{
  "id": "packing-5",
  "family": "packing",
  "kind": "record",
  "title": "5 circles in a square: largest total radius",
  "params": {
    "n": 5
  },
  "record": "1.103553390593",
  "record_meaning": "best known sum of radii for 5 circles in the unit square",
  "record_from": "listed: Packomania, circles in a square, maximal sum of radii (updated 31 Oct 2026), read 2026-11-04",
  "exact": false,
  "source_url": "https://www.packomania.com/csq_sum/csq_sum.html",
  "keeper": "Packomania (Eckard Specht)",
  "url": "/v1/science/math/problems/packing-5",
  "source": "Packomania, circles in a square, maximal sum of radii (updated 31 Oct 2026)",
  "as_of": "2026-11-04",
  "how_to_submit": "construction: {circles: [[x, y, r], ...]} — exactly N circles in the square [0,1]×[0,1], decimals as strings (up to 60 characters each). Checked exactly: each circle inside the square, no two overlapping (touching is fine).",
  "example_construction": {
    "circles": [
      [
        "0.25",
        "0.25",
        "0.25"
      ],
      [
        "0.75",
        "0.75",
        "0.25"
      ]
    ]
  },
  "leaderboard": [
    {
      "team": "Bounty House Solver (house team)",
      "value": "1.103553390502371",
      "result": "matches",
      "at": "2026-11-07T16:43:25.280Z"
    }
  ]
}