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FA-80311 / Typography line breaking / Open access

URL line breaking: double slash integrity · case 01

URLs are broken between the two slashes of "//".

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

ROOT CAUSE

Any position before a slash is a break opportunity.

THE FAILURE

Any position before a slash is a break opportunity.

Unsuccessful approach: Checking the previous character but not the next still splits "x//y" before the pair.

Case contract

Input [url, width]. Break opportunities (no hyphen added): after ":"; after "//" (never between its slashes); before a single "/"; before . - _ ? # % ~; before or after = and &. While the rest exceeds the width, break at the latest opportunity within width characters, else hard-break at width. 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):
    url, width = x
    n = len(url)
    ok = set()
    for p in range(1, n):
        a, b = url[p - 1], url[p]
        if a == ':':
            ok.add(p)
        elif a == '/' and url[p - 2:p] == '//':
            ok.add(p)
        elif b == '/':
            ok.add(p)
        elif b in '.-_?#%~':
            ok.add(p)
        elif a in '=&' or b in '=&':
            ok.add(p)
    lines = []
    start = 0
    while n - start > width:
        cands = [p for p in ok if start < p <= start + width]
        cut = max(cands) if cands else start + width
        lines.append(url[start:cut])
        start = cut
    lines.append(url[start:])
    return lines
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: double slash integrity', ['https://x.io/search?term=line%20break&lang=en', 7], ['https:', '//x.io', '/search', '?term=', 'line', '%20brea', 'k&lang=', 'en']), ('regression: double slash integrity', ['https://example.com/path/to/page.html', 7], ['https:', '//', 'example', '.com', '/path', '/to', '/page', '.html']), ('regression: double slash integrity', ['http://a.b.org/x//y?q=1&r=2', 9], ['http://a', '.b.org', '/x//y?q=1', '&r=2']), ('regression: double slash integrity', ['http://a.b.org/x//y?q=1&r=2', 9], ['http://a', '.b.org', '/x//y?q=1', '&r=2']), ('double slash inside path', ['http://a.b.org/x//y?q=1&r=2', 10], ['http://a.b', '.org/x//y', '?q=1&r=2']), ('break after scheme', ['https://example.com/path/to/page.html', 8], ['https://', 'example', '.com', '/path/to', '/page', '.html']), ('control layout', ['https://w.org/a=b/c&d', 5], ['https', '://w', '.org', '/a=b', '/c&d']), ('control layout', ['file:///usr/local/share/doc', 14], ['file:///usr', '/local/share', '/doc'])], [('regression: double slash integrity', ['https://www.docs.io/a/b/c#sec-3', 7], ['https:', '//www', '.docs', '.io/a/b', '/c#sec', '-3']), ('regression: double slash integrity', ['http://a.b.org/x//y?q=1&r=2', 6], ['http:', '//a.b', '.org', '/x//y', '?q=1&r', '=2']), ('regression: double slash integrity', ['http://a.b.org/x//y?q=1&r=2', 9], ['http://a', '.b.org', '/x//y?q=1', '&r=2']), ('regression: double slash integrity', ['http://a.b.org/x//y?q=1&r=2', 8], ['http://a', '.b.org', '/x//y?q=', '1&r=2']), ('double slash inside path', ['http://a.b.org/x//y?q=1&r=2', 10], ['http://a.b', '.org/x//y', '?q=1&r=2']), ('break after scheme', ['https://example.com/path/to/page.html', 8], ['https://', 'example', '.com', '/path/to', '/page', '.html']), ('control layout', ['https://www.docs.io/a/b/c#sec-3', 4], ['http', 's://', 'www', '.doc', 's.io', '/a/b', '/c', '#sec', '-3']), ('control layout', ['https://t.co/AbCdEf', 5], ['https', '://t', '.co', '/AbCd', 'Ef'])], [('regression: double slash integrity', ['https://example.com/path/to/page.html', 7], ['https:', '//', 'example', '.com', '/path', '/to', '/page', '.html']), ('regression: double slash integrity', ['http://a.b.org/x//y?q=1&r=2', 