{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:XQJMJLIUDTZUDBKXW2BT6QZPOQ","short_pith_number":"pith:XQJMJLIU","schema_version":"1.0","canonical_sha256":"bc12c4ad141cf3418557b6833f432f742452834b56a514584559ac0642560218","source":{"kind":"arxiv","id":"2606.10295","version":1},"attestation_state":"computed","paper":{"title":"$k$-Nearest Neighbors in Gromov--Wasserstein Space","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","math.ST","stat.TH"],"primary_cat":"stat.ML","authors_text":"Caroline Moosmueller, Kaitlyn Hohmeier, Nicolas Fraiman","submitted_at":"2026-06-09T01:33:01Z","abstract_excerpt":"The Gromov--Wasserstein (GW) distance provides a framework for comparing metric measure spaces, regardless of their underlying structure or geometry. For network-based data, it enables direct comparisons of graphs with different numbers of nodes, without requiring an embedding or other abstraction. Furthermore, through a variant of GW known as fused Gromov--Wasserstein (fGW), it is also possible to incorporate node features in addition to graph structure. In this work, we implement $k$-nearest neighbors ($k$-NN) classification using the GW and fGW distances. We prove the universal consistency "},"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":"2606.10295","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2026-06-09T01:33:01Z","cross_cats_sorted":["cs.LG","math.ST","stat.TH"],"title_canon_sha256":"eb02f86157a1a8381b93ed390760b4a4a5db86eefc28da29ff1aecc61a5d808d","abstract_canon_sha256":"3429ec2ba7bdbe23da7956890482454f34a78c3f7ed4f417c8a7937640805cb9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-10T01:10:10.187515Z","signature_b64":"bDoa73EcyBuJ+mbVTM4W3594CbsnOTO6Ci+Mg9Np/Isg81AyIiNb07W23giZ3P7dQniAVJ28UlFdFAK1Hu7cCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bc12c4ad141cf3418557b6833f432f742452834b56a514584559ac0642560218","last_reissued_at":"2026-06-10T01:10:10.186613Z","signature_status":"signed_v1","first_computed_at":"2026-06-10T01:10:10.186613Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$k$-Nearest Neighbors in Gromov--Wasserstein Space","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","math.ST","stat.TH"],"primary_cat":"stat.ML","authors_text":"Caroline Moosmueller, Kaitlyn Hohmeier, Nicolas Fraiman","submitted_at":"2026-06-09T01:33:01Z","abstract_excerpt":"The Gromov--Wasserstein (GW) distance provides a framework for comparing metric measure spaces, regardless of their underlying structure or geometry. For network-based data, it enables direct comparisons of graphs with different numbers of nodes, without requiring an embedding or other abstraction. Furthermore, through a variant of GW known as fused Gromov--Wasserstein (fGW), it is also possible to incorporate node features in addition to graph structure. In this work, we implement $k$-nearest neighbors ($k$-NN) classification using the GW and fGW distances. We prove the universal consistency "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.10295","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/2606.10295/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":"2606.10295","created_at":"2026-06-10T01:10:10.186754+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.10295v1","created_at":"2026-06-10T01:10:10.186754+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.10295","created_at":"2026-06-10T01:10:10.186754+00:00"},{"alias_kind":"pith_short_12","alias_value":"XQJMJLIUDTZU","created_at":"2026-06-10T01:10:10.186754+00:00"},{"alias_kind":"pith_short_16","alias_value":"XQJMJLIUDTZUDBKX","created_at":"2026-06-10T01:10:10.186754+00:00"},{"alias_kind":"pith_short_8","alias_value":"XQJMJLIU","created_at":"2026-06-10T01:10:10.186754+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/XQJMJLIUDTZUDBKXW2BT6QZPOQ","json":"https://pith.science/pith/XQJMJLIUDTZUDBKXW2BT6QZPOQ.json","graph_json":"https://pith.science/api/pith-number/XQJMJLIUDTZUDBKXW2BT6QZPOQ/graph.json","events_json":"https://pith.science/api/pith-number/XQJMJLIUDTZUDBKXW2BT6QZPOQ/events.json","paper":"https://pith.science/paper/XQJMJLIU"},"agent_actions":{"view_html":"https://pith.science/pith/XQJMJLIUDTZUDBKXW2BT6QZPOQ","download_json":"https://pith.science/pith/XQJMJLIUDTZUDBKXW2BT6QZPOQ.json","view_paper":"https://pith.science/paper/XQJMJLIU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.10295&json=true","fetch_graph":"https://pith.science/api/pith-number/XQJMJLIUDTZUDBKXW2BT6QZPOQ/graph.json","fetch_events":"https://pith.science/api/pith-number/XQJMJLIUDTZUDBKXW2BT6QZPOQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XQJMJLIUDTZUDBKXW2BT6QZPOQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XQJMJLIUDTZUDBKXW2BT6QZPOQ/action/storage_attestation","attest_author":"https://pith.science/pith/XQJMJLIUDTZUDBKXW2BT6QZPOQ/action/author_attestation","sign_citation":"https://pith.science/pith/XQJMJLIUDTZUDBKXW2BT6QZPOQ/action/citation_signature","submit_replication":"https://pith.science/pith/XQJMJLIUDTZUDBKXW2BT6QZPOQ/action/replication_record"}},"created_at":"2026-06-10T01:10:10.186754+00:00","updated_at":"2026-06-10T01:10:10.186754+00:00"}