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FA-80061 / Typography line breaking / Open access

Box-glue-penalty breakpoints: overflow trigger · case 01

Lines that exactly fill the measure are broken early.

Verified by executionVariant 1 · 8 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The overflow test uses >= width.

THE FAILURE

The overflow test uses >= width.

Unsuccessful approach: Allowing one extra unit produces overfull lines.

Case contract

Input [items, width]; items are ["b",w], ["g",w] or ["p",w,cost,flag]. Legal breaks: glue immediately after a box; penalty with cost < 10000 (width counted only if broken there); cost <= -10000 forces a break. Discardable glue/penalties at a line start are dropped. First-fit: when the running width exceeds the measure, break at the last legal breakpoint. Return [[line width, break kind]] with kinds glue/penalty/forced/end.

Why this case matters

Line breaking decides where paragraphs wrap on screen and in print; a wrong decision point shifts every following line.

1 / The failure

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(x):
    items, width = x
    lines = []
    start = 0
    n = len(items)
    while start < n:
        while start < n and items[start][0] != 'b':
            start += 1
        if start >= n:
            break
        total = 0
        last = None
        result = None
        i = start
        while i < n:
            it = items[i]
            if it[0] == 'p':
                if it[2] <= -10000:
                    result = (i, total + it[1], 'forced')
                    break
                if it[2] < 10000:
                    last = (i, total + it[1], 'penalty')
            elif it[0] == 'g':
                if items[i - 1][0] == 'b':
                    last = (i, total, 'glue')
                total += it[1]
            else:
                total += it[1]
            if total >= width and last is not None:
                result = last
                break
            i += 1
        if result is None:
            lines.append([total, 'end'])
            break
        lines.append([result[1], result[2]])
        start = result[0] + 1
    return lines
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: overflow trigger', [[['b', 2], ['g', 1], ['b', 6], ['g', 2], ['b', 4], ['p', 0, 9999, False], ['g', 1], ['b', 1], ['g', 1], ['b', 5], ['g', 2], ['b', 4], ['p', 0, 10000, False], ['g', 2], ['b', 1], ['p', 1, 50, True], ['g', 1]], 9], [[9, 'glue'], [6, 'glue'], [5, 'glue'], [8, 'end']]), ('regression: overflow trigger', [[['b', 5], ['p', 0, -10000, False], ['g', 1], ['b', 5], ['g', 2], ['b', 2], ['p', 1, 50, True], ['g', 2], ['b', 2], ['p', 0, 10000, False], ['g', 2], ['b', 7], ['g', 1], ['g', 1], ['b', 7], ['g', 1], ['b', 5], ['g', 1], ['b', 1], ['g', 1], ['b', 2], ['g', 1]], 7], [[5, 'forced'], [5, 'glue'], [3, 'penalty'], [11, 'glue'], [7, 'glue'], [7, 'glue'], [3, 'end']]), ('regression: overflow trigger', [[['b', 6], ['g', 1], ['b', 3], ['g', 1], ['b', 1], ['p', 1, 50, True], ['g', 2], ['b', 7], ['g', 1], ['b', 1], ['g', 1], ['b', 7], ['p', 0, -10000, False], ['g', 1], ['g', 1], ['b', 1], ['p', 1, 50, True], ['p', 1, 50, True], ['g', 1]], 9], [[6, 'glue'], [6, 'penalty'], [9, 'glue'], [7, 'forced'], [2, 'end']]), ('partial-repair probe', [[['b', 4], ['p', 0, -10000, False], ['g', 1], ['b', 4], ['g', 1], ['b', 4], ['g', 1], ['b', 5], ['p', 1, 50, True], ['g', 2], ['b', 2], ['p', 1, 50, True], ['g', 1], ['b', 2], ['p', 