{
  "abstract": "We consider the matrix model of a seven-dimensional quantum space built from concentric fuzzy $CP^3$'s of increasing matrix size, and show that its continuum limit is the metric cone $C(CP^3)$ over $CP^3$, not flat $R^7$. Every ingredient is fixed before any comparison, so this geometry is a prediction rather than an input. The two geometries agree in the $s$ wave ($p=0$) but separate in the higher angular sectors (harmonics on $CP^3$ of degree $p\\geq1$): in each sector tested, the spectrum of the free Laplacian converges at second order to that of the cone, and at 20480 layers the cone is matched to $1\\times10^{-9}$ for $p\\leq8$, whereas flat space misses by 8-18%. The free propagator converges to that of the cone at the same order, and heat diffusion reproduces the $r^6$ measure and the Bessel spectrum of the cone. The maps between neighbouring layers are obtained in closed form from the polar decomposition of the second-quantized Schwinger-boson lift, using a known operator identity, and coincide with the Kováčik-Tekel coefficient-copying prescription. For $CP^1$ the construction reduces, away from the outer boundary, to the Kováčik-Tekel fuzzy onion. Modes along the twistor fibre are exactly degenerate with the harmonics on $S^4$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.17807",
  "author_total": 2,
  "authors": [
    {
      "name": "Kohei Uno"
    },
    {
      "name": "Tomohiro Inagaki"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0vte7ex9wg665.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.17807",
  "fulltext_url": null,
  "id": "0vte7ex9wg665",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.17807",
  "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",
      "hep-th"
    ],
    [
      "openalex",
      "3109|Noncommutative and Quantum Gravity Theories"
    ]
  ],
  "openalex": "W7221766977",
  "pdf_url": "https://arxiv.org/pdf/2610.17807",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0vte7ex9wg665.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:11Z",
      "native_id": "2610.17807",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.17807"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Construction and geometric properties of the fuzzy $CP^3$ onion",
  "title_text": "Construction and geometric properties of the fuzzy CP^3 onion",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:11Z",
  "url": "https://research.draconitic.com/paper/0vte7ex9wg665",
  "venue": "arXiv",
  "versions": []
}