{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:DAELCE4N2LQ7EA4L5FR7MBMDVB","short_pith_number":"pith:DAELCE4N","schema_version":"1.0","canonical_sha256":"1808b1138dd2e1f2038be963f60583a85db9b8b8cc41d10cf0d476965c07bb29","source":{"kind":"arxiv","id":"1104.4223","version":1},"attestation_state":"computed","paper":{"title":"Generalized Orlicz spaces and Wasserstein distances for convex-concave scale functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.FA","authors_text":"Karl-Theodor Sturm","submitted_at":"2011-04-21T10:19:24Z","abstract_excerpt":"Given a strictly increasing, continuous function $\\vartheta:\\R_+\\to\\R_+$, based on the cost functional $\\int_{X\\times X}\\vartheta(d(x,y))\\,d q(x,y)$, we define the $L^\\vartheta$-Wasserstein distance $W_\\vartheta(\\mu,\\nu)$ between probability measures $\\mu,\\nu$ on some metric space $(X,d)$. The function $\\vartheta$ will be assumed to admit a representation $\\vartheta=\\phi\\circ\\psi$ as a composition of a convex and a concave function $\\phi$ and $\\psi$, resp. Besides convex functions and concave functions this includes all $\\mathcal C^2$ functions.\n  For such functions $\\vartheta$ we extend the c"},"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":"1104.4223","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-04-21T10:19:24Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"09bab009e91ffae8c9e4c86c6604c7a0a58abd708d835381140e6441d6efba2a","abstract_canon_sha256":"6cab0b3c489d2091791cc928d381134528a2d5b12afb24ad2408888c05730f43"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:23:44.825230Z","signature_b64":"rVHycF8cjrfoUyxHcmFCzCn3cOjfRBCfhUcjRQx0wqSC9xIsA8ru2pmdOLd5JlE57EpOUP1UrAeFRhI4uS41BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1808b1138dd2e1f2038be963f60583a85db9b8b8cc41d10cf0d476965c07bb29","last_reissued_at":"2026-05-18T04:23:44.824466Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:23:44.824466Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generalized Orlicz spaces and Wasserstein distances for convex-concave scale functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.FA","authors_text":"Karl-Theodor Sturm","submitted_at":"2011-04-21T10:19:24Z","abstract_excerpt":"Given a strictly increasing, continuous function $\\vartheta:\\R_+\\to\\R_+$, based on the cost functional $\\int_{X\\times X}\\vartheta(d(x,y))\\,d q(x,y)$, we define the $L^\\vartheta$-Wasserstein distance $W_\\vartheta(\\mu,\\nu)$ between probability measures $\\mu,\\nu$ on some metric space $(X,d)$. The function $\\vartheta$ will be assumed to admit a representation $\\vartheta=\\phi\\circ\\psi$ as a composition of a convex and a concave function $\\phi$ and $\\psi$, resp. Besides convex functions and concave functions this includes all $\\mathcal C^2$ functions.\n  For such functions $\\vartheta$ we extend the c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.4223","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1104.4223","created_at":"2026-05-18T04:23:44.824601+00:00"},{"alias_kind":"arxiv_version","alias_value":"1104.4223v1","created_at":"2026-05-18T04:23:44.824601+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.4223","created_at":"2026-05-18T04:23:44.824601+00:00"},{"alias_kind":"pith_short_12","alias_value":"DAELCE4N2LQ7","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_16","alias_value":"DAELCE4N2LQ7EA4L","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_8","alias_value":"DAELCE4N","created_at":"2026-05-18T12:26:26.731475+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/DAELCE4N2LQ7EA4L5FR7MBMDVB","json":"https://pith.science/pith/DAELCE4N2LQ7EA4L5FR7MBMDVB.json","graph_json":"https://pith.science/api/pith-number/DAELCE4N2LQ7EA4L5FR7MBMDVB/graph.json","events_json":"https://pith.science/api/pith-number/DAELCE4N2LQ7EA4L5FR7MBMDVB/events.json","paper":"https://pith.science/paper/DAELCE4N"},"agent_actions":{"view_html":"https://pith.science/pith/DAELCE4N2LQ7EA4L5FR7MBMDVB","download_json":"https://pith.science/pith/DAELCE4N2LQ7EA4L5FR7MBMDVB.json","view_paper":"https://pith.science/paper/DAELCE4N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1104.4223&json=true","fetch_graph":"https://pith.science/api/pith-number/DAELCE4N2LQ7EA4L5FR7MBMDVB/graph.json","fetch_events":"https://pith.science/api/pith-number/DAELCE4N2LQ7EA4L5FR7MBMDVB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DAELCE4N2LQ7EA4L5FR7MBMDVB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DAELCE4N2LQ7EA4L5FR7MBMDVB/action/storage_attestation","attest_author":"https://pith.science/pith/DAELCE4N2LQ7EA4L5FR7MBMDVB/action/author_attestation","sign_citation":"https://pith.science/pith/DAELCE4N2LQ7EA4L5FR7MBMDVB/action/citation_signature","submit_replication":"https://pith.science/pith/DAELCE4N2LQ7EA4L5FR7MBMDVB/action/replication_record"}},"created_at":"2026-05-18T04:23:44.824601+00:00","updated_at":"2026-05-18T04:23:44.824601+00:00"}