{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:L44Z2VRG5L27OBBB3RXC4M7BXX","short_pith_number":"pith:L44Z2VRG","canonical_record":{"source":{"id":"1702.08433","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-02-27T18:52:04Z","cross_cats_sorted":[],"title_canon_sha256":"f4f17d50c477a21713740f4a3ccbf6b592af8b218bc92bc605e7a9c34d62ffdd","abstract_canon_sha256":"4d1428255ea14522ededd1aecc1495395f2b051a337d7dd4726e72f7fc08a999"},"schema_version":"1.0"},"canonical_sha256":"5f399d5626eaf5f70421dc6e2e33e1bdd2870d5d6c296f2266a64b88de5e68a1","source":{"kind":"arxiv","id":"1702.08433","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.08433","created_at":"2026-05-18T00:49:53Z"},{"alias_kind":"arxiv_version","alias_value":"1702.08433v1","created_at":"2026-05-18T00:49:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.08433","created_at":"2026-05-18T00:49:53Z"},{"alias_kind":"pith_short_12","alias_value":"L44Z2VRG5L27","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"L44Z2VRG5L27OBBB","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"L44Z2VRG","created_at":"2026-05-18T12:31:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:L44Z2VRG5L27OBBB3RXC4M7BXX","target":"record","payload":{"canonical_record":{"source":{"id":"1702.08433","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-02-27T18:52:04Z","cross_cats_sorted":[],"title_canon_sha256":"f4f17d50c477a21713740f4a3ccbf6b592af8b218bc92bc605e7a9c34d62ffdd","abstract_canon_sha256":"4d1428255ea14522ededd1aecc1495395f2b051a337d7dd4726e72f7fc08a999"},"schema_version":"1.0"},"canonical_sha256":"5f399d5626eaf5f70421dc6e2e33e1bdd2870d5d6c296f2266a64b88de5e68a1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:53.009879Z","signature_b64":"+MPk8uTwBJyBq9HTdbHTP8tV57boQiPuQ2c9C0j03Jz/689nacewJOb7QAsM4H9VMei3NI1JL/NLsXP8ez+nAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5f399d5626eaf5f70421dc6e2e33e1bdd2870d5d6c296f2266a64b88de5e68a1","last_reissued_at":"2026-05-18T00:49:53.009281Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:53.009281Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.08433","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":"2026-05-18T00:49:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t5rlzNxnS23rmpc6WBxhSSKLBBZqgvortWFAbeFHqYGPpPhKkS5mKDF2s1FONFY72NZjJpNhHtIfO4RAJO4hDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T04:46:22.115284Z"},"content_sha256":"40e1a8026c8ad6bc8651690df7c1b42851115d5fbf23d9bbdf4345de7eed5af3","schema_version":"1.0","event_id":"sha256:40e1a8026c8ad6bc8651690df7c1b42851115d5fbf23d9bbdf4345de7eed5af3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:L44Z2VRG5L27OBBB3RXC4M7BXX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Structure of martingale transports in finite dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jan Ob\\l\\'oj, Pietro Siorpaes","submitted_at":"2017-02-27T18:52:04Z","abstract_excerpt":"We study the structure of martingale transports in finite dimensions. We consider the family $\\mathcal{M}(\\mu,\\nu) $ of martingale measures on $\\mathbb{R}^N \\times \\mathbb{R}^N$ with given marginals $\\mu,\\nu$, and construct a family of relatively open convex sets $\\{C_x:x\\in \\mathbb{R}^N \\}$, which forms a partition of $\\mathbb{R}^N$, and such that any martingale transport in $\\mathcal{M}(\\mu,\\nu) $ sends mass from $x$ to within $\\overline{C_x}$, $\\mu(dx)$--a.e. Our results extend the analogous one-dimensional results of M. Beiglb\\\"ock and N. Juillet (2016) and M. Beiglb\\\"ock, M. Nutz, and N. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.08433","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":"2026-05-18T00:49:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yzFp8XvIkjxTtxl+T7LCLR/LI6GQnxF/F2qT4D7tyrDBkkvVfw6F6q7H9AvK5KH2nEqygMkeDleGOimlJmXyAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T04:46:22.115798Z"},"content_sha256":"112d548943c853e77b2915c566a242458ba70aefbdf2514d7f7267f27cf2e9db","schema_version":"1.0","event_id":"sha256:112d548943c853e77b2915c566a242458ba70aefbdf2514d7f7267f27cf2e9db"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L44Z2VRG5L27OBBB3RXC4M7BXX/bundle.json","state_url":"https