{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:YQBKNUN5UOR3LH3VH2NNYYYDMB","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":"58e73454bf158d2bfaa9c31a1565be3b03ea98daa758f05aeed2e4e84e50816f","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-06-19T21:51:54Z","title_canon_sha256":"62361b642949715f0eeae08954b0df26dbf51e0149ba12961b03be33e8b6dbe7"},"schema_version":"1.0","source":{"id":"1706.06189","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.06189","created_at":"2026-05-18T00:42:04Z"},{"alias_kind":"arxiv_version","alias_value":"1706.06189v1","created_at":"2026-05-18T00:42:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.06189","created_at":"2026-05-18T00:42:04Z"},{"alias_kind":"pith_short_12","alias_value":"YQBKNUN5UOR3","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"YQBKNUN5UOR3LH3V","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"YQBKNUN5","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:fa9265ed324f93481db5b59bec8943b76341a34e2a1f4989a5ce0b2000369b51","target":"graph","created_at":"2026-05-18T00:42:04Z","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 continue investigating spectral properties of a Hermitised random matrix product, which, contrary to previous product ensembles, allows for eigenvalues on the full real line. When a GUE matrix with an external source is involved, we prove that the eigenvalues of the product form a determinantal point process and derive a double integral representation for correlation kernel. As the source changes, we observe a critical value and establish the existence of a phase transition for scaled eigenvalues at the origin. Particularly in the critical case, we obtain a new family of Pearcey-type kernel","authors_text":"Dang-Zheng Liu","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-06-19T21:51:54Z","title":"Spectral statistics for product matrix ensembles of Hermite type with external source"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.06189","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:a929f5236d67b49c7eec4b63053106d5a4d9cb48a0a38c661e1d7085c3c2ea76","target":"record","created_at":"2026-05-18T00:42:04Z","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":"58e73454bf158d2bfaa9c31a1565be3b03ea98daa758f05aeed2e4e84e50816f","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-06-19T21:51:54Z","title_canon_sha256":"62361b642949715f0eeae08954b0df26dbf51e0149ba12961b03be33e8b6dbe7"},"schema_version":"1.0","source":{"id":"1706.06189","kind":"arxiv","version":1}},"canonical_sha256":"c402a6d1bda3a3b59f753e9adc6303604c95da5fb1a7d3928f2feb19701be6c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c402a6d1bda3a3b59f753e9adc6303604c95da5fb1a7d3928f2feb19701be6c5","first_computed_at":"2026-05-18T00:42:04.013363Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:04.013363Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LZV4RT5j2kyiuuFU5rF6LazUq6ExUmNWcJP7SHjkjkarjHq5KFaHmliUvIJn1QBmgefeQiEKLx1Na0g5IDXMDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:04.014040Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.06189","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a929f5236d67b49c7eec4b63053106d5a4d9cb48a0a38c661e1d7085c3c2ea76","sha256:fa9265ed324f93481db5b59bec8943b76341a34e2a1f4989a5ce0b2000369b51"],"state_sha256":"1665178803cc48bb39ea96d4e2e8442f4c6fd92fb6c230f627f0829c52e6db73"}