{
  "schemaVersion": 1,
  "name": "Print sheet layout benchmark: 24 reproducible constructions",
  "description": "A curated, finite geometry benchmark comparing constructed layouts with independently calculated uniform grids and usable-area upper bounds. JSON includes every footprint and trim coordinate; CSV summarises each case.",
  "caseCount": 24,
  "method": {
    "id": "paper-and-scale-rectangular-layout-benchmark",
    "version": "1",
    "engineSha256": "f793e2478837d147b87452862474b17b5611b95454dbe3dc316868b44c23d409",
    "units": "millimetres",
    "coordinateOrigin": "sheet top-left; x rightward and y downward",
    "arithmetic": "Dimensions and placements are checked as integer thousandths of a millimetre.",
    "candidateFamilies": [
      "uniform-upright",
      "uniform-rotated",
      "mixed-rows",
      "mixed-columns",
      "pinwheel-tiles"
    ],
    "gapDefinition": "Required axis separation between every pair of complete bleed footprints.",
    "areaUpperBound": "floor(usable_width × usable_height / ((trim_width + 2 × bleed) × (trim_height + 2 × bleed))); gaps are ignored, so this is an upper bound, not a fit prediction.",
    "certification": "A verified construction is a proved maximum only when its count reaches the independently recomputed valid area bound. Other cases remain constructions, not claimed optima.",
    "verification": "The standalone verifier checks inputs, counts, uniform baselines, bounds, rotations, bleed and trim shapes, every pair gap, and the content checksum. It does not rerun the packing search.",
    "selection": "Five sheet/item families under four settings, two A4 full-bleed comparisons, and two explicitly synthetic algorithm controls. The suite is illustrative, not a representative sample of all print jobs."
  },
  "provenance": [
    {
      "id": "iso-216",
      "url": "https://www.iso.org/standard/36631.html",
      "role": "Standard defining trimmed A-series formats; the numerical fixtures use the published nominal dimensions below."
    },
    {
      "id": "adobe-nominal-sizes",
      "url": "https://www.adobe.com/uk/creativecloud/design/discover/a6-format.html",
      "role": "Published nominal A3, A4 and A6 millimetre dimensions."
    },
    {
      "id": "fujifilm-sra3",
      "url": "https://asset-fb.fujifilm.com/www/fbsg/files/2025-07/6f108f52370caed349a76a825b9103d0/product_fujifilm_uncoated_hr_01.pdf",
      "role": "Manufacturer catalogue listing SRA3 as 450 × 320 mm."
    },
    {
      "id": "adobe-bleed",
      "url": "https://www.adobe.com/learn/indesign/web/set-print-bleed?locale=en",
      "role": "Explains bleed extending beyond finished trim. Benchmark margins, bleed and gaps are chosen test inputs, not universal machine requirements."
    },
    {
      "id": "chosen-fixtures",
      "role": "The 85 × 55 mm card, 20 mm pinwheel sheet, and 0.001 mm boundary gap are deliberately chosen geometry fixtures. No product standard, physical printing test or press suitability is claimed."
    }
  ],
  "cases": [
    {
      "id": "a6-on-a4-nominal",
      "label": "A6 on A4: no allowances",
      "family": "A6 on A4",
      "configuration": "nominal",
      "input": {
        "sheetWidth": 210,
        "sheetHeight": 297,
        "itemWidth": 105,
        "itemHeight": 148,
        "margin": 0,
        "bleed": 0,
        "gap": 0,
        "targetCount": 1,
        "allowRotation": true
      },
      "metrics": {
        "constructedCount": 4,
        "uniformCount": 4,
        "areaUpperBound": 4,
        "gainOverUniform": 0,
        "usableWidthMm": 210,
        "usableHeightMm": 297,
        "footprintWidthMm": 105,
        "footprintHeightMm": 148,
        "trimCoveragePercent": 99.663
      },
      "method": "uniform-upright",
      "areaBoundMet": true,
      "positions": [
        {
          "x": 0,
          "y": 0,
          "width": 105,
          "height": 148,
          "rotation": 0,
          "trim": {
            "x": 0,
            "y": 0,
            "width": 105,
            "height": 148
          }
        },
        {
          "x": 105,
          "y": 0,
          "width": 105,
          "height": 148,
          "rotation": 0,
          "trim": {
            "x": 105,
            "y": 0,
            "width": 105,
            "height": 148
          }
        },
        {
          "x": 0,
          "y": 148,
          "width": 105,
          "height": 148,
          "rotation": 0,
          "trim": {
            "x": 0,
            "y": 148,
            "width": 105,
            "height": 148
          }
        },
        {
          "x": 105,
          "y": 148,
          "width": 105,
          "height": 148,
          "rotation": 0,
