{
  "abstract": "We study obstacle-constrained variational problems whose reduced energies depend on a probability law through a lower-level optimizer. Uniform strong convexity yields a single-valued Lipschitz follower response, while convexity and a Poincare inequality give a unique upper-level policy. A type-Lipschitz reduced marginal then implies Lipschitz continuity of the policy map from the 1-Wasserstein metric to the energy space. In a one-dimensional linear-obstacle subclass, the policy derivative is the positive part of a cumulative forcing. Single crossing makes the coincidence set an interval. An algebraic crossing of order m gives a $W_1^{1/m}$ modulus for its endpoint; odd-power examples show that this exponent is sharp, while a transversal crossing recovers Lipschitz stability. For empirical laws on compact subsets of $\\mathbb{R}^k$, dimension-dependent Wasserstein bounds yield finite-sample rates for policies and thresholds. At a transversal population root, the empirical threshold is asymptotically linear, with an explicit influence function and central limit theorem. For higher-dimensional regular patches, a conditional level-set argument gives local Hausdorff stability when a nondegenerate switching function is available. An explicit quadratic firm response produces a nonlinear corporate-tax schedule with an endogenous zero-tax region and a Wasserstein-stable threshold. The tax illustration is analytic and uses no empirical calibration.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08454",
  "author_total": 1,
  "authors": [
    {
      "name": "Kun Huang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fn0vr0wmtebjh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08454",
  "fulltext_url": null,
  "id": "fn0vr0wmtebjh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08454",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7212059794",
  "pdf_url": "https://arxiv.org/pdf/2609.08454",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fn0vr0wmtebjh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.08454",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08454"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Wasserstein Stability and Free Boundaries in Measure-Parameterized Bilevel Obstacle Problems",
  "title_text": "Wasserstein Stability and Free Boundaries in Measure-Parameterized Bilevel Obstacle Problems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/fn0vr0wmtebjh",
  "venue": "arXiv",
  "versions": []
}