{
  "abstract": "We extend the discrete gauge rigidity of time-scaled intertwining cocycles to operator networks over a connected manifold M and classify the holonomy that the continuous setting admits. For dissipative semigroups $S_x(t)=e^{-tA_x}$ linked by transport operators $K_γS_{γ(0)}(t)=S_{γ(1)}(λ(γ)t)K_γ$ along paths $γ$, we prove that the scaling field carries no monodromy: $λ(x,y)=τ(x)/τ(y)$ for a continuous positive function $τ$, unique up to a multiplicative constant, with multiplicativity forced by the intertwining relation rather than assumed. For regular cocycles the transport defines a bounded operator connection on a Hilbert bundle over M; the holonomy of a closed loop is confined to the commutant of the generator and decomposes into spectral sectors, on each of which it is adiabatic (Berry-Wilczek-Zee) transport twisted by an independent commutant-valued sector potential; for flat unitary cocycles the holonomy is classified by unitary representations of $π_1(M)$ in the commutant. An explicit rotating network over $S^1$ exhibits holonomy equal to the parity operator while the Berry connection one-form of every level vanishes identically: the monodromy is carried by $\\mathbb{Z}_2$ orientation classes of Moebius eigenline bundles.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11965",
  "author_total": 1,
  "authors": [
    {
      "name": "Anton Alexa"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/96j704jwgwrn0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11965",
  "fulltext_url": null,
  "id": "96j704jwgwrn0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11965",
  "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-ph"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7213187155",
  "pdf_url": "https://arxiv.org/pdf/2609.11965",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/96j704jwgwrn0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:07Z",
      "native_id": "2609.11965",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11965"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Gauge Rigidity and Holonomy Classification of Time-Scaled Intertwining Cocycles on Hilbert Bundles",
  "title_text": "Gauge Rigidity and Holonomy Classification of Time-Scaled Intertwining Cocycles on Hilbert Bundles",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/96j704jwgwrn0",
  "venue": "arXiv",
  "versions": []
}