          "trim": {
            "x": 105,
            "y": 148,
            "width": 105,
            "height": 148
          }
        }
      ]
    },
    {
      "id": "a6-on-a4-bleed-only",
      "label": "A6 on A4: 3 mm bleed only",
      "family": "A6 on A4",
      "configuration": "bleed-only",
      "input": {
        "sheetWidth": 210,
        "sheetHeight": 297,
        "itemWidth": 105,
        "itemHeight": 148,
        "margin": 0,
        "bleed": 3,
        "gap": 0,
        "targetCount": 1,
        "allowRotation": true
      },
      "metrics": {
        "constructedCount": 2,
        "uniformCount": 2,
        "areaUpperBound": 3,
        "gainOverUniform": 0,
        "usableWidthMm": 210,
        "usableHeightMm": 297,
        "footprintWidthMm": 111,
        "footprintHeightMm": 154,
        "trimCoveragePercent": 49.832
      },
      "method": "uniform-rotated",
      "areaBoundMet": false,
      "positions": [
        {
          "x": 0,
          "y": 0,
          "width": 154,
          "height": 111,
          "rotation": 90,
          "trim": {
            "x": 3,
            "y": 3,
            "width": 148,
            "height": 105
          }
        },
        {
          "x": 0,
          "y": 111,
          "width": 154,
          "height": 111,
          "rotation": 90,
          "trim": {
            "x": 3,
            "y": 114,
            "width": 148,
            "height": 105
          }
        }
      ]
    },
    {
      "id": "a6-on-a4-margin-gap",
      "label": "A6 on A4: 5 mm margins and 3 mm gaps",
      "family": "A6 on A4",
      "configuration": "margin-gap",
      "input": {
        "sheetWidth": 210,
        "sheetHeight": 297,
        "itemWidth": 105,
        "itemHeight": 148,
        "margin": 5,
        "bleed": 0,
        "gap": 3,
        "targetCount": 1,
        "allowRotation": true
      },
      "metrics": {
        "constructedCount": 2,
        "uniformCount": 2,
        "areaUpperBound": 3,
        "gainOverUniform": 0,
        "usableWidthMm": 200,
        "usableHeightMm": 287,
        "footprintWidthMm": 105,
        "footprintHeightMm": 148,
        "trimCoveragePercent": 49.832
      },
      "method": "uniform-rotated",
      "areaBoundMet": false,
      "positions": [
        {
          "x": 5,
          "y": 5,
          "width": 148,
          "height": 105,
          "rotation": 90,
          "trim": {
            "x": 5,
            "y": 5,
            "width": 148,
            "height": 105
          }
        },
        {
          "x": 5,
          "y": 113,
          "width": 148,
          "height": 105,
          "rotation": 90,
          "trim": {
            "x": 5,
            "y": 113,
            "width": 148,
            "height": 105
          }
        }
      ]
    },
    {
      "id": "a6-on-a4-full-allowances",
      "label": "A6 on A4: 5 mm margins, 3 mm bleed and gaps",
      "family": "A6 on A4",
      "configuration": "full-allowances",
      "input": {
        "sheetWidth": 210,
        "sheetHeight": 297,
        "itemWidth": 105,
        "itemHeight": 148,
        "margin": 5,
        "bleed": 3,
        "gap": 3,
        "targetCount": 1,
        "allowRotation": true
      },
      "metrics": {
        "constructedCount": 2,
        "uniformCount": 2,
        "areaUpperBound": 3,
        "gainOverUniform": 0,
        "usableWidthMm": 200,
        "usableHeightMm": 287,
        "footprintWidthMm": 111,
        "footprintHeightMm": 154,
        "trimCoveragePercent": 49.832
      },
      "method": "uniform-rotated",
      "areaBoundMet": false,
      "positions": [
        {
          "x": 5,
          "y": 5,
          "width": 154,
          "height": 111,
          "rotation": 90,
          "trim": {
            "x": 8,
            "y": 8,
            "width": 148,
            "height": 105
          }
        },
        {
          "x": 5,
          "y": 119,
          "width": 154,
          "height": 111,
          "rotation": 90,
          "trim": {
            "x": 8,
            "y": 122,
            "width": 148,
            "height": 105
          }
        }
      ]
    },
    {
      "id": "a6-on-a3-nominal",
      "label": "A6 on A3: no allowances",
      "family": "A6 on A3",
      "configuration": "nominal",
      "input": {
        "sheetWidth": 297,
        "sheetHeight": 420,
        "itemWidth": 105,
        "itemHeight": 148,
        "margin": 0,
        "bleed": 0,
        "gap": 0,
        "targetCount": 1,
        "allowRotation": true
      },
      "metrics": {
        "constructedCount": 8,
        "uniformCount": 8,
        "areaUpperBound": 8,
        "gainOverUniform": 0,