://pith.science/pith/L44Z2VRG5L27OBBB3RXC4M7BXX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L44Z2VRG5L27OBBB3RXC4M7BXX/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":"2026-05-27T04:46:22Z","links":{"resolver":"https://pith.science/pith/L44Z2VRG5L27OBBB3RXC4M7BXX","bundle":"https://pith.science/pith/L44Z2VRG5L27OBBB3RXC4M7BXX/bundle.json","state":"https://pith.science/pith/L44Z2VRG5L27OBBB3RXC4M7BXX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L44Z2VRG5L27OBBB3RXC4M7BXX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:L44Z2VRG5L27OBBB3RXC4M7BXX","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":"4d1428255ea14522ededd1aecc1495395f2b051a337d7dd4726e72f7fc08a999","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-02-27T18:52:04Z","title_canon_sha256":"f4f17d50c477a21713740f4a3ccbf6b592af8b218bc92bc605e7a9c34d62ffdd"},"schema_version":"1.0","source":{"id":"1702.08433","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.08433","created_at":"2026-05-18T00:49:53Z"},{"alias_kind":"arxiv_version","alias_value":"1702.08433v1","created_at":"2026-05-18T00:49:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.08433","created_at":"2026-05-18T00:49:53Z"},{"alias_kind":"pith_short_12","alias_value":"L44Z2VRG5L27","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"L44Z2VRG5L27OBBB","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"L44Z2VRG","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:112d548943c853e77b2915c566a242458ba70aefbdf2514d7f7267f27cf2e9db","target":"graph","created_at":"2026-05-18T00:49:53Z","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 study the structure of martingale transports in finite dimensions. We consider the family $\\mathcal{M}(\\mu,\\nu) $ of martingale measures on $\\mathbb{R}^N \\times \\mathbb{R}^N$ with given marginals $\\mu,\\nu$, and construct a family of relatively open convex sets $\\{C_x:x\\in \\mathbb{R}^N \\}$, which forms a partition of $\\mathbb{R}^N$, and such that any martingale transport in $\\mathcal{M}(\\mu,\\nu) $ sends mass from $x$ to within $\\overline{C_x}$, $\\mu(dx)$--a.e. Our results extend the analogous one-dimensional results of M. Beiglb\\\"ock and N. Juillet (2016) and M. Beiglb\\\"ock, M. Nutz, and N. ","authors_text":"Jan Ob\\l\\'oj, Pietro Siorpaes","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-02-27T18:52:04Z","title":"Structure of martingale transports in finite dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.08433","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":"sha256:40e1a8026c8ad6bc8651690df7c1b42851115d5fbf23d9bbdf4345de7eed5af3","target":"record","created_at":"2026-05-18T00:49:53Z","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":"4d1428255ea14522ededd1aecc1495395f2b051a337d7dd4726e72f7fc08a999","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-02-27T18:52:04Z","title_canon_sha256":"f4f17d50c477a21713740f4a3ccbf6b592af8b218bc92bc605e7a9c34d62ffdd"},"schema_version":"1.0","source":{"id":"1702.08433","kind":"arxiv","version":1}},"canonical_sha256":"5f399d5626eaf5f70421dc6e2e33e1bdd2870d5d6c296f2266a64b88de5e68a1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5f399d5626eaf5f70421dc6e2e33e1bdd2870d5d6c296f2266a64b88de5e68a1","first_computed_at":"2026-05-18T00:49:53.009281Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:53.009281Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+MPk8uTwBJyBq9HTdbHTP8tV57boQiPuQ2c9C0j03Jz/689nacewJOb7QAsM4H9VMei3NI1JL/NLsXP8ez+nAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:53.009879Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.08433","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:40e1a8026c8ad6bc8651690df7c1b42851115d5fbf23d9bbdf4345de7eed5af3","sha256:112d548943c853e77b2915c566a242458ba70aefbdf2514d7f7267f27cf2e9db"],"state_sha256":"0956f41f24608712a88239773c8970de277937fb3eb683f47d45629e6e5dd30c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cF7S+eC3YzU2+r9E7TIFPi/LNR8H6LtCydo7cPeRLgQs9gNgMrDW7VqVAbwSc6U2pIYoiRVDYP1RPH64pwPPCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T04:46:22.118799Z","bundle_sha256":"81d6b9b37b974375f33e17b786929fa5a6d53e75361800fd56fa39bc97d615fb"}}