{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:JOUJIGSCYB4REV2DVCXQ5SMGF3","short_pith_number":"pith:JOUJIGSC","schema_version":"1.0","canonical_sha256":"4ba8941a42c079125743a8af0ec9862ece91c176729fd530b6026d1065868b1f","source":{"kind":"arxiv","id":"1707.01337","version":1},"attestation_state":"computed","paper":{"title":"An algorithm for optimal transport between a simplex soup and a point cloud","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"cs.CG","authors_text":"Boris Thibert, Jocelyn Meyron, Quentin M\\'erigot","submitted_at":"2017-07-05T11:57:47Z","abstract_excerpt":"We propose a numerical method to find the optimal transport map between a measure supported on a lower-dimensional subset of R^d and a finitely supported measure. More precisely, the source measure is assumed to be supported on a simplex soup, i.e. on a union of simplices of arbitrary dimension between 2 and d. As in [Aurenhammer, Hoffman, Aronov, Algorithmica 20 (1), 1998, 61--76] we recast this optimal transport problem as the resolution of a non-linear system where one wants to prescribe the quantity of mass in each cell of the so-called Laguerre diagram. We prove the convergence with linea"},"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":"1707.01337","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2017-07-05T11:57:47Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"8e29966a40292817c33e54d4bbf46b6733d84cb40cde312303c1f90193a752de","abstract_canon_sha256":"4be07c8b0867c6c04250692886b735ef0f8cc0318871f97049f299ecbcd738d8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:53.111803Z","signature_b64":"XBe4KW5KMO3QqJ0X+PfJx+RQpFn35kxdalYh3qrFjmHujTAwUbk/WEF6Fa9oJ7FOq8pGKbiJM5jegcn8aWFvBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4ba8941a42c079125743a8af0ec9862ece91c176729fd530b6026d1065868b1f","last_reissued_at":"2026-05-18T00:40:53.111285Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:53.111285Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An algorithm for optimal transport between a simplex soup and a point cloud","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"cs.CG","authors_text":"Boris Thibert, Jocelyn Meyron, Quentin M\\'erigot","submitted_at":"2017-07-05T11:57:47Z","abstract_excerpt":"We propose a numerical method to find the optimal transport map between a measure supported on a lower-dimensional subset of R^d and a finitely supported measure. More precisely, the source measure is assumed to be supported on a simplex soup, i.e. on a union of simplices of arbitrary dimension between 2 and d. As in [Aurenhammer, Hoffman, Aronov, Algorithmica 20 (1), 1998, 61--76] we recast this optimal transport problem as the resolution of a non-linear system where one wants to prescribe the quantity of mass in each cell of the so-called Laguerre diagram. We prove the convergence with linea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.01337","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":"1707.01337","created_at":"2026-05-18T00:40:53.111374+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.01337v1","created_at":"2026-05-18T00:40:53.111374+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.01337","created_at":"2026-05-18T00:40:53.111374+00:00"},{"alias_kind":"pith_short_12","alias_value":"JOUJIGSCYB4R","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_16","alias_value":"JOUJIGSCYB4REV2D","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_8","alias_value":"JOUJIGSC","created_at":"2026-05-18T12:31:24.725408+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/JOUJIGSCYB4REV2DVCXQ5SMGF3","json":"https://pith.science/pith/JOUJIGSCYB4REV2DVCXQ5SMGF3.json","graph_json":"https://pith.science/api/pith-number/JOUJIGSCYB4REV2DVCXQ5SMGF3/graph.json","events_json":"https://pith.science/api/pith-number/JOUJIGSCYB4REV2DVCXQ5SMGF3/events.json","paper":"https://pith.science/paper/JOUJIGSC"},"agent_actions":{"view_html":"https://pith.science/pith/JOUJIGSCYB4REV2DVCXQ5SMGF3","download_json":"https://pith.science/pith/JOUJIGSCYB4REV2DVCXQ5SMGF3.json","view_paper":"https://pith.science/paper/JOUJIGSC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.01337&json=true","fetch_graph":"https://pith.science/api/pith-number/JOUJIGSCYB4REV2DVCXQ5SMGF3/graph.json","fetch_events":"https://pith.science/api/pith-number/JOUJIGSCYB4REV2DVCXQ5SMGF3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JOUJIGSCYB4REV2DVCXQ5SMGF3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JOUJIGSCYB4REV2DVCXQ5SMGF3/action/storage_attestation","attest_author":"https://pith.science/pith/JOUJIGSCYB4REV2DVCXQ5SMGF3/action/author_attestation","sign_citation":"https://pith.science/pith/JOUJIGSCYB4REV2DVCXQ5SMGF3/action/citation_signature","submit_replication":"https://pith.science/pith/JOUJIGSCYB4REV2DVCXQ5SMGF3/action/replication_record"}},"created_at":"2026-05-18T00:40:53.111374+00:00","updated_at":"2026-05-18T00:40:53.111374+00:00"}