        "usableWidthMm": 297,
        "usableHeightMm": 420,
        "footprintWidthMm": 105,
        "footprintHeightMm": 148,
        "trimCoveragePercent": 99.663
      },
      "method": "uniform-rotated",
      "areaBoundMet": true,
      "positions": [
        {
          "x": 0,
          "y": 0,
          "width": 148,
          "height": 105,
          "rotation": 90,
          "trim": {
            "x": 0,
            "y": 0,
            "width": 148,
            "height": 105
          }
        },
        {
          "x": 148,
          "y": 0,
          "width": 148,
          "height": 105,
          "rotation": 90,
          "trim": {
            "x": 148,
            "y": 0,
            "width": 148,
            "height": 105
          }
        },
        {
          "x": 0,
          "y": 105,
          "width": 148,
          "height": 105,
          "rotation": 90,
          "trim": {
            "x": 0,
            "y": 105,
            "width": 148,
            "height": 105
          }
        },
        {
          "x": 148,
          "y": 105,
          "width": 148,
          "height": 105,
          "rotation": 90,
          "trim": {
            "x": 148,
            "y": 105,
            "width": 148,
            "height": 105
          }
        },
        {
          "x": 0,
          "y": 210,
          "width": 148,
          "height": 105,
          "rotation": 90,
          "trim": {
            "x": 0,
            "y": 210,
            "width": 148,
            "height": 105
          }
        },
        {
          "x": 148,
          "y": 210,
          "width": 148,
          "height": 105,
          "rotation": 90,
          "trim": {
            "x": 148,
            "y": 210,
            "width": 148,
            "height": 105
          }
        },
        {
          "x": 0,
          "y": 315,
          "width": 148,
          "height": 105,
          "rotation": 90,
          "trim": {
            "x": 0,
            "y": 315,
            "width": 148,
            "height": 105
          }
        },
        {
          "x": 148,
          "y": 315,
          "width": 148,
          "height": 105,
          "rotation": 90,
          "trim": {
            "x": 148,
            "y": 315,
            "width": 148,
            "height": 105
          }
        }
      ]
    },
    {
      "id": "a6-on-a3-bleed-only",
      "label": "A6 on A3: 3 mm bleed only",
      "family": "A6 on A3",
      "configuration": "bleed-only",
      "input": {
        "sheetWidth": 297,
        "sheetHeight": 420,
        "itemWidth": 105,
        "itemHeight": 148,
        "margin": 0,
        "bleed": 3,
        "gap": 0,
        "targetCount": 1,
        "allowRotation": true
      },
      "metrics": {
        "constructedCount": 5,
        "uniformCount": 4,
        "areaUpperBound": 7,
        "gainOverUniform": 1,
        "usableWidthMm": 297,
        "usableHeightMm": 420,
        "footprintWidthMm": 111,
        "footprintHeightMm": 154,
        "trimCoveragePercent": 62.29
      },
      "method": "mixed-rows",
      "areaBoundMet": false,
      "positions": [
        {
          "x": 0,
          "y": 0,
          "width": 111,
          "height": 154,
          "rotation": 0,
          "trim": {
            "x": 3,
            "y": 3,
            "width": 105,
            "height": 148
          }
        },
        {
          "x": 111,
          "y": 0,
          "width": 111,
          "height": 154,
          "rotation": 0,
          "trim": {
            "x": 114,
            "y": 3,
            "width": 105,
            "height": 148
          }
        },
        {
          "x": 0,
          "y": 154,
          "width": 111,
          "height": 154,
          "rotation": 0,
          "trim": {
            "x": 3,
            "y": 157,
            "width": 105,
            "height": 148
          }
        },
        {
          "x": 111,
          "y": 154,
          "width": 111,
          "height": 154,
          "rotation": 0,
          "trim": {
            "x": 114,
            "y": 157,
            "width": 105,
            "height": 148
          }
        },
        {
          "x": 0,
          "y": 308,
          "width": 154,
          "height": 111,
          "rotation": 90,
          "trim": {
            "x": 3,
            "y": 311,
            "width": 148,
            "height": 105
          }
        }
      ]
    },
    {
      "id": "a6-on-a3-margin-gap",
      "label": "A6 on A3: 5 mm margins and 3 mm gaps",
      "family": "A6 on A3",
      "configuration": "margin-gap",
      "input": {
        "sheetWidth": 297,
        "sheetHeight": 420,
        "itemWidth": 105,
