{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:DRK32572NUQVTZMK4H3QK4SZLR","short_pith_number":"pith:DRK32572","schema_version":"1.0","canonical_sha256":"1c55bd77fa6d2159e58ae1f70572595c46b8b8ee5829be2d85564e3860b1e85c","source":{"kind":"arxiv","id":"2404.09332","version":3},"attestation_state":"computed","paper":{"title":"A generalized Liouville equation and magnetic stability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","nlin.SI"],"primary_cat":"math.AP","authors_text":"Alireza Ataei, Dinh-Thi Nguyen, Douglas Lundholm","submitted_at":"2024-04-14T19:09:03Z","abstract_excerpt":"This work considers two related families of nonlinear and nonlocal problems in the plane $\\mathbb{R}^2$. The first main result derives the general integrable solution to a generalized Liouville equation using the Wronskian of two coprime complex polynomials. The second main result concerns an application to a generalized Ladyzhenskaya-Gagliardo-Nirenberg interpolation inequality, with a single real parameter $\\beta$ interpreted as the strength of a magnetic self-interaction. The optimal constant of the inequality and the corresponding minimizers of the quotient are studied and it is proved tha"},"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":"2404.09332","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-04-14T19:09:03Z","cross_cats_sorted":["math-ph","math.MP","nlin.SI"],"title_canon_sha256":"05a4b50b7e9058ce66b8e5674cc4603364214942147e61a5200b437823ddec5c","abstract_canon_sha256":"65202e0fd5fb53ad52b6b54136d27c4cc47e9a73c430455bf23f2d49922abecb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:48:15.383856Z","signature_b64":"vyfuAaiF7H0W01Fn2jEIw1Kb9VD7KdCY0D9LPUMV9Y1NairFRmm49+2yQ01vlfxr4FrTSMFs/bn2tVx/Kf4iCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1c55bd77fa6d2159e58ae1f70572595c46b8b8ee5829be2d85564e3860b1e85c","last_reissued_at":"2026-07-05T10:48:15.383341Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:48:15.383341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A generalized Liouville equation and magnetic stability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","nlin.SI"],"primary_cat":"math.AP","authors_text":"Alireza Ataei, Dinh-Thi Nguyen, Douglas Lundholm","submitted_at":"2024-04-14T19:09:03Z","abstract_excerpt":"This work considers two related families of nonlinear and nonlocal problems in the plane $\\mathbb{R}^2$. The first main result derives the general integrable solution to a generalized Liouville equation using the Wronskian of two coprime complex polynomials. The second main result concerns an application to a generalized Ladyzhenskaya-Gagliardo-Nirenberg interpolation inequality, with a single real parameter $\\beta$ interpreted as the strength of a magnetic self-interaction. The optimal constant of the inequality and the corresponding minimizers of the quotient are studied and it is proved tha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.09332","kind":"arxiv","version":3},"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/2404.09332/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":"2404.09332","created_at":"2026-07-05T10:48:15.383391+00:00"},{"alias_kind":"arxiv_version","alias_value":"2404.09332v3","created_at":"2026-07-05T10:48:15.383391+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.09332","created_at":"2026-07-05T10:48:15.383391+00:00"},{"alias_kind":"pith_short_12","alias_value":"DRK32572NUQV","created_at":"2026-07-05T10:48:15.383391+00:00"},{"alias_kind":"pith_short_16","alias_value":"DRK32572NUQVTZMK","created_at":"2026-07-05T10:48:15.383391+00:00"},{"alias_kind":"pith_short_8","alias_value":"DRK32572","created_at":"2026-07-05T10:48:15.383391+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.01102","citing_title":"Average-field approximation for very dilute almost-bosonic anyon gases","ref_index":3,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DRK32572NUQVTZMK4H3QK4SZLR","json":"https://pith.science/pith/DRK32572NUQVTZMK4H3QK4SZLR.json","graph_json":"https://pith.science/api/pith-number/DRK32572NUQVTZMK4H3QK4SZLR/graph.json","events_json":"https://pith.science/api/pith-number/DRK32572NUQVTZMK4H3QK4SZLR/events.json","paper":"https://pith.science/paper/DRK32572"},"agent_actions":{"view_html":"https://pith.science/pith/DRK32572NUQVTZMK4H3QK4SZLR","download_json":"https://pith.science/pith/DRK32572NUQVTZMK4H3QK4SZLR.json","view_paper":"https://pith.science/paper/DRK32572","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2404.09332&json=true","fetch_graph":"https://pith.science/api/pith-number/DRK32572NUQVTZMK4H3QK4SZLR/graph.json","fetch_events":"https://pith.science/api/pith-number/DRK32572NUQVTZMK4H3QK4SZLR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DRK32572NUQVTZMK4H3QK4SZLR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DRK32572NUQVTZMK4H3QK4SZLR/action/storage_attestation","attest_author":"https://pith.science/pith/DRK32572NUQVTZMK4H3QK4SZLR/action/author_attestation","sign_citation":"https://pith.science/pith/DRK32572NUQVTZMK4H3QK4SZLR/action/citation_signature","submit_replication":"https://pith.science/pith/DRK32572NUQVTZMK4H3QK4SZLR/action/replication_record"}},"created_at":"2026-07-05T10:48:15.383391+00:00","updated_at":"2026-07-05T10:48:15.383391+00:00"}