{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:FLAAM2RBDJGBXHSW7H67CIKG3T","short_pith_number":"pith:FLAAM2RB","canonical_record":{"source":{"id":"1610.02940","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-10-10T14:46:09Z","cross_cats_sorted":["q-fin.MF"],"title_canon_sha256":"10f04e5b5b3e1c29ae00d7ed664b40c19070234121e9044e244ede7b709af5c0","abstract_canon_sha256":"3a210f5255145bcd2ce9c2852148c7ded23e568ab2796e3883b105174b24487c"},"schema_version":"1.0"},"canonical_sha256":"2ac0066a211a4c1b9e56f9fdf12146dcdc32e36766b75682f1e21c862f461aaa","source":{"kind":"arxiv","id":"1610.02940","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.02940","created_at":"2026-05-18T00:32:14Z"},{"alias_kind":"arxiv_version","alias_value":"1610.02940v2","created_at":"2026-05-18T00:32:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.02940","created_at":"2026-05-18T00:32:14Z"},{"alias_kind":"pith_short_12","alias_value":"FLAAM2RBDJGB","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FLAAM2RBDJGBXHSW","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FLAAM2RB","created_at":"2026-05-18T12:30:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:FLAAM2RBDJGBXHSW7H67CIKG3T","target":"record","payload":{"canonical_record":{"source":{"id":"1610.02940","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-10-10T14:46:09Z","cross_cats_sorted":["q-fin.MF"],"title_canon_sha256":"10f04e5b5b3e1c29ae00d7ed664b40c19070234121e9044e244ede7b709af5c0","abstract_canon_sha256":"3a210f5255145bcd2ce9c2852148c7ded23e568ab2796e3883b105174b24487c"},"schema_version":"1.0"},"canonical_sha256":"2ac0066a211a4c1b9e56f9fdf12146dcdc32e36766b75682f1e21c862f461aaa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:14.648410Z","signature_b64":"FVZO+HsISnHV92clP5HaO/cbr8DoDXuVQQieE48L1BBrzmhco4ubINYbv5O0KL7rfcsGEIjQx7jdGfSKDiEoBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2ac0066a211a4c1b9e56f9fdf12146dcdc32e36766b75682f1e21c862f461aaa","last_reissued_at":"2026-05-18T00:32:14.647808Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:14.647808Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.02940","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":"2026-05-18T00:32:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B4MUw3hCjKCrkzH00/JEP3VtWlcDCJpbSIpoCVqST315R2aomStuw4l2tbGg2KkVMSCqmQLI6YnVS+56d6UOAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T21:20:36.003989Z"},"content_sha256":"946e5f31be6c0d97dfc843125d687517dd4bcc9313a59073cc25c346c396b2aa","schema_version":"1.0","event_id":"sha256:946e5f31be6c0d97dfc843125d687517dd4bcc9313a59073cc25c346c396b2aa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:FLAAM2RBDJGBXHSW7H67CIKG3T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Constrained Optimal Transport","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-fin.MF"],"primary_cat":"math.FA","authors_text":"H. Mete Soner, Ibrahim Ekren","submitted_at":"2016-10-10T14:46:09Z","abstract_excerpt":"The classical duality theory of Kantorovich and Kellerer for the classical optimal transport is generalized to an abstract framework and a characterization of the dual elements is provided. This abstract generalization is set in a Banach lattice $\\cal{X}$ with a order unit. The primal problem is given as the supremum over a convex subset of the positive unit sphere of the topological dual of $\\cal{X}$ and the dual problem is defined on the bi-dual of $\\cal{X}$. These results are then applied to several extensions of the classical optimal transport."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.02940","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":"2026-05-18T00:32:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KN4BCfg8BnK3LSYu641YZNLUr7ZbbntRVej8iq5Ecw9JLRXCxa72WtH8djHLGyMgEltH955dhIHABQ7Xq4BTDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T21:20:36.004373Z"},"content_sha256":"d83b81eb0e0e3116188f017753f4df60a6e4758201ceb6aa11d6b4595915c3e6","schema_version":"1.0","event_id":"sha256:d83b81eb0e0e3116188f017753f4df60a6e4758201ceb6aa11d6b4595915c3e6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FLAAM2RBDJGBXHSW7H67CIKG3T/bundle.json","state_url":"https://pith