{
  "abstract": "We construct the first-law-consistent entropy of a geometrically minimal-length-deformed Schwarzschild spacetime, obtained via the areal-radius substitution $R(r)=\\sqrt{r^{2}+\\ell^{2}}$ on $r\\in[0,+\\infty)$ with $f(R)=1-2M/R$, whose nonvanishing Einstein tensor sources an effective geometric fluid with no classical matter counterpart. Integrating the first law gives $S=π[r_{h}R_{h}+\\ell^{2}\\ln((r_{h}+R_{h})/\\ell)]$. This coincides in functional form with the semiclassical term found independently by Joshi and Joshi, but we fix its boundary condition $S(r_h=0)=0$ on independent physical grounds and adopt it, rather than the Bekenstein--Hawking area law, as the complete entropy of the model, building the free energy, geometrothermodynamics, and mode-stability analysis on it. Evaporation, governed by the Helmholtz free energy $F(M)$, terminates at $M_{\\min}=\\ell/2$ in a previously unrecognised endpoint: a degenerate extremal regular black hole, where the regular centre coincides with a degenerate Killing horizon of quadratic order, $f\\approx r^{2}/(2\\ell^{2})$, at areal radius $\\ell$, with $T_{H}\\to 0$, $S\\to 0$, $C\\to 0^{+}$, and finite curvature everywhere; we display its Penrose--Carter structure for the first time. The same entropy, with $\\ell$, defines the equilibrium state space of a Legendre-invariant geometrothermodynamic (GTD) description whose curvature scalar diverges independently at the Davies-type transition $M^{*}=\\ell/\\sqrt{2}$ and at $M_{\\min}$, a divergence with no counterpart in the minimal-length black hole literature, specific to a genuine horizon at $S=0$. We embed this remnant within the observational discriminant noted qualitatively by Tsukamoto: exact shadow degeneracy combined with a measurable photon-ring flux enhancement $r_{n}=e^{-2π/a}>e^{-2π}$, accessible to next-generation very-long-baseline interferometry.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17588",
  "author_total": 4,
  "authors": [
    {
      "name": "T. Toghrai"
    },
    {
      "name": "N. Mansour"
    },
    {
      "name": "A. Daassou"
    },
    {
      "name": "R. Benbrik"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9ez0x4s8e2w58.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17588",
  "fulltext_url": null,
  "id": "9ez0x4s8e2w58",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17588",
  "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",
      "gr-qc"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7213527386",
  "pdf_url": "https://arxiv.org/pdf/2609.17588",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9ez0x4s8e2w58.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:01Z",
      "native_id": "2609.17588",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17588"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "First-Law Entropy and a Degenerate Extremal Remnant in a Minimal-Length Simpson--Visser-Type Regular Black Hole: Geometrothermodynamics, Phase Structure, and Observational Discriminants",
  "title_text": "First-Law Entropy and a Degenerate Extremal Remnant in a Minimal-Length Simpson--Visser-Type Regular Black Hole: Geometrothermodynamics, Phase Structure, and Observational Discriminants",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:01Z",
  "url": "https://research.draconitic.com/paper/9ez0x4s8e2w58",
  "venue": "arXiv",
  "versions": []
}