0, 10000, False], ['g', 1], ['b', 7], ['p', 1, 50, True], ['g', 1], ['b', 7], ['p', 0, 9999, False], ['g', 1], ['b', 2], ['g', 2]], 8], [[4, 'forced'], [4, 'glue'], [4, 'glue'], [6, 'penalty'], [3, 'penalty'], [11, 'penalty'], [7, 'penalty'], [4, 'end']]), ('hyphen penalty taken', [[['b', 5], ['p', 1, 50, True], ['b', 4], ['g', 1], ['b', 3]], 7], [[6, 'penalty'], [4, 'glue'], [3, 'end']]), ('inhibited penalty', [[['b', 5], ['p', 0, 10000, False], ['b', 4], ['g', 1], ['b', 3]], 7], [[9, 'glue'], [3, 'end']]), ('control layout', [[['b', 2], ['g', 2], ['b', 2], ['g', 1], ['b', 3], ['g', 2], ['b', 7], ['p', 0, 9999, False], ['g', 1], ['b', 6], ['p', 1, 50, True], ['g', 2], ['b', 3], ['p', 0, 10000, False], ['g', 2], ['b', 4], ['p', 1, 50, True], ['g', 1], ['b', 7], ['g', 1], ['g', 1], ['b', 2], ['p', 0, 900, False], ['p', 1, 50, True], ['g', 1]], 15], [[10, 'glue'], [15, 'penalty'], [10, 'penalty'], [12, 'end']]), ('control layout', [[['b', 7], ['g', 2], ['b', 7], ['p', 0, 9999, False], ['g', 1], ['b', 5], ['g', 1], ['b', 7], ['g', 2], ['b', 5], ['g', 2], ['b', 1], ['p', 0, 900, False], ['g', 2], ['b', 3], ['p', 1, 50, True], ['g', 2]], 10], [[7, 'glue'], [7, 'penalty'], [5, 'glue'], [7, 'glue'], [8, 'penalty'], [5, 'end']])], [('regression: overflow trigger', [[['b', 1], ['g', 1], ['b', 5], ['g', 2], ['b', 4], ['g', 1], ['b', 6], ['g', 1], ['b', 1], ['p', 0, -10000, False], ['g', 1], ['b', 4], ['g', 2], ['b', 1], ['g', 1], ['b', 4], ['p', 0, 9999, False], ['g', 2], ['b', 6], ['p', 0, -5000, False], ['g', 1], ['g', 1], ['b', 3], ['p', 1, 50, True], ['g', 2]], 7], [[7, 'glue'], [4, 'glue'], [6, 'glue'], [1, 'forced'], [7, 'glue'], [4, 'penalty'], [6, 'penalty'], [5, 'end']]), ('regression: overflow trigger', [[['b', 5], ['p', 1, 50, True], ['g', 1], ['b', 5], ['g', 2], ['b', 2], ['g', 1], ['b', 2], ['g', 2], ['b', 5], ['p', 1, 50, True], ['g', 1], ['b', 6], ['p', 0, -10000, False], ['g', 1], ['b', 4], ['g', 1], ['g', 1], ['b', 4], ['g', 1], ['b', 6], ['g', 1], ['g', 1]], 8], [[6, 'penalty'], [5, 'glue'], [5, 'glue'], [6, 'penalty'], [6, 'forced'], [4, 'glue'], [4, 'glue'], [8, 'end']]), ('partial-repair probe', [[['b', 1], ['g', 2], ['b', 5], ['p', 1, 50, True], ['g', 2], ['b', 6], ['p', 1, 50, True], ['g', 1], ['b', 7], ['p', 1, 50, True], ['g', 1], ['b', 2], ['g', 1], ['b', 2], ['g', 2], ['b', 4], ['g', 2]], 12], [[9, 'penalty'], [7, 'penalty'], [10, 'glue'], [10, 'end']]), ('regression: overflow trigger', [[['b', 6], ['p', 1, 50, True], ['g', 1], ['g', 1], ['b', 6], ['p', 0, 10000, False], ['g', 1], ['b', 2], ['p', 0, -10000, False], ['g', 2], ['b', 1], ['p', 0, 10000, False], ['g', 2], ['b', 7], ['g', 2], ['b', 1], ['p', 0, -10000, False], ['g', 1], ['b', 3], ['g', 2], ['b', 2], ['p', 0, 900, False], ['g', 2], ['b', 1], ['p', 1, 50, True], ['g', 1], ['b', 6], ['g', 2]], 7], [[7, 'penalty'], [9, 'forced'], [10, 'glue'], [1, 'forced'], [7, 'penalty'], [2, 'penalty'], [6, 'glue']]), ('hyphen penalty taken', [[['b', 5], ['p', 1, 50, True], ['b', 4], ['g', 1], ['b', 3]], 7], [[6, 'penalty'], [4, 'glue'], [3, 'end']]), ('inhibited penalty', [[['b', 5], ['p', 0, 10000, False], ['b', 4], ['g', 1], ['b', 3]], 7], [[9, 'glue'], [3, 'end']]), ('control layout', [[['b', 4], ['g', 2], ['b', 4], ['g', 2], ['b', 3], ['p', 0, -10000, False], ['g', 1], ['g', 1], ['b', 6], ['p', 1, 50, True], ['g', 2], ['b', 1], ['g', 2], ['b', 2], ['p', 0, -10000, False], ['g', 2], ['b', 5], ['g', 2], ['b', 2], ['p', 0, 10000, False], ['g', 1], ['b', 3], ['p', 