{
  "abstract": "We develop a branch-complete classical free-spectrum analysis of local parity-even symmetric teleparallel gravity containing all pure-gravity nonmetricity operators through four derivatives. After canonicalisation and integration by parts, the nonlinear action contains 116 independent operators distributed as $5+13+29+69$ among $Q^2$, $(\\nabla Q)^2$, $Q^2\\nabla Q$ and $Q^4$. Around Minkowski spacetime in the coincident gauge only the first two sectors contribute to the quadratic action, which reduces to four two-derivative and five four-derivative bilinears. We map the original coefficients to this nine-dimensional basis, construct the Hessian and momentum kernel, and classify local linear gauge symmetries. Unrestricted linearised diffeomorphism invariance imposes six independent relations and leaves a three-parameter family $(A,B,C)$. We also recover TDiff, Weyl, WTDiff and additional accidental symmetry branches. Barnes--Rivers decomposition, gauge fixing, exact inversion and conserved-source saturation reduce the physical exchange to spin-two and scalar factors $A+2Cq$ and $2A+(3B-2C)q$. The generic regular spectrum contains a massless graviton, a massive spin-two state and a massive scalar, with eight degrees of freedom. The massive spin-two residue is necessarily opposite to that of the healthy massless graviton. The regular classification leaves only GR/STEGR, $A>0$ with $B=C=0$, and the scalar extension, $A>0$, $B>0$, $C=0$, as fully healthy Minkowski loci. The latter has three degrees of freedom and mixed ultraviolet behaviour, with tensor exchange scaling as $k^{-2}$ and scalar exchange as $k^{-4}$. Thus, within this finite local metric theory, full four-derivative tensor suppression requires the finite massive spin-two pole with opposite residue.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.04448",
  "author_total": 1,
  "authors": [
    {
      "name": "Caglar Pala"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5vjh7wz09maxm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.04448",
  "fulltext_url": null,
  "id": "5vjh7wz09maxm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.04448",
  "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",
      "gr-qc"
    ],
    [
      "openalex",
      "3103|Cosmology and Gravitation Theories"
    ]
  ],
  "openalex": "W7211916199",
  "pdf_url": "https://arxiv.org/pdf/2609.04448",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5vjh7wz09maxm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:14Z",
      "native_id": "2609.04448",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.04448"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    }
  ],
  "title": "From Nonmetricity Operators to the Physical Spectrum: A Branch-Complete Analysis of Local Four-Derivative Symmetric Teleparallel Gravity",
  "title_text": "From Nonmetricity Operators to the Physical Spectrum: A Branch-Complete Analysis of Local Four-Derivative Symmetric Teleparallel Gravity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:14Z",
  "url": "https://research.draconitic.com/paper/5vjh7wz09maxm",
  "venue": "arXiv",
  "versions": []
}