{"paper":{"title":"Universal formulae for correlators of a broad class of models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Correlators of many models arise from the same universal formulae by choosing a model-specific defining function.","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Clifford V. Johnson","submitted_at":"2026-04-13T18:00:15Z","abstract_excerpt":"A simple method is presented for deriving universal formulae for the correlators, frequently denoted $W_{g,n}(\\{z_i\\}), i=1,..n$, of a wide range of models of physical and mathematical interest. While many alternative methods exist for constructing such correlators, these formulae can be simply written in terms of one defining function and its derivatives. The method has been applied to the Airy and Bessel models, various minimal string and superstring theories, and their associated intersection theory settings, ordinary and various kinds of supersymmetric Weil-Petersson volumes, and more besi"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"their W_{g,n}({z_i}) are just all specializations of the same universal formulae","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the models in question all admit a defining function whose derivatives generate the correlators through the same universal expressions, relying on the underlying KdV integrable structure and Gel'fand-Dikii equation.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Correlators of diverse models are expressed via universal formulae derived from a single defining function using KdV flows and the Gel'fand-Dikii equation.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Correlators of many models arise from the same universal formulae by choosing a model-specific defining function.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"98ef64010aed3af38e0985a05e6fa06e0b6b701816c294de1783c0ef4001bb2f"},"source":{"id":"2604.11902","kind":"arxiv","version":2},"verdict":{"id":"dcf4e7d6-e675-40a5-99bc-40447f39135f","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T15:09:29.926537Z","strongest_claim":"their W_{g,n}({z_i}) are just all specializations of the same universal formulae","one_line_summary":"Correlators of diverse models are expressed via universal formulae derived from a single defining function using KdV flows and the Gel'fand-Dikii equation.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the models in question all admit a defining function whose derivatives generate the correlators through the same universal expressions, relying on the underlying KdV integrable structure and Gel'fand-Dikii equation.","pith_extraction_headline":"Correlators of many models arise from the same universal formulae by choosing a model-specific defining function."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.11902/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"}