{
  "abstract": "A recognizer that compares rotation-invariant descriptors sees a surface only up to the fiber of the descriptor. We measure this fiber by its radius in the orbit distance from the enrolled surface. A large radius admits decoys, that is, distant shapes that pass the matcher. A small radius discloses the enrolled shape to anyone who captures the stored value. For star-shaped surfaces truncated to spherical harmonics of degree at most $L$, with $n$ coefficients, a descriptor of generic rank $r$ has generic fibers of dimension $n-3-r$ modulo rotations. The standard pool of band powers, even bispectra, and three invariants of the degree-three band therefore admits decoy families of dimension $5$, $13$, $20$ at $L=4,6,8$. Its rank first reaches $n-3$ at $L=16$, and a mirror decoy remains at every $L$. The odd bispectra remove the mirror decoy generically for $L \\geq 4$. Yet at fixed mean radius the same pool determines the enclosed volume exactly, and it does not determine whether a surface meets a clearance requirement. We certify two cases by exact and interval arithmetic. At $L=6$ a decoy matches all $32$ invariants to relative precision $2 \\cdot 10^{-18}$ at orbit distance at least $0.87$ times the norm of the enrolled tuple. For the radar shape model of asteroid (101955) Bennu, the pool recovers the modeled volume, misses the handedness, and leaves the keep-out radius uncertain by more than $7 \\, \\mathrm{m}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.08410",
  "author_total": 2,
  "authors": [
    {
      "name": "Tanush Shaska"
    },
    {
      "name": "Lubjana Beshaj"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/enpftd320e7b9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.08410",
  "fulltext_url": null,
  "id": "enpftd320e7b9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.08410",
  "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",
      "astro-ph.EP"
    ],
    [
      "arxiv",
      "cs.CR"
    ],
    [
      "arxiv",
      "cs.CV"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "openalex",
      "1703|Topological and Geometric Data Analysis"
    ]
  ],
  "openalex": "W7220922612",
  "pdf_url": "https://arxiv.org/pdf/2610.08410",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/enpftd320e7b9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:22Z",
      "native_id": "2610.08410",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.08410"
    }
  ],
  "subjects": [
    {
      "field": "astronomy",
      "origin": "arxiv:astro-ph.EP",
      "subfield": "planetary"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Decoy and disclosure radii of invariant shape descriptors",
  "title_text": "Decoy and disclosure radii of invariant shape descriptors",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/enpftd320e7b9",
  "venue": "arXiv",
  "versions": []
}