{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:PENUXFQR7K3OR4AJFX3ILMP6DW","short_pith_number":"pith:PENUXFQR","schema_version":"1.0","canonical_sha256":"791b4b9611fab6e8f0092df685b1fe1d8b861feed01c2bee2193b0d6bf15e84e","source":{"kind":"arxiv","id":"1706.06008","version":5},"attestation_state":"computed","paper":{"title":"Next-order asymptotic expansion for N-marginal optimal transport with Coulomb and Riesz costs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Codina Cotar, Mircea Petrache","submitted_at":"2017-06-19T15:20:35Z","abstract_excerpt":"Motivated by a problem arising from Density Functional Theory, we provide the sharp next-order asymptotics for a class of multimarginal optimal transport problems with cost given by singular, long-range pairwise interaction potentials. More precisely, we consider an $N$-marginal optimal transport problem with $N$ equal marginals supported on $\\mathbb R^d$ and with cost of the form $\\sum_{i\\neq j}|x_i-x_j|^{-s}$. In this setting we determine the second-order term in the $N\\to\\infty$ asymptotic expansion of the minimum energy, for the long-range interactions corresponding to all exponents $0<s<d"},"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":"1706.06008","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-06-19T15:20:35Z","cross_cats_sorted":["math.AP","math.MP","math.PR"],"title_canon_sha256":"94ee293059c2ebbe4f3deb71e2e7fc1724274cc1a675de0dc1a9578930dfd29d","abstract_canon_sha256":"35a7280b1583d71fce250d3e2f0b98a7772d4a59da05933b35c13167701f83d6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:19.679520Z","signature_b64":"YcbQXDGHVqjM6L8ScY5E1v1dnQzcfDsyM0btQVaFqZR7goL2u66Y1j0VvYWZ+fcfKLsmOEmwpTjfRZnU09IKCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"791b4b9611fab6e8f0092df685b1fe1d8b861feed01c2bee2193b0d6bf15e84e","last_reissued_at":"2026-05-17T23:58:19.678999Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:19.678999Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Next-order asymptotic expansion for N-marginal optimal transport with Coulomb and Riesz costs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Codina Cotar, Mircea Petrache","submitted_at":"2017-06-19T15:20:35Z","abstract_excerpt":"Motivated by a problem arising from Density Functional Theory, we provide the sharp next-order asymptotics for a class of multimarginal optimal transport problems with cost given by singular, long-range pairwise interaction potentials. More precisely, we consider an $N$-marginal optimal transport problem with $N$ equal marginals supported on $\\mathbb R^d$ and with cost of the form $\\sum_{i\\neq j}|x_i-x_j|^{-s}$. In this setting we determine the second-order term in the $N\\to\\infty$ asymptotic expansion of the minimum energy, for the long-range interactions corresponding to all exponents $0<s<d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.06008","kind":"arxiv","version":5},"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":"1706.06008","created_at":"2026-05-17T23:58:19.679078+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.06008v5","created_at":"2026-05-17T23:58:19.679078+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.06008","created_at":"2026-05-17T23:58:19.679078+00:00"},{"alias_kind":"pith_short_12","alias_value":"PENUXFQR7K3O","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_16","alias_value":"PENUXFQR7K3OR4AJ","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_8","alias_value":"PENUXFQR","created_at":"2026-05-18T12:31:37.085036+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/PENUXFQR7K3OR4AJFX3ILMP6DW","json":"https://pith.science/pith/PENUXFQR7K3OR4AJFX3ILMP6DW.json","graph_json":"https://pith.science/api/pith-number/PENUXFQR7K3OR4AJFX3ILMP6DW/graph.json","events_json":"https://pith.science/api/pith-number/PENUXFQR7K3OR4AJFX3ILMP6DW/events.json","paper":"https://pith.science/paper/PENUXFQR"},"agent_actions":{"view_html":"https://pith.science/pith/PENUXFQR7K3OR4AJFX3ILMP6DW","download_json":"https://pith.science/pith/PENUXFQR7K3OR4AJFX3ILMP6DW.json","view_paper":"https://pith.science/paper/PENUXFQR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.06008&json=true","fetch_graph":"https://pith.science/api/pith-number/PENUXFQR7K3OR4AJFX3ILMP6DW/graph.json","fetch_events":"https://pith.science/api/pith-number/PENUXFQR7K3OR4AJFX3ILMP6DW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PENUXFQR7K3OR4AJFX3ILMP6DW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PENUXFQR7K3OR4AJFX3ILMP6DW/action/storage_attestation","attest_author":"https://pith.science/pith/PENUXFQR7K3OR4AJFX3ILMP6DW/action/author_attestation","sign_citation":"https://pith.science/pith/PENUXFQR7K3OR4AJFX3ILMP6DW/action/citation_signature","submit_replication":"https://pith.science/pith/PENUXFQR7K3OR4AJFX3ILMP6DW/action/replication_record"}},"created_at":"2026-05-17T23:58:19.679078+00:00","updated_at":"2026-05-17T23:58:19.679078+00:00"}