{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:JCA4HIQVCKXAUCKBTWVXKU5OOG","short_pith_number":"pith:JCA4HIQV","canonical_record":{"source":{"id":"1905.05663","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-05-14T15:17:36Z","cross_cats_sorted":["math.NA","math.ST","q-fin.CP","stat.TH"],"title_canon_sha256":"5e850de0e3f2a117bc80141e749f1f31c0813e3d721e567f891b76709e3e680c","abstract_canon_sha256":"d3a1bac64e1e99249bd2b7aca889398adeef49249c31959fe5dc348b2baa2937"},"schema_version":"1.0"},"canonical_sha256":"4881c3a21512ae0a09419dab7553ae71b5cf3d1ba6a0c9fe4589b889ce6ff91f","source":{"kind":"arxiv","id":"1905.05663","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.05663","created_at":"2026-05-17T23:46:13Z"},{"alias_kind":"arxiv_version","alias_value":"1905.05663v1","created_at":"2026-05-17T23:46:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.05663","created_at":"2026-05-17T23:46:13Z"},{"alias_kind":"pith_short_12","alias_value":"JCA4HIQVCKXA","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"JCA4HIQVCKXAUCKB","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"JCA4HIQV","created_at":"2026-05-18T12:33:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:JCA4HIQVCKXAUCKBTWVXKU5OOG","target":"record","payload":{"canonical_record":{"source":{"id":"1905.05663","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-05-14T15:17:36Z","cross_cats_sorted":["math.NA","math.ST","q-fin.CP","stat.TH"],"title_canon_sha256":"5e850de0e3f2a117bc80141e749f1f31c0813e3d721e567f891b76709e3e680c","abstract_canon_sha256":"d3a1bac64e1e99249bd2b7aca889398adeef49249c31959fe5dc348b2baa2937"},"schema_version":"1.0"},"canonical_sha256":"4881c3a21512ae0a09419dab7553ae71b5cf3d1ba6a0c9fe4589b889ce6ff91f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:13.910713Z","signature_b64":"yKGBLteQooOkxsWvjVemLu9KLIDSIQOWlG4Vl/iTS5t8uzHbli5nbHRNUalJfeBlsar74OTAAbOtekZEGAs9Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4881c3a21512ae0a09419dab7553ae71b5cf3d1ba6a0c9fe4589b889ce6ff91f","last_reissued_at":"2026-05-17T23:46:13.910121Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:13.910121Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1905.05663","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":"2026-05-17T23:46:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Yjgs6Llcpp/9XBYvVfghpyda6e57cVMVl5orXe1WZ4/YXUMe1wl5jAuOkfxWgHDyVBKXV4glSpd5y/4q6j3JDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T05:13:25.779990Z"},"content_sha256":"677e8cddd33b1821a673ed133b082de28cae912693eb16331a550e2e8aaf8e27","schema_version":"1.0","event_id":"sha256:677e8cddd33b1821a673ed133b082de28cae912693eb16331a550e2e8aaf8e27"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:JCA4HIQVCKXAUCKBTWVXKU5OOG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximation of Optimal Transport problems with marginal moments constraints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA","math.ST","q-fin.CP","stat.TH"],"primary_cat":"math.PR","authors_text":"Aur\\'elien Alfonsi, Damiano Lombardi, Rafa\\\"el Coyaud, Virginie Ehrlacher","submitted_at":"2019-05-14T15:17:36Z","abstract_excerpt":"Optimal Transport (OT) problems arise in a wide range of applications, from physics to economics. Getting numerical approximate solution of these problems is a challenging issue of practical importance. In this work, we investigate the relaxation of the OT problem when the marginal constraints are replaced by some moment constraints. Using Tchakaloff's theorem, we show that the Moment Constrained Optimal Transport problem (MCOT) is achieved by a finite discrete measure. Interestingly, for multimarginal OT problems, the number of points weighted by this measure scales linearly with the number