        "itemHeight": 148,
        "margin": 5,
        "bleed": 0,
        "gap": 3,
        "targetCount": 1,
        "allowRotation": true
      },
      "metrics": {
        "constructedCount": 5,
        "uniformCount": 4,
        "areaUpperBound": 7,
        "gainOverUniform": 1,
        "usableWidthMm": 287,
        "usableHeightMm": 410,
        "footprintWidthMm": 105,
        "footprintHeightMm": 148,
        "trimCoveragePercent": 62.29
      },
      "method": "mixed-rows",
      "areaBoundMet": false,
      "positions": [
        {
          "x": 5,
          "y": 5,
          "width": 105,
          "height": 148,
          "rotation": 0,
          "trim": {
            "x": 5,
            "y": 5,
            "width": 105,
            "height": 148
          }
        },
        {
          "x": 113,
          "y": 5,
          "width": 105,
          "height": 148,
          "rotation": 0,
          "trim": {
            "x": 113,
            "y": 5,
            "width": 105,
            "height": 148
          }
        },
        {
          "x": 5,
          "y": 156,
          "width": 105,
          "height": 148,
          "rotation": 0,
          "trim": {
            "x": 5,
            "y": 156,
            "width": 105,
            "height": 148
          }
        },
        {
          "x": 113,
          "y": 156,
          "width": 105,
          "height": 148,
          "rotation": 0,
          "trim": {
            "x": 113,
            "y": 156,
            "width": 105,
            "height": 148
          }
        },
        {
          "x": 5,
          "y": 307,
          "width": 148,
          "height": 105,
          "rotation": 90,
          "trim": {
            "x": 5,
            "y": 307,
            "width": 148,
            "height": 105
          }
        }
      ]
    },
    {
      "id": "a6-on-a3-full-allowances",
      "label": "A6 on A3: 5 mm margins, 3 mm bleed and gaps",
      "family": "A6 on A3",
      "configuration": "full-allowances",
      "input": {
        "sheetWidth": 297,
        "sheetHeight": 420,
        "itemWidth": 105,
        "itemHeight": 148,
        "margin": 5,
        "bleed": 3,
        "gap": 3,
        "targetCount": 1,
        "allowRotation": true
      },
      "metrics": {
        "constructedCount": 5,
        "uniformCount": 4,
        "areaUpperBound": 6,
        "gainOverUniform": 1,
        "usableWidthMm": 287,
        "usableHeightMm": 410,
        "footprintWidthMm": 111,
        "footprintHeightMm": 154,
        "trimCoveragePercent": 62.29
      },
      "method": "mixed-columns",
      "areaBoundMet": false,
      "positions": [
        {
          "x": 5,
          "y": 5,
          "width": 111,
          "height": 154,
          "rotation": 0,
          "trim": {
            "x": 8,
            "y": 8,
            "width": 105,
            "height": 148
          }
        },
        {
          "x": 5,
          "y": 162,
          "width": 111,
          "height": 154,
          "rotation": 0,
          "trim": {
            "x": 8,
            "y": 165,
            "width": 105,
            "height": 148
          }
        },
        {
          "x": 119,
          "y": 5,
          "width": 154,
          "height": 111,
          "rotation": 90,
          "trim": {
            "x": 122,
            "y": 8,
            "width": 148,
            "height": 105
          }
        },
        {
          "x": 119,
          "y": 119,
          "width": 154,
          "height": 111,
          "rotation": 90,
          "trim": {
            "x": 122,
            "y": 122,
            "width": 148,
            "height": 105
          }
        },
        {
          "x": 119,
          "y": 233,
          "width": 154,
          "height": 111,
          "rotation": 90,
          "trim": {
            "x": 122,
            "y": 236,
            "width": 148,
            "height": 105
          }
        }
      ]
    },
    {
      "id": "a6-on-sra3-nominal",
      "label": "A6 on SRA3: no allowances",
      "family": "A6 on SRA3",
      "configuration": "nominal",
      "input": {
        "sheetWidth": 320,
        "sheetHeight": 450,
        "itemWidth": 105,
        "itemHeight": 148,
        "margin": 0,
        "bleed": 0,
        "gap": 0,
        "targetCount": 1,
        "allowRotation": true
      },
      "metrics": {
        "constructedCount": 9,
        "uniformCount": 9,
        "areaUpperBound": 9,
        "gainOverUniform": 0,
        "usableWidthMm": 320,
        "usableHeightMm": 450,
        "footprintWidthMm": 105,
        "footprintHeightMm": 148,
        "trimCoveragePercent": 97.125
      },
      "method": "uniform-upright",
