touzi, Pierre Henry-Labordere","cross_cats":["q-fin.MF"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-24T09:21:36Z","title":"Monotone Martingale Transport Plans and Skorohod Embedding"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06779","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:b315a2d58b35e78f78cb6ebc1d7217eb257bf1c293326855a444411eb3264a61","target":"record","created_at":"2026-05-18T00:52:12Z","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":"3ad198da8cf1ffb93c7d824ec05908b682afc5bc7b4a3b3c0d0888eb1552bd47","cross_cats_sorted":["q-fin.MF"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-24T09:21:36Z","title_canon_sha256":"87bfa9c686f25ea7910e581228495d4c0d28cba7a31e4720ba5da0a88249b853"},"schema_version":"1.0","source":{"id":"1701.06779","kind":"arxiv","version":1}},"canonical_sha256":"13a2de52443044df5c07c72e001c2daf8941deda979f6ae53509c5e92873821a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"13a2de52443044df5c07c72e001c2daf8941deda979f6ae53509c5e92873821a","first_computed_at":"2026-05-18T00:52:12.198081Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:12.198081Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uDGKFdZcCSF1/CAkCiV+H3I/yqDv8vPnFXbGQzwpP+Nb0z9tmbGfWwd7VlQozuvWwHi9riVgV87UQqo+ApifCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:12.198565Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.06779","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b315a2d58b35e78f78cb6ebc1d7217eb257bf1c293326855a444411eb3264a61","sha256:810d1453ba9d1a8675d58b509725d8efa06467fb1f49626081b95f74921c7ce4"],"state_sha256":"6b72c91f01d301b406080a50a6f7d6fd6d2801f7287822aab4d9531e006b90bc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mtTwBOAQO9zZVZqGBN0T/vzpTSaO7w1C8C0m3m8/5qx5/TWQK9tI6wMl8W4lTFE7XykJntpA35iuoMXo3fglDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T20:24:23.170939Z","bundle_sha256":"6f3ec4483bee4a7274da93ed99ec45a2992ab9ed7c5a85ebc01464afd357c6dd"}}