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FA-80131 / Typography line breaking / Open access

Runt last-line prevention: repeated rebalancing · case 01

A runt is only partly fixed when one moved word is not enough.

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

ROOT CAUSE

The rebalancing loop exits after moving a single word.

VERIFIED REPAIR

Keep moving words while the last line is still a runt.

Unsuccessful approach: Stopping once the donor line has fewer than three words still leaves runts.

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 not cur:
            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
        break
    return lines
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: repeated rebalancing', [['the', 'the', 'is', 'ink', 'serif', 'on', 'on', 'ink'], 14, 8], ['the the is ink', 'serif', 'on on ink']), ('regression: repeated rebalancing', [['the', 'measure', 'a', 'x'], 14, 6], ['the', 'measure a x']), ('regression: repeated rebalancing', [['measure', 'is', 'on', 'grid', 'is', 'measure', 'ink', 'ink', 'serif', 'x', 'on'], 13, 9], ['measure is on', 'grid is', 'measure ink', 'ink', 'serif x on']), ('regression: repeated rebalancing', [['ink', 'the', 'of', 'of', 'of', 'on', 'at'], 10, 9], ['ink the of', 'of', 'of on at']), ('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', [['on', 'ink', 'type', 'a'], 12, 4], ['on ink', 'type a']), ('control layout', [['kerning', 'grid', 'a', 'kerning', 'serif', 'is', 'the', 'kerning', 'baseline', 'serif'], 7, 4], ['kerning', 'grid a', 'kerning', 'serif', 'is the', 'kerning', 'baseline', 'serif'])], [('regression: repeated rebalancing', [['x', 'on', 'is', 'the', 'is', 'is', 'ink'], 18, 7], ['x on is the', 'is is ink']), ('regression: repeated rebalancing', [['is', 'serif', 'on', 'a', 'type'], 14, 7], ['is serif', 'on a type']), ('regression: repeated rebalancing', [['grid', 'the', 'the', 'kerning', 'kerning', 'x', 'a'], 17, 7], ['grid the the', 'kerning', 'kerning x a']), ('regression: repeated rebalancing', [['is', 'baseline', 'measure', 'the', 'baseline', 'a', 'the', 'x'], 15, 8], ['is baseline', 'measure the', 'baseline', 'a the x']), ('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', [['serif', 'measure', 'type'], 11, 5], ['serif', 'measure', 'type']), ('control layout', [['of', 'at', 'x', 'on', 'measure', 'type', 'a', 'measure'], 19, 4], ['of at x on measure', 'type a measure'])], [('regression: repeated rebalancing', [['serif', 'the', 'is', 'is', 'of', 'grid', 'at', 'is', 'a'], 10, 7], ['serif the', 'is is of', 'grid', 'at is a']), ('regression: repeated rebalancing', [['measure', 'is', 'on', 'grid', 'is', 'measure', 'ink', 'ink', 'serif', 'x', 'on'], 13, 9], ['measure is on', 'grid is', 'measure ink', 'ink', 'serif x on']), ('regression: repeated rebalancing', [['ink', 'the', 'of', 'of', 'of', 'on', 'at'], 10, 9], ['ink the of', 'of', 'of on at']), ('regression: repeated rebalancing', [['measure', 'type', 