8], ['http://a', '.b.org', '/x//y?q=', '1&r=2']), ('regression: double slash integrity', ['http://a.b.org/x//y?q=1&r=2', 8], ['http://a', '.b.org', '/x//y?q=', '1&r=2']), ('regression: double slash integrity', ['http://a.b.org/x//y?q=1&r=2', 6], ['http:', '//a.b', '.org', '/x//y', '?q=1&r', '=2']), ('double slash inside path', ['http://a.b.org/x//y?q=1&r=2', 10], ['http://a.b', '.org/x//y', '?q=1&r=2']), ('break after scheme', ['https://example.com/path/to/page.html', 8], ['https://', 'example', '.com', '/path/to', '/page', '.html']), ('control layout', ['file:///usr/local/share/doc', 7], ['file://', '/usr', '/local', '/share', '/doc']), ('control layout', ['https://www.docs.io/a/b/c#sec-3', 14], ['https://www', '.docs.io/a/b/c', '#sec-3'])], [('regression: double slash integrity', ['ftp://files.site.net/pub/file-name_v2.tar.gz', 5], ['ftp:', '//', 'files', '.site', '.net', '/pub', '/file', '-name', '_v2', '.tar', '.gz']), ('regression: double slash integrity', ['https://t.co/AbCdEf', 7], ['https:', '//t.co', '/AbCdEf']), ('regression: double slash integrity', ['http://a.b.org/x//y?q=1&r=2', 9], ['http://a', '.b.org', '/x//y?q=1', '&r=2']), ('regression: double slash integrity', ['http://a.b.org/x//y?q=1&r=2', 8], ['http://a', '.b.org', '/x//y?q=', '1&r=2']), ('double slash inside path', ['http://a.b.org/x//y?q=1&r=2', 10], ['http://a.b', '.org/x//y', '?q=1&r=2']), ('break after scheme', ['https://example.com/path/to/page.html', 8], ['https://', 'example', '.com', '/path/to', '/page', '.html']), ('control layout', ['https://w.org/a=b/c&d', 16], ['https://w.org/a=', 'b/c&d']), ('control layout', ['https://example.com/path/to/page.html', 11], ['https://', 'example.com', '/path/to', '/page.html'])], [('regression: double slash integrity', ['https://example.com/path/to/page.html', 7], ['https:', '//', 'example', '.com', '/path', '/to', '/page', '.html']), ('regression: double slash integrity', ['file:///usr/local/share/doc', 6], ['file:', '///usr', '/local', '/share', '/doc']), ('regression: double slash integrity', ['http://a.b.org/x//y?q=1&r=2', 8], ['http://a', '.b.org', '/x//y?q=', '1&r=2']), ('regression: double slash integrity', ['http://a.b.org/x//y?q=1&r=2', 16], ['http://a.b.org', '/x//y?q=1&r=2']), ('double slash inside path', ['http://a.b.org/x//y?q=1&r=2', 10], ['http://a.b', '.org/x//y', '?q=1&r=2']), ('break after scheme', ['https://example.com/path/to/page.html', 8], ['https://', 'example', '.com', '/path/to', '/page', '.html']), ('control layout', ['mailto:someone@example.com', 15], ['mailto:', 'someone@example', '.com']), ('control layout', ['file:///usr/local/share/doc', 12], ['file:///usr', '/local/share', '/doc'])]]
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: double slash integrity['https:/', '/x.io', '/search', '?term=', 'line', '%20brea', 'k&lang=', 'en']['https:', '//x.io', '/search', '?term=', 'line', '%20brea', 'k&lang=', 'en']Failed
regression: double slash integrity['https:/', '/', 'example', '.com', '/path', '/to', '/page', '.html']['https:', '//', 'example', '.com', '/path', '/to', '/page', '.html']Failed
regression: double slash integrity['http://a', '.b.org/x/', '/y?q=1&r=', '2']['http://a', '.b.org', '/x//y?q=1', '&r=2']Failed
regression: double slash integrity['http://a', '.b.org/x/', '/y?q=1&r=', '2']['http://a', '.b.org', '/x//y?q=1', '&r=2']Failed
double slash inside path['http://a.b', '.org/x//y', '?q=1&r=2']['http://a.b', '.org/x//y', '?q=1&r=2']Passed
break after scheme['https://', 'example', '.com', '/path/to', '/page', '.html']['https://', 'example', '.com', '/path/to', '/page', '.html']Passed
control layout['https', '://w', '.org', '/a=b', '/c&d']['https', '://w', '.org', '/a=b', '/c&d']Passed
control layout['file:///usr', '/local/share', '/doc']['file:///usr', '/local/share', '/doc']Passed

