{
 "source_of_best_known": {
  "title": "Squares in Squares",
  "by": "David Ellsworth, from the original by Erich Friedman",
  "url": "https://kingbird.myphotos.cc/packing/squares_in_squares.html"
 },
 "rule": "A match: the certificate passes the exact check, and |L - best known| <= 1E-11, the difference published unrounded for each size. L is the side of the certificate's box, rounded up at 15 decimals.",
 "epsilon": "1E-11",
 "unit": "CSV and sides: one square's side = 1. DXF and DWG: millimetres, squares of 100 mm",
 "verify": "python verify_exact.py --records=records.json",
 "records": [
  {
   "squares": 1,
   "side": "1.000000000000000",
   "side_10_decimals": "1.0000000000",
   "best_known": "1.0",
   "best_known_10_decimals": "1.0000000000",
   "difference": "0",
   "valid": true,
   "found_by": "A plain grid",
   "year": "",
   "history": [],
   "plain_grid": true,
   "long_search": false,
   "fastest_seconds": null,
   "median_seconds": null,
   "timed_runs": null,
   "threads": null,
   "cpu": null,
   "upright": 1,
   "turned": 0,
   "files": {
    "svg": "1/1-squares-in-a-square.svg",
    "dxf": "1/1-squares-in-a-square.dxf",
    "dwg": "1/1-squares-in-a-square.dwg",
    "csv": "1/1-squares-in-a-square.csv"
   }
  },
  {
   "squares": 2,
   "side": "2.000000000000000",
   "side_10_decimals": "2.0000000000",
   "best_known": "2.0",
   "best_known_10_decimals": "2.0000000000",
   "difference": "0",
   "valid": true,
   "found_by": "Proved optimal by Frits Göbel",
   "year": "1979",
   "history": [],
   "plain_grid": true,
   "long_search": false,
   "fastest_seconds": null,
   "median_seconds": null,
   "timed_runs": null,
   "threads": null,
   "cpu": null,
   "upright": 2,
   "turned": 0,
   "files": {
    "svg": "2/2-squares-in-a-square.svg",
    "dxf": "2/2-squares-in-a-square.dxf",
    "dwg": "2/2-squares-in-a-square.dwg",
    "csv": "2/2-squares-in-a-square.csv"
   }
  },
  {
   "squares": 3,
   "side": "2.000000000000000",
   "side_10_decimals": "2.0000000000",
   "best_known": "2.0",
   "best_known_10_decimals": "2.0000000000",
   "difference": "0",
   "valid": true,
   "found_by": "Proved optimal by Frits Göbel",
   "year": "1979",
   "history": [],
   "plain_grid": true,
   "long_search": false,
   "fastest_seconds": null,
   "median_seconds": null,
   "timed_runs": null,
   "threads": null,
   "cpu": null,
   "upright": 3,
   "turned": 0,
   "files": {
    "svg": "3/3-squares-in-a-square.svg",
    "dxf": "3/3-squares-in-a-square.dxf",
    "dwg": "3/3-squares-in-a-square.dwg",
    "csv": "3/3-squares-in-a-square.csv"
   }
  },
  {
   "squares": 4,
   "side": "2.000000000000000",
   "side_10_decimals": "2.0000000000",
   "best_known": "2.0",
   "best_known_10_decimals": "2.0000000000",
   "difference": "0",
   "valid": true,
   "found_by": "A plain grid",
   "year": "",
   "history": [],
   "plain_grid": true,
   "long_search": false,
   "fastest_seconds": null,
   "median_seconds": null,
   "timed_runs": null,
   "threads": null,
   "cpu": null,
   "upright": 4,
   "turned": 0,
   "files": {
    "svg": "4/4-squares-in-a-square.svg",
    "dxf": "4/4-squares-in-a-square.dxf",
    "dwg": "4/4-squares-in-a-square.dwg",
    "csv": "4/4-squares-in-a-square.csv"
   }
  },
  {
   "squares": 5,
   "side": "2.707106781186910",
   "side_10_decimals": "2.7071067812",
   "best_known": "2.70710678118654",
   "best_known_10_decimals": "2.7071067812",
   "difference": "+3.700E-13",
   "valid": true,
   "found_by": "Frits Göbel",
