{
  "abstract": "Quantum mechanics carries two uncertainty relations usually taught as one. This paper reads them as the real and imaginary parts of a single complex exponent e^(λ+i)θ. Position–momentum (ΔxΔp ≥ ℏ/2) is an i-phenomenon — Fourier conjugacy, substance-independent, importing ℏ/2 without deriving it; the slogan that uncertainty is \"the equation of state of the atomic realm\" is named and refused. Energy–time is different: not a conjugate-operator relation (t is not an operator; Pauli) but lifetime–linewidth, ΔE ≈ ℏΓ, the complex energy E₀ − iΓ/2 of Gamow and Weisskopf–Wigner — the inward λ-drain at the atomic floor of the nesting ladder, with Γ = −2ωλ from Entropy on the Spiral. This is the real equation of state the exponent discloses: a relation carrying a measurable rate. The framework is then stress-tested where most exposed — number–phase uncertainty against the absence of a self-adjoint phase operator (Dirac; Susskind–Glogower; Pegg–Barnett) — and the result is logged as a wall, not rescued. One organizing arrangement, one logged obstruction, no new number. The parent cosmology's falsification is reprinted.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Nicholas Archer Sanders",
      "orcid": "0009-0006-6427-1450"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6849ynvzanykk.bib",
  "cited_by": 8,
  "doi": "10.5281/zenodo.21131949",
  "fulltext_url": null,
  "id": "6849ynvzanykk",
  "issns": [],
  "landing_url": "https://doi.org/10.5281/zenodo.21131949",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "3107|Quantum Mechanics and Applications"
    ]
  ],
  "openalex": "W7167080902",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-07-02",
  "publisher": "European Organization for Nuclear Research",
  "ris": "https://research.draconitic.com/paper/6849ynvzanykk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:18Z",
      "native_id": "W7167080902",
      "source": "openalex",
      "url": "https://doi.org/10.5281/zenodo.21131949"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "openalex:3107|Quantum Mechanics and Applications",
      "subfield": "amo"
    }
  ],
  "title": "Uncertainty on the Spiral: The Real and Imaginary Parts of the Quantum Exponent",
  "title_text": "Uncertainty on the Spiral: The Real and Imaginary Parts of the Quantum Exponent",
  "type": "preprint",
  "updated_at": "2026-11-04T13:21:02Z",
  "url": "https://research.draconitic.com/paper/6849ynvzanykk",
  "venue": "Zenodo (CERN European Organization for Nuclear Research)",
  "versions": []
}