1, 50, True], ['g', 2], ['b', 3], ['p', 0, 10000, False], ['g', 2]], 18], [[15, 'forced'], [13, 'forced'], [14, 'penalty'], [5, 'end']]), ('control layout', [[['b', 3], ['g', 2], ['b', 5], ['g', 2], ['b', 2], ['g', 1], ['b', 7], ['g', 1], ['b', 7], ['g', 2], ['b', 2], ['g', 1], ['g', 1], ['b', 7], ['p', 1, 50, True], ['g', 1]], 16], [[14, 'glue'], [15, 'glue'], [12, 'end']])], [('regression: overflow trigger', [[['b', 2], ['g', 1], ['b', 4], ['g', 2], ['b', 1], ['p', 1, 50, True], ['g', 1], ['b', 6], ['g', 2], ['b', 6], ['g', 1], ['b', 7], ['g', 2], ['b', 6], ['g', 1]], 16], [[11, 'penalty'], [14, 'glue'], [16, 'end']]), ('regression: overflow trigger', [[['b', 5], ['p', 1, 50, True], ['g', 2], ['b', 3], ['g', 1], ['b', 2], ['g', 2], ['b', 5], ['g', 1], ['b', 2], ['g', 2], ['b', 7], ['g', 1], ['g', 1]], 17], [[13, 'glue'], [17, 'glue']]), ('partial-repair probe', [[['b', 5], ['p', 0, -5000, False], ['g', 2], ['b', 7], ['g', 2], ['b', 4], ['p', 1, 50, True], ['g', 1], ['g', 1], ['b', 5], ['g', 1], ['b', 7], ['g', 2], ['b', 6], ['p', 1, 50, True], ['g', 1]], 12], [[5, 'penalty'], [7, 'glue'], [11, 'glue'], [7, 'glue'], [7, 'end']]), ('partial-repair probe', [[['b', 2], ['g', 1], ['b', 3], ['p', 1, 50, True], ['g', 1], ['b', 6], ['p', 0, 900, False], ['g', 1], ['b', 7], ['g', 1], ['b', 7], ['g', 1]], 7], [[7, 'penalty'], [6, 'penalty'], [7, 'glue'], [7, 'glue']]), ('inhibited penalty', [[['b', 5], ['p', 0, 10000, False], ['b', 4], ['g', 1], ['b', 3]], 7], [[9, 'glue'], [3, 'end']]), ('hyphen penalty taken', [[['b', 5], ['p', 1, 50, True], ['b', 4], ['g', 1], ['b', 3]], 7], [[6, 'penalty'], [4, 'glue'], [3, 'end']]), ('control layout', [[['b', 4], ['g', 1], ['b', 5], ['g', 1], ['b', 4], ['g', 1], ['b', 2], ['g', 2], ['b', 2], ['g', 1], ['b', 5], ['g', 1]], 12], [[10, 'glue'], [11, 'glue'], [6, 'end']]), ('control layout', [[['b', 6], ['g', 1], ['g', 1], ['b', 4], ['g', 1], ['b', 5], ['p', 0, -10000, False], ['g', 1], ['b', 4], ['p', 1, 50, True], ['g', 1], ['b', 1], ['p', 1, 50, True], ['g', 2]], 14], [[12, 'glue'], [5, 'forced'], [8, 'end']])], [('regression: overflow trigger', [[['b', 5], ['g', 1], ['g', 1], ['b', 4], ['g', 1], ['b', 3], ['p', 0, -5000, False], ['g', 2], ['b', 4], ['p', 1, 50, True], ['g', 1], ['b', 4], ['g', 2], ['b', 5], ['g', 2]], 11], [[11, 'glue'], [10, 'penalty'], [11, 'glue']]), ('regression: overflow trigger', [[['b', 2], ['g', 1], ['b', 6], ['g', 1], ['b', 1], ['g', 1], ['b', 5], ['g', 2], ['b', 4], ['p', 1, 50, True], ['g', 2], ['b', 7], ['p', 1, 50, True], ['g', 1], ['b', 4], ['g', 1]], 8], [[2, 'glue'], [8, 'glue'], [5, 'glue'], [5, 'penalty'], [8, 'penalty'], [5, 'end']]), ('regression: overflow trigger', [[['b', 2], ['g', 1], ['b', 4], ['g', 2], ['b', 1], ['p', 1, 50, True], ['g', 1], ['b', 6], ['g', 2], ['b', 6], ['g', 1], ['b', 7], ['g', 2], ['b', 6], ['g', 1]], 16], [[11, 'penalty'], [14, 'glue'], [16, 'end']]), ('partial-repair probe', [[['b', 3], ['g', 1], ['b', 6], ['g', 1], ['b', 7], ['g', 1], ['b', 6], ['p', 1, 50, True], ['g', 1], ['b', 5], ['p', 1, 50, True], ['g', 1], ['b', 2], ['g', 2], ['b', 3], ['g', 1], ['g', 1]], 17], [[10, 'glue'], [15, 'penalty'], [15, 'end']]), ('forced break', [[['b', 2], ['g', 1], ['b', 2], ['p', 0, -10000, False], ['b', 3]], 20], [[5, 'forced'], [3, 'end']]), ('hyphen penalty taken', [[['b', 5], ['p', 1, 50, True], ['b', 4], ['g', 1], ['b', 3]], 7], [[6, 'penalty'], [4, 'glue'], [3, 'end']]), ('control layout', [[['b', 4], ['p', 1, 50, True], ['g', 2], ['b', 