{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:HLYPGRAA42DAAOSXOWCLX665AN","short_pith_number":"pith:HLYPGRAA","canonical_record":{"source":{"id":"1609.02867","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-09T17:25:51Z","cross_cats_sorted":["math.OC","q-fin.MF"],"title_canon_sha256":"b5bb8be423ffb01889e9bf1b8b89e4a278755b6fba501e648f1a979155eb0b8b","abstract_canon_sha256":"3e196a95039e4bd46da18c8e43e3d015cf94ac5c65b96ad872bf20ce80ebee40"},"schema_version":"1.0"},"canonical_sha256":"3af0f34400e686003a577584bbfbdd035e1028c976be87bb48b8d65644634904","source":{"kind":"arxiv","id":"1609.02867","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.02867","created_at":"2026-05-18T00:29:39Z"},{"alias_kind":"arxiv_version","alias_value":"1609.02867v2","created_at":"2026-05-18T00:29:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.02867","created_at":"2026-05-18T00:29:39Z"},{"alias_kind":"pith_short_12","alias_value":"HLYPGRAA42DA","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"HLYPGRAA42DAAOSX","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"HLYPGRAA","created_at":"2026-05-18T12:30:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:HLYPGRAA42DAAOSXOWCLX665AN","target":"record","payload":{"canonical_record":{"source":{"id":"1609.02867","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-09T17:25:51Z","cross_cats_sorted":["math.OC","q-fin.MF"],"title_canon_sha256":"b5bb8be423ffb01889e9bf1b8b89e4a278755b6fba501e648f1a979155eb0b8b","abstract_canon_sha256":"3e196a95039e4bd46da18c8e43e3d015cf94ac5c65b96ad872bf20ce80ebee40"},"schema_version":"1.0"},"canonical_sha256":"3af0f34400e686003a577584bbfbdd035e1028c976be87bb48b8d65644634904","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:39.532575Z","signature_b64":"6JJEONA1vX1ulli4LkK+KSrbTSOhleSKEzWG/0jVrp6mPfxVxkaVYwCTThgb6D8U1vmE1j6+6J1aL4HfPC2ADg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3af0f34400e686003a577584bbfbdd035e1028c976be87bb48b8d65644634904","last_reissued_at":"2026-05-18T00:29:39.532050Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:39.532050Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.02867","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":"2026-05-18T00:29:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LsTbJf7bjZz0Hn3QVG2STwuIno4H4GQz35e2k2pFXG8GeuiBrQICy0SC4hu9WDCHre2p/AV7Nr5/VkpGhufsCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T06:02:36.143616Z"},"content_sha256":"0c8000fe1baf8e7e3a66026a7c32ffb32dd530806c6cbe45e9df9c2971b6a3e1","schema_version":"1.0","event_id":"sha256:0c8000fe1baf8e7e3a66026a7c32ffb32dd530806c6cbe45e9df9c2971b6a3e1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:HLYPGRAA42DAAOSXOWCLX665AN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Canonical Supermartingale Couplings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","q-fin.MF"],"primary_cat":"math.PR","authors_text":"Florian Stebegg, Marcel Nutz","submitted_at":"2016-09-09T17:25:51Z","abstract_excerpt":"Two probability distributions $\\mu$ and $\\nu$ in second stochastic order can be coupled by a supermartingale, and in fact by many. Is there a canonical choice? We construct and investigate two couplings which arise as optimizers for constrained Monge-Kantorovich optimal transport problems where only supermartingales are allowed as transports. Much like the Hoeffding-Fr\\'echet coupling of classical transport and its symmetric counterpart, the antitone coupling, these can be characterized by order-theoretic minimality properties, as simultaneous optimal transports for certain classes of reward ("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.02867","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":"2026-05-18T00:29:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qsUTSqXsLupcB3q3yjR4bgZrS4rtFaZJ5dnBrcEba9LpnSOif9Lbmc7GCiS5CUsEbP+a4Id6s0IJsESBRBlqDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T06:02:36.144266Z"},"content_sha256":"127d25d0e33e0f282204386c1f2f1f6758a8719c04c00ff344b2d2c989e4469f","schema_version":"1.0","event_id":"sha256:127d25d0e33e0f282204386c1f2f1f6758a8719c04c00ff344b2d2c989e4469f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HLYPGRAA42DAAOSXOWCLX665AN/bundle.json","state_url":"https://pith.science