'is', 'serif', 'at', 'the'], 13, 8], ['measure type', 'is', 'serif at the']), ('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', [['serif', 'is', 'a', 'x', 'kerning', 'kerning'], 7, 4], ['serif', 'is a x', 'kerning', 'kerning']), ('control layout', [['grid', 'kerning', 'is', 'serif', 'ink'], 17, 7], ['grid kerning is', 'serif ink'])], [('regression: repeated rebalancing', [['the', 'on', 'a', 'a', 'of'], 10, 8], ['the', 'on a a of']), ('regression: repeated rebalancing', [['grid', 'the', 'the', 'kerning', 'kerning', 'x', 'a'], 17, 7], ['grid the the', 'kerning', 'kerning x a']), ('regression: repeated rebalancing', [['the', 'measure', 'a', 'x'], 14, 6], ['the', 'measure a x']), ('regression: repeated rebalancing', [['ink', 'the', 'of', 'of', 'of', 'on', 'at'], 10, 9], ['ink the of', 'of', 'of on at']), ('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', [['on', 'of', 'at', 'ink', 'measure'], 12, 5], ['on of at ink', 'measure']), ('control layout', [['kerning', 'is', 'type', 'of', 'type', 'of', 'baseline', 'a', 'baseline'], 14, 8], ['kerning is', 'type of type', 'of baseline a', 'baseline'])], [('regression: repeated rebalancing', [['the', 'on', 'a', 'a', 'of'], 10, 8], ['the', 'on a a of']), ('regression: repeated rebalancing', [['the', 'the', 'is', 'ink', 'serif', 'on', 'on', 'ink'], 14, 8], ['the the is ink', 'serif', 'on on ink']), ('regression: repeated rebalancing', [['is', 'baseline', 'measure', 'the', 'baseline', 'a', 'the', 'x'], 15, 8], ['is baseline', 'measure the', 'baseline', 'a the x']), ('regression: repeated rebalancing', [['grid', 'the', 'the', 'kerning', 'kerning', 'x', 'a'], 17, 7], ['grid the the', 'kerning', 'kerning x 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', [['type', 'ink', 'the', 'ink', 'the', 'of', 'kerning', 'a', 'of'], 13, 9], ['type ink the', 'ink the of', 'kerning a of']), ('control layout', [['x', 'baseline', 'grid', 'is', 'baseline', 'on', 'on', 'at', 'on', 'grid', 'grid'], 20, 3], ['x baseline grid is', 'baseline on on at on', 'grid grid'])]]
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: repeated rebalancing['the the is ink', 'serif on', 'on ink']['the the is ink', 'serif', 'on on ink']Failed
regression: repeated rebalancing['the measure', 'a x']['the', 'measure a x']Failed
regression: repeated rebalancing['measure is on', 'grid is', 'measure ink', 'ink serif', 'x on']['measure is on', 'grid is', 'measure ink', 'ink', 'serif x on']Failed
regression: repeated rebalancing['ink the of', 'of of', 'on at']['ink the of', 'of', 'of on at']Failed
runt limited by width['kerning', 'baseline x']['kerning', 'baseline x']Passed
one-word runt pulled down['the type', 'grid is a']['the type', 'grid is a']Passed
control layout['on ink', 'type a']['on ink', 'type a']Passed
control layout['kerning', 'grid a', 'kerning', 'serif', 'is the', 'kerning', 'baseline', 'serif']['kerning', 'grid a', 'kerning', 'serif', 'is the', 'kerning', 'baseline', 'serif']Passed