1], ['g', 1], ['g', 1], ['b', 6], ['g', 1], ['b', 1], ['p', 0, -10000, False], ['g', 1], ['b', 7], ['g', 2], ['b', 5], ['g', 1]], 10], [[7, 'glue'], [8, 'forced'], [7, 'glue'], [6, 'end']]), ('control layout', [[['b', 2], ['p', 1, 50, True], ['g', 1], ['b', 5], ['g', 2], ['b', 6], ['g', 2], ['b', 6], ['g', 1], ['b', 1], ['g', 1], ['b', 1], ['p', 1, 50, True], ['g', 1]], 17], [[16, 'glue'], [11, 'end']])], [('regression: overflow trigger', [[['b', 6], ['g', 2], ['b', 3], ['p', 1, 50, True], ['g', 2], ['b', 4], ['g', 2], ['b', 6], ['g', 1], ['b', 7], ['g', 1]], 12], [[12, 'penalty'], [12, 'glue'], [8, 'end']]), ('regression: overflow trigger', [[['b', 3], ['g', 1], ['b', 6], ['g', 1], ['b', 1], ['g', 2], ['b', 3], ['p', 1, 50, True], ['g', 1], ['b', 3], ['g', 1]], 8], [[3, 'glue'], [8, 'glue'], [8, 'end']]), ('regression: overflow trigger', [[['b', 3], ['p', 0, 10000, False], ['g', 2], ['b', 6], ['g', 1], ['b', 7], ['g', 1], ['b', 1], ['p', 1, 50, True], ['g', 1]], 9], [[11, 'glue'], [10, 'penalty']]), ('regression: overflow trigger', [[['b', 6], ['g', 1], ['b', 6], ['g', 2], ['b', 3], ['p', 0, 10000, False], ['g', 1], ['g', 1], ['b', 1], ['p', 0, 10000, False], ['g', 2], ['b', 4], ['g', 1], ['b', 2], ['g', 2], ['b', 5], ['g', 1], ['b', 2], ['g', 1], ['g', 1]], 13], [[13, 'glue'], [12, 'glue'], [12, 'glue']]), ('hyphen penalty taken', [[['b', 5], ['p', 1, 50, True], ['b', 4], ['g', 1], ['b', 3]], 7], [[6, 'penalty'], [4, 'glue'], [3, 'end']]), ('forced break', [[['b', 2], ['g', 1], ['b', 2], ['p', 0, -10000, False], ['b', 3]], 20], [[5, 'forced'], [3, 'end']]), ('control layout', [[['b', 3], ['g', 2], ['b', 3], ['g', 1], ['g', 1], ['b', 3], ['p', 0, 10000, False], ['g', 2], ['b', 1], ['g', 1], ['b', 3], ['g', 1]], 14], [[8, 'glue'], [11, 'end']]), ('control layout', [[['b', 7], ['g', 2], ['b', 7], ['g', 1], ['b', 7], ['g', 1], ['b', 1], ['p', 0, 10000, False], ['g', 1], ['b', 6], ['g', 2], ['b', 7], ['p', 1, 50, True], ['g', 2]], 10], [[7, 'glue'], [7, 'glue'], [7, 'glue'], [8, 'glue'], [9, 'end']])]]
for label, args, expected in fixtures[N - 1]:
    check(label, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
regression: overflow trigger[[2, 'glue'], [6, 'glue'], [6, 'glue'], [5, 'glue'], [8, 'end']][[9, 'glue'], [6, 'glue'], [5, 'glue'], [8, 'end']]Failed
regression: overflow trigger[[5, 'forced'], [5, 'glue'], [3, 'penalty'], [11, 'glue'], [7, 'glue'], [5, 'glue'], [5, 'end']][[5, 'forced'], [5, 'glue'], [3, 'penalty'], [11, 'glue'], [7, 'glue'], [7, 'glue'], [3, 'end']]Failed
regression: overflow trigger[[6, 'glue'], [6, 'penalty'], [7, 'glue'], [1, 'glue'], [7, 'forced'], [2, 'end']][[6, 'glue'], [6, 'penalty'], [9, 'glue'], [7, 'forced'], [2, 'end']]Failed
partial-repair probe[[4, 'forced'], [4, 'glue'], [4, 'glue'], [6, 'penalty'], [3, 'penalty'], [11, 'penalty'], [7, 'penalty'], [4, 'end']][[4, 'forced'], [4, 'glue'], [4, 'glue'], [6, 'penalty'], [3, 'penalty'], [11, 'penalty'], [7, 'penalty'], [4, 'end']]Passed
hyphen penalty taken[[6, 'penalty'], [4, 'glue'], [3, 'end']][[6, 'penalty'], [4, 'glue'], [3, 'end']]Passed
inhibited penalty[[9, 'glue'], [3, 'end']][[9, 'glue'], [3, 'end']]Passed
control layout[[10, 'glue'], [15, 'penalty'], [10, 'penalty'], [12, 'end']][[10, 'glue'], [15, 'penalty'], [10, 'penalty'], [12, 'end']]Passed
control layout[[7, 'glue'], [7, 'penalty'], [5, 'glue'], [7, 'glue'], [8, 'penalty'], [5, 'end']][[7, 'glue'], [7, 'penalty'], [5, 'glue'], [7, 'glue'], [8, 'penalty'], [5, 'end']]Passed

