{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:MVXYULL7I4TCKFYUL35RZTH65N","short_pith_number":"pith:MVXYULL7","schema_version":"1.0","canonical_sha256":"656f8a2d7f47262517145efb1cccfeeb43a409731a67b1a88f0be00f9fd90178","source":{"kind":"arxiv","id":"1412.7597","version":2},"attestation_state":"computed","paper":{"title":"The supercritical regime in the normal matrix model with cubic potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Alexander Tovbis, Arno B.J. Kuijlaars","submitted_at":"2014-12-24T04:13:32Z","abstract_excerpt":"The normal matrix model with a cubic potential is ill-defined and it develops a critical behavior in finite time. We follow the approach of Bleher and Kuijlaars to reformulate the model in terms of orthogonal polynomials with respect to a Hermitian form. This reformulation was shown to capture the essential features of the normal matrix model in the subcritical regime, namely that the zeros of the polynomials tend to a number of segments (the motherbody) inside a domain (the droplet) that attracts the eigenvalues in the normal matrix model.\n  In the present paper we analyze the supercritical r"},"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":"1412.7597","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-12-24T04:13:32Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"9dddb2f5c29264cc3708e93d1f3f095b4cb014814c8f5ba1f9031ad260854a52","abstract_canon_sha256":"e38db7750df2d8f49f2c8e59738c76f253f2d49c73f69c9f57e5ea390cb33ff4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:47.443921Z","signature_b64":"Bwslm05c5tCVvhxOJ2TN3sSbGHWt30GSlZi8uWArrDrSOjShOi023DrEZs1a2hoIMzxlWXe/Z8mQKqUMApCNBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"656f8a2d7f47262517145efb1cccfeeb43a409731a67b1a88f0be00f9fd90178","last_reissued_at":"2026-05-17T23:50:47.443211Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:47.443211Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The supercritical regime in the normal matrix model with cubic potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Alexander Tovbis, Arno B.J. Kuijlaars","submitted_at":"2014-12-24T04:13:32Z","abstract_excerpt":"The normal matrix model with a cubic potential is ill-defined and it develops a critical behavior in finite time. We follow the approach of Bleher and Kuijlaars to reformulate the model in terms of orthogonal polynomials with respect to a Hermitian form. This reformulation was shown to capture the essential features of the normal matrix model in the subcritical regime, namely that the zeros of the polynomials tend to a number of segments (the motherbody) inside a domain (the droplet) that attracts the eigenvalues in the normal matrix model.\n  In the present paper we analyze the supercritical r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7597","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1412.7597","created_at":"2026-05-17T23:50:47.443335+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.7597v2","created_at":"2026-05-17T23:50:47.443335+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.7597","created_at":"2026-05-17T23:50:47.443335+00:00"},{"alias_kind":"pith_short_12","alias_value":"MVXYULL7I4TC","created_at":"2026-05-18T12:28:38.356838+00:00"},{"alias_kind":"pith_short_16","alias_value":"MVXYULL7I4TCKFYU","created_at":"2026-05-18T12:28:38.356838+00:00"},{"alias_kind":"pith_short_8","alias_value":"MVXYULL7","created_at":"2026-05-18T12:28:38.356838+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/MVXYULL7I4TCKFYUL35RZTH65N","json":"https://pith.science/pith/MVXYULL7I4TCKFYUL35RZTH65N.json","graph_json":"https://pith.science/api/pith-number/MVXYULL7I4TCKFYUL35RZTH65N/graph.json","events_json":"https://pith.science/api/pith-number/MVXYULL7I4TCKFYUL35RZTH65N/events.json","paper":"https://pith.science/paper/MVXYULL7"},"agent_actions":{"view_html":"https://pith.science/pith/MVXYULL7I4TCKFYUL35RZTH65N","download_json":"https://pith.science/pith/MVXYULL7I4TCKFYUL35RZTH65N.json","view_paper":"https://pith.science/paper/MVXYULL7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.7597&json=true","fetch_graph":"https://pith.science/api/pith-number/MVXYULL7I4TCKFYUL35RZTH65N/graph.json","fetch_events":"https://pith.science/api/pith-number/MVXYULL7I4TCKFYUL35RZTH65N/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MVXYULL7I4TCKFYUL35RZTH65N/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MVXYULL7I4TCKFYUL35RZTH65N/action/storage_attestation","attest_author":"https://pith.science/pith/MVXYULL7I4TCKFYUL35RZTH65N/action/author_attestation","sign_citation":"https://pith.science/pith/MVXYULL7I4TCKFYUL35RZTH65N/action/citation_signature","submit_replication":"https://pith.science/pith/MVXYULL7I4TCKFYUL35RZTH65N/action/replication_record"}},"created_at":"2026-05-17T23:50:47.443335+00:00","updated_at":"2026-05-17T23:50:47.443335+00:00"}