{
  "abstract": "Complex experiments infer theory parameters through a coupled chain of physical models and data reduction. We formulate the theoretical--operational model (TOM) as a typed factorization of this forward prediction and study how changes of preparation, phenomenon modelling, readout, backgrounds, and analysis project onto the local manifold generated by the physics parameters. For a smooth prediction and a locally identifiable weighted least-squares estimate, the resulting response map separates each model deformation into a parameter-equivalent component and a residual component that cannot be absorbed by a change of the fitted physics parameters. This gives local criteria for robustness, exact degeneracy, and partial degeneracy of parameter inference. The construction is applied to charged-lepton-flavour-violating muon--electron conversion in aluminium. A one-bin conversion-rate model exhibits an exact normalization degeneracy. In a two-template model of the elastic--inelastic spectrum, a common signal normalization is absorbed by the fitted conversion rate without changing an operator-sensitive nuclear-response ratio, whereas a relative elastic--inelastic efficiency change is exactly parameter-equivalent to a change of that ratio at first order. A numerical Run-I example based on published Mu2e spectra shows that a \\(100\\,\\mathrm{keV}/c\\) momentum-scale mismatch is only partially parameter-equivalent: its projection ratio onto the local tangent space generated by the elastic normalization \\(R_0\\) and the logarithmic inelastic-to-elastic response ratio \\(ρ\\) is \\(η=0.331\\), while most of the weighted spectral deformation remains as a residual shape. TOM thereby provides a local theoretical description of parameter robustness and degeneracy at the interface of particle/nuclear phenomenology and experimental realization.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17581",
  "author_total": 1,
  "authors": [
    {
      "name": "Vitaly Pronskikh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2h7hc2gpk0ek2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17581",
  "fulltext_url": null,
  "id": "2h7hc2gpk0ek2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17581",
  "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",
      "hep-ex"
    ],
    [
      "arxiv",
      "hep-ph"
    ],
    [
      "arxiv",
      "physics.data-an"
    ],
    [
      "openalex",
      "3106|Particle physics theoretical and experimental studies"
    ]
  ],
  "openalex": "W7213522520",
  "pdf_url": "https://arxiv.org/pdf/2609.17581",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2h7hc2gpk0ek2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:01Z",
      "native_id": "2609.17581",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17581"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.data-an",
      "subfield": "computational"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-ex",
      "subfield": "high-energy"
    }
  ],
  "title": "Theoretical--operational modelling of complex experiments: parameter robustness and degeneracy in muon--electron conversion",
  "title_text": "Theoretical--operational modelling of complex experiments: parameter robustness and degeneracy in muon--electron conversion",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:01Z",
  "url": "https://research.draconitic.com/paper/2h7hc2gpk0ek2",
  "venue": "arXiv",
  "versions": []
}