THE REPRODUCIBLE WORKBENCH
What fits. What can be checked.
Twenty-four finite test cases, complete placement coordinates and an independent geometry verifier. Compare constructed print layouts with a simple uniform grid, then inspect the limits of each result.
The result, with its limits
In this curated suite, the planner constructs more pieces than its best uniform grid in 9 of 24 cases. The largest improvement is 3 pieces per sheet. Every published placement passes separate checks for dimensions, usable bounds, rotation, bleed and the gap between every pair of pieces.
8 cases reach a valid area upper bound. Those constructions establish a maximum for the stated dimensions and allowances. The remaining cases are feasible arrangements, not claims that no better packing exists. These are deliberately selected examples, not a representative survey of print work and not a performance score.
What changes when allowances are added?
Each of five common sheet/item families appears under four settings: no allowances; 3 mm bleed only; 5 mm margins with 3 mm gaps; and all three allowances together. The finished trim size remains unchanged. The last four cases compare A4 full-bleed stock choices and exercise two synthetic boundary conditions.
The table below compares the constructed count without allowances with the full-allowance result. The final column is the independently recalculated uniform baseline under those same full allowances.
| Sheet and item | No allowances | All allowances | Uniform, all allowances |
|---|---|---|---|
| A6 on A4 | 4 | 2 | 2 |
| A6 on A3 | 8 | 5 | 4 |
| A6 on SRA3 | 9 | 5 | 4 |
| 85 × 55 mm cards on A4 | 11 | 9 | 9 |
| 85 × 55 mm cards on A3 | 24 | 18 | 18 |
A construction is different from a maximum
The planner tests upright and rotated uniform grids, two-zone mixed rows and columns, and repeated four-piece pinwheels. For example, the A6-on-A3 worked plan constructs five pieces where the best uniform grid fits four, with 5 mm margins, 3 mm bleed and 3 mm gaps. That improvement is real geometry; it does not prove that every possible arrangement has been searched.
Our independent upper bound divides the usable sheet area by one complete bleed footprint's area, then rounds down. It ignores gutters, so it can overestimate what fits. If a verified construction reaches that bound, however, another arrangement cannot fit an extra footprint into the available area. Otherwise the difference between construction and bound remains unresolved by this benchmark.
The synthetic pinwheel uses a 20 × 20 mm sheet and 12 × 8 mm pieces. Its four-piece arrangement reaches an area bound of four. The separate 0.001 mm-gap case deliberately checks that a small positive gap is not rounded away at an exact-fit boundary. Neither control describes a recommended print specification.
All 24 cases
Counts are pieces per sheet. Select a case to load its inputs in the planner. JSON retains every coordinate; CSV contains one summary row per case.
| Stable case | Uniform | Constructed | Area bound | Certification | Chosen method |
|---|---|---|---|---|---|
| A6 on A4: no allowances | 4 | 4 | 4 | Area bound met | uniform-upright |
| A6 on A4: 3 mm bleed only | 2 | 2 | 3 | Construction only | uniform-rotated |
| A6 on A4: 5 mm margins and 3 mm gaps | 2 | 2 | 3 | Construction only | uniform-rotated |
| A6 on A4: 5 mm margins, 3 mm bleed and gaps | 2 | 2 | 3 | Construction only | uniform-rotated |
| A6 on A3: no allowances | 8 | 8 | 8 | Area bound met | uniform-rotated |
| A6 on A3: 3 mm bleed only | 4 | 5 | 7 | Construction only | mixed-rows |
| A6 on A3: 5 mm margins and 3 mm gaps | 4 | 5 | 7 | Construction only | mixed-rows |
| A6 on A3: 5 mm margins, 3 mm bleed and gaps | 4 | 5 | 6 | Construction only | mixed-columns |
| A6 on SRA3: no allowances | 9 | 9 | 9 | Area bound met | uniform-upright |
| A6 on SRA3: 3 mm bleed only | 8 | 8 | 8 | Area bound met | uniform-rotated |
| A6 on SRA3: 5 mm margins and 3 mm gaps | 8 | 8 | 8 | Area bound met | uniform-rotated |
| A6 on SRA3: 5 mm margins, 3 mm bleed and gaps | 4 | 5 | 7 | Construction only | mixed-rows |
| 85 × 55 mm cards on A4: no allowances | 10 | 11 | 13 | Construction only | mixed-columns |
| 85 × 55 mm cards on A4: 3 mm bleed only | 9 | 9 | 11 | Construction only | uniform-rotated |
| 85 × 55 mm cards on A4: 5 mm margins and 3 mm gaps | 10 | 10 | 12 | Construction only | uniform-upright |
| 85 × 55 mm cards on A4: 5 mm margins, 3 mm bleed and gaps | 9 | 9 | 10 | Construction only | uniform-rotated |
| 85 × 55 mm cards on A3: no allowances | 21 | 24 | 26 | Construction only | mixed-rows |
| 85 × 55 mm cards on A3: 3 mm bleed only | 18 | 19 | 22 | Construction only | mixed-rows |
| 85 × 55 mm cards on A3: 5 mm margins and 3 mm gaps | 21 | 23 | 25 | Construction only | mixed-rows |
| 85 × 55 mm cards on A3: 5 mm margins, 3 mm bleed and gaps | 18 | 18 | 21 | Construction only | uniform-upright |
| A4 on A3: 5 mm margins, 3 mm bleed and gaps | 1 | 1 | 1 | Area bound met | uniform-upright |
| A4 on SRA3: 5 mm margins, 3 mm bleed and gaps | 2 | 2 | 2 | Area bound met | uniform-rotated |
| Synthetic pinwheel: 12 × 8 mm in a 20 mm square | 2 | 4 | 4 | Area bound met | pinwheel-tiles |
| Exact-fit boundary: 50 mm squares with a 0.001 mm gap | 1 | 1 | 4 | Construction only | uniform-upright |
Verify the published coordinates
Download the JSON and verifier into the same folder. With current Node.js, run node verify-layout-benchmark.mjs layout-benchmark.json. A browser can import the same module and call verifyBenchmark(data) and await verifyChecksum(data). There are no third-party dependencies or remote calls in the verifier.
The check uses integer thousandths of a millimetre. It recomputes the best uniform count and usable-area bound, checks every footprint and trim box, and requires the full stated gutter on at least one axis between every pair. It also verifies the JSON's SHA-256 content checksum. It validates the published constructions rather than rerunning the packing search or establishing an unknown optimum.
Benchmark schema and method version: 1. Engine source SHA-256: f793e2478837d147b87452862474b17b5611b95454dbe3dc316868b44c23d409. The JSON includes a separate checksum over its content, excluding its checksum object, using recursively sorted object keys and retained array order. Rebuilding unchanged inputs and engine source preserves the result.
Sources and assumptions
A3, A4 and A6 use nominal millimetre dimensions from Adobe's published A-series table, under the trimmed-format scope of ISO 216. SRA3 uses the 320 × 450 mm listing in Fujifilm's paper catalogue. The 85 × 55 mm card is a chosen fixture, not a claim about every business-card standard.
Bleed is added outside each trim edge; gutter is additional separation between complete bleed footprints. See the region definitions and Adobe's bleed setup guidance. Margins and gaps here are test inputs. Printer limits, crop marks, gripper, grain, artwork, cutting order and physical tolerances are not detected. Use the result for planning and measure a test at actual size.