{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:3E6KLFPDR5YF7FOGIBOLDHIQKE","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":"3851b145589abfbdfef0c1401020efddcbd7d586097ac46b92d60f435102ece3","cross_cats_sorted":["cond-mat.dis-nn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-01-22T08:06:52Z","title_canon_sha256":"68f6cf0e7b6bb3818ac2ed5ed7b4a93b8c773573c213905e042fe24bde88db64"},"schema_version":"1.0","source":{"id":"1001.3935","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.3935","created_at":"2026-05-18T02:09:31Z"},{"alias_kind":"arxiv_version","alias_value":"1001.3935v1","created_at":"2026-05-18T02:09:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.3935","created_at":"2026-05-18T02:09:31Z"},{"alias_kind":"pith_short_12","alias_value":"3E6KLFPDR5YF","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"3E6KLFPDR5YF7FOG","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"3E6KLFPD","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:d63230e41d3131757b6f4bc661779c9cb917c4431f02efa3f450b6dc2280a677","target":"graph","created_at":"2026-05-18T02:09:31Z","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":"A methodology to analyze the properties of the first (largest) eigenvalue and its eigenvector is developed for large symmetric random sparse matrices utilizing the cavity method of statistical mechanics. Under a tree approximation, which is plausible for infinitely large systems, in conjunction with the introduction of a Lagrange multiplier for constraining the length of the eigenvector, the eigenvalue problem is reduced to a bunch of optimization problems of a quadratic function of a single variable, and the coefficients of the first and the second order terms of the functions act as cavity f","authors_text":"Hisanao Takahashi, Osamu Watanabe, Yoshiyuki Kabashima","cross_cats":["cond-mat.dis-nn"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-01-22T08:06:52Z","title":"Cavity approach to the first eigenvalue problem in a family of symmetric random sparse matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.3935","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:c470c5262802057f678ec55f5d39bc7f75fe10eb99f1bd2fa6bb7c52ae37aa94","target":"record","created_at":"2026-05-18T02:09:31Z","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":"3851b145589abfbdfef0c1401020efddcbd7d586097ac46b92d60f435102ece3","cross_cats_sorted":["cond-mat.dis-nn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-01-22T08:06:52Z","title_canon_sha256":"68f6cf0e7b6bb3818ac2ed5ed7b4a93b8c773573c213905e042fe24bde88db64"},"schema_version":"1.0","source":{"id":"1001.3935","kind":"arxiv","version":1}},"canonical_sha256":"d93ca595e38f705f95c6405cb19d10510fc0473abd2581a14638f626a5dc949a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d93ca595e38f705f95c6405cb19d10510fc0473abd2581a14638f626a5dc949a","first_computed_at":"2026-05-18T02:09:31.249305Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:09:31.249305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FvcqJvbY6gwXRs0POnhN0AdjS0FBsXU72a8/26s6SgSsUMyrbb4zmlPTP5nPRQjaxwSnvfNXAzzPSQPA3nZ3Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:09:31.249878Z","signed_message":"canonical_sha256_bytes"},"source_id":"1001.3935","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c470c5262802057f678ec55f5d39bc7f75fe10eb99f1bd2fa6bb7c52ae37aa94","sha256:d63230e41d3131757b6f4bc661779c9cb917c4431f02efa3f450b6dc2280a677"],"state_sha256":"86e25753c73cbbfb7664dd6e8cd19debd91e9172bbf3b56c6fc45e1c54340a9c"}