{
  "abstract": "We investigate pair-weighted lattice energies constructed from the reciprocal ratio cost $J(x)=\\frac{1}{2}(x+x^{-1})-1$ and their connection to the von Weizsäcker kinetic-energy functional. When the pair weight depends only on the common multiplicative amplitude scale and is quadratic under uniform amplitude rescaling, it takes the form $B(u,v)=Cuv$. For the normalization $C=1$, the weighted edge cost reduces exactly to $\\frac{1}{2}(u-v)^2$ for arbitrary positive neighboring amplitudes, without requiring a small-deviation expansion. On a Cartesian lattice, the resulting discrete energy converges to $\\frac{1}{2}\\int |\\nabla u|^2,d\\mathbf r$, with leading correction $-\\frac{h^2}{24}\\sum_k\\int(\\partial_k^2u)^2,d\\mathbf r+O(h^4)$ under the stated regularity conditions. Identifying $u=\\sqrtρ$ and restoring the factor $\\hbar^2/m$ yields the von Weizsäcker functional. By contrast, the unweighted ratio cost approaches a scale-invariant log-Dirichlet action and does not have kinetic-energy dimensions. Numerical benchmarks confirm the expected lattice convergence and assess the discretization error in smooth, nodal, cusp, and molecular cases. For $\\mathrm{H}_2^+$ densities obtained from aug-cc-pV5Z orbitals, a four-grid least-squares $h^2+h^4$ extrapolation agrees with orbital kinetic energies within $1.5\\times10^{-4}$ relative over $R=1$--$6,a_0$. Alternative extrapolations indicate a conservative sensitivity of up to approximately $5\\times10^{-4}$. The construction therefore provides a conditional exact discrete representation of the von Weizsäcker sector rather than an approximation to the complete noninteracting kinetic functional.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.03677",
  "author_total": 2,
  "authors": [
    {
      "name": "Megan Simons"
    },
    {
      "name": "Jonathan Washburn"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a2fww4h97wt3v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03677",
  "fulltext_url": null,
  "id": "a2fww4h97wt3v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03677",
  "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",
      "physics.chem-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.03677",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a2fww4h97wt3v.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:25Z",
      "native_id": "2611.03677",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03677"
    }
  ],
  "subjects": [
    {
      "field": "chemistry",
      "origin": "arxiv:physics.chem-ph",
      "subfield": "physical"
    }
  ],
  "title": "A Pair-Weighted Reciprocal-Cost Representation of the von Weizsäcker Functional",
  "title_text": "A Pair-Weighted Reciprocal-Cost Representation of the von Weizsäcker Functional",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/a2fww4h97wt3v",
  "venue": "arXiv",
  "versions": []
}