{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:K7X2NMKX6XMMIBL43RAPJIDQAE","short_pith_number":"pith:K7X2NMKX","schema_version":"1.0","canonical_sha256":"57efa6b157f5d8c4057cdc40f4a070011057643ac5af140098be03cd3586792e","source":{"kind":"arxiv","id":"1805.01748","version":1},"attestation_state":"computed","paper":{"title":"Critical measures for vector energy: asymptotics of non-diagonal multiple orthogonal polynomials for a cubic weight","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.CV","authors_text":"Andrei Mart\\'inez-Finkelshtein, Guilherme Silva","submitted_at":"2018-05-04T12:54:46Z","abstract_excerpt":"We consider the type I multiple orthogonal polynomials (MOPs) $(A_{n,m}, B_{n,m})$ and type II MOPs $P_{n,m}$, satisfying non-hermitian orthogonality with respect to the weight $e^{-z^3}$ on two unbounded contours on $\\mathbb C$. Under the assumption that $$ n,m \\to \\infty, \\quad \\frac{n}{n+m}\\to \\alpha \\in (0, 1) $$ we find the detailed asymptotics of the MOPs, and describe the phase transitions of this limit behavior as a function of $\\alpha$. This description is given in terms of vector critical measures, which are saddle points of an energy functional comprising both attracting and repelli"},"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":"1805.01748","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-05-04T12:54:46Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"1b36db065abddffdf660ddfd8de10c669c14b1c9b7b04a53fe91319a71279018","abstract_canon_sha256":"a2e2f0f6762707ee1c5f24af293a52ee4d29eede69efed0cd890f33df9c7f673"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:46.846844Z","signature_b64":"W9SZEdxesjfw/++XQpveVQAbexfEw2YwbPQWFVh/AdVLjHoMLOznXk+/PG3PPmu2ERHOy9/aB3e1AwGt9lrQDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"57efa6b157f5d8c4057cdc40f4a070011057643ac5af140098be03cd3586792e","last_reissued_at":"2026-05-18T00:16:46.846195Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:46.846195Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Critical measures for vector energy: asymptotics of non-diagonal multiple orthogonal polynomials for a cubic weight","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.CV","authors_text":"Andrei Mart\\'inez-Finkelshtein, Guilherme Silva","submitted_at":"2018-05-04T12:54:46Z","abstract_excerpt":"We consider the type I multiple orthogonal polynomials (MOPs) $(A_{n,m}, B_{n,m})$ and type II MOPs $P_{n,m}$, satisfying non-hermitian orthogonality with respect to the weight $e^{-z^3}$ on two unbounded contours on $\\mathbb C$. Under the assumption that $$ n,m \\to \\infty, \\quad \\frac{n}{n+m}\\to \\alpha \\in (0, 1) $$ we find the detailed asymptotics of the MOPs, and describe the phase transitions of this limit behavior as a function of $\\alpha$. This description is given in terms of vector critical measures, which are saddle points of an energy functional comprising both attracting and repelli"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.01748","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":""},"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":"1805.01748","created_at":"2026-05-18T00:16:46.846277+00:00"},{"alias_kind":"arxiv_version","alias_value":"1805.01748v1","created_at":"2026-05-18T00:16:46.846277+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.01748","created_at":"2026-05-18T00:16:46.846277+00:00"},{"alias_kind":"pith_short_12","alias_value":"K7X2NMKX6XMM","created_at":"2026-05-18T12:32:33.847187+00:00"},{"alias_kind":"pith_short_16","alias_value":"K7X2NMKX6XMMIBL4","created_at":"2026-05-18T12:32:33.847187+00:00"},{"alias_kind":"pith_short_8","alias_value":"K7X2NMKX","created_at":"2026-05-18T12:32:33.847187+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/K7X2NMKX6XMMIBL43RAPJIDQAE","json":"https://pith.science/pith/K7X2NMKX6XMMIBL43RAPJIDQAE.json","graph_json":"https://pith.science/api/pith-number/K7X2NMKX6XMMIBL43RAPJIDQAE/graph.json","events_json":"https://pith.science/api/pith-number/K7X2NMKX6XMMIBL43RAPJIDQAE/events.json","paper":"https://pith.science/paper/K7X2NMKX"},"agent_actions":{"view_html":"https://pith.science/pith/K7X2NMKX6XMMIBL43RAPJIDQAE","download_json":"https://pith.science/pith/K7X2NMKX6XMMIBL43RAPJIDQAE.json","view_paper":"https://pith.science/paper/K7X2NMKX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1805.01748&json=true","fetch_graph":"https://pith.science/api/pith-number/K7X2NMKX6XMMIBL43RAPJIDQAE/graph.json","fetch_events":"https://pith.science/api/pith-number/K7X2NMKX6XMMIBL43RAPJIDQAE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/K7X2NMKX6XMMIBL43RAPJIDQAE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/K7X2NMKX6XMMIBL43RAPJIDQAE/action/storage_attestation","attest_author":"https://pith.science/pith/K7X2NMKX6XMMIBL43RAPJIDQAE/action/author_attestation","sign_citation":"https://pith.science/pith/K7X2NMKX6XMMIBL43RAPJIDQAE/action/citation_signature","submit_replication":"https://pith.science/pith/K7X2NMKX6XMMIBL43RAPJIDQAE/action/replication_record"}},"created_at":"2026-05-18T00:16:46.846277+00:00","updated_at":"2026-05-18T00:16:46.846277+00:00"}