/pith/HLYPGRAA42DAAOSXOWCLX665AN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HLYPGRAA42DAAOSXOWCLX665AN/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":"2026-06-02T06:02:36Z","links":{"resolver":"https://pith.science/pith/HLYPGRAA42DAAOSXOWCLX665AN","bundle":"https://pith.science/pith/HLYPGRAA42DAAOSXOWCLX665AN/bundle.json","state":"https://pith.science/pith/HLYPGRAA42DAAOSXOWCLX665AN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HLYPGRAA42DAAOSXOWCLX665AN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:HLYPGRAA42DAAOSXOWCLX665AN","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":"3e196a95039e4bd46da18c8e43e3d015cf94ac5c65b96ad872bf20ce80ebee40","cross_cats_sorted":["math.OC","q-fin.MF"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-09T17:25:51Z","title_canon_sha256":"b5bb8be423ffb01889e9bf1b8b89e4a278755b6fba501e648f1a979155eb0b8b"},"schema_version":"1.0","source":{"id":"1609.02867","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.02867","created_at":"2026-05-18T00:29:39Z"},{"alias_kind":"arxiv_version","alias_value":"1609.02867v2","created_at":"2026-05-18T00:29:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.02867","created_at":"2026-05-18T00:29:39Z"},{"alias_kind":"pith_short_12","alias_value":"HLYPGRAA42DA","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"HLYPGRAA42DAAOSX","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"HLYPGRAA","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:127d25d0e33e0f282204386c1f2f1f6758a8719c04c00ff344b2d2c989e4469f","target":"graph","created_at":"2026-05-18T00:29:39Z","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":"Two probability distributions $\\mu$ and $\\nu$ in second stochastic order can be coupled by a supermartingale, and in fact by many. Is there a canonical choice? We construct and investigate two couplings which arise as optimizers for constrained Monge-Kantorovich optimal transport problems where only supermartingales are allowed as transports. Much like the Hoeffding-Fr\\'echet coupling of classical transport and its symmetric counterpart, the antitone coupling, these can be characterized by order-theoretic minimality properties, as simultaneous optimal transports for certain classes of reward (","authors_text":"Florian Stebegg, Marcel Nutz","cross_cats":["math.OC","q-fin.MF"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-09T17:25:51Z","title":"Canonical Supermartingale Couplings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.02867","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":"sha256:0c8000fe1baf8e7e3a66026a7c32ffb32dd530806c6cbe45e9df9c2971b6a3e1","target":"record","created_at":"2026-05-18T00:29:39Z","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":"3e196a95039e4bd46da18c8e43e3d015cf94ac5c65b96ad872bf20ce80ebee40","cross_cats_sorted":["math.OC","q-fin.MF"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-09T17:25:51Z","title_canon_sha256":"b5bb8be423ffb01889e9bf1b8b89e4a278755b6fba501e648f1a979155eb0b8b"},"schema_version":"1.0","source":{"id":"1609.02867","kind":"arxiv","version":2}},"canonical_sha256":"3af0f34400e686003a577584bbfbdd035e1028c976be87bb48b8d65644634904","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3af0f34400e686003a577584bbfbdd035e1028c976be87bb48b8d65644634904","first_computed_at":"2026-05-18T00:29:39.532050Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:39.532050Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6JJEONA1vX1ulli4LkK+KSrbTSOhleSKEzWG/0jVrp6mPfxVxkaVYwCTThgb6D8U1vmE1j6+6J1aL4HfPC2ADg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:39.532575Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.02867","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c8000fe1baf8e7e3a66026a7c32ffb32dd530806c6cbe45e9df9c2971b6a3e1","sha256:127d25d0e33e0f282204386c1f2f1f6758a8719c04c00ff344b2d2c989e4469f"],"state_sha256":"c8031de729be20f95731464c4df0025109d443f2c7f0636a03f61c5a1c2e27a8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XtoBPfmn1JO1tXSDbqMQTEM4X1PVNUPF7WS9UjqOVQU91OjNlxRjR9PsOTGLosVIgjP2Wga8Vj7w0Y/mZ/iCCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T06:02:36.146685Z","bundle_sha256":"f4a11df27d89ea4861a26c0f5f4723ad0c97723048cc8cfdfa4bfc61095eead9"}}