   "year": "1979",
   "history": [
    "Proved by Frits Göbel, early 1979"
   ],
   "plain_grid": false,
   "long_search": false,
   "fastest_seconds": 0.05,
   "median_seconds": 0.05,
   "timed_runs": 1,
   "threads": 16,
   "cpu": "Intel Core i5-12600K, 10 cores, 16 threads",
   "upright": 4,
   "turned": 1,
   "files": {
    "svg": "5/5-squares-in-a-square.svg",
    "dxf": "5/5-squares-in-a-square.dxf",
    "dwg": "5/5-squares-in-a-square.dwg",
    "csv": "5/5-squares-in-a-square.csv"
   }
  },
  {
   "squares": 6,
   "side": "3.000000000000000",
   "side_10_decimals": "3.0000000000",
   "best_known": "3.0",
   "best_known_10_decimals": "3.0000000000",
   "difference": "0",
   "valid": true,
   "found_by": "Proved optimal by Michael Kearney and Peter Shiu",
   "year": "2001",
   "history": [],
   "plain_grid": true,
   "long_search": false,
   "fastest_seconds": null,
   "median_seconds": null,
   "timed_runs": null,
   "threads": null,
   "cpu": null,
   "upright": 6,
   "turned": 0,
   "files": {
    "svg": "6/6-squares-in-a-square.svg",
    "dxf": "6/6-squares-in-a-square.dxf",
    "dwg": "6/6-squares-in-a-square.dwg",
    "csv": "6/6-squares-in-a-square.csv"
   }
  },
  {
   "squares": 7,
   "side": "3.000000000000000",
   "side_10_decimals": "3.0000000000",
   "best_known": "3.0",
   "best_known_10_decimals": "3.0000000000",
   "difference": "0",
   "valid": true,
   "found_by": "Proved optimal by Erich Friedman",
   "year": "1999",
   "history": [],
   "plain_grid": true,
   "long_search": false,
   "fastest_seconds": null,
   "median_seconds": null,
   "timed_runs": null,
   "threads": null,
   "cpu": null,
   "upright": 7,
   "turned": 0,
   "files": {
    "svg": "7/7-squares-in-a-square.svg",
    "dxf": "7/7-squares-in-a-square.dxf",
    "dwg": "7/7-squares-in-a-square.dwg",
    "csv": "7/7-squares-in-a-square.csv"
   }
  },
  {
   "squares": 8,
   "side": "3.000000000000000",
   "side_10_decimals": "3.0000000000",
   "best_known": "3.0",
   "best_known_10_decimals": "3.0000000000",
   "difference": "0",
   "valid": true,
   "found_by": "Proved optimal by Erich Friedman",
   "year": "1999",
   "history": [],
   "plain_grid": true,
   "long_search": false,
   "fastest_seconds": null,
   "median_seconds": null,
   "timed_runs": null,
   "threads": null,
   "cpu": null,
   "upright": 8,
   "turned": 0,
   "files": {
    "svg": "8/8-squares-in-a-square.svg",
    "dxf": "8/8-squares-in-a-square.dxf",
    "dwg": "8/8-squares-in-a-square.dwg",
    "csv": "8/8-squares-in-a-square.csv"
   }
  },
  {
   "squares": 9,
   "side": "3.000000000000000",
   "side_10_decimals": "3.0000000000",
   "best_known": "3.0",
   "best_known_10_decimals": "3.0000000000",
   "difference": "0",
   "valid": true,
   "found_by": "A plain grid",
   "year": "",
   "history": [],
   "plain_grid": true,
   "long_search": false,
   "fastest_seconds": null,
   "median_seconds": null,
   "timed_runs": null,
   "threads": null,
   "cpu": null,
   "upright": 9,
   "turned": 0,
   "files": {
    "svg": "9/9-squares-in-a-square.svg",
    "dxf": "9/9-squares-in-a-square.dxf",
    "dwg": "9/9-squares-in-a-square.dwg",
    "csv": "9/9-squares-in-a-square.csv"
   }
  },
  {
   "squares": 10,
   "side": "3.707106781187110",
   "side_10_decimals": "3.7071067812",
   "best_known": "3.70710678118654",
   "best_known_10_decimals": "3.7071067812",
   "difference": "+5.700E-13",
   "valid": true,
   "found_by": "Frits Göbel",
   "year": "1979",
   "history": [
    "Found by Frits Göbel, early 1979",