SHA-256 / 2a2a9c058d4ef12af05c8b33abf6f00d6d515c44eb229150447ce2d66bae04ca

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(x):
    items, width = x
    lines = []
    start = 0
    n = len(items)
    while start < n:
        while start < n and items[start][0] != 'b':
            start += 1
        if start >= n:
            break
        total = 0
        last = None
        result = None
        i = start
        while i < n:
            it = items[i]
            if it[0] == 'p':
                if it[2] <= -10000:
                    result = (i, total + it[1], 'forced')
                    break
                if it[2] < 10000:
                    last = (i, total + it[1], 'penalty')
            elif it[0] == 'g':
                if items[i - 1][0] == 'b':
                    last = (i, total, 'glue')
                total += it[1]
            else:
                total += it[1]
            if total > width + 1 and last is not None:
                result = last
                break
            i += 1
        if result is None:
            lines.append([total, 'end'])
            break
        lines.append([result[1], result[2]])
        start = result[0] + 1
    return lines
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: overflow trigger', [[['b', 2], ['g', 1], ['b', 6], ['g', 2], ['b', 4], ['p', 0, 9999, False], ['g', 1], ['b', 1], ['g', 1], ['b', 5], ['g', 2], ['b', 4], ['p', 0, 10000, False], ['g', 2], ['b', 1], ['p', 1, 50, True], ['g', 1]], 9], [[9, 'glue'], [6, 'glue'], [5, 'glue'], [8, 'end']]), ('regression: overflow trigger', [[['b', 5], ['p', 0, -10000, False], ['g', 1], ['b', 5], ['g', 2], ['b', 2], ['p', 1, 50, True], ['g', 2], ['b', 2], ['p', 0, 10000, False], ['g', 2], ['b', 7], ['g', 1], ['g', 1], ['b', 7], ['g', 1], ['b', 5], ['g', 1], ['b', 1], ['g', 1], ['b', 2], ['g', 1]], 7], [[5, 'forced'], [5, 'glue'], [3, 'penalty'], [11, 'glue'], [7, 'glue'], [7, 'glue'], [3, 'end']]), ('regression: overflow trigger', [[['b', 6], ['g', 1], ['b', 3], ['g', 1], ['b', 1], ['p', 1, 50, True], ['g', 2], ['b', 7], ['g', 1], ['b', 1], ['g', 1], ['b', 7], ['p', 0, -10000, False], ['g', 1], ['g', 1], ['b', 1], ['p', 1, 50, True], ['p', 1, 50, True], ['g', 1]], 9], [[6, 'glue'], [6, 'penalty'], [9, 'glue'], [7, 'forced'], [2, 'end']]), ('partial-repair probe', [[['b', 4], ['p', 0, -10000, False], ['g', 1], ['b', 4], ['g', 1], ['b', 4], ['g', 1], ['b', 5], ['p', 1, 50, True], ['g', 2], ['b', 2], ['p', 1, 50, True], ['g', 1], ['b', 2], ['p', 0, 10000, False], ['g', 1], ['b', 7], ['p', 1, 50, True], ['g', 1], ['b', 7], ['p', 0, 9999, False], ['g', 1], ['b', 2], ['g', 2]], 8], [[4, 'forced'], [4, 'glue'], [4, 'glue'], [6, 'penalty'], [3, 'penalty'], [11, 'penalty'], [7, 'penalty'], [4, 'end']]), ('hyphen penalty taken', [[['b', 5], ['p', 1, 50, True], ['b', 4], ['g', 1], ['b', 3]], 7], [[6, 'penalty'], [4, 'glue'], [3, 'end']]), ('inhibited penalty', [[['b', 5], ['p', 0, 10000, False], ['b', 4], ['g', 1], ['b', 3]], 7], [[9, 'glue'], [3, 'end']]), ('control layout', [[['b', 2], ['g', 2], ['b', 2], ['g', 1], ['b', 3], ['g', 2], ['b', 7], ['p', 0, 9999, False], ['g', 1], ['b', 6], ['p', 1, 50, True], ['g', 2], ['b', 3], ['p', 0, 10000, False], ['g', 2], ['b', 4], ['p', 1, 50, True], ['g', 1], ['b', 7], ['g', 1], ['g', 1], ['b', 2], ['p', 0, 900, False], ['p', 1, 50, True], ['g', 1]], 15], [[10, 