{
  "abstract": "We prove the spacetime Penrose inequality for asymptotically flat initial data sets $(M^n,g,k)$ in all dimensions $n\\geq 3$, under the dominant energy condition, for data admitting the 'maximally parameterized form' defined in equation (4.7). In this case, the second fundamental form $k$ is locally parameterized by $n(n+1)/2$ functions, giving the same formal local functional degrees of freedom as an arbitrary symmetric $2$-tensor. The proof is based on a new 1-parameter family of generalized Schoen-Yau identities and their gauge-invariant specialization, inspired by the generalized Jang framework of Bray-Khuri [8, 9]. For maximally parameterized data, these identities produce a Riemannian comparison metric \\[ \\bar g=g+β\\otimesβ\\] with nonnegative scalar curvature $R_{\\bar{g}} \\geq 0$. Under a natural nondegeneracy condition (5.7) at the apparent horizon, the comparison metric admits a smooth minimal completion up to $\\partial M^n$. Together with suitable asymptotic control, this reduces the Penrose inequality to its Riemannian counterpart. The all-dimensional conclusion uses the Riemannian Penrose theorem of Bi-Zhu [6], together with a minimizing enclosure argument that allows singular boundaries. More generally, in the spirit of [8, 9], we note that the Penrose conjecture follows whenever a certain system of PDEs (3.18) involving $k$ can be solved, in which case our new identity (3.15) immediately implies $R_{\\bar{g}} \\geq 0$. A natural problem is thus to regularize our degenerate system to prove a general existence theory, thereby proving the Penrose conjecture. Essentially, we believe this is what the OpenAI paper [27] posted last week on October 6, 2026 claims to have done.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.20559",
  "author_total": 4,
  "authors": [
    {
      "name": "Hubert Bray"
    },
    {
      "name": "Tuan Dolmen"
    },
    {
      "name": "Marcus Khuri"
    },
    {
      "name": "David Schmidt"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cy5xrdw97m7bt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.20559",
  "fulltext_url": null,
  "id": "cy5xrdw97m7bt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.20559",
  "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",
      "math.DG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7222112045",
  "pdf_url": "https://arxiv.org/pdf/2610.20559",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cy5xrdw97m7bt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.20559",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.20559"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Proof of the Penrose Conjecture for Maximally Parameterized Initial Data Sets",
  "title_text": "Proof of the Penrose Conjecture for Maximally Parameterized Initial Data Sets",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/cy5xrdw97m7bt",
  "venue": "arXiv",
  "versions": []
}