{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:A5NX4UWCUUOFV23S227KDUMZTS","short_pith_number":"pith:A5NX4UWC","schema_version":"1.0","canonical_sha256":"075b7e52c2a51c5aeb72d6bea1d1999c95cb43c86f9b4a539c05c0d5e89b11af","source":{"kind":"arxiv","id":"2607.27810","version":1},"attestation_state":"computed","paper":{"title":"Perturbed Beta Corners Process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Jiaming Xu, Leonid Petrov","submitted_at":"2026-07-30T07:48:39Z","abstract_excerpt":"We introduce and study the perturbed $\\beta$-corners process, a deformation of the classical $\\beta$-corners process. The latter is a probability measure on interlacing arrays of real numbers that, for the classical values $\\beta=1,2,4$, describes the joint distribution of eigenvalues of principal submatrices of a Gaussian random matrix with the corresponding GOE/GUE/GSE symmetry.\n  For classical $\\beta$, the perturbed process arises from adding a deterministic diagonal matrix $A=diag(a_1,...,a_N)$ to a GOE/GUE/GSE matrix. The eigenvalues of the resulting random matrix depend symmetrically on "},"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":"2607.27810","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-07-30T07:48:39Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"583776edcac83c98f746b28c48b1098fc64d03e5632006dc1501ba78b45c3c1e","abstract_canon_sha256":"8dd0531f85a12696773e26c03a7789bca0751c981f060d3ae53a290b39c21b1b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"075b7e52c2a51c5aeb72d6bea1d1999c95cb43c86f9b4a539c05c0d5e89b11af","last_reissued_at":"2026-07-31T01:34:15.243543Z","signature_status":"unsigned_v0","first_computed_at":"2026-07-31T01:34:15.243543Z"},"graph_snapshot":{"paper":{"title":"Perturbed Beta Corners Process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Jiaming Xu, Leonid Petrov","submitted_at":"2026-07-30T07:48:39Z","abstract_excerpt":"We introduce and study the perturbed $\\beta$-corners process, a deformation of the classical $\\beta$-corners process. The latter is a probability measure on interlacing arrays of real numbers that, for the classical values $\\beta=1,2,4$, describes the joint distribution of eigenvalues of principal submatrices of a Gaussian random matrix with the corresponding GOE/GUE/GSE symmetry.\n  For classical $\\beta$, the perturbed process arises from adding a deterministic diagonal matrix $A=diag(a_1,...,a_N)$ to a GOE/GUE/GSE matrix. The eigenvalues of the resulting random matrix depend symmetrically on "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.27810","kind":"arxiv","version":1},"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/2607.27810/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":"2607.27810","created_at":"2026-07-31T01:34:15.246666+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.27810v1","created_at":"2026-07-31T01:34:15.246666+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.27810","created_at":"2026-07-31T01:34:15.246666+00:00"},{"alias_kind":"pith_short_12","alias_value":"A5NX4UWCUUOF","created_at":"2026-07-31T01:34:15.246666+00:00"},{"alias_kind":"pith_short_16","alias_value":"A5NX4UWCUUOFV23S","created_at":"2026-07-31T01:34:15.246666+00:00"},{"alias_kind":"pith_short_8","alias_value":"A5NX4UWC","created_at":"2026-07-31T01:34:15.246666+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/A5NX4UWCUUOFV23S227KDUMZTS","json":"https://pith.science/pith/A5NX4UWCUUOFV23S227KDUMZTS.json","graph_json":"https://pith.science/api/pith-number/A5NX4UWCUUOFV23S227KDUMZTS/graph.json","events_json":"https://pith.science/api/pith-number/A5NX4UWCUUOFV23S227KDUMZTS/events.json","paper":"https://pith.science/paper/A5NX4UWC"},"agent_actions":{"view_html":"https://pith.science/pith/A5NX4UWCUUOFV23S227KDUMZTS","download_json":"https://pith.science/pith/A5NX4UWCUUOFV23S227KDUMZTS.json","view_paper":"https://pith.science/paper/A5NX4UWC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.27810&json=true","fetch_graph":"https://pith.science/api/pith-number/A5NX4UWCUUOFV23S227KDUMZTS/graph.json","fetch_events":"https://pith.science/api/pith-number/A5NX4UWCUUOFV23S227KDUMZTS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/A5NX4UWCUUOFV23S227KDUMZTS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/A5NX4UWCUUOFV23S227KDUMZTS/action/storage_attestation","attest_author":"https://pith.science/pith/A5NX4UWCUUOFV23S227KDUMZTS/action/author_attestation","sign_citation":"https://pith.science/pith/A5NX4UWCUUOFV23S227KDUMZTS/action/citation_signature","submit_replication":"https://pith.science/pith/A5NX4UWCUUOFV23S227KDUMZTS/action/replication_record"}},"created_at":"2026-07-31T01:34:15.246666+00:00","updated_at":"2026-07-31T01:34:15.246666+00:00"}