SHA-256 / 59087e45d671414ed15c566d5f4ff831d379e52975f3a1e38557368618390af5

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(x):
    url, width = x
    n = len(url)
    ok = set()
    for p in range(1, n):
        a, b = url[p - 1], url[p]
        if a == ':':
            ok.add(p)
        elif a == '/' and url[p - 2:p] == '//':
            ok.add(p)
        elif b == '/' and a != '/':
            ok.add(p)
        elif b in '.-_?#%~':
            ok.add(p)
        elif a in '=&' or b in '=&':
            ok.add(p)
    lines = []
    start = 0
    while n - start > width:
        cands = [p for p in ok if start < p <= start + width]
        cut = max(cands) if cands else start + width
        lines.append(url[start:cut])
        start = cut
    lines.append(url[start:])
    return lines
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: double slash integrity', ['https://x.io/search?term=line%20break&lang=en', 7], ['https:', '//x.io', '/search', '?term=', 'line', '%20brea', 'k&lang=', 'en']), ('regression: double slash integrity', ['https://example.com/path/to/page.html', 7], ['https:', '//', 'example', '.com', '/path', '/to', '/page', '.html']), ('regression: double slash integrity', ['http://a.b.org/x//y?q=1&r=2', 9], ['http://a', '.b.org', '/x//y?q=1', '&r=2']), ('regression: double slash integrity', ['http://a.b.org/x//y?q=1&r=2', 9], ['http://a', '.b.org', '/x//y?q=1', '&r=2']), ('double slash inside path', ['http://a.b.org/x//y?q=1&r=2', 10], ['http://a.b', '.org/x//y', '?q=1&r=2']), ('break after scheme', ['https://example.com/path/to/page.html', 8], ['https://', 'example', '.com', '/path/to', '/page', '.html']), ('control layout', ['https://w.org/a=b/c&d', 5], ['https', '://w', '.org', '/a=b', '/c&d']), ('control layout', ['file:///usr/local/share/doc', 14], ['file:///usr', '/local/share', '/doc'])], [('regression: double slash integrity', ['https://www.docs.io/a/b/c#sec-3', 7], ['https:', '//www', '.docs', '.io/a/b', '/c#sec', '-3']), ('regression: double slash integrity', ['http://a.b.org/x//y?q=1&r=2', 6], ['http:', '//a.b', '.org', '/x//y', '?q=1&r', '=2']), ('regression: double slash integrity', ['http://a.b.org/x//y?q=1&r=2', 9], ['http://a', '.b.org', '/x//y?q=1', '&r=2']), ('regression: double slash integrity', ['http://a.b.org/x//y?q=1&r=2', 8], ['http://a', '.b.org', '/x//y?q=', '1&r=2']), ('double slash inside path', ['http://a.b.org/x//y?q=1&r=2', 10], ['http://a.b', '.org/x//y', '?q=1&r=2']), ('break after scheme', ['https://example.com/path/to/page.html', 8], ['https://', 'example', '.com', '/path/to', '/page', '.html']), ('control layout', ['https://www.docs.io/a/b/c#sec-3', 4], ['http', 's://', 'www', '.doc', 's.io', '/a/b', '/c', '#sec', '-3']), ('control layout', ['https://t.co/AbCdEf', 5], ['https', '://t', '.co', '/AbCd', 'Ef'])], [('regression: double slash integrity', ['https://example.com/path/to/page.html', 7], ['https:', '//', 'example', '.com', '/path', '/to', '/page', '.html']), ('regression: