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FA-80151 / Typography line breaking / Open access

Runt last-line prevention: overwide word isolation · case 01

Overwide words are attached to the current line or leave empty lines.

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

ROOT CAUSE

Overwide words are appended to a non-empty line instead of starting their own.

THE FAILURE

Overwide words are appended to a non-empty line instead of starting their own.

Unsuccessful approach: Special-casing only the first word still merges later overwide words.

Case contract

Input [words, width, minimum last-line length]. Greedy fill (unit spaces; overwide word alone). Then while there are at least two lines and the last line string is shorter than the minimum, move the last word of the previous line down if that line keeps at least one word and the new last line fits. Return lines.

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):
    words, width, min_last = x
    lines = []
    cur = ''
    for w in words:
        cand = w if not cur else cur + ' ' + w
        if len(cand) <= width or len(w) > width:
            cur = cand
        else:
            lines.append(cur)
            cur = w
    lines.append(cur)
    while len(lines) >= 2 and len(lines[-1]) < min_last:
        prev = lines[-2].split(' ')
        if len(prev) < 2:
            break
        moved = prev[-1] + ' ' + lines[-1]
        if len(moved) > width:
            break
        lines[-2] = ' '.join(prev[:-1])
        lines[-1] = moved
    return lines
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: overwide word isolation', [['on', 'ink', 'x', 'at', 'a', 'kerning', 'serif', 'measure', 'at', 'baseline'], 7, 3], ['on ink', 'x at a', 'kerning', 'serif', 'measure', 'at', 'baseline']), ('regression: overwide word isolation', [['on', 'of', 'kerning', 'on', 'kerning', 'grid', 'baseline', 'grid', 'a', 'measure', 'at', 'measure'], 5, 4], ['on of', 'kerning', 'on', 'kerning', 'grid', 'baseline', 'grid', 'a', 'measure', 'at', 'measure']), ('partial-repair probe', [['a', 'ink', 'measure', 'serif', 'baseline'], 14, 5], ['a ink measure', 'serif baseline']), ('partial-repair probe', [['baseline', 'on', 'grid', 'kerning', 'a', 'ink', 'baseline', 'measure', 'a'], 10, 3], ['baseline', 'on grid', 'kerning a', 'ink', 'baseline', 'measure a']), ('one-word runt pulled down', [['the', 'type', 'grid', 'is', 'a'], 12, 5], ['the type', 'grid is a']), ('runt limited by width', [['kerning', 'baseline', 'x'], 10, 4], ['kerning', 'baseline x']), ('control layout', [['a', 'x', 'grid'], 13, 9], ['a x grid']), ('control layout', [['serif', 'a', 'the'], 17, 4], ['serif a the'])], [('regression: overwide word isolation', [['serif', 'baseline', 'grid', 'of', 'is', 'kerning'], 5, 8], ['serif', 'baseline', 'grid', 'of is', 'kerning']), ('regression: overwide word isolation', [['a', 'baseline', 'the', 'a', 'type', 'kerning', 'is', 'serif', 'a', 'grid', 'the'], 6, 3], ['a', 'baseline', 'the a', 'type', 'kerning', 'is', 'serif', 'a grid', 'the']), ('partial-repair probe', [['on', 'ink', 'type', 'a'], 12, 4], ['on ink', 'type a']), ('regression: overwide word isolation', [['baseline', 'a', 'a', 'is', 'a', 'type', 'on', 'baseline', 'serif', 'baseline', 'serif'], 7, 8], ['baseline', 'a a is', 'a type', 'on', 'baseline', 'serif', 'baseline', 'serif']), ('one-word runt pulled down', [['the', 'type', 'grid', 'is', 'a'], 12, 5], ['the type', 'grid is a']), ('runt limited by width', [['kerning', 'baseline', 'x'], 10, 4], ['kerning', 'baseline x']), ('control layout', [['on', 'is', 'at'], 17, 3], ['on is at']), ('control layout', [['x', 'on', 'serif'], 18, 4], ['x on serif'])], [('regression: overwide word isolation', [['kerning', 'grid', 'a', 'kerning', 'serif', 'is', 'the', 'kerning', 'baseline', 'serif'], 7, 4], ['kerning', 'grid a', 'kerning', 'serif', 'is the', 'kerning', 'baseline', 