{
  "abstract": "A shoreline-search path starts at the origin and must meet an unknown affine line, without knowing either its normal or its distance. We first establish a self-similar reduction theorem for homogeneous search problems whose historical information is a record profile updated by pointwise maximum. Two quasi-returns of the normalized state delimit a block that renews the required profile by itself; a short connector closes this block into a cell. Every finite-ratio path can therefore be approximated, with arbitrarily small loss, by repetitions of a single cell at all scales. The main chain is then made effective. A finite coding of the state space computably bounds the scale factor and normalized length of a nearly optimal cell. For planar Shoreline search, the support function of the convex hull gives an exact cell functional. A one-sided polygonalization then reduces the problem to a computable number of vertices, after which quantifier elimination decides whether a polygonal cell exists below a rational threshold. It follows that the optimal deterministic planar Shoreline value $C_2^*$ is a computable real: for every rational $ε>0$, an algorithm terminates with a rational interval of width at most $ε$ containing $C_2^*$. Additional results---sliding memory, Bellman transitions, deadlines, geometric filters, and relative equilibria---are presented separately as a toolbox for certified computation and for the study of spiral rigidity; they are not used in the computability proof.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.29032",
  "author_total": 1,
  "authors": [
    {
      "name": "Florentin Koch"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/de8sdyyqvq6ma.bib",
  "cited_by": 1,
  "doi": "10.48550/arxiv.2608.29032",
  "fulltext_url": null,
  "id": "de8sdyyqvq6ma",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.29032",
  "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",
      "cs.CG"
    ],
    [
      "arxiv",
      "math.MG"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1705|Optimization and Search Problems"
    ]
  ],
  "openalex": "W7204624998",
  "pdf_url": "https://arxiv.org/pdf/2608.29032",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/de8sdyyqvq6ma.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.29032",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.29032"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Bellman Search in Arbitrary Finite Dimension: A Self-Similar Cell Theorem and Effective Computability of Planar Shoreline Search",
  "title_text": "Bellman Search in Arbitrary Finite Dimension: A Self-Similar Cell Theorem and Effective Computability of Planar Shoreline Search",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/de8sdyyqvq6ma",
  "venue": "arXiv",
  "versions": []
}