{"paper":{"title":"An explicit four-corner dictionary for (2,p) minimal Liouville gravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"A. Alexandrov, V. Belavin","submitted_at":"2026-08-09T12:23:56Z","abstract_excerpt":"(2,p) minimal Liouville gravity admits four algebraic descriptions interrelated by dualities. On the Frobenius manifold (FM) side the theory is built either on the $A_{1}$ manifold of $Q(y)=y^{2}+u_{1}$ ($y$-side) or on the $A_{p-1}$ manifold in the variable $x$ ($x$-side). On the spectral curve / topological recursion (SC) side the analogous choice is the Chebyshev curve and its $x \\leftrightarrow y$ swap. FM-$y$, SC-$y$ require a resonance transformation between the KdV times and the Liouville couplings, while the other two do not. We work out the explicit correspondence between the four app"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.08669","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/2608.08669/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"}