SHA-256 / 3b25c0fe5a669ccd598fa0cb4d669afc984640972409a3abfbfe1ffa246b48d5

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 cur:
            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
        if len(prev) < 4:
            break
    return lines
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: repeated rebalancing', [['the', 'the', 'is', 'ink', 'serif', 'on', 'on', 'ink'], 14, 8], ['the the is ink', 'serif', 'on on ink']), ('regression: repeated rebalancing', [['the', 'measure', 'a', 'x'], 14, 6], ['the', 'measure a x']), ('regression: repeated rebalancing', [['measure', 'is', 'on', 'grid', 'is', 'measure', 'ink', 'ink', 'serif', 'x', 'on'], 13, 9], ['measure is on', 'grid is', 'measure ink', 'ink', 'serif x on']), ('regression: repeated rebalancing', [['ink', 'the', 'of', 'of', 'of', 'on', 'at'], 10, 9], ['ink the of', 'of', 'of on at']), ('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', [['on', 'ink', 'type', 'a'], 12, 4], ['on ink', 'type a']), ('control layout', [['kerning', 'grid', 'a', 'kerning', 'serif', 'is', 'the', 'kerning', 'baseline', 'serif'], 7, 4], ['kerning', 'grid a', 'kerning', 'serif', 'is the', 'kerning', 'baseline', 'serif'])], [('regression: repeated rebalancing', [['x', 'on', 'is', 'the', 'is', 'is', 'ink'], 18, 7], ['x on is the', 'is is ink']), ('regression: repeated rebalancing', [['is', 'serif', 'on', 'a', 'type'], 14, 7], ['is serif', 'on a type']), ('regression: repeated rebalancing', [['grid', 'the', 'the', 'kerning', 'kerning', 'x', 'a'], 17, 7], ['grid the the', 'kerning', 'kerning x a']), ('regression: repeated rebalancing', [['is', 'baseline', 'measure', 'the', 'baseline', 'a', 'the', 'x'], 15, 8], ['is baseline', 'measure the', 'baseline', 'a the x']), ('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', [['serif', 'measure', 'type'], 11, 5], ['serif', 'measure', 'type']), ('control layout', [['of', 'at', 'x', 'on', 'measure', 'type', 'a', 'measure'], 19, 4], ['of at x on measure', 'type a measure'])], [('regression: repeated rebalancing', [['serif', 'the', 'is', 'is', 'of', 'grid', 'at', 'is', 'a'], 10, 7], ['serif the', 'is is of', 'grid', 'at is a']), ('regression: repeated rebalancing', [['measure', 'is', 'on', 'grid', 'is', 'measure', 'ink', 'ink', 'serif', 'x', 'on'], 13, 9], ['measure is on', 'grid is', 'measure ink', 'ink', 'serif x on']), ('regression: repeated rebalancing', [['ink', 'the', 'of', 'of', 'of', 'on', 'at'], 10, 9], ['ink the of', 'of', 'of on at']), ('regression: repeated rebalancing', [['measure', 'type', 'is', 'serif', 'at', 'the'], 13, 8], ['measure type', 'is', 'serif at the']), ('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', [['serif', 'is', 'a', 'x', 'kerning', 'kerning'], 7, 4], ['serif', 'is a x', 'kerning', 'kerning']), ('control layout', [['grid', 'kerning', 'is', 'serif', 'ink'], 17, 7], ['grid kerning is', 'serif ink'])], [('regression: repeated rebalancing', [['the', 'on', 'a', 'a', 'of'], 10, 8], ['the', 'on a a of']), ('regression: repeated rebalancing', [['grid', 'the', 'the', 'kerning', 'kerning', 'x', 'a'], 17, 7], ['grid the the', 'kerning', 'kerning x a']), ('regression: repeated rebalancing', [['the', 'measure', 'a', 'x'], 14, 6], ['the', 'measure a x']), ('regression: repeated rebalancing', [['ink', 'the', 'of', 'of', 'of', 'on', 'at'], 10, 9], ['ink the of', 'of', 'of on at']), ('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', [['on', 'of', 'at', 'ink', 'measure'], 12, 5], ['on of at ink', 'measure']), ('control layout', [['kerning', 'is', 'type', 'of', 'type', 'of', 'baseline', 'a', 'baseline'], 14, 8], ['kerning is', 'type of type', 'of baseline a', 'baseline'])], [('regression: repeated rebalancing', [['the', 'on', 'a', 'a', 'of'], 10, 8], ['the', 'on a a of']), ('regression: repeated rebalancing', [['the', 'the', 'is', 'ink', 'serif', 'on', 'on', 'ink'], 14, 8], ['the the is ink', 'serif', 'on on ink']), ('regression: repeated rebalancing', [['is', 'baseline', 'measure', 'the', 'baseline', 'a', 'the', 'x'], 15, 8], ['is baseline', 'measure the', 'baseline', 'a the x']), ('regression: repeated rebalancing', [['grid', 'the', 'the', 'kerning', 'kerning', 'x', 'a'], 17, 7], ['grid the the', 'kerning', 'kerning x 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', [['type', 'ink', 'the', 'ink', 'the', 'of', 'kerning', 'a', 'of'], 13, 9], ['type ink the', 'ink the of', 'kerning a of']), ('control layout', [['x', 'baseline', 'grid', 'is', 'baseline', 'on', 'on', 'at', 'on', 'grid', 'grid'], 20, 3], ['x baseline grid is', 'baseline on on at on', 'grid grid'])]]
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: repeated rebalancing['the the is ink', 'serif on', 'on ink']['the the is ink', 'serif', 'on on ink']Failed
regression: repeated rebalancing['the measure', 'a x']['the', 'measure a x']Failed
regression: repeated rebalancing['measure is on', 'grid is', 'measure ink', 'ink serif', 'x on']['measure is on', 'grid is', 'measure ink', 'ink', 'serif x on']Failed
regression: repeated rebalancing['ink the of', 'of of', 'on at']['ink the of', 'of', 'of on at']Failed
runt limited by width['kerning', 'baseline x']['kerning', 'baseline x']Passed
one-word runt pulled down['the type', 'grid is a']['the type', 'grid is a']Passed
control layout['on ink', 'type a']['on ink', 'type a']Passed
control layout['kerning', 'grid a', 'kerning', 'serif', 'is the', 'kerning', 'baseline', 'serif']['kerning', 'grid a', 'kerning', 'serif', 'is the', 'kerning', 'baseline', 'serif']Passed

