{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:72CBQUAQ2TU2EZMGUHWTTZ6W4N","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":"9b9e41595de78fb9096cb29b347d2474e61e037cca2ebde8ca385b253b385229","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2010-06-06T21:49:04Z","title_canon_sha256":"0dad1060750954021dfd66d39d8cfcf674b6c5daed4a68081368044325ae416b"},"schema_version":"1.0","source":{"id":"1006.1141","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.1141","created_at":"2026-05-18T03:23:48Z"},{"alias_kind":"arxiv_version","alias_value":"1006.1141v3","created_at":"2026-05-18T03:23:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.1141","created_at":"2026-05-18T03:23:48Z"},{"alias_kind":"pith_short_12","alias_value":"72CBQUAQ2TU2","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"72CBQUAQ2TU2EZMG","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"72CBQUAQ","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:9c2d766c03e99da282b38574ab66f25b04b61d31360f28754b2e93f5d0fe9142","target":"graph","created_at":"2026-05-18T03:23:48Z","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":"Recently we introduced a family of $U(N)$ invariant Random Matrix Ensembles which is characterized by a parameter $\\lambda$ describing logarithmic soft-confinement potentials $V(H) \\sim [\\ln H]^{(1+\\lambda)} \\:(\\lambda>0$). We showed that we can study eigenvalue correlations of these \"$\\lambda$-ensembles\" based on the numerical construction of the corresponding orthogonal polynomials with respect to the weight function $\\exp[- (\\ln x)^{1+\\lambda}]$. In this work, we expand our previous work and show that: i) the eigenvalue density is given by a power-law of the form $\\rho(x) \\propto [\\ln x]^{\\","authors_text":"Jinmyung Choi, K.A. Muttalib","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2010-06-06T21:49:04Z","title":"Universality of a family of Random Matrix Ensembles with logarithmic soft-confinement potentials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.1141","kind":"arxiv","version":3},"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":"sha256:5697dade37bb8f96165d78f79338e8aeee4a4f76ce51d498e86dd46072594670","target":"record","created_at":"2026-05-18T03:23:48Z","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":"9b9e41595de78fb9096cb29b347d2474e61e037cca2ebde8ca385b253b385229","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2010-06-06T21:49:04Z","title_canon_sha256":"0dad1060750954021dfd66d39d8cfcf674b6c5daed4a68081368044325ae416b"},"schema_version":"1.0","source":{"id":"1006.1141","kind":"arxiv","version":3}},"canonical_sha256":"fe84185010d4e9a26586a1ed39e7d6e37b706721b8607a34d2dec30c17332683","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fe84185010d4e9a26586a1ed39e7d6e37b706721b8607a34d2dec30c17332683","first_computed_at":"2026-05-18T03:23:48.493760Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:23:48.493760Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dweWaRlBhxAaDNvj71fTWVs/JJzoCNDJITVbiuJO7+LYX66c2HEQG/LO54VRJOjjO7qQN2n3uiV6OzaCAwsXBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:23:48.494410Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.1141","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5697dade37bb8f96165d78f79338e8aeee4a4f76ce51d498e86dd46072594670","sha256:9c2d766c03e99da282b38574ab66f25b04b61d31360f28754b2e93f5d0fe9142"],"state_sha256":"921810290f354b1e5215eaf0466adbbccb90535fe4d8106cd5271b464dd5ddea"}