o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.05663","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":"2026-05-17T23:46:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nhQpKaLhZtXS/S+Pn8l9lsPzG8aU+zbrSimfgF20YIQNsijEnm7nQtHRCjII8tYOm3ZJZzauSqo3a83XFZ+BDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T05:13:25.780672Z"},"content_sha256":"62fd779931a647badd8c0be73be9dc0b5716f08b1e436540aebca9129f3f7144","schema_version":"1.0","event_id":"sha256:62fd779931a647badd8c0be73be9dc0b5716f08b1e436540aebca9129f3f7144"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JCA4HIQVCKXAUCKBTWVXKU5OOG/bundle.json","state_url":"https://pith.science/pith/JCA4HIQVCKXAUCKBTWVXKU5OOG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JCA4HIQVCKXAUCKBTWVXKU5OOG/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":"2026-06-10T05:13:25Z","links":{"resolver":"https://pith.science/pith/JCA4HIQVCKXAUCKBTWVXKU5OOG","bundle":"https://pith.science/pith/JCA4HIQVCKXAUCKBTWVXKU5OOG/bundle.json","state":"https://pith.science/pith/JCA4HIQVCKXAUCKBTWVXKU5OOG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JCA4HIQVCKXAUCKBTWVXKU5OOG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:JCA4HIQVCKXAUCKBTWVXKU5OOG","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":"d3a1bac64e1e99249bd2b7aca889398adeef49249c31959fe5dc348b2baa2937","cross_cats_sorted":["math.NA","math.ST","q-fin.CP","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-05-14T15:17:36Z","title_canon_sha256":"5e850de0e3f2a117bc80141e749f1f31c0813e3d721e567f891b76709e3e680c"},"schema_version":"1.0","source":{"id":"1905.05663","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.05663","created_at":"2026-05-17T23:46:13Z"},{"alias_kind":"arxiv_version","alias_value":"1905.05663v1","created_at":"2026-05-17T23:46:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.05663","created_at":"2026-05-17T23:46:13Z"},{"alias_kind":"pith_short_12","alias_value":"JCA4HIQVCKXA","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"JCA4HIQVCKXAUCKB","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"JCA4HIQV","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:62fd779931a647badd8c0be73be9dc0b5716f08b1e436540aebca9129f3f7144","target":"graph","created_at":"2026-05-17T23:46:13Z","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":"Optimal Transport (OT) problems arise in a wide range of applications, from physics to economics. Getting numerical approximate solution of these problems is a challenging issue of practical importance. In this work, we investigate the relaxation of the OT problem when the marginal constraints are replaced by some moment constraints. Using Tchakaloff's theorem, we show that the Moment Constrained Optimal Transport problem (MCOT) is achieved by a finite discrete measure. Interestingly, for multimarginal OT problems, the number of points weighted by this measure scales linearly with the number o","authors_text":"Aur\\'elien Alfonsi, Damiano Lombardi, Rafa\\\"el Coyaud, Virginie Ehrlacher","cross_cats":["math.NA","math.ST","q-fin.CP","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-05-14T15:17:36Z","title":"Approximation of Optimal Transport problems with marginal moments constraints"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.05663","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":"sha256:677e8cddd33b1821a673ed133b082de28cae912693eb16331a550e2e8aaf8e27","target":"record","created_at":"2026-05-17T23:46:13Z","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":"d3a1bac64e1e99249bd2b7aca889398adeef49249c31959fe5dc348b2baa2937","cross_cats_sorted":["math.NA","math.ST","q-fin.CP","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-05-14T15:17:36Z","title_canon_sha256":"5e850de0e3f2a117bc80141e749f1f31c0813e3d721e567f891b76709e3e680c"},"schema_version":"1.0","source":{"id":"1905.05663","kind":"arxiv","version":1}},"canonical_sha256":"4881c3a21512ae0a09419dab7553ae71b5cf3d1ba6a0c9fe4589b889ce6ff91f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4881c3a21512ae0a09419dab7553ae71b5cf3d1ba6a0c9fe4589b889ce6ff91f","first_computed_at":"2026-05-17T23:46:13.910121Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:13.910121Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yKGBLteQooOkxsWvjVemLu9KLIDSIQOWlG4Vl/iTS5t8uzHbli5nbHRNUalJfeBlsar74OTAAbOtekZEGAs9Ag==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:13.910713Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.05663","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:677e8cddd33b1821a673ed133b082de28cae912693eb16331a550e2e8aaf8e27","sha256:62fd779931a647badd8c0be73be9dc0b5716f08b1e436540aebca9129f3f7144"],"state_sha256":"6eb3ebfe08e60cd11cbe3e73e20e215ba30b54c4f532e031637965d7739379fa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QsVOCjVbrO4hX+MtV8HqeJC+Cn+Ux8TI2d/OB2WaGXZEZMbN6sD/7PZfw2Za8gCFzJaerOOsCD10wy7bx9hBDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T05:13:25.784572Z","bundle_sha256":"3c70bc782156e819aee851f9fd1ff1c32942745b5e6a375af580dc49367fbe3b"}}