      "areaBoundMet": true,
      "positions": [
        {
          "x": 0,
          "y": 0,
          "width": 105,
          "height": 148,
          "rotation": 0,
          "trim": {
            "x": 0,
            "y": 0,
            "width": 105,
            "height": 148
          }
        },
        {
          "x": 105,
          "y": 0,
          "width": 105,
          "height": 148,
          "rotation": 0,
          "trim": {
            "x": 105,
            "y": 0,
            "width": 105,
            "height": 148
          }
        },
        {
          "x": 210,
          "y": 0,
          "width": 105,
          "height": 148,
          "rotation": 0,
          "trim": {
            "x": 210,
            "y": 0,
            "width": 105,
            "height": 148
          }
        },
        {
          "x": 0,
          "y": 148,
          "width": 105,
          "height": 148,
          "rotation": 0,
          "trim": {
            "x": 0,
            "y": 148,
            "width": 105,
            "height": 148
          }
        },
        {
          "x": 105,
          "y": 148,
          "width": 105,
          "height": 148,
          "rotation": 0,
          "trim": {
            "x": 105,
            "y": 148,
            "width": 105,
            "height": 148
          }
        },
        {
          "x": 210,
          "y": 148,
          "width": 105,
          "height": 148,
          "rotation": 0,
          "trim": {
            "x": 210,
            "y": 148,
            "width": 105,
            "height": 148
          }
        },
        {
          "x": 0,
          "y": 296,
          "width": 105,
          "height": 148,
          "rotation": 0,
          "trim": {
            "x": 0,
            "y": 296,
            "width": 105,
            "height": 148
          }
        },
        {
          "x": 105,
          "y": 296,
          "width": 105,
          "height": 148,
          "rotation": 0,
          "trim": {
            "x": 105,
            "y": 296,
            "width": 105,
            "height": 148
          }
        },
        {
          "x": 210,
          "y": 296,
          "width": 105,
          "height": 148,
          "rotation": 0,
          "trim": {
            "x": 210,
            "y": 296,
            "width": 105,
            "height": 148
          }
        }
      ]
    },
    {
      "id": "a6-on-sra3-bleed-only",
      "label": "A6 on SRA3: 3 mm bleed only",
      "family": "A6 on SRA3",
      "configuration": "bleed-only",
      "input": {
        "sheetWidth": 320,
        "sheetHeight": 450,
        "itemWidth": 105,
        "itemHeight": 148,
        "margin": 0,
        "bleed": 3,
        "gap": 0,
        "targetCount": 1,
        "allowRotation": true
      },
      "metrics": {
        "constructedCount": 8,
        "uniformCount": 8,
        "areaUpperBound": 8,
        "gainOverUniform": 0,
        "usableWidthMm": 320,
        "usableHeightMm": 450,
        "footprintWidthMm": 111,
        "footprintHeightMm": 154,
        "trimCoveragePercent": 86.333
      },
      "method": "uniform-rotated",
      "areaBoundMet": true,
      "positions": [
        {
          "x": 0,
          "y": 0,
          "width": 154,
          "height": 111,
          "rotation": 90,
          "trim": {
            "x": 3,
            "y": 3,
            "width": 148,
            "height": 105
          }
        },
        {
          "x": 154,
          "y": 0,
          "width": 154,
          "height": 111,
          "rotation": 90,
          "trim": {
            "x": 157,
            "y": 3,
            "width": 148,
            "height": 105
          }
        },
        {
          "x": 0,
          "y": 111,
          "width": 154,
          "height": 111,
          "rotation": 90,
          "trim": {
            "x": 3,
            "y": 114,
            "width": 148,
            "height": 105
          }
        },
        {
          "x": 154,
          "y": 111,
          "width": 154,
          "height": 111,
          "rotation": 90,
          "trim": {
            "x": 157,
            "y": 114,
            "width": 148,
            "height": 105
          }
        },
        {
          "x": 0,
          "y": 222,
          "width": 154,
          "height": 111,
          "rotation": 90,
          "trim": {
            "x": 3,
            "y": 225,
            "width": 148,
            "height": 105
          }
        },
        {
          "x": 154,
          "y": 222,
          "width": 154,
          "height": 111,
          "rotation": 90,
          "trim": {
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