{"paper":{"title":"Almost sure local well-posedness for the nonlinear Schr\\\"odinger equations on $\\Bbb T^d$ with non-algebraic nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Yongming Luo","submitted_at":"2026-08-05T10:01:32Z","abstract_excerpt":"We study the Cauchy problem for the nonlinear Schr\\\"odinger equation on $\\mathbb T^d$ with random initial data and a general non-algebraic power-type nonlinearity. We establish almost sure local well-posedness in every spatial dimension and for the whole mass-supercritical range allowed by the natural condition $0<s_{\\mathrm c}<1+a$. The main new ingredient is a frequency-gaining probabilistic refinement of the Galilean bilinear estimates recently developed by Kwak and Kwon \\cite{KwakKwon}. In the random setting, the gauge decomposition gives rise to three new types of terms: a mean-free coeff"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.04643","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/2608.04643/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"}