{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:NIBK45JSQN4W2UGGRMTH7XVNRN","short_pith_number":"pith:NIBK45JS","schema_version":"1.0","canonical_sha256":"6a02ae753283796d50c68b267fdead8b57ec3f89dfac31ee9bc53c8bd978f547","source":{"kind":"arxiv","id":"2607.09026","version":1},"attestation_state":"computed","paper":{"title":"Geometric planted matchings in high dimensions: The power of multiple views","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"Cheng Mao, Kaylee Y. Yang, Timothy L. H. Wee, Zhou Fan","submitted_at":"2026-07-10T01:17:10Z","abstract_excerpt":"We study the problem of recovering the correspondence between a collection of $n$ points in $\\mathbb{R}^d$ and a noisy, permuted version of those points. In the high-dimensional regime $d=\\omega(\\log n)$, under a Gaussian model with noise variance $\\sigma^2=d/(b\\log n)$, prior work identifies $b=2$ as the threshold for almost exact recovery. We prove that this threshold is all-or-nothing: for every fixed $b<2$, no estimator recovers a positive fraction of the matching, and even estimating the matched point cloud in Euclidean distance is asymptotically no better than ignoring the correspondence"},"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":"2607.09026","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2026-07-10T01:17:10Z","cross_cats_sorted":["cs.DS","math.PR","stat.TH"],"title_canon_sha256":"553dd2c5c7f7b9fd730214aaf3d3d8921d4aa0d634b27abc09a67536c3923b85","abstract_canon_sha256":"271c99fff06a3a2943e3ed1183d802a1343b7895f9b1087294da63118476db86"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-13T00:17:35.353996Z","signature_b64":"CjoFTqcfUbf20qZJ4FqM2JC3pddxgWT3p6LaSIOXHZ1CqfzT4XRvILvdySZ/Xx4OrFgcTpeqVNspwUvD007LCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a02ae753283796d50c68b267fdead8b57ec3f89dfac31ee9bc53c8bd978f547","last_reissued_at":"2026-07-13T00:17:35.351711Z","signature_status":"signed_v1","first_computed_at":"2026-07-13T00:17:35.351711Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Geometric planted matchings in high dimensions: The power of multiple views","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"Cheng Mao, Kaylee Y. Yang, Timothy L. H. Wee, Zhou Fan","submitted_at":"2026-07-10T01:17:10Z","abstract_excerpt":"We study the problem of recovering the correspondence between a collection of $n$ points in $\\mathbb{R}^d$ and a noisy, permuted version of those points. In the high-dimensional regime $d=\\omega(\\log n)$, under a Gaussian model with noise variance $\\sigma^2=d/(b\\log n)$, prior work identifies $b=2$ as the threshold for almost exact recovery. We prove that this threshold is all-or-nothing: for every fixed $b<2$, no estimator recovers a positive fraction of the matching, and even estimating the matched point cloud in Euclidean distance is asymptotically no better than ignoring the correspondence"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.09026","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/2607.09026/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":"2607.09026","created_at":"2026-07-13T00:17:35.352744+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.09026v1","created_at":"2026-07-13T00:17:35.352744+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.09026","created_at":"2026-07-13T00:17:35.352744+00:00"},{"alias_kind":"pith_short_12","alias_value":"NIBK45JSQN4W","created_at":"2026-07-13T00:17:35.352744+00:00"},{"alias_kind":"pith_short_16","alias_value":"NIBK45JSQN4W2UGG","created_at":"2026-07-13T00:17:35.352744+00:00"},{"alias_kind":"pith_short_8","alias_value":"NIBK45JS","created_at":"2026-07-13T00:17:35.352744+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/NIBK45JSQN4W2UGGRMTH7XVNRN","json":"https://pith.science/pith/NIBK45JSQN4W2UGGRMTH7XVNRN.json","graph_json":"https://pith.science/api/pith-number/NIBK45JSQN4W2UGGRMTH7XVNRN/graph.json","events_json":"https://pith.science/api/pith-number/NIBK45JSQN4W2UGGRMTH7XVNRN/events.json","paper":"https://pith.science/paper/NIBK45JS"},"agent_actions":{"view_html":"https://pith.science/pith/NIBK45JSQN4W2UGGRMTH7XVNRN","download_json":"https://pith.science/pith/NIBK45JSQN4W2UGGRMTH7XVNRN.json","view_paper":"https://pith.science/paper/NIBK45JS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.09026&json=true","fetch_graph":"https://pith.science/api/pith-number/NIBK45JSQN4W2UGGRMTH7XVNRN/graph.json","fetch_events":"https://pith.science/api/pith-number/NIBK45JSQN4W2UGGRMTH7XVNRN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NIBK45JSQN4W2UGGRMTH7XVNRN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NIBK45JSQN4W2UGGRMTH7XVNRN/action/storage_attestation","attest_author":"https://pith.science/pith/NIBK45JSQN4W2UGGRMTH7XVNRN/action/author_attestation","sign_citation":"https://pith.science/pith/NIBK45JSQN4W2UGGRMTH7XVNRN/action/citation_signature","submit_replication":"https://pith.science/pith/NIBK45JSQN4W2UGGRMTH7XVNRN/action/replication_record"}},"created_at":"2026-07-13T00:17:35.352744+00:00","updated_at":"2026-07-13T00:17:35.352744+00:00"}