{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R206",
  "content_hash": null,
  "slug": "ddg9-attempt-literature-audit",
  "type": "attempt",
  "title": "Prior work covers the distance-only problem",
  "summary": "The grid distinct-distance problem is classical, and a compiled exact table independently gives the required upper bound.",
  "relevance": "This records a line of attack on the target problem, including what it establishes and where it stops.",
  "relevance_source": "derived",
  "body": "Lefmann and Thiele define \\(f_2(n)\\) as the maximum size of a subset of the \\(n\\times n\\) grid with all mutual Euclidean distances distinct. Their 1995 paper develops asymptotic lower bounds and also studies distinct-distance selection when the ambient point set is in general position. It does not report the combined fixed-grid value \\(G_9\\).\n\nOEIS A193838 records the inverse distance-only parameter: the smallest square grid supporting eight points is \\(9\\times9\\), while nine points first occur in a \\(10\\times10\\) grid. This compiled table independently rules out nine distance-distinct points in the present grid, even without imposing general position. Its displayed eight-point example contains a collinear triple, so a separate witness is still needed for the lower bound in this entry.\n\nThe targeted search covered distinct-distance grid subsets, Golomb squares, no-three-in-line sets, and general-position distance selection. It located no primary source tabulating the exact combined value. The exhaustive artifact provides a self-contained upper-bound certificate, and the verified witness supplies the lower bound.",
  "status": "completed",
  "evidence_grade": "sourced",
  "scope": {
    "kind": "bounded",
    "statement": "published and compiled results concerning distinct-distance subsets and general-position subsets of a 9 by 9 lattice grid",
    "bounds": {
      "grid_side": {
        "min": 9,
        "max": 9
      }
    },
    "exhaustive": false
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://doi.org/10.1007/BF01299744",
      "locator": "Hanno Lefmann and Torsten Thiele, Point sets with distinct distances, Combinatorica 15 (1995), 379-408, DOI 10.1007/BF01299744; OEIS A193838, Size of smallest square grid supporting n points with distinct mutual distances, https://oeis.org/A193838; search performed 2026-07-24"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.1007/BF01299744",
    "locator": "Hanno Lefmann and Torsten Thiele, Point sets with distinct distances, Combinatorica 15 (1995), 379-408, DOI 10.1007/BF01299744; OEIS A193838, Size of smallest square grid supporting n points with distinct mutual distances, https://oeis.org/A193838; search performed 2026-07-24"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R208",
      "title": "The exact value is G_9=8",
      "object_type": "claim",
      "relation": "corroborates",
      "direction": "outgoing"
    },
    {
      "slug": "distinct-distance-grid-9",
      "title": "distinct distance grid 9",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}