.science/pith/FLAAM2RBDJGBXHSW7H67CIKG3T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FLAAM2RBDJGBXHSW7H67CIKG3T/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":"2026-05-30T21:20:36Z","links":{"resolver":"https://pith.science/pith/FLAAM2RBDJGBXHSW7H67CIKG3T","bundle":"https://pith.science/pith/FLAAM2RBDJGBXHSW7H67CIKG3T/bundle.json","state":"https://pith.science/pith/FLAAM2RBDJGBXHSW7H67CIKG3T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FLAAM2RBDJGBXHSW7H67CIKG3T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:FLAAM2RBDJGBXHSW7H67CIKG3T","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":"3a210f5255145bcd2ce9c2852148c7ded23e568ab2796e3883b105174b24487c","cross_cats_sorted":["q-fin.MF"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-10-10T14:46:09Z","title_canon_sha256":"10f04e5b5b3e1c29ae00d7ed664b40c19070234121e9044e244ede7b709af5c0"},"schema_version":"1.0","source":{"id":"1610.02940","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.02940","created_at":"2026-05-18T00:32:14Z"},{"alias_kind":"arxiv_version","alias_value":"1610.02940v2","created_at":"2026-05-18T00:32:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.02940","created_at":"2026-05-18T00:32:14Z"},{"alias_kind":"pith_short_12","alias_value":"FLAAM2RBDJGB","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FLAAM2RBDJGBXHSW","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FLAAM2RB","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:d83b81eb0e0e3116188f017753f4df60a6e4758201ceb6aa11d6b4595915c3e6","target":"graph","created_at":"2026-05-18T00:32:14Z","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 classical duality theory of Kantorovich and Kellerer for the classical optimal transport is generalized to an abstract framework and a characterization of the dual elements is provided. This abstract generalization is set in a Banach lattice $\\cal{X}$ with a order unit. The primal problem is given as the supremum over a convex subset of the positive unit sphere of the topological dual of $\\cal{X}$ and the dual problem is defined on the bi-dual of $\\cal{X}$. These results are then applied to several extensions of the classical optimal transport.","authors_text":"H. Mete Soner, Ibrahim Ekren","cross_cats":["q-fin.MF"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-10-10T14:46:09Z","title":"Constrained Optimal Transport"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.02940","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":"sha256:946e5f31be6c0d97dfc843125d687517dd4bcc9313a59073cc25c346c396b2aa","target":"record","created_at":"2026-05-18T00:32:14Z","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":"3a210f5255145bcd2ce9c2852148c7ded23e568ab2796e3883b105174b24487c","cross_cats_sorted":["q-fin.MF"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-10-10T14:46:09Z","title_canon_sha256":"10f04e5b5b3e1c29ae00d7ed664b40c19070234121e9044e244ede7b709af5c0"},"schema_version":"1.0","source":{"id":"1610.02940","kind":"arxiv","version":2}},"canonical_sha256":"2ac0066a211a4c1b9e56f9fdf12146dcdc32e36766b75682f1e21c862f461aaa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2ac0066a211a4c1b9e56f9fdf12146dcdc32e36766b75682f1e21c862f461aaa","first_computed_at":"2026-05-18T00:32:14.647808Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:14.647808Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FVZO+HsISnHV92clP5HaO/cbr8DoDXuVQQieE48L1BBrzmhco4ubINYbv5O0KL7rfcsGEIjQx7jdGfSKDiEoBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:14.648410Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.02940","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:946e5f31be6c0d97dfc843125d687517dd4bcc9313a59073cc25c346c396b2aa","sha256:d83b81eb0e0e3116188f017753f4df60a6e4758201ceb6aa11d6b4595915c3e6"],"state_sha256":"00a3a3670a12acc30ccad0eafa2101639233f19bfce2fbf6c2fe85bd47b8a496"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MDwZeL63Zn6QI8y7dvBQeSd8+y54uRL7+47hSbtfqu66vRI9374xdFYcPu3Omfrd0uY07EH7J/Rde5zmg41qDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T21:20:36.006362Z","bundle_sha256":"713f5a611eee3709b3af7190dbf36ded2d6a5b26081b39226236e52a00054ee0"}}