{
  "abstract": "The Rytova–Keldysh potential V(r) = (π/2r₀)[H₀ − Y₀](r/r₀) describes the in-plane interaction in a monolayer transition-metal dichalcogenide. We give a human proof (Tier C, not machine-checked) that, as a function of t = r², it is a positive mixture of Gaussians, with weight w(a) = r₀⁻¹ erfcx(√a/r₀). It is therefore completely monotone in the squared distance, which is the class covered by the openai/math theorem on universal optimality of the triangular lattice. Every claim is filed in an Elenchus claim ledger with tiers A (kernel-checked Lean), L (cited literature, quoted verbatim), C (human argument, not machine-checked) and X (floating-point exploration, which never supports a claim).\n\nTier A (Lean 4.34.1, pinned openai/math and Mathlib; axioms within propext, Classical.choice, Quot.sound; planted sorry and planted-axiom controls caught):\n\na generic lemma: positive exponential mixtures with finite moments are AdmissiblePotential;\n\nadmissibility and strict positivity of the mixture-defined Keldysh potential, and of its Gaussian regularisation;\n\nthe triangular-lattice energy inequalities obtained from upstream's universal_energy_minimum.\n\nThese corollaries are conditional on the upstream theorem, which is AI-generated and not peer reviewed, and on the fidelity of its definitions. The unregularised inequality is expected to read ⊤ ≤ ⊤ (Tier C). Finiteness of the regularised energy is not proved.\n\nTier C: the identification of the Lean mixture with the Struve form, given as a step-by-step human demonstration written for undergraduates. Its main route uses only positive integrands: DLMF 11.5.2, the subordination formula (used without a citation) and an elementary erfcx integral.\n\nTier X: a new rusty-SUNDIALS module computes Keldysh-jellium Madelung energies of triangular and square Wigner lattices by an Ewald split in the mixture variable. It reproduces the Coulomb values at r₀ = 0 and the Dedekind-eta log-gas gap at large r₀, and both negative controls are caught. The square lattice lies above the triangular one at all 51 sampled points. Material curves for MoS₂, MoSe₂, WS₂ and WSe₂ in vacuum take r₀ = 2πχ2D from Berkelbach et al. (Tier L). The HuggingFace dataset colabfit/JARVIS_C2DB (CC-BY-4.0) is used only to identify the 2H phases and to cross-check lattice constants; it contains no polarizabilities. All of this is static and classical, and compares two lattices only.\n\nNo breakthrough is claimed: complete monotonicity follows quickly from textbook integrals. The ledger gate reports 0 blocking findings and 9 flags, one for each Tier A row whose statement adequacy no human has audited. The work was produced by AI agents (Claude) under the author's direction; the author is responsible for the content.",
  "abstract_shown": true,
  "affiliations": [
    "SocrateAI Lab"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Xavier Callens"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3membsbam1f6d.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23646107",
  "fulltext_url": null,
  "id": "3membsbam1f6d",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23646107",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [],
  "openalex": null,
  "pdf_url": "https://zenodo.org/api/records/23646107/files/ar_keldysh_tmd.pdf/content",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3membsbam1f6d.ris",
  "sources": [
    {
      "first_seen": "2026-11-08T12:21:05Z",
      "native_id": "23646107",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23646107"
    }
  ],
  "subjects": [],
  "title": "The Rytova-Keldysh interaction is a positive Gaussian mixture: kernel-checked admissibility for planar universal optimality and Keldysh-jellium Madelung energies of TMD Wigner lattices",
  "title_text": "The Rytova-Keldysh interaction is a positive Gaussian mixture: kernel-checked admissibility for planar universal optimality and Keldysh-jellium Madelung energies of TMD Wigner lattices",
  "type": "preprint",
  "updated_at": "2026-11-08T12:21:05Z",
  "url": "https://research.draconitic.com/paper/3membsbam1f6d",
  "venue": "Zenodo",
  "versions": []
}