{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:I7BSBQ667424S6W5NS6ISO2LTI","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":"9b79a698a3457313781a3686a8e3e4e8cdd14e11c0ecbda2e0e2095d42d5563d","cross_cats_sorted":["cs.LG","math.SP","math.ST","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-07-20T23:50:02Z","title_canon_sha256":"57b4395f05d39b69fc3611e34db03deba68f6ac0d2a2ac96bd81ff2bb9e56c00"},"schema_version":"1.0","source":{"id":"1907.08883","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.08883","created_at":"2026-05-17T23:40:02Z"},{"alias_kind":"arxiv_version","alias_value":"1907.08883v1","created_at":"2026-05-17T23:40:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.08883","created_at":"2026-05-17T23:40:02Z"},{"alias_kind":"pith_short_12","alias_value":"I7BSBQ667424","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"I7BSBQ667424S6W5","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"I7BSBQ66","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:dd9adce4c54edd25ed4c490d621ad1dddae9fe39f554235481dfc74195b5e51f","target":"graph","created_at":"2026-05-17T23:40:02Z","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"},"paper":{"abstract_excerpt":"We analyze a new spectral graph matching algorithm, GRAph Matching by Pairwise eigen-Alignments (GRAMPA), for recovering the latent vertex correspondence between two unlabeled, edge-correlated weighted graphs. Extending the exact recovery guarantees established in the companion paper for Gaussian weights, in this work, we prove the universality of these guarantees for a general correlated Wigner model. In particular, for two Erd\\H{o}s-R\\'enyi graphs with edge correlation coefficient $1-\\sigma^2$ and average degree at least $\\operatorname{polylog}(n)$, we show that GRAMPA exactly recovers the l","authors_text":"Cheng Mao, Jiaming Xu, Yihong Wu, Zhou Fan","cross_cats":["cs.LG","math.SP","math.ST","stat.ML","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-07-20T23:50:02Z","title":"Spectral Graph Matching and Regularized Quadratic Relaxations II: Erd\\H{o}s-R\\'enyi Graphs and Universality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.08883","kind":"arxiv","version":1},"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":"sha256:800b32bb124b96aa1500bdde2b068899364dc38bb153e4c0c3effdf45a2bff8c","target":"record","created_at":"2026-05-17T23:40:02Z","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":"9b79a698a3457313781a3686a8e3e4e8cdd14e11c0ecbda2e0e2095d42d5563d","cross_cats_sorted":["cs.LG","math.SP","math.ST","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-07-20T23:50:02Z","title_canon_sha256":"57b4395f05d39b69fc3611e34db03deba68f6ac0d2a2ac96bd81ff2bb9e56c00"},"schema_version":"1.0","source":{"id":"1907.08883","kind":"arxiv","version":1}},"canonical_sha256":"47c320c3deff35c97add6cbc893b4b9a1d7b95365cb644e1a65d83bdeaf5b4ff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"47c320c3deff35c97add6cbc893b4b9a1d7b95365cb644e1a65d83bdeaf5b4ff","first_computed_at":"2026-05-17T23:40:02.855462Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:02.855462Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"76QyhN+UpWpmcXyUlYQGyVpjRojbeJa4nBva50pO626AZJPVZazIp0z8kcspUOVwuIDwsV49wvi23mDL8xBeDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:02.856191Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.08883","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:800b32bb124b96aa1500bdde2b068899364dc38bb153e4c0c3effdf45a2bff8c","sha256:dd9adce4c54edd25ed4c490d621ad1dddae9fe39f554235481dfc74195b5e51f"],"state_sha256":"e815d76a1b8fefac47beb1bde9dbb00fc1f0e2336bff6c89243100ddb8347481"}