{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:BUFSILF4FT3IGVVCMFADFVACUI","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":"053e4e021078a1039323ea371b6dfbeb74e3bde20297070dbb4ea5eca67fceff","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2020-02-05T03:09:23Z","title_canon_sha256":"28ee059a95406890bd7e9428e811e941fb65a796168fe6a68d13bf55636bacc6"},"schema_version":"1.0","source":{"id":"2002.01615","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2002.01615","created_at":"2026-07-05T02:14:09Z"},{"alias_kind":"arxiv_version","alias_value":"2002.01615v3","created_at":"2026-07-05T02:14:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2002.01615","created_at":"2026-07-05T02:14:09Z"},{"alias_kind":"pith_short_12","alias_value":"BUFSILF4FT3I","created_at":"2026-07-05T02:14:09Z"},{"alias_kind":"pith_short_16","alias_value":"BUFSILF4FT3IGVVC","created_at":"2026-07-05T02:14:09Z"},{"alias_kind":"pith_short_8","alias_value":"BUFSILF4","created_at":"2026-07-05T02:14:09Z"}],"graph_snapshots":[{"event_id":"sha256:52dfcb59582de53c16134d5858d94411712bd4b4a1f3143db37b13f5d665bc96","target":"graph","created_at":"2026-07-05T02:14:09Z","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/2002.01615/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Comparing two probability measures supported on heterogeneous spaces is an increasingly important problem in machine learning. Such problems arise when comparing for instance two populations of biological cells, each described with its own set of features, or when looking at families of word embeddings trained across different corpora/languages. For such settings, the Gromov Wasserstein (GW) distance is often presented as the gold standard. GW is intuitive, as it quantifies whether one measure can be isomorphically mapped to the other. However, its exact computation is intractable, and most al","authors_text":"Hisashi Kashima, Makoto Yamada, Marco Cuturi, Ryoma Sato","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2020-02-05T03:09:23Z","title":"Fast and Robust Comparison of Probability Measures in Heterogeneous Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2002.01615","kind":"arxiv","version":3},"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:c3719c2e795cca473cb8e04b6869204d576a5f7582a335cb2e90f6e78e30fc9a","target":"record","created_at":"2026-07-05T02:14:09Z","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":"053e4e021078a1039323ea371b6dfbeb74e3bde20297070dbb4ea5eca67fceff","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2020-02-05T03:09:23Z","title_canon_sha256":"28ee059a95406890bd7e9428e811e941fb65a796168fe6a68d13bf55636bacc6"},"schema_version":"1.0","source":{"id":"2002.01615","kind":"arxiv","version":3}},"canonical_sha256":"0d0b242cbc2cf68356a2614032d402a220b431121a5e8549d6edb2e6acf2a057","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0d0b242cbc2cf68356a2614032d402a220b431121a5e8549d6edb2e6acf2a057","first_computed_at":"2026-07-05T02:14:09.286421Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:14:09.286421Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DAtjbxg9ShfnWWPW32b73vnZG3X3u9BogGzfU5o4tobyW+LVJXNVs5jiCGETCZhQQy8qVDNJpH7vtRjByRagAA==","signature_status":"signed_v1","signed_at":"2026-07-05T02:14:09.286987Z","signed_message":"canonical_sha256_bytes"},"source_id":"2002.01615","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c3719c2e795cca473cb8e04b6869204d576a5f7582a335cb2e90f6e78e30fc9a","sha256:52dfcb59582de53c16134d5858d94411712bd4b4a1f3143db37b13f5d665bc96"],"state_sha256":"504f9cb1e9faa8a9e62ea9219f442e7368fa50a8d0a0129088029ebf3687e175"}