{
  "abstract": "Elimination geometry studies the exact nonnegative defect left after an auxiliary variable is optimized out. Part~II audits this certified-elimination interface through three theorem families. For integrability, local gaps form a repeated partial-elimination tower precisely under nonnegativity, touching, and zero elementary-square circulation. Hodge projection constructs nearest finite-space repairs and separates curvature, certification, and global period taxes. For representation and price, a descent gate characterizes surjective refinements and rules out strictly convex separable, duplication-invariant weight penalties. Dummy and target-calling lifts show that unrestricted lift design is vacuous, whereas the Fidelity-coherence frontier isolates irreducible cost. A modal Gram block classifies unconstrained quadratic lift-coupling germs and yields aligned Gaussian risk ledgers. Bernstein spectral functions preserve graph-Laplacian structure. Graph-universal Markov resolvents exist exactly up to first-order fractional qualification, and universal polynomial spectral penalties reduce to nonnegative Laplacian multiples. This linear limit does not preclude Part~I's nonlinear CDF repair and sharp CRPS theory. For converses, finite-order target-jet preservation uniquely requires subtraction of the corresponding defect jet, up to flat terms; approximate jets yield quasi-descent and stationary limits. Fixed-marginal coupling obeys a dependence-benefit frontier. Reversing certified KL in entropy-regularized control eliminates dimension-free guarantees, while a fixed measurement preserves all Umegaki defects of a faithful Gibbs family exactly when that family commutes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30145",
  "author_total": 2,
  "authors": [
    {
      "name": "Mian Huang"
    },
    {
      "name": "Xueqin Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cjmrfhta0a2sc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30145",
  "fulltext_url": null,
  "id": "cjmrfhta0a2sc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30145",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "openalex",
      "1703|Polynomial and algebraic computation"
    ]
  ],
  "openalex": "W7223265805",
  "pdf_url": "https://arxiv.org/pdf/2610.30145",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cjmrfhta0a2sc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.30145",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30145"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Elimination Geometry II: Integrability, Representation, and Structural Limits",
  "title_text": "Elimination Geometry II: Integrability, Representation, and Structural Limits",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:43Z",
  "url": "https://research.draconitic.com/paper/cjmrfhta0a2sc",
  "venue": "arXiv",
  "versions": []
}