{
  "abstract": "Let $G$ be a finite connected simple graph, let $uv$ be a nonedge, and let $s$ be a starting vertex. We study the exact change in the expected cover time of simple random walk when $uv$ is inserted. A killed Green matrix update, combined with target-set inclusion-exclusion, gives an exact formula using only the original graph. The response can have either sign. Our main result is a nonlocality theorem. For every radius $r\\geq 1$, we construct two marked configurations whose ambient-degree-labelled radius-$r$ neighbourhoods at $s,u,v$ are isomorphic but whose fixed-start cover-time responses have opposite signs. The construction also matches the three marked degrees, the marked distance, and the effective resistance $R_{uv}$. The two graphs have different orders; equal-order nonlocality remains open. We complement this result with a conductance interpolation theorem and an occupation interpretation of its high-conductance coefficient. After contracting $u$ and $v$, that coefficient is a positive multiple of the expected pre-cover occupation of the contracted vertex, and its zero case is classified exactly. A path with two pendant insertion endpoints is solved for all starting vertices and shows a sharp change of sign across the start set.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.27474",
  "author_total": 1,
  "authors": [
    {
      "name": "Ian Meng Si"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ezfz71xxey12m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.27474",
  "fulltext_url": null,
  "id": "ezfz71xxey12m",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.27474",
  "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.CO"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7204755618",
  "pdf_url": "https://arxiv.org/pdf/2608.27474",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ezfz71xxey12m.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:28Z",
      "native_id": "2608.27474",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.27474"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Nonlocality of Cover-Time Changes Under Edge Addition",
  "title_text": "Nonlocality of Cover-Time Changes Under Edge Addition",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:28Z",
  "url": "https://research.draconitic.com/paper/ezfz71xxey12m",
  "venue": "arXiv",
  "versions": []
}