{
  "abstract": "We expand the Einstein--Hilbert action to cubic order about the Schwarzschild horizon, in the even Regge--Wheeler gauge of the Gaddam--Groenenboom--'t~Hooft near-horizon framework, and derive the cubic graviton self-interaction. Our central result is a vanishing theorem: at leading soft order the self-coupling of the purely traceless longitudinal polarizations is identically zero. This is a framework-specific statement: even RW gauge, GGV sector, leading soft order. The surviving interaction lives in the trace sector; its on-shell equal-$\\ell$ weight $W(λ,λ,λ)=-3λ(2λ^2+λ+3)/(λ+1)^2$, follows from two independent derivations agreeing to machine precision. We simulate the resulting Hamiltonian at two complementary scales. On IBM Qiskit/Aer, with exact cross-checks, the hardware-format circuits confirm quantitatively what two structural facts already predict, a conserved charge that only the cubic vertex violates (opening $ϕϕ\\to hh\\to4ϕ$) and a resonance-free boost spectrum (gap $\\to1/2$): the longitudinal channel is perturbatively rigid, and the simulation measures the residual dressing ($d_{\\rm eff}=1.06$; multiplicity far from thermal, Poisson, and Haar). A symmetry-graded matrix-product-state evolution then climbs the multipole ladder to sixty modes, the $120$-qubit register, and settles the one question the multiplet cannot: on a late-time measure common to both engines the inelasticity converges to $\\barη_\\infty\\simeq0.16$ (understated by the single multiplet), the dressing stays area-law with peak entanglement $\\simeq0.45$ nats far below the Page value, and the result is cutoff-converged and robust to $96$ qubits at larger occupation. The rigidity therefore persists rather than scrambling as the register grows.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.21066",
  "author_total": 1,
  "authors": [
    {
      "name": "Ayanendu Dutta"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9yf31rrs9m15s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.21066",
  "fulltext_url": null,
  "id": "9yf31rrs9m15s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.21066",
  "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"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7170503469",
  "pdf_url": "https://arxiv.org/pdf/2607.21066",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9yf31rrs9m15s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:41Z",
      "native_id": "2607.21066",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.21066"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "The leading-soft cubic graviton self-interaction on the black-hole horizon",
  "title_text": "The leading-soft cubic graviton self-interaction on the black-hole horizon",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:41Z",
  "url": "https://research.draconitic.com/paper/9yf31rrs9m15s",
  "venue": "arXiv",
  "versions": []
}