'glue'], [15, 'penalty'], [10, 'penalty'], [12, 'end']]), ('control layout', [[['b', 7], ['g', 2], ['b', 7], ['p', 0, 9999, False], ['g', 1], ['b', 5], ['g', 1], ['b', 7], ['g', 2], ['b', 5], ['g', 2], ['b', 1], ['p', 0, 900, False], ['g', 2], ['b', 3], ['p', 1, 50, True], ['g', 2]], 10], [[7, 'glue'], [7, 'penalty'], [5, 'glue'], [7, 'glue'], [8, 'penalty'], [5, 'end']])], [('regression: overflow trigger', [[['b', 1], ['g', 1], ['b', 5], ['g', 2], ['b', 4], ['g', 1], ['b', 6], ['g', 1], ['b', 1], ['p', 0, -10000, False], ['g', 1], ['b', 4], ['g', 2], ['b', 1], ['g', 1], ['b', 4], ['p', 0, 9999, False], ['g', 2], ['b', 6], ['p', 0, -5000, False], ['g', 1], ['g', 1], ['b', 3], ['p', 1, 50, True], ['g', 2]], 7], [[7, 'glue'], [4, 'glue'], [6, 'glue'], [1, 'forced'], [7, 'glue'], [4, 'penalty'], [6, 'penalty'], [5, 'end']]), ('regression: overflow trigger', [[['b', 5], ['p', 1, 50, True], ['g', 1], ['b', 5], ['g', 2], ['b', 2], ['g', 1], ['b', 2], ['g', 2], ['b', 5], ['p', 1, 50, True], ['g', 1], ['b', 6], ['p', 0, -10000, False], ['g', 1], ['b', 4], ['g', 1], ['g', 1], ['b', 4], ['g', 1], ['b', 6], ['g', 1], ['g', 1]], 8], [[6, 'penalty'], [5, 'glue'], [5, 'glue'], [6, 'penalty'], [6, 'forced'], [4, 'glue'], [4, 'glue'], [8, 'end']]), ('partial-repair probe', [[['b', 1], ['g', 2], ['b', 5], ['p', 1, 50, True], ['g', 2], ['b', 6], ['p', 1, 50, True], ['g', 1], ['b', 7], ['p', 1, 50, True], ['g', 1], ['b', 2], ['g', 1], ['b', 2], ['g', 2], ['b', 4], ['g', 2]], 12], [[9, 'penalty'], [7, 'penalty'], [10, 'glue'], [10, 'end']]), ('regression: overflow trigger', [[['b', 6], ['p', 1, 50, True], ['g', 1], ['g', 1], ['b', 6], ['p', 0, 10000, False], ['g', 1], ['b', 2], ['p', 0, -10000, False], ['g', 2], ['b', 1], ['p', 0, 10000, False], ['g', 2], ['b', 7], ['g', 2], ['b', 1], ['p', 0, -10000, False], ['g', 1], ['b', 3], ['g', 2], ['b', 2], ['p', 0, 900, False], ['g', 2], ['b', 1], ['p', 1, 50, True], ['g', 1], ['b', 6], ['g', 2]], 7], [[7, 'penalty'], [9, 'forced'], [10, 'glue'], [1, 'forced'], [7, 'penalty'], [2, 'penalty'], [6, 'glue']]), ('hyphen penalty taken', [[['b', 5], ['p', 1, 50, True], ['b', 4], ['g', 1], ['b', 3]], 7], [[6, 'penalty'], [4, 'glue'], [3, 'end']]), ('inhibited penalty', [[['b', 5], ['p', 0, 10000, False], ['b', 4], ['g', 1], ['b', 3]], 7], [[9, 'glue'], [3, 'end']]), ('control layout', [[['b', 4], ['g', 2], ['b', 4], ['g', 2], ['b', 3], ['p', 0, -10000, False], ['g', 1], ['g', 1], ['b', 6], ['p', 1, 50, True], ['g', 2], ['b', 1], ['g', 2], ['b', 2], ['p', 0, -10000, False], ['g', 2], ['b', 5], ['g', 2], ['b', 2], ['p', 0, 10000, False], ['g', 1], ['b', 3], ['p', 1, 50, True], ['g', 2], ['b', 3], ['p', 0, 10000, False], ['g', 2]], 18], [[15, 'forced'], [13, 'forced'], [14, 'penalty'], [5, 'end']]), ('control layout', [[['b', 3], ['g', 2], ['b', 5], ['g', 2], ['b', 2], ['g', 1], ['b', 7], ['g', 1], ['b', 7], ['g', 2], ['b', 2], ['g', 1], ['g', 1], ['b', 7], ['p', 1, 50, True], ['g', 1]], 16], [[14, 'glue'], [15, 'glue'], [12, 'end']])], [('regression: overflow trigger', [[['b', 2], ['g', 1], ['b', 4], ['g', 2], ['b', 1], ['p', 1, 50, True], ['g', 1], ['b', 6], ['g', 2], ['b', 6], ['g', 1], ['b', 7], ['g', 2], ['b', 6], ['g', 1]], 16], [[11, 'penalty'], [14, 'glue'], [16, 'end']]), ('regression: overflow trigger', [[['b', 5], ['p', 1, 50, True], ['g', 2], ['b', 3], ['g', 1], ['b', 2], ['g', 2], ['b', 5], ['g', 