'serif']), ('regression: overwide word isolation', [['on', 'at', 'grid', 'measure', 'type', 'measure', 'on', 'x', 'at', 'a', 'baseline'], 7, 5], ['on at', 'grid', 'measure', 'type', 'measure', 'on x at', 'a', 'baseline']), ('partial-repair probe', [['grid', 'serif', 'at', 'measure'], 15, 3], ['grid serif at', 'measure']), ('partial-repair probe', [['ink', 'the', 'kerning', 'x', 'kerning'], 18, 7], ['ink the kerning x', 'kerning']), ('one-word runt pulled down', [['the', 'type', 'grid', 'is', 'a'], 12, 5], ['the type', 'grid is a']), ('runt limited by width', [['kerning', 'baseline', 'x'], 10, 4], ['kerning', 'baseline x']), ('control layout', [['is', 'measure', 'at'], 19, 4], ['is measure at']), ('control layout', [['measure', 'on', 'x', 'ink'], 16, 7], ['measure on x ink'])], [('regression: overwide word isolation', [['the', 'serif', 'baseline', 'x', 'a', 'baseline', 'measure', 'ink', 'of', 'measure', 'the'], 6, 8], ['the', 'serif', 'baseline', 'x a', 'baseline', 'measure', 'ink of', 'measure', 'the']), ('regression: overwide word isolation', [['on', 'of', 'kerning', 'on', 'kerning', 'grid', 'baseline', 'grid', 'a', 'measure', 'at', 'measure'], 5, 4], ['on of', 'kerning', 'on', 'kerning', 'grid', 'baseline', 'grid', 'a', 'measure', 'at', 'measure']), ('partial-repair probe', [['at', 'a', 'on', 'grid', 'grid', 'measure', 'the', 'x', 'at', 'at', 'type'], 20, 8], ['at a on grid grid', 'measure the x', 'at at type']), ('regression: overwide word isolation', [['serif', 'of', 'at', 'the', 'measure', 'ink', 'ink', 'a', 'x'], 5, 8], ['serif', 'of at', 'the', 'measure', 'ink', 'ink', 'a x']), ('one-word runt pulled down', [['the', 'type', 'grid', 'is', 'a'], 12, 5], ['the type', 'grid is a']), ('runt limited by width', [['kerning', 'baseline', 'x'], 10, 4], ['kerning', 'baseline x']), ('control layout', [['x', 'on', 'serif'], 18, 4], ['x on serif']), ('control layout', [['is', 'the', 'serif'], 12, 9], ['is the serif'])], [('regression: overwide word isolation', [['baseline', 'serif', 'is', 'baseline', 'x', 'x', 'at', 'is', 'serif', 'at', 'at'], 6, 9], ['baseline', 'serif', 'is', 'baseline', 'x x at', 'is', 'serif', 'at at']), ('regression: overwide word isolation', [['on', 'at', 'a', 'at', 'type', 'of', 'a', 'baseline', 'ink', 'ink', 'serif', 'baseline'], 5, 7], ['on at', 'a at', 'type', 'of a', 'baseline', 'ink', 'ink', 'serif', 'baseline']), ('partial-repair probe', [['of', 'at', 'ink', 'measure', 'at', 'the', 'measure', 'ink'], 11, 6], ['of at ink', 'measure at', 'the', 'measure ink']), ('partial-repair probe', [['ink', 'kerning', 'ink'], 8, 9], ['ink', 'kerning', 'ink']), ('runt limited by width', [['kerning', 'baseline', 'x'], 10, 4], ['kerning', 'baseline x']), ('one-word runt pulled down', [['the', 'type', 'grid', 'is', 'a'], 12, 5], ['the type', 'grid is a']), ('control layout', [['type', 'the', 'a'], 18, 3], ['type the a']), ('control layout', [['a', 'is', 'serif'], 11, 3], ['a is serif'])]]
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: overwide word isolation['on ink', 'x at a', 'kerning', 'serif', 'measure', 'at baseline']['on ink', 'x at a', 'kerning', 'serif', 'measure', 'at', 'baseline']Failed
regression: overwide word isolation['on of kerning', 'on kerning', 'grid baseline', 'grid', 'a measure', 'at measure']['on of', 'kerning', 'on', 'kerning', 'grid', 'baseline', 'grid', 'a', 'measure', 'at', 'measure']Failed
partial-repair probe['a ink measure', 'serif baseline']['a ink measure', 'serif baseline']Passed
partial-repair probe['baseline', 'on grid', 'kerning a', 'ink', 'baseline', 'measure a']['baseline', 'on grid', 'kerning a', 'ink', 'baseline', 'measure a']Passed
one-word runt pulled down['the type', 'grid is a']['the type', 'grid is a']Passed
runt limited by width['kerning', 'baseline x']['kerning', 'baseline x']Passed
control layout['a x grid']['a x grid']Passed
control layout['serif a the']['serif a the']Passed

