{
  "abstract": "Let $P$ be a short-range projector on $\\ell^2(\\mathbb{Z}^{2n},\\mathbb{C}^m)$ and $U=(U_1,\\dots,U_{2n})$ be a transverse family of open subsets of $\\mathbb{R}^{2n}$. We give an elementary proof of a recent result of Martinian-Stoiber, which extends a two-dimensional result of Drouot-Zhu to all even dimensions. Specifically, using only Stokes' theorem and the Poincaré lemma, we show that the geometric Kubo formula $\\operatorname{Tr}\\big(P[P,\\mathbf{1}_{U_1}]\\wedge\\cdots\\wedge[P,\\mathbf{1}_{U_{2n}}]\\big)$ is the product of a topological integer $\\mathcal{X}_U$, which depends only on the relative positions of $U_1, \\dots, U_{2n}$, and of the bulk conductance of $P$. Our proof writes the geometric bulk conductance as the pairing of $P$ with a cochain on $\\mathbb{Z}^{2n}$ - an idea originally due to Kitaev - and deforms the cochain rather than the sets $(U_1, \\dots, U_{2n})$. The proof presented in this paper is due to Claude Opus 5.5.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.16208",
  "author_total": 1,
  "authors": [
    {
      "name": "Alexis Drouot"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0fk6qp2y526kj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.16208",
  "fulltext_url": null,
  "id": "0fk6qp2y526kj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.16208",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "3107|Topological Materials and Phenomena"
    ]
  ],
  "openalex": "W7221801398",
  "pdf_url": "https://arxiv.org/pdf/2610.16208",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0fk6qp2y526kj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:06Z",
      "native_id": "2610.16208",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.16208"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Geometric bulk conductances in even dimensions",
  "title_text": "Geometric bulk conductances in even dimensions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/0fk6qp2y526kj",
  "venue": "arXiv",
  "versions": []
}