1], ['b', 2], ['g', 2], ['b', 7], ['g', 1], ['g', 1]], 17], [[13, 'glue'], [17, 'glue']]), ('partial-repair probe', [[['b', 5], ['p', 0, -5000, False], ['g', 2], ['b', 7], ['g', 2], ['b', 4], ['p', 1, 50, True], ['g', 1], ['g', 1], ['b', 5], ['g', 1], ['b', 7], ['g', 2], ['b', 6], ['p', 1, 50, True], ['g', 1]], 12], [[5, 'penalty'], [7, 'glue'], [11, 'glue'], [7, 'glue'], [7, 'end']]), ('partial-repair probe', [[['b', 2], ['g', 1], ['b', 3], ['p', 1, 50, True], ['g', 1], ['b', 6], ['p', 0, 900, False], ['g', 1], ['b', 7], ['g', 1], ['b', 7], ['g', 1]], 7], [[7, 'penalty'], [6, 'penalty'], [7, 'glue'], [7, 'glue']]), ('inhibited penalty', [[['b', 5], ['p', 0, 10000, False], ['b', 4], ['g', 1], ['b', 3]], 7], [[9, 'glue'], [3, 'end']]), ('hyphen penalty taken', [[['b', 5], ['p', 1, 50, True], ['b', 4], ['g', 1], ['b', 3]], 7], [[6, 'penalty'], [4, 'glue'], [3, 'end']]), ('control layout', [[['b', 4], ['g', 1], ['b', 5], ['g', 1], ['b', 4], ['g', 1], ['b', 2], ['g', 2], ['b', 2], ['g', 1], ['b', 5], ['g', 1]], 12], [[10, 'glue'], [11, 'glue'], [6, 'end']]), ('control layout', [[['b', 6], ['g', 1], ['g', 1], ['b', 4], ['g', 1], ['b', 5], ['p', 0, -10000, False], ['g', 1], ['b', 4], ['p', 1, 50, True], ['g', 1], ['b', 1], ['p', 1, 50, True], ['g', 2]], 14], [[12, 'glue'], [5, 'forced'], [8, 'end']])], [('regression: overflow trigger', [[['b', 5], ['g', 1], ['g', 1], ['b', 4], ['g', 1], ['b', 3], ['p', 0, -5000, False], ['g', 2], ['b', 4], ['p', 1, 50, True], ['g', 1], ['b', 4], ['g', 2], ['b', 5], ['g', 2]], 11], [[11, 'glue'], [10, 'penalty'], [11, 'glue']]), ('regression: overflow trigger', [[['b', 2], ['g', 1], ['b', 6], ['g', 1], ['b', 1], ['g', 1], ['b', 5], ['g', 2], ['b', 4], ['p', 1, 50, True], ['g', 2], ['b', 7], ['p', 1, 50, True], ['g', 1], ['b', 4], ['g', 1]], 8], [[2, 'glue'], [8, 'glue'], [5, 'glue'], [5, 'penalty'], [8, 'penalty'], [5, 'end']]), ('regression: overflow trigger', [[['b', 2], ['g', 1], ['b', 4], ['g', 2], ['b', 1], ['p', 1, 50, True], ['g', 1], ['b', 6], ['g', 2], ['b', 6], ['g', 1], ['b', 7], ['g', 2], ['b', 6], ['g', 1]], 16], [[11, 'penalty'], [14, 'glue'], [16, 'end']]), ('partial-repair probe', [[['b', 3], ['g', 1], ['b', 6], ['g', 1], ['b', 7], ['g', 1], ['b', 6], ['p', 1, 50, True], ['g', 1], ['b', 5], ['p', 1, 50, True], ['g', 1], ['b', 2], ['g', 2], ['b', 3], ['g', 1], ['g', 1]], 17], [[10, 'glue'], [15, 'penalty'], [15, 'end']]), ('forced break', [[['b', 2], ['g', 1], ['b', 2], ['p', 0, -10000, False], ['b', 3]], 20], [[5, 'forced'], [3, 'end']]), ('hyphen penalty taken', [[['b', 5], ['p', 1, 50, True], ['b', 4], ['g', 1], ['b', 3]], 7], [[6, 'penalty'], [4, 'glue'], [3, 'end']]), ('control layout', [[['b', 4], ['p', 1, 50, True], ['g', 2], ['b', 1], ['g', 1], ['g', 1], ['b', 6], ['g', 1], ['b', 1], ['p', 0, -10000, False], ['g', 1], ['b', 7], ['g', 2], ['b', 5], ['g', 1]], 10], [[7, 'glue'], [8, 'forced'], [7, 'glue'], [6, 'end']]), ('control layout', [[['b', 2], ['p', 1, 50, True], ['g', 1], ['b', 5], ['g', 2], ['b', 6], ['g', 2], ['b', 6], ['g', 1], ['b', 1], ['g', 1], ['b', 1], ['p', 1, 50, True], ['g', 1]], 17], [[16, 'glue'], [11, 'end']])], [('regression: overflow trigger', [[['b', 6], ['g', 2], ['b', 3], ['p', 1, 50, True], ['g', 2], ['b', 4], ['g', 2], ['b', 6], ['g', 1], ['b', 7], ['g', 1]], 12], [[12, 'penalty'], [12, 'glue'], [8, 'end']]), ('regression: overflow