SHA-256 / a636b396cd6c5b50bf453463b240c6779fd9ea6f39c12d31f9167f3c0480d240

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(x):
    words, width, min_last = x
    lines = []
    cur = ''
    for w in words:
        cand = w if not cur else cur + ' ' + w
        if len(cand) <= width or not lines:
            cur = cand
        else:
            lines.append(cur)
            cur = w
    lines.append(cur)
    while len(lines) >= 2 and len(lines[-1]) < min_last:
        prev = lines[-2].split(' ')
        if len(prev) < 2:
            break
        moved = prev[-1] + ' ' + lines[-1]
        if len(moved) > width:
            break
        lines[-2] = ' '.join(prev[:-1])
        lines[-1] = moved
    return lines
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: overwide word isolation', [['on', 'ink', 'x', 'at', 'a', 'kerning', 'serif', 'measure', 'at', 'baseline'], 7, 3], ['on ink', 'x at a', 'kerning', 'serif', 'measure', 'at', 'baseline']), ('regression: overwide word isolation', [['on', 'of', 'kerning', 'on', 'kerning', 'grid', 'baseline', 'grid', 'a', 'measure', 'at', 'measure'], 5, 4], ['on of', 'kerning', 'on', 'kerning', 'grid', 'baseline', 'grid', 'a', 'measure', 'at', 'measure']), ('partial-repair probe', [['a', 'ink', 'measure', 'serif', 'baseline'], 14, 5], ['a ink measure', 'serif baseline']), ('partial-repair probe', [['baseline', 'on', 'grid', 'kerning', 'a', 'ink', 'baseline', 'measure', 'a'], 10, 3], ['baseline', 'on grid', 'kerning a', 'ink', 'baseline', 'measure a']), ('one-word runt pulled down', [['the', 'type', 'grid', 'is', 'a'], 12, 5], ['the type', 'grid is a']), ('runt limited by width', [['kerning', 'baseline', 'x'], 10, 4], ['kerning', 'baseline x']), ('control layout', [['a', 'x', 'grid'], 13, 9], ['a x grid']), ('control layout', [['serif', 'a', 'the'], 17, 4], ['serif a the'])], [('regression: overwide word isolation', [['serif', 'baseline', 'grid', 'of', 'is', 'kerning'], 5, 8], ['serif', 'baseline', 'grid', 'of is', 'kerning']), ('regression: overwide word isolation', [['a', 'baseline', 'the', 'a', 'type', 'kerning', 'is', 'serif', 'a', 'grid', 'the'], 6, 3], ['a', 'baseline', 'the a', 'type', 'kerning', 'is', 'serif', 'a grid', 'the']), ('partial-repair probe', [['on', 'ink', 'type', 'a'], 12, 4], ['on ink', 'type a']), ('regression: overwide word isolation', [['baseline', 'a', 'a', 'is', 'a', 'type', 'on', 'baseline', 'serif', 'baseline', 'serif'], 7, 8], ['baseline', 'a a is', 'a type', 'on', 'baseline', 'serif', 'baseline', 'serif']), ('one-word runt pulled down', [['the', 'type', 'grid', 'is', 'a'], 12, 5], ['the type', 'grid is a']), ('runt limited by width', [['kerning', 'baseline', 'x'], 10, 4], ['kerning', 'baseline x']), ('control layout', [['on', 'is', 'at'], 17, 3], ['on is at']), ('control layout', [['x', 'on', 'serif'], 18, 4], ['x on serif'])], [('regression: overwide word isolation', [['kerning', 'grid', 'a', 'kerning', 'serif', 'is', 'the', 'kerning', 'baseline', 'serif'], 7, 4], ['kerning', 'grid a', 'kerning', 'serif', 'is the', 'kerning', 'baseline', 'serif']), ('regression: overwide word isolation', [['on', 'at', 'grid', 'measure', 'type', 'measure', 'on', 'x', 'at', 'a', 'baseline'], 7, 5], ['on at', 'grid', 'measure', 'type', 'measure', 'on x at', 'a', 'baseline']), ('partial-repair probe', [['grid', 'serif', 'at', 'measure'], 15, 3], ['grid serif at', 'measure']), ('partial-repair probe', [['ink', 'the', 'kerning', 'x', 'kerning'], 18, 7], ['ink the kerning x', 'kerning']), ('one-word runt pulled down', [['the', 'type', 'grid', 'is', 'a'], 12, 5], ['the