{"paper":{"title":"On the spatio-temporal increments of nonlinear parabolic SPDEs and the open KPZ equation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Nonlinear parabolic SPDEs on bounded intervals have exact local and uniform spatio-temporal moduli of continuity.","cross_cats":[],"primary_cat":"math.PR","authors_text":"Cheuk Yin Lee, Jingwu Hu","submitted_at":"2025-08-07T05:12:52Z","abstract_excerpt":"We study spatio-temporal increments of the solutions to nonlinear parabolic SPDEs on a bounded interval with Dirichlet, Neumann, or Robin boundary conditions. We identify the exact local and uniform spatio-temporal moduli of continuity for the sample functions of the solutions. These moduli of continuity results imply the existence of random points in space-time at which spatio-temporal oscillations are exceptionally large. We also establish small-ball probability estimates and Chung-type laws of the iterated logarithm for spatio-temporal increments. Our method yields extension of some of thes"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We identify the exact local and uniform spatio-temporal moduli of continuity for the sample functions of the solutions to nonlinear parabolic SPDEs on a bounded interval with Dirichlet, Neumann, or Robin boundary conditions.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The results rest on new strong local non-determinism properties for the linear stochastic heat equation under the various boundary conditions, together with detailed control of linearization errors for the nonlinear increments, as stated in the abstract.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Exact spatio-temporal moduli of continuity, small-ball estimates, and iterated logarithm laws are established for nonlinear parabolic SPDEs and extended to the open KPZ equation on the unit interval.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Nonlinear parabolic SPDEs on bounded intervals have exact local and uniform spatio-temporal moduli of continuity.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"12d93d225ea4856fdcb2b05b124a79137b7dee0c431ed15975849e62239f6f97"},"source":{"id":"2508.05032","kind":"arxiv","version":3},"verdict":{"id":"94294d79-4853-4055-89c0-c6d7672423e7","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T00:50:09.822339Z","strongest_claim":"We identify the exact local and uniform spatio-temporal moduli of continuity for the sample functions of the solutions to nonlinear parabolic SPDEs on a bounded interval with Dirichlet, Neumann, or Robin boundary conditions.","one_line_summary":"Exact spatio-temporal moduli of continuity, small-ball estimates, and iterated logarithm laws are established for nonlinear parabolic SPDEs and extended to the open KPZ equation on the unit interval.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The results rest on new strong local non-determinism properties for the linear stochastic heat equation under the various boundary conditions, together with detailed control of linearization errors for the nonlinear increments, as stated in the abstract.","pith_extraction_headline":"Nonlinear parabolic SPDEs on bounded intervals have exact local and uniform spatio-temporal moduli of continuity."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2508.05032/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":2,"snapshot_sha256":"279530641c34300e9568fb28a6bd62856352f1306be0c5ac7e4dadc7582adb8c"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}