{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:BRPQQKAGRNRVD3SHVMAHMLEUQ7","short_pith_number":"pith:BRPQQKAG","schema_version":"1.0","canonical_sha256":"0c5f0828068b6351ee47ab00762c9487fc7d2f9e3810da05ef7abf95e80723be","source":{"kind":"arxiv","id":"1907.08880","version":1},"attestation_state":"computed","paper":{"title":"Spectral Graph Matching and Regularized Quadratic Relaxations I: The Gaussian Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.PR","math.SP","math.ST","stat.TH"],"primary_cat":"stat.ML","authors_text":"Cheng Mao, Jiaming Xu, Yihong Wu, Zhou Fan","submitted_at":"2019-07-20T23:36:41Z","abstract_excerpt":"Graph matching aims at finding the vertex correspondence between two unlabeled graphs that maximizes the total edge weight correlation. This amounts to solving a computationally intractable quadratic assignment problem. In this paper we propose a new spectral method, GRAph Matching by Pairwise eigen-Alignments (GRAMPA). Departing from prior spectral approaches that only compare top eigenvectors, or eigenvectors of the same order, GRAMPA first constructs a similarity matrix as a weighted sum of outer products between all pairs of eigenvectors of the two graphs, with weights given by a Cauchy ke"},"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":"1907.08880","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2019-07-20T23:36:41Z","cross_cats_sorted":["cs.LG","math.PR","math.SP","math.ST","stat.TH"],"title_canon_sha256":"52b13a3f44d922b2b12d38c25e5183209f1e67a82c50df91ce342030da6ae931","abstract_canon_sha256":"f9c3c776e0deef4b519faab40cbd3b61165caf015bd9a494f864911cabf3f4d3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:02.872171Z","signature_b64":"IM6lKoapD+2pOvjzyhurHVI1CVcdlW2Av2dC8Me1O+qGGYEzFZ2Sxgc7xYgJH1sByA74Og7lHf5o46iimygFAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0c5f0828068b6351ee47ab00762c9487fc7d2f9e3810da05ef7abf95e80723be","last_reissued_at":"2026-05-17T23:40:02.871579Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:02.871579Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectral Graph Matching and Regularized Quadratic Relaxations I: The Gaussian Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.PR","math.SP","math.ST","stat.TH"],"primary_cat":"stat.ML","authors_text":"Cheng Mao, Jiaming Xu, Yihong Wu, Zhou Fan","submitted_at":"2019-07-20T23:36:41Z","abstract_excerpt":"Graph matching aims at finding the vertex correspondence between two unlabeled graphs that maximizes the total edge weight correlation. This amounts to solving a computationally intractable quadratic assignment problem. In this paper we propose a new spectral method, GRAph Matching by Pairwise eigen-Alignments (GRAMPA). Departing from prior spectral approaches that only compare top eigenvectors, or eigenvectors of the same order, GRAMPA first constructs a similarity matrix as a weighted sum of outer products between all pairs of eigenvectors of the two graphs, with weights given by a Cauchy ke"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.08880","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":""},"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":"1907.08880","created_at":"2026-05-17T23:40:02.871659+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.08880v1","created_at":"2026-05-17T23:40:02.871659+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.08880","created_at":"2026-05-17T23:40:02.871659+00:00"},{"alias_kind":"pith_short_12","alias_value":"BRPQQKAGRNRV","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_16","alias_value":"BRPQQKAGRNRVD3SH","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_8","alias_value":"BRPQQKAG","created_at":"2026-05-18T12:33:12.712433+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"2502.17142","citing_title":"The feasibility of multi-graph alignment: a Bayesian approach","ref_index":15,"is_internal_anchor":true},{"citing_arxiv_id":"2502.17142","citing_title":"The feasibility of multi-graph alignment: a Bayesian approach","ref_index":15,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BRPQQKAGRNRVD3SHVMAHMLEUQ7","json":"https://pith.science/pith/BRPQQKAGRNRVD3SHVMAHMLEUQ7.json","graph_json":"https://pith.science/api/pith-number/BRPQQKAGRNRVD3SHVMAHMLEUQ7/graph.json","events_json":"https://pith.science/api/pith-number/BRPQQKAGRNRVD3SHVMAHMLEUQ7/events.json","paper":"https://pith.science/paper/BRPQQKAG"},"agent_actions":{"view_html":"https://pith.science/pith/BRPQQKAGRNRVD3SHVMAHMLEUQ7","download_json":"https://pith.science/pith/BRPQQKAGRNRVD3SHVMAHMLEUQ7.json","view_paper":"https://pith.science/paper/BRPQQKAG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.08880&json=true","fetch_graph":"https://pith.science/api/pith-number/BRPQQKAGRNRVD3SHVMAHMLEUQ7/graph.json","fetch_events":"https://pith.science/api/pith-number/BRPQQKAGRNRVD3SHVMAHMLEUQ7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BRPQQKAGRNRVD3SHVMAHMLEUQ7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BRPQQKAGRNRVD3SHVMAHMLEUQ7/action/storage_attestation","attest_author":"https://pith.science/pith/BRPQQKAGRNRVD3SHVMAHMLEUQ7/action/author_attestation","sign_citation":"https://pith.science/pith/BRPQQKAGRNRVD3SHVMAHMLEUQ7/action/citation_signature","submit_replication":"https://pith.science/pith/BRPQQKAGRNRVD3SHVMAHMLEUQ7/action/replication_record"}},"created_at":"2026-05-17T23:40:02.871659+00:00","updated_at":"2026-05-17T23:40:02.871659+00:00"}