    "Proved by Walter Stromquist, 2003"
   ],
   "plain_grid": false,
   "long_search": false,
   "fastest_seconds": 0.075,
   "median_seconds": 0.075,
   "timed_runs": 1,
   "threads": 16,
   "cpu": "Intel Core i5-12600K, 10 cores, 16 threads",
   "upright": 7,
   "turned": 3,
   "files": {
    "svg": "10/10-squares-in-a-square.svg",
    "dxf": "10/10-squares-in-a-square.dxf",
    "dwg": "10/10-squares-in-a-square.dwg",
    "csv": "10/10-squares-in-a-square.csv"
   }
  },
  {
   "squares": 11,
   "side": "3.877083590023390",
   "side_10_decimals": "3.8770835900",
   "best_known": "3.87708359002281",
   "best_known_10_decimals": "3.8770835900",
   "difference": "+5.800E-13",
   "valid": true,
   "found_by": "Walter Trump",
   "year": "1979",
   "history": [
    "Found by Walter Trump, 1979"
   ],
   "plain_grid": false,
   "long_search": false,
   "fastest_seconds": 1.762,
   "median_seconds": 1.762,
   "timed_runs": 1,
   "threads": 16,
   "cpu": "Intel Core i5-12600K, 10 cores, 16 threads",
   "upright": 6,
   "turned": 5,
   "files": {
    "svg": "11/11-squares-in-a-square.svg",
    "dxf": "11/11-squares-in-a-square.dxf",
    "dwg": "11/11-squares-in-a-square.dwg",
    "csv": "11/11-squares-in-a-square.csv"
   }
  },
  {
   "squares": 12,
   "side": "4.000000000000000",
   "side_10_decimals": "4.0000000000",
   "best_known": "4.0",
   "best_known_10_decimals": "4.0000000000",
   "difference": "0",
   "valid": true,
   "found_by": "A plain grid",
   "year": "",
   "history": [],
   "plain_grid": true,
   "long_search": false,
   "fastest_seconds": null,
   "median_seconds": null,
   "timed_runs": null,
   "threads": null,
   "cpu": null,
   "upright": 12,
   "turned": 0,
   "files": {
    "svg": "12/12-squares-in-a-square.svg",
    "dxf": "12/12-squares-in-a-square.dxf",
    "dwg": "12/12-squares-in-a-square.dwg",
    "csv": "12/12-squares-in-a-square.csv"
   }
  },
  {
   "squares": 13,
   "side": "4.000000000000000",
   "side_10_decimals": "4.0000000000",
   "best_known": "4.0",
   "best_known_10_decimals": "4.0000000000",
   "difference": "0",
   "valid": true,
   "found_by": "Proved optimal by Wolfram Bentz",
   "year": "2009",
   "history": [],
   "plain_grid": true,
   "long_search": false,
   "fastest_seconds": null,
   "median_seconds": null,
   "timed_runs": null,
   "threads": null,
   "cpu": null,
   "upright": 13,
   "turned": 0,
   "files": {
    "svg": "13/13-squares-in-a-square.svg",
    "dxf": "13/13-squares-in-a-square.dxf",
    "dwg": "13/13-squares-in-a-square.dwg",
    "csv": "13/13-squares-in-a-square.csv"
   }
  },
  {
   "squares": 14,
   "side": "4.000000000000000",
   "side_10_decimals": "4.0000000000",
   "best_known": "4.0",
   "best_known_10_decimals": "4.0000000000",
   "difference": "0",
   "valid": true,
   "found_by": "Proved optimal by Erich Friedman",
   "year": "1999",
   "history": [],
   "plain_grid": true,
   "long_search": false,
   "fastest_seconds": null,
   "median_seconds": null,
   "timed_runs": null,
   "threads": null,
   "cpu": null,
   "upright": 14,
   "turned": 0,
   "files": {
    "svg": "14/14-squares-in-a-square.svg",
    "dxf": "14/14-squares-in-a-square.dxf",
    "dwg": "14/14-squares-in-a-square.dwg",
    "csv": "14/14-squares-in-a-square.csv"
   }
  },
  {
   "squares": 15,
   "side": "4.000000000000000",
   "side_10_decimals": "4.0000000000",
   "best_known": "4.0",
   "best_known_10_decimals": "4.0000000000",
   "difference": "0",
   "valid": true,
   "found_by": "Proved optimal by Erich Friedman",