trigger', [[['b', 3], ['g', 1], ['b', 6], ['g', 1], ['b', 1], ['g', 2], ['b', 3], ['p', 1, 50, True], ['g', 1], ['b', 3], ['g', 1]], 8], [[3, 'glue'], [8, 'glue'], [8, 'end']]), ('regression: overflow trigger', [[['b', 3], ['p', 0, 10000, False], ['g', 2], ['b', 6], ['g', 1], ['b', 7], ['g', 1], ['b', 1], ['p', 1, 50, True], ['g', 1]], 9], [[11, 'glue'], [10, 'penalty']]), ('regression: overflow trigger', [[['b', 6], ['g', 1], ['b', 6], ['g', 2], ['b', 3], ['p', 0, 10000, False], ['g', 1], ['g', 1], ['b', 1], ['p', 0, 10000, False], ['g', 2], ['b', 4], ['g', 1], ['b', 2], ['g', 2], ['b', 5], ['g', 1], ['b', 2], ['g', 1], ['g', 1]], 13], [[13, 'glue'], [12, 'glue'], [12, 'glue']]), ('hyphen penalty taken', [[['b', 5], ['p', 1, 50, True], ['b', 4], ['g', 1], ['b', 3]], 7], [[6, 'penalty'], [4, 'glue'], [3, 'end']]), ('forced break', [[['b', 2], ['g', 1], ['b', 2], ['p', 0, -10000, False], ['b', 3]], 20], [[5, 'forced'], [3, 'end']]), ('control layout', [[['b', 3], ['g', 2], ['b', 3], ['g', 1], ['g', 1], ['b', 3], ['p', 0, 10000, False], ['g', 2], ['b', 1], ['g', 1], ['b', 3], ['g', 1]], 14], [[8, 'glue'], [11, 'end']]), ('control layout', [[['b', 7], ['g', 2], ['b', 7], ['g', 1], ['b', 7], ['g', 1], ['b', 1], ['p', 0, 10000, False], ['g', 1], ['b', 6], ['g', 2], ['b', 7], ['p', 1, 50, True], ['g', 2]], 10], [[7, 'glue'], [7, 'glue'], [7, 'glue'], [8, 'glue'], [9, 'end']])]]
for label, args, expected in fixtures[N - 1]:
    check(label, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
regression: overflow trigger[[9, 'glue'], [6, 'glue'], [5, 'glue'], [8, 'end']][[9, 'glue'], [6, 'glue'], [5, 'glue'], [8, 'end']]Passed
regression: overflow trigger[[5, 'forced'], [5, 'glue'], [3, 'penalty'], [11, 'glue'], [7, 'glue'], [7, 'glue'], [3, 'end']][[5, 'forced'], [5, 'glue'], [3, 'penalty'], [11, 'glue'], [7, 'glue'], [7, 'glue'], [3, 'end']]Passed
regression: overflow trigger[[10, 'glue'], [10, 'glue'], [9, 'forced'], [2, 'end']][[6, 'glue'], [6, 'penalty'], [9, 'glue'], [7, 'forced'], [2, 'end']]Failed
partial-repair probe[[4, 'forced'], [9, 'glue'], [10, 'penalty'], [11, 'penalty'], [7, 'penalty'], [4, 'end']][[4, 'forced'], [4, 'glue'], [4, 'glue'], [6, 'penalty'], [3, 'penalty'], [11, 'penalty'], [7, 'penalty'], [4, 'end']]Failed
hyphen penalty taken[[6, 'penalty'], [8, 'end']][[6, 'penalty'], [4, 'glue'], [3, 'end']]Failed
inhibited penalty[[9, 'glue'], [3, 'end']][[9, 'glue'], [3, 'end']]Passed
control layout[[10, 'glue'], [15, 'penalty'], [10, 'penalty'], [12, 'end']][[10, 'glue'], [15, 'penalty'], [10, 'penalty'], [12, 'end']]Passed
control layout[[7, 'glue'], [7, 'penalty'], [5, 'glue'], [7, 'glue'], [8, 'penalty'], [5, 'end']][[7, 'glue'], [7, 'penalty'], [5, 'glue'], [7, 'glue'], [8, 'penalty'], [5, 'end']]Passed

SHA-256 / 3cf6e4cacb85ed9585f620820380795c68dbd544d366b7709406671da02e107c

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 8 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

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Verification & scope

A deterministic toy typesetting model with integer widths and a stipulated rule set; it does not claim conformance to any engine. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.

Observations recorded using Python 3.12.14 at 2026-09-29T14:49:50.298466+00:00.

Case digest / 19c0c250dbe35c3a133a2313f70b3816fe4115ad4a30cc57eb5e327aa28f71fd