{"paper":{"title":"Neural variational framework for random Young-diagram limit shapes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","physics.data-an"],"primary_cat":"cond-mat.stat-mech","authors_text":"Bo-Xuan Ge, Qian Chen","submitted_at":"2026-07-29T15:52:00Z","abstract_excerpt":"We develop a structure-preserving neural variational framework for random Young-diagram ensembles, with representations adapted to the structure and scaling of each measure. The method is validated on the Plancherel, uniform, minimal-difference, and fixed-\\(q\\) \\(q\\)-Plancherel ensembles, using known asymptotic profiles only for post-training comparison. We then study a quartically deformed hook-length ensemble without assuming an analytical saddle shape. Large-\\(n\\) neural profiles are compared with finite-size MAP profiles obtained from exact-action searches and with mean profiles obtained f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.27061","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/2607.27061/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"}