{
  "abstract": "We study preservation of finite gauge-energy flows under local network repair after Bernoulli edge failures. A macroscopic demand network records terminal pairs to be routed, while a microscopic physical network contains local backup routes, bypasses and shared corridors. We prove a deterministic gauge-energy repair theorem: if the usable demand network $\\mathcal{B}^{\\sharp}$ carries a finite $Φ$-energy flow $θ$, then the repaired physical network $H$ carries a lifted finite $Φ$-energy flow $Θ$ with $$ \\mathcal{E}^Φ_H(Θ) \\le L\\,β_Φ(K)\\,\\mathcal{E}^Φ_{\\mathcal{B}^{\\sharp}}(θ), $$ where $L$ bounds route length, $K$ bounds routing congestion, $\\mathcal{E}$ marks energy, and $β_Φ$ is the gauge dilation constant. We then convert this comparison into probabilistic repair criteria: finite-dependent local repair is handled via domination by product measures, and random repair lengths via a variable-cost formulation compatible with chemical-distance estimates. As a main application, we prove a finite-dependent local bypass theorem: any macroscopic network whose supercritical percolation cluster supports a finite gauge-energy flow remains gauge-energy stable after bounded-range local reinforcement, provided the local repair probability is sufficiently high. This yields reinforced lattice and wedge-type examples and provides a potential-theoretic framework for random network repair beyond tree-like or edge-disjoint constructions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.39587",
  "author_total": 2,
  "authors": [
    {
      "name": "Zhenyuan Sun"
    },
    {
      "name": "Dayue Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/befec2v275g65.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.39587",
  "fulltext_url": null,
  "id": "befec2v275g65",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.39587",
  "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.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7215061881",
  "pdf_url": "https://arxiv.org/pdf/2609.39587",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/befec2v275g65.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.39587",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.39587"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Gauge-energy preservation under congestion-controlled network repair",
  "title_text": "Gauge-energy preservation under congestion-controlled network repair",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/befec2v275g65",
  "venue": "arXiv",
  "versions": []
}