{
  "abstract": "The unknown coefficient $c_{5,1}$ controls the first omitted fifth-order term in fixed-order analyses of inclusive hadronic $τ$ decays. We determine what the four known Adler coefficients can actually test. For any normalized polynomial weight, the fixed-order Adler-to-moment map is triangular with unit diagonal. Hence one common Adler-coefficient error reaches every moment with the same absolute size, and a multi-weight relative test reduces to one absolute tolerance. For three representative weights, a ten-percent test resolves $c_{5,1}$ only to about $\\pm24$; the closest contour-improved test is weaker by more than an order of magnitude. Moreover, any continuation that preserves the observed sign of the direct Padé/Shanks defects gives $c_{5,1}\\geq378.03$, so values near $280$ require additional structure. A calibration-and-falsification protocol applied to a simplified Beneke--Jamin-type pure-power ansatz gives the conditional estimate $c_{5,1}=248\\pm30\\,(\\mathrm{struct})\\pm74\\,(\\mathrm{method})=248\\pm80$. At the physical order its central value coincides algebraically with the exact four-parameter fit; the protocol adds a falsifiable admissibility test and a method uncertainty, not new coefficient information. We also clarify that the often-quoted Beneke--Jamin value $283$ is a linear extrapolation of total-width FOPT te",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06824",
  "author_total": 4,
  "authors": [
    {
      "name": "Gauhar Abbas"
    },
    {
      "name": "Debabina Biswas"
    },
    {
      "name": "Pratham Dadhich"
    },
    {
      "name": "Vartika Singh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3v2nbks68v2vc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06824",
  "fulltext_url": null,
  "id": "3v2nbks68v2vc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06824",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "hep-ex"
    ],
    [
      "arxiv",
      "hep-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.06824",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3v2nbks68v2vc.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:20:56Z",
      "native_id": "2611.06824",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06824"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-ex",
      "subfield": "high-energy"
    }
  ],
  "title": "Cross-Moment Consistency and the Fifth Adler Coefficient in Hadronic Tau Decays",
  "title_text": "Cross-Moment Consistency and the Fifth Adler Coefficient in Hadronic Tau Decays",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:21Z",
  "url": "https://research.draconitic.com/paper/3v2nbks68v2vc",
  "venue": "arXiv",
  "versions": []
}