{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:OIXERKS5DI7ZJZRRBMFFJLIWA2","short_pith_number":"pith:OIXERKS5","schema_version":"1.0","canonical_sha256":"722e48aa5d1a3f94e6310b0a54ad1606ae79af53a55f2ec2c9af1fc5659ee026","source":{"kind":"arxiv","id":"1912.00231","version":2},"attestation_state":"computed","paper":{"title":"Spectral Alignment of Correlated Gaussian matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"math.PR","authors_text":"Laurent Massouli\\'e, Luca Ganassali, Marc Lelarge","submitted_at":"2019-11-30T16:45:33Z","abstract_excerpt":"In this paper we analyze a simple spectral method (EIG1) for the problem of matrix alignment, consisting in aligning their leading eigenvectors: given two matrices $A$ and $B$, we compute $v_1$ and $v'_1$ two corresponding leading eigenvectors. The algorithm returns the permutation $\\hat{\\pi}$ such that the rank of coordinate $\\hat{\\pi}(i)$ in $v_1$ and that of coordinate $i$ in $v'_1$ (up to the sign of $v'_1$) are the same. We consider a model of weighted graphs where the adjacency matrix $A$ belongs to the Gaussian Orthogonal Ensemble (GOE) of size $N \\times N$, and $B$ is a noisy version o"},"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":"1912.00231","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-11-30T16:45:33Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"2e96ebbcd813f96e2a828f76ef653c29fb7322134c64b427806e967fe7908f11","abstract_canon_sha256":"a934354e070c917962e4ac6029b8825239853ba84de1e9647981319884843c4a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:03:12.761912Z","signature_b64":"4rT86kcueeq1R1LmliIpbCV1DcxUuvwH6QLG8ObiY5KSSeN758Rowf7X6SUsZhXcWqsbyyh0+Cn86Vtv5MO9Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"722e48aa5d1a3f94e6310b0a54ad1606ae79af53a55f2ec2c9af1fc5659ee026","last_reissued_at":"2026-07-05T09:03:12.761416Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:03:12.761416Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectral Alignment of Correlated Gaussian matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"math.PR","authors_text":"Laurent Massouli\\'e, Luca Ganassali, Marc Lelarge","submitted_at":"2019-11-30T16:45:33Z","abstract_excerpt":"In this paper we analyze a simple spectral method (EIG1) for the problem of matrix alignment, consisting in aligning their leading eigenvectors: given two matrices $A$ and $B$, we compute $v_1$ and $v'_1$ two corresponding leading eigenvectors. The algorithm returns the permutation $\\hat{\\pi}$ such that the rank of coordinate $\\hat{\\pi}(i)$ in $v_1$ and that of coordinate $i$ in $v'_1$ (up to the sign of $v'_1$) are the same. We consider a model of weighted graphs where the adjacency matrix $A$ belongs to the Gaussian Orthogonal Ensemble (GOE) of size $N \\times N$, and $B$ is a noisy version o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.00231","kind":"arxiv","version":2},"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/1912.00231/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":"1912.00231","created_at":"2026-07-05T09:03:12.761478+00:00"},{"alias_kind":"arxiv_version","alias_value":"1912.00231v2","created_at":"2026-07-05T09:03:12.761478+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1912.00231","created_at":"2026-07-05T09:03:12.761478+00:00"},{"alias_kind":"pith_short_12","alias_value":"OIXERKS5DI7Z","created_at":"2026-07-05T09:03:12.761478+00:00"},{"alias_kind":"pith_short_16","alias_value":"OIXERKS5DI7ZJZRR","created_at":"2026-07-05T09:03:12.761478+00:00"},{"alias_kind":"pith_short_8","alias_value":"OIXERKS5","created_at":"2026-07-05T09:03:12.761478+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2502.17142","citing_title":"The feasibility of multi-graph alignment: a Bayesian approach","ref_index":17,"is_internal_anchor":false},{"citing_arxiv_id":"2502.17142","citing_title":"The feasibility of multi-graph alignment: a Bayesian approach","ref_index":17,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OIXERKS5DI7ZJZRRBMFFJLIWA2","json":"https://pith.science/pith/OIXERKS5DI7ZJZRRBMFFJLIWA2.json","graph_json":"https://pith.science/api/pith-number/OIXERKS5DI7ZJZRRBMFFJLIWA2/graph.json","events_json":"https://pith.science/api/pith-number/OIXERKS5DI7ZJZRRBMFFJLIWA2/events.json","paper":"https://pith.science/paper/OIXERKS5"},"agent_actions":{"view_html":"https://pith.science/pith/OIXERKS5DI7ZJZRRBMFFJLIWA2","download_json":"https://pith.science/pith/OIXERKS5DI7ZJZRRBMFFJLIWA2.json","view_paper":"https://pith.science/paper/OIXERKS5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1912.00231&json=true","fetch_graph":"https://pith.science/api/pith-number/OIXERKS5DI7ZJZRRBMFFJLIWA2/graph.json","fetch_events":"https://pith.science/api/pith-number/OIXERKS5DI7ZJZRRBMFFJLIWA2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OIXERKS5DI7ZJZRRBMFFJLIWA2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OIXERKS5DI7ZJZRRBMFFJLIWA2/action/storage_attestation","attest_author":"https://pith.science/pith/OIXERKS5DI7ZJZRRBMFFJLIWA2/action/author_attestation","sign_citation":"https://pith.science/pith/OIXERKS5DI7ZJZRRBMFFJLIWA2/action/citation_signature","submit_replication":"https://pith.science/pith/OIXERKS5DI7ZJZRRBMFFJLIWA2/action/replication_record"}},"created_at":"2026-07-05T09:03:12.761478+00:00","updated_at":"2026-07-05T09:03:12.761478+00:00"}