SHA-256 / 3bfed405395df87b0fb8183ad7165a19b84e601e2bd3c03b9f237b6940c55246

3 / The verified repair

Exit 0
"""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 cur:
            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: repeated rebalancing', [['the', 'the', 'is', 'ink', 'serif', 'on', 'on', 'ink'], 14, 8], ['the the is ink', 'serif', 'on on ink']), ('regression: repeated rebalancing', [['the', 'measure', 'a', 'x'], 14, 6], ['the', 'measure a x']), ('regression: repeated rebalancing', [['measure', 'is', 'on', 'grid', 'is', 'measure', 'ink', 'ink', 'serif', 'x', 'on'], 13, 9], ['measure is on', 'grid is', 'measure ink', 'ink', 'serif x on']), ('regression: repeated rebalancing', [['ink', 'the', 'of', 'of', 'of', 'on', 'at'], 10, 9], ['ink the of', 'of', 'of on at']), ('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', [['on', 'ink', 'type', 'a'], 12, 4], ['on ink', 'type a']), ('control layout', [['kerning', 'grid', 'a', 'kerning', 'serif', 'is', 'the', 'kerning', 'baseline', 'serif'], 7, 4], ['kerning', 'grid a', 'kerning', 'serif', 'is the', 'kerning', 'baseline', 'serif'])], [('regression: repeated rebalancing', [['x', 'on', 'is', 'the', 'is', 'is', 'ink'], 18, 7], ['x on is the', 'is is ink']), ('regression: repeated rebalancing', [['is', 'serif', 'on', 'a', 'type'], 14, 7], ['is serif', 'on a type']), ('regression: repeated rebalancing', [['grid', 'the', 'the', 'kerning', 'kerning', 'x', 'a'], 17, 7], ['grid the the', 'kerning', 'kerning x a']), ('regression: repeated rebalancing', [['is', 'baseline', 'measure', 'the', 'baseline', 'a', 'the', 'x'], 15, 8], ['is baseline', 'measure the', 'baseline', 'a the x']), ('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', [['serif', 'measure', 'type'], 11, 5], ['serif', 'measure', 'type']), ('control layout', [['of', 'at', 'x', 'on', 'measure', 'type', 'a', 'measure'], 19, 4], ['of at x on measure', 'type a measure'])], [('regression: repeated rebalancing', [['serif', 'the', 'is', 'is', 'of', 'grid', 'at', 'is', 'a'], 10, 7], ['serif the', 'is is of', 'grid', 'at is a']), ('regression: repeated rebalancing', [['measure', 'is', 'on', 'grid', 'is', 'measure', 'ink', 'ink', 'serif', 'x', 'on'], 13, 9], ['measure is on', 'grid is', 'measure ink', 'ink', 'serif x on']), ('regression: repeated rebalancing', [['ink', 'the', 'of', 'of', 'of', 'on', 'at'], 10, 9], ['ink the of', 'of', 'of on at']), ('regression: repeated rebalancing', [['measure', 'type', 'is', 'serif', 'at', 'the'], 13, 8], ['measure type', 'is', 'serif at the']), ('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', [['serif', 'is', 'a', 'x', 'kerning', 'kerning'], 7, 4], ['serif', 'is a x', 'kerning', 'kerning']), ('control layout', [['grid', 'kerning', 'is', 'serif', 'ink'], 17, 7], ['grid kerning is', 'serif ink'])], [('regression: repeated