   "year": "1999",
   "history": [],
   "plain_grid": true,
   "long_search": false,
   "fastest_seconds": null,
   "median_seconds": null,
   "timed_runs": null,
   "threads": null,
   "cpu": null,
   "upright": 15,
   "turned": 0,
   "files": {
    "svg": "15/15-squares-in-a-square.svg",
    "dxf": "15/15-squares-in-a-square.dxf",
    "dwg": "15/15-squares-in-a-square.dwg",
    "csv": "15/15-squares-in-a-square.csv"
   }
  },
  {
   "squares": 16,
   "side": "4.000000000000000",
   "side_10_decimals": "4.0000000000",
   "best_known": "4.0",
   "best_known_10_decimals": "4.0000000000",
   "difference": "0",
   "valid": true,
   "found_by": "A plain grid",
   "year": "",
   "history": [],
   "plain_grid": true,
   "long_search": false,
   "fastest_seconds": null,
   "median_seconds": null,
   "timed_runs": null,
   "threads": null,
   "cpu": null,
   "upright": 16,
   "turned": 0,
   "files": {
    "svg": "16/16-squares-in-a-square.svg",
    "dxf": "16/16-squares-in-a-square.dxf",
    "dwg": "16/16-squares-in-a-square.dwg",
    "csv": "16/16-squares-in-a-square.csv"
   }
  },
  {
   "squares": 17,
   "side": "4.675530093605300",
   "side_10_decimals": "4.6755300936",
   "best_known": "4.67553009360455",
   "best_known_10_decimals": "4.6755300936",
   "difference": "+7.500E-13",
   "valid": true,
   "found_by": "John Bidwell",
   "year": "1998",
   "history": [
    "Found by John Bidwell, 1998"
   ],
   "plain_grid": false,
   "long_search": false,
   "fastest_seconds": 4.838,
   "median_seconds": 4.838,
   "timed_runs": 1,
   "threads": 16,
   "cpu": "Intel Core i5-12600K, 10 cores, 16 threads",
   "upright": 10,
   "turned": 7,
   "files": {
    "svg": "17/17-squares-in-a-square.svg",
    "dxf": "17/17-squares-in-a-square.dxf",
    "dwg": "17/17-squares-in-a-square.dwg",
    "csv": "17/17-squares-in-a-square.csv"
   }
  },
  {
   "squares": 18,
   "side": "4.822875655533110",
   "side_10_decimals": "4.8228756555",
   "best_known": "4.82287565553229",
   "best_known_10_decimals": "4.8228756555",
   "difference": "+8.200E-13",
   "valid": true,
   "found_by": "Pertti Hämäläinen",
   "year": "1980",
   "history": [
    "Found by Pertti Hämäläinen, 1980"
   ],
   "plain_grid": false,
   "long_search": false,
   "fastest_seconds": 0.471,
   "median_seconds": 0.471,
   "timed_runs": 1,
   "threads": 16,
   "cpu": "Intel Core i5-12600K, 10 cores, 16 threads",
   "upright": 12,
   "turned": 6,
   "files": {
    "svg": "18/18-squares-in-a-square.svg",
    "dxf": "18/18-squares-in-a-square.dxf",
    "dwg": "18/18-squares-in-a-square.dwg",
    "csv": "18/18-squares-in-a-square.csv"
   }
  },
  {
   "squares": 19,
   "side": "4.885618083164925",
   "side_10_decimals": "4.8856180832",
   "best_known": "4.88561808316412",
   "best_known_10_decimals": "4.8856180832",
   "difference": "+8.050E-13",
   "valid": true,
   "found_by": "Robert Wainwright",
   "year": "1979",
   "history": [
    "Found first by Robert Wainwright, late 1979"
   ],
   "plain_grid": false,
   "long_search": false,
   "fastest_seconds": 13.528,
   "median_seconds": 13.528,
   "timed_runs": 1,
   "threads": 16,
   "cpu": "Intel Core i5-12600K, 10 cores, 16 threads",
   "upright": 10,
   "turned": 9,
   "files": {
    "svg": "19/19-squares-in-a-square.svg",
    "dxf": "19/19-squares-in-a-square.dxf",
    "dwg": "19/19-squares-in-a-square.dwg",
    "csv": "19/19-squares-in-a-square.csv"
   }
  },
  {
   "squares": 20,
   "side": "5.000000000000000",
