{"paper":{"title":"Hyperbolic sine-Gordon model beyond the first threshold","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR"],"primary_cat":"math.AP","authors_text":"Younes Zine","submitted_at":"2025-04-10T17:53:59Z","abstract_excerpt":"We study the hyperbolic sine-Gordon model, with a parameter $\\be^2 > 0$, and its associated Gibbs dynamics on the two-dimensional torus. By introducing a physical space approach to the Fourier restriction norm method and establishing nonlinear dispersive smoothing for the imaginary multiplicative Gaussian chaos, we construct invariant Gibbs dynamics for the hyperbolic sine-Gordon model beyond the first threshold $\\be^2 = 2\\pi$. The deterministic step of our argument hinges on establishing key bilinear estimates, featuring weighted bounds for cone multipliers. Moreover, the probabilistic compon"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.07944","kind":"arxiv","version":2},"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/2504.07944/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"}