{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:QBC2BQUPJLATIHIKQLLRBYDXKX","short_pith_number":"pith:QBC2BQUP","schema_version":"1.0","canonical_sha256":"8045a0c28f4ac1341d0a82d710e07755e5a5885a94a386dfcfe15735b278f81e","source":{"kind":"arxiv","id":"1708.02469","version":1},"attestation_state":"computed","paper":{"title":"Multiscale Strategies for Computing Optimal Transport","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Mauro Maggioni, Samuel Gerber","submitted_at":"2017-08-08T12:54:27Z","abstract_excerpt":"This paper presents a multiscale approach to efficiently compute approximate optimal transport plans between point sets. It is particularly well-suited for point sets that are in high-dimensions, but are close to being intrinsically low-dimensional. The approach is based on an adaptive multiscale decomposition of the point sets. The multiscale decomposition yields a sequence of optimal transport problems, that are solved in a top-to-bottom fashion from the coarsest to the finest scale. We provide numerical evidence that this multiscale approach scales approximately linearly, in time and memory"},"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":"1708.02469","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-08-08T12:54:27Z","cross_cats_sorted":[],"title_canon_sha256":"265777ac94aac2822280295d9c813abef0987f568f5a01a89c4b1efa2ab89ffd","abstract_canon_sha256":"44dbcb6ae3cfc094c713ea459bae87e605e10e452de92c1eab325e6ab398b508"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:30:54.033950Z","signature_b64":"p+Wa2wll0VLORQDQeBNSdZOjWZWNDY7Bb2p+b18Vu4SjZ4DXxH7cF9Ex8EQ2Bdmxmcs0lWFL/Q3SzP9AxSo5AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8045a0c28f4ac1341d0a82d710e07755e5a5885a94a386dfcfe15735b278f81e","last_reissued_at":"2026-07-05T02:30:54.033516Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:30:54.033516Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multiscale Strategies for Computing Optimal Transport","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Mauro Maggioni, Samuel Gerber","submitted_at":"2017-08-08T12:54:27Z","abstract_excerpt":"This paper presents a multiscale approach to efficiently compute approximate optimal transport plans between point sets. It is particularly well-suited for point sets that are in high-dimensions, but are close to being intrinsically low-dimensional. The approach is based on an adaptive multiscale decomposition of the point sets. The multiscale decomposition yields a sequence of optimal transport problems, that are solved in a top-to-bottom fashion from the coarsest to the finest scale. We provide numerical evidence that this multiscale approach scales approximately linearly, in time and memory"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.02469","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1708.02469/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1708.02469","created_at":"2026-07-05T02:30:54.033585+00:00"},{"alias_kind":"arxiv_version","alias_value":"1708.02469v1","created_at":"2026-07-05T02:30:54.033585+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.02469","created_at":"2026-07-05T02:30:54.033585+00:00"},{"alias_kind":"pith_short_12","alias_value":"QBC2BQUPJLAT","created_at":"2026-07-05T02:30:54.033585+00:00"},{"alias_kind":"pith_short_16","alias_value":"QBC2BQUPJLATIHIK","created_at":"2026-07-05T02:30:54.033585+00:00"},{"alias_kind":"pith_short_8","alias_value":"QBC2BQUP","created_at":"2026-07-05T02:30:54.033585+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.01394","citing_title":"Learning to Transport with Neural Networks","ref_index":5,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QBC2BQUPJLATIHIKQLLRBYDXKX","json":"https://pith.science/pith/QBC2BQUPJLATIHIKQLLRBYDXKX.json","graph_json":"https://pith.science/api/pith-number/QBC2BQUPJLATIHIKQLLRBYDXKX/graph.json","events_json":"https://pith.science/api/pith-number/QBC2BQUPJLATIHIKQLLRBYDXKX/events.json","paper":"https://pith.science/paper/QBC2BQUP"},"agent_actions":{"view_html":"https://pith.science/pith/QBC2BQUPJLATIHIKQLLRBYDXKX","download_json":"https://pith.science/pith/QBC2BQUPJLATIHIKQLLRBYDXKX.json","view_paper":"https://pith.science/paper/QBC2BQUP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1708.02469&json=true","fetch_graph":"https://pith.science/api/pith-number/QBC2BQUPJLATIHIKQLLRBYDXKX/graph.json","fetch_events":"https://pith.science/api/pith-number/QBC2BQUPJLATIHIKQLLRBYDXKX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QBC2BQUPJLATIHIKQLLRBYDXKX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QBC2BQUPJLATIHIKQLLRBYDXKX/action/storage_attestation","attest_author":"https://pith.science/pith/QBC2BQUPJLATIHIKQLLRBYDXKX/action/author_attestation","sign_citation":"https://pith.science/pith/QBC2BQUPJLATIHIKQLLRBYDXKX/action/citation_signature","submit_replication":"https://pith.science/pith/QBC2BQUPJLATIHIKQLLRBYDXKX/action/replication_record"}},"created_at":"2026-07-05T02:30:54.033585+00:00","updated_at":"2026-07-05T02:30:54.033585+00:00"}