   "side_10_decimals": "5.0000000000",
   "best_known": "5.0",
   "best_known_10_decimals": "5.0000000000",
   "difference": "0",
   "valid": true,
   "found_by": "A plain grid",
   "year": "",
   "history": [],
   "plain_grid": true,
   "long_search": false,
   "fastest_seconds": null,
   "median_seconds": null,
   "timed_runs": null,
   "threads": null,
   "cpu": null,
   "upright": 20,
   "turned": 0,
   "files": {
    "svg": "20/20-squares-in-a-square.svg",
    "dxf": "20/20-squares-in-a-square.dxf",
    "dwg": "20/20-squares-in-a-square.dwg",
    "csv": "20/20-squares-in-a-square.csv"
   }
  },
  {
   "squares": 21,
   "side": "5.000000000000000",
   "side_10_decimals": "5.0000000000",
   "best_known": "5.0",
   "best_known_10_decimals": "5.0000000000",
   "difference": "0",
   "valid": true,
   "found_by": "A plain grid",
   "year": "",
   "history": [],
   "plain_grid": true,
   "long_search": false,
   "fastest_seconds": null,
   "median_seconds": null,
   "timed_runs": null,
   "threads": null,
   "cpu": null,
   "upright": 21,
   "turned": 0,
   "files": {
    "svg": "21/21-squares-in-a-square.svg",
    "dxf": "21/21-squares-in-a-square.dxf",
    "dwg": "21/21-squares-in-a-square.dwg",
    "csv": "21/21-squares-in-a-square.csv"
   }
  },
  {
   "squares": 22,
   "side": "5.000000000000000",
   "side_10_decimals": "5.0000000000",
   "best_known": "5.0",
   "best_known_10_decimals": "5.0000000000",
   "difference": "0",
   "valid": true,
   "found_by": "Proved optimal by Wolfram Bentz",
   "year": "2018",
   "history": [],
   "plain_grid": true,
   "long_search": false,
   "fastest_seconds": null,
   "median_seconds": null,
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   "upright": 22,
   "turned": 0,
   "files": {
    "svg": "22/22-squares-in-a-square.svg",
    "dxf": "22/22-squares-in-a-square.dxf",
    "dwg": "22/22-squares-in-a-square.dwg",
    "csv": "22/22-squares-in-a-square.csv"
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  },
  {
   "squares": 23,
   "side": "5.000000000000000",
   "side_10_decimals": "5.0000000000",
   "best_known": "5.0",
   "best_known_10_decimals": "5.0000000000",
   "difference": "0",
   "valid": true,
   "found_by": "Proved optimal by Hiroshi Nagamochi",
   "year": "2005",
   "history": [],
   "plain_grid": true,
   "long_search": false,
   "fastest_seconds": null,
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   "upright": 23,
   "turned": 0,
   "files": {
    "svg": "23/23-squares-in-a-square.svg",
    "dxf": "23/23-squares-in-a-square.dxf",
    "dwg": "23/23-squares-in-a-square.dwg",
    "csv": "23/23-squares-in-a-square.csv"
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  },
  {
   "squares": 24,
   "side": "5.000000000000000",
   "side_10_decimals": "5.0000000000",
   "best_known": "5.0",
   "best_known_10_decimals": "5.0000000000",
   "difference": "0",
   "valid": true,
   "found_by": "Proved optimal by Erich Friedman",
   "year": "1999",
   "history": [],
   "plain_grid": true,
   "long_search": false,
   "fastest_seconds": null,
   "median_seconds": null,
   "timed_runs": null,
   "threads": null,
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   "upright": 24,
   "turned": 0,
   "files": {
    "svg": "24/24-squares-in-a-square.svg",
    "dxf": "24/24-squares-in-a-square.dxf",
    "dwg": "24/24-squares-in-a-square.dwg",
    "csv": "24/24-squares-in-a-square.csv"
   }
  },
  {
   "squares": 25,
   "side": "5.000000000000000",
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