type', 'grid is a']), ('runt limited by width', [['kerning', 'baseline', 'x'], 10, 4], ['kerning', 'baseline x']), ('control layout', [['is', 'measure', 'at'], 19, 4], ['is measure at']), ('control layout', [['measure', 'on', 'x', 'ink'], 16, 7], ['measure on x ink'])], [('regression: overwide word isolation', [['the', 'serif', 'baseline', 'x', 'a', 'baseline', 'measure', 'ink', 'of', 'measure', 'the'], 6, 8], ['the', 'serif', 'baseline', 'x a', 'baseline', 'measure', 'ink of', 'measure', 'the']), ('regression: overwide word isolation', [['on', 'of', 'kerning', 'on', 'kerning', 'grid', 'baseline', 'grid', 'a', 'measure', 'at', 'measure'], 5, 4], ['on of', 'kerning', 'on', 'kerning', 'grid', 'baseline', 'grid', 'a', 'measure', 'at', 'measure']), ('partial-repair probe', [['at', 'a', 'on', 'grid', 'grid', 'measure', 'the', 'x', 'at', 'at', 'type'], 20, 8], ['at a on grid grid', 'measure the x', 'at at type']), ('regression: overwide word isolation', [['serif', 'of', 'at', 'the', 'measure', 'ink', 'ink', 'a', 'x'], 5, 8], ['serif', 'of at', 'the', 'measure', 'ink', 'ink', 'a x']), ('one-word runt pulled down', [['the', 'type', 'grid', 'is', 'a'], 12, 5], ['the type', 'grid is a']), ('runt limited by width', [['kerning', 'baseline', 'x'], 10, 4], ['kerning', 'baseline x']), ('control layout', [['x', 'on', 'serif'], 18, 4], ['x on serif']), ('control layout', [['is', 'the', 'serif'], 12, 9], ['is the serif'])], [('regression: overwide word isolation', [['baseline', 'serif', 'is', 'baseline', 'x', 'x', 'at', 'is', 'serif', 'at', 'at'], 6, 9], ['baseline', 'serif', 'is', 'baseline', 'x x at', 'is', 'serif', 'at at']), ('regression: overwide word isolation', [['on', 'at', 'a', 'at', 'type', 'of', 'a', 'baseline', 'ink', 'ink', 'serif', 'baseline'], 5, 7], ['on at', 'a at', 'type', 'of a', 'baseline', 'ink', 'ink', 'serif', 'baseline']), ('partial-repair probe', [['of', 'at', 'ink', 'measure', 'at', 'the', 'measure', 'ink'], 11, 6], ['of at ink', 'measure at', 'the', 'measure ink']), ('partial-repair probe', [['ink', 'kerning', 'ink'], 8, 9], ['ink', 'kerning', 'ink']), ('runt limited by width', [['kerning', 'baseline', 'x'], 10, 4], ['kerning', 'baseline x']), ('one-word runt pulled down', [['the', 'type', 'grid', 'is', 'a'], 12, 5], ['the type', 'grid is a']), ('control layout', [['type', 'the', 'a'], 18, 3], ['type the a']), ('control layout', [['a', 'is', 'serif'], 11, 3], ['a is serif'])]]
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: overwide word isolation['on ink x at a kerning serif measure at baseline']['on ink', 'x at a', 'kerning', 'serif', 'measure', 'at', 'baseline']Failed
regression: overwide word isolation['on of kerning on kerning grid baseline grid a measure at measure']['on of', 'kerning', 'on', 'kerning', 'grid', 'baseline', 'grid', 'a', 'measure', 'at', 'measure']Failed
partial-repair probe['a ink measure serif baseline']['a ink measure', 'serif baseline']Failed
partial-repair probe['baseline on grid kerning a ink baseline measure a']['baseline', 'on grid', 'kerning a', 'ink', 'baseline', 'measure a']Failed
one-word runt pulled down['the type grid is a']['the type', 'grid is a']Failed
runt limited by width['kerning baseline x']['kerning', 'baseline x']Failed
control layout['a x grid']['a x grid']Passed
control layout['serif a the']['serif a the']Passed

SHA-256 / 09a54d9d37a4e5ce15044c3740b0df134e68368b0790e133b7baec9f615e0354

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 2026-09-29T14:49:51.156284+00:00.

Case digest / 17b456ea38cdc8c3d6706b5e8e010cc90fb69610e1bef73441e15b5658150d16