{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:QBC2BQUPJLATIHIKQLLRBYDXKX","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"44dbcb6ae3cfc094c713ea459bae87e605e10e452de92c1eab325e6ab398b508","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-08-08T12:54:27Z","title_canon_sha256":"265777ac94aac2822280295d9c813abef0987f568f5a01a89c4b1efa2ab89ffd"},"schema_version":"1.0","source":{"id":"1708.02469","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.02469","created_at":"2026-07-05T02:30:54Z"},{"alias_kind":"arxiv_version","alias_value":"1708.02469v1","created_at":"2026-07-05T02:30:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.02469","created_at":"2026-07-05T02:30:54Z"},{"alias_kind":"pith_short_12","alias_value":"QBC2BQUPJLAT","created_at":"2026-07-05T02:30:54Z"},{"alias_kind":"pith_short_16","alias_value":"QBC2BQUPJLATIHIK","created_at":"2026-07-05T02:30:54Z"},{"alias_kind":"pith_short_8","alias_value":"QBC2BQUP","created_at":"2026-07-05T02:30:54Z"}],"graph_snapshots":[{"event_id":"sha256:efcacc71f77bd351c9940b307e8c4179fb8ea23d1b33fcfe2ce79edf14098159","target":"graph","created_at":"2026-07-05T02:30:54Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1708.02469/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Mauro Maggioni, Samuel Gerber","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-08-08T12:54:27Z","title":"Multiscale Strategies for Computing Optimal Transport"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.02469","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:912dbfd20a959af3d6261f454d9ad645f1580cad4da4c13470868884b26cb371","target":"record","created_at":"2026-07-05T02:30:54Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"44dbcb6ae3cfc094c713ea459bae87e605e10e452de92c1eab325e6ab398b508","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-08-08T12:54:27Z","title_canon_sha256":"265777ac94aac2822280295d9c813abef0987f568f5a01a89c4b1efa2ab89ffd"},"schema_version":"1.0","source":{"id":"1708.02469","kind":"arxiv","version":1}},"canonical_sha256":"8045a0c28f4ac1341d0a82d710e07755e5a5885a94a386dfcfe15735b278f81e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8045a0c28f4ac1341d0a82d710e07755e5a5885a94a386dfcfe15735b278f81e","first_computed_at":"2026-07-05T02:30:54.033516Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:30:54.033516Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p+Wa2wll0VLORQDQeBNSdZOjWZWNDY7Bb2p+b18Vu4SjZ4DXxH7cF9Ex8EQ2Bdmxmcs0lWFL/Q3SzP9AxSo5AQ==","signature_status":"signed_v1","signed_at":"2026-07-05T02:30:54.033950Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.02469","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:912dbfd20a959af3d6261f454d9ad645f1580cad4da4c13470868884b26cb371","sha256:efcacc71f77bd351c9940b307e8c4179fb8ea23d1b33fcfe2ce79edf14098159"],"state_sha256":"0bd726fd57a628070f10ad91e85a826dddcf03c9593d6d83da62be4c91cba111"}