{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:T6C4IT2UMSHKSKXCIPCSYUPPFK","short_pith_number":"pith:T6C4IT2U","schema_version":"1.0","canonical_sha256":"9f85c44f54648ea92ae243c52c51ef2a9ccddbda6259ff86f3f645d759df61d7","source":{"kind":"arxiv","id":"1311.1918","version":2},"attestation_state":"computed","paper":{"title":"On Sudakov's type decomposition of transference plans with norm costs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Sara Daneri, Stefano Bianchini","submitted_at":"2013-11-08T10:02:48Z","abstract_excerpt":"We consider the original strategy proposed by Sudakov for solving the Monge transportation problem with norm cost $|\\cdot|_{D^*}$ \\[ \\min \\bigg\\{\\int |\\mathtt T(x) - x|_{D^*} d\\mu(x), \\ \\mathtt T : \\mathbb R^d \\to \\mathbb R^d, \\ \\nu = \\mathtt T_\\# \\mu \\bigg\\}, \\] with $\\mu$, $\\nu$ probability measures in $\\mathbb R^d$ and $\\mu$ absolutely continuous w.r.t. $\\mathcal L^d$. The key idea in this approach is to decompose (via disintegration of measures) the Kantorovich optimal transportation problem into a family of transportation problems in $Z_\\mathfrak a\\times\\mathbb R^d$, where $\\{Z_\\mathfrak "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1311.1918","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-11-08T10:02:48Z","cross_cats_sorted":[],"title_canon_sha256":"fab33bcd0eb75c8f452e28a39f77d3114221cab0c5a6a0ee472151232c7782da","abstract_canon_sha256":"47e6510bb5b6653bb84c9a6cdbbfb4bd881cb9bf7093f50a2f5947cb59e590be"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:03:09.594068Z","signature_b64":"lG2OuVX3S63Mb852e+hDdFFrTOqApEpe3GHSMOyFREM7H3rnYOC//1Go78ui6tFTsv/SlF14geskjriIMvKAAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f85c44f54648ea92ae243c52c51ef2a9ccddbda6259ff86f3f645d759df61d7","last_reissued_at":"2026-05-18T03:03:09.593457Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:03:09.593457Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Sudakov's type decomposition of transference plans with norm costs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Sara Daneri, Stefano Bianchini","submitted_at":"2013-11-08T10:02:48Z","abstract_excerpt":"We consider the original strategy proposed by Sudakov for solving the Monge transportation problem with norm cost $|\\cdot|_{D^*}$ \\[ \\min \\bigg\\{\\int |\\mathtt T(x) - x|_{D^*} d\\mu(x), \\ \\mathtt T : \\mathbb R^d \\to \\mathbb R^d, \\ \\nu = \\mathtt T_\\# \\mu \\bigg\\}, \\] with $\\mu$, $\\nu$ probability measures in $\\mathbb R^d$ and $\\mu$ absolutely continuous w.r.t. $\\mathcal L^d$. The key idea in this approach is to decompose (via disintegration of measures) the Kantorovich optimal transportation problem into a family of transportation problems in $Z_\\mathfrak a\\times\\mathbb R^d$, where $\\{Z_\\mathfrak "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.1918","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1311.1918","created_at":"2026-05-18T03:03:09.593532+00:00"},{"alias_kind":"arxiv_version","alias_value":"1311.1918v2","created_at":"2026-05-18T03:03:09.593532+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.1918","created_at":"2026-05-18T03:03:09.593532+00:00"},{"alias_kind":"pith_short_12","alias_value":"T6C4IT2UMSHK","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_16","alias_value":"T6C4IT2UMSHKSKXC","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_8","alias_value":"T6C4IT2U","created_at":"2026-05-18T12:27:59.945178+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/T6C4IT2UMSHKSKXCIPCSYUPPFK","json":"https://pith.science/pith/T6C4IT2UMSHKSKXCIPCSYUPPFK.json","graph_json":"https://pith.science/api/pith-number/T6C4IT2UMSHKSKXCIPCSYUPPFK/graph.json","events_json":"https://pith.science/api/pith-number/T6C4IT2UMSHKSKXCIPCSYUPPFK/events.json","paper":"https://pith.science/paper/T6C4IT2U"},"agent_actions":{"view_html":"https://pith.science/pith/T6C4IT2UMSHKSKXCIPCSYUPPFK","download_json":"https://pith.science/pith/T6C4IT2UMSHKSKXCIPCSYUPPFK.json","view_paper":"https://pith.science/paper/T6C4IT2U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1311.1918&json=true","fetch_graph":"https://pith.science/api/pith-number/T6C4IT2UMSHKSKXCIPCSYUPPFK/graph.json","fetch_events":"https://pith.science/api/pith-number/T6C4IT2UMSHKSKXCIPCSYUPPFK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/T6C4IT2UMSHKSKXCIPCSYUPPFK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/T6C4IT2UMSHKSKXCIPCSYUPPFK/action/storage_attestation","attest_author":"https://pith.science/pith/T6C4IT2UMSHKSKXCIPCSYUPPFK/action/author_attestation","sign_citation":"https://pith.science/pith/T6C4IT2UMSHKSKXCIPCSYUPPFK/action/citation_signature","submit_replication":"https://pith.science/pith/T6C4IT2UMSHKSKXCIPCSYUPPFK/action/replication_record"}},"created_at":"2026-05-18T03:03:09.593532+00:00","updated_at":"2026-05-18T03:03:09.593532+00:00"}