rebalancing', [['the', 'on', 'a', 'a', 'of'], 10, 8], ['the', 'on a a of']), ('regression: repeated rebalancing', [['grid', 'the', 'the', 'kerning', 'kerning', 'x', 'a'], 17, 7], ['grid the the', 'kerning', 'kerning x a']), ('regression: repeated rebalancing', [['the', 'measure', 'a', 'x'], 14, 6], ['the', 'measure a x']), ('regression: repeated rebalancing', [['ink', 'the', 'of', 'of', 'of', 'on', 'at'], 10, 9], ['ink the of', 'of', 'of on at']), ('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', [['on', 'of', 'at', 'ink', 'measure'], 12, 5], ['on of at ink', 'measure']), ('control layout', [['kerning', 'is', 'type', 'of', 'type', 'of', 'baseline', 'a', 'baseline'], 14, 8], ['kerning is', 'type of type', 'of baseline a', 'baseline'])], [('regression: repeated rebalancing', [['the', 'on', 'a', 'a', 'of'], 10, 8], ['the', 'on a a of']), ('regression: repeated rebalancing', [['the', 'the', 'is', 'ink', 'serif', 'on', 'on', 'ink'], 14, 8], ['the the is ink', 'serif', 'on on ink']), ('regression: repeated rebalancing', [['is', 'baseline', 'measure', 'the', 'baseline', 'a', 'the', 'x'], 15, 8], ['is baseline', 'measure the', 'baseline', 'a the x']), ('regression: repeated rebalancing', [['grid', 'the', 'the', 'kerning', 'kerning', 'x', 'a'], 17, 7], ['grid the the', 'kerning', 'kerning x 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', [['type', 'ink', 'the', 'ink', 'the', 'of', 'kerning', 'a', 'of'], 13, 9], ['type ink the', 'ink the of', 'kerning a of']), ('control layout', [['x', 'baseline', 'grid', 'is', 'baseline', 'on', 'on', 'at', 'on', 'grid', 'grid'], 20, 3], ['x baseline grid is', 'baseline on on at on', 'grid grid'])]]
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: repeated rebalancing['the the is ink', 'serif', 'on on ink']['the the is ink', 'serif', 'on on ink']Passed
regression: repeated rebalancing['the', 'measure a x']['the', 'measure a x']Passed
regression: repeated rebalancing['measure is on', 'grid is', 'measure ink', 'ink', 'serif x on']['measure is on', 'grid is', 'measure ink', 'ink', 'serif x on']Passed
regression: repeated rebalancing['ink the of', 'of', 'of on at']['ink the of', 'of', 'of on at']Passed
runt limited by width['kerning', 'baseline x']['kerning', 'baseline x']Passed
one-word runt pulled down['the type', 'grid is a']['the type', 'grid is a']Passed
control layout['on ink', 'type a']['on ink', 'type a']Passed
control layout['kerning', 'grid a', 'kerning', 'serif', 'is the', 'kerning', 'baseline', 'serif']['kerning', 'grid a', 'kerning', 'serif', 'is the', 'kerning', 'baseline', 'serif']Passed

SHA-256 / 1c223ca8eaa09ad4095cb5333edbbe63151b72f6a203285c0ab94c7f35cc5423

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 2026-09-29T14:49:50.962282+00:00.

Case digest / 611e15401ce3408340b50bc6fa9359ae8b385000cf1497cd639be0e365df459e