{
  "abstract": "Measured voltage and current waveforms may be represented in a reference frame whose frequency differs from the physical fundamental frequency. Reactive-power readouts calculated from such frequency-shifted coordinates may change if their readout operators are not transformed consistently. This paper presents a frequency-frame covariance formulation for finite-spectrum, zero-mean periodic waveforms with complete harmonic information over one physical period. A necessary and sufficient covariance condition is derived, requiring the readout operator to transform consistently with the waveform representation. Consequently, frequency-dependent harmonic weights must be evaluated at physical harmonic orders rather than relative frame labels. In particular, the derivative/Iliovici readout equals a relative-derivative contribution plus an explicit reference contribution. The formulation also separates readout-operator errors from errors caused by changes in the physical components retained by waveform projections. Three analytical cases illustrate conditional carrier recovery for a memoryless resistor, physical-frequency weighting at relative zero in an RLC branch, and the possibility that an exact reactive-power scalar can coexist with a substantial waveform error after projection. The scope is deterministic calculation consistency in frequency-shifted coordinates rather than instrument measurement uncertainty.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.05913",
  "author_total": 1,
  "authors": [
    {
      "name": "Kai Sun"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b6y2h4gym5eqg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.05913",
  "fulltext_url": null,
  "id": "b6y2h4gym5eqg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.05913",
  "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",
      "cs.SY"
    ],
    [
      "arxiv",
      "eess.SP"
    ],
    [
      "arxiv",
      "eess.SY"
    ],
    [
      "arxiv",
      "math-ph"
    ],
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      "arxiv",
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    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.05913",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b6y2h4gym5eqg.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:20:56Z",
      "native_id": "2611.05913",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.05913"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Frequency-Frame Covariance for Reactive-Power Scalarization",
  "title_text": "Frequency-Frame Covariance for Reactive-Power Scalarization",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:30Z",
  "url": "https://research.draconitic.com/paper/b6y2h4gym5eqg",
  "venue": "arXiv",
  "versions": []
}