double slash integrity', ['http://a.b.org/x//y?q=1&r=2', 8], ['http://a', '.b.org', '/x//y?q=', '1&r=2']), ('regression: double slash integrity', ['http://a.b.org/x//y?q=1&r=2', 8], ['http://a', '.b.org', '/x//y?q=', '1&r=2']), ('regression: double slash integrity', ['http://a.b.org/x//y?q=1&r=2', 6], ['http:', '//a.b', '.org', '/x//y', '?q=1&r', '=2']), ('double slash inside path', ['http://a.b.org/x//y?q=1&r=2', 10], ['http://a.b', '.org/x//y', '?q=1&r=2']), ('break after scheme', ['https://example.com/path/to/page.html', 8], ['https://', 'example', '.com', '/path/to', '/page', '.html']), ('control layout', ['file:///usr/local/share/doc', 7], ['file://', '/usr', '/local', '/share', '/doc']), ('control layout', ['https://www.docs.io/a/b/c#sec-3', 14], ['https://www', '.docs.io/a/b/c', '#sec-3'])], [('regression: double slash integrity', ['ftp://files.site.net/pub/file-name_v2.tar.gz', 5], ['ftp:', '//', 'files', '.site', '.net', '/pub', '/file', '-name', '_v2', '.tar', '.gz']), ('regression: double slash integrity', ['https://t.co/AbCdEf', 7], ['https:', '//t.co', '/AbCdEf']), ('regression: double slash integrity', ['http://a.b.org/x//y?q=1&r=2', 9], ['http://a', '.b.org', '/x//y?q=1', '&r=2']), ('regression: double slash integrity', ['http://a.b.org/x//y?q=1&r=2', 8], ['http://a', '.b.org', '/x//y?q=', '1&r=2']), ('double slash inside path', ['http://a.b.org/x//y?q=1&r=2', 10], ['http://a.b', '.org/x//y', '?q=1&r=2']), ('break after scheme', ['https://example.com/path/to/page.html', 8], ['https://', 'example', '.com', '/path/to', '/page', '.html']), ('control layout', ['https://w.org/a=b/c&d', 16], ['https://w.org/a=', 'b/c&d']), ('control layout', ['https://example.com/path/to/page.html', 11], ['https://', 'example.com', '/path/to', '/page.html'])], [('regression: double slash integrity', ['https://example.com/path/to/page.html', 7], ['https:', '//', 'example', '.com', '/path', '/to', '/page', '.html']), ('regression: double slash integrity', ['file:///usr/local/share/doc', 6], ['file:', '///usr', '/local', '/share', '/doc']), ('regression: double slash integrity', ['http://a.b.org/x//y?q=1&r=2', 8], ['http://a', '.b.org', '/x//y?q=', '1&r=2']), ('regression: double slash integrity', ['http://a.b.org/x//y?q=1&r=2', 16], ['http://a.b.org', '/x//y?q=1&r=2']), ('double slash inside path', ['http://a.b.org/x//y?q=1&r=2', 10], ['http://a.b', '.org/x//y', '?q=1&r=2']), ('break after scheme', ['https://example.com/path/to/page.html', 8], ['https://', 'example', '.com', '/path/to', '/page', '.html']), ('control layout', ['mailto:someone@example.com', 15], ['mailto:', 'someone@example', '.com']), ('control layout', ['file:///usr/local/share/doc', 12], ['file:///usr', '/local/share', '/doc'])]]
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: double slash integrity['https:', '//x.io', '/search', '?term=', 'line', '%20brea', 'k&lang=', 'en']['https:', '//x.io', '/search', '?term=', 'line', '%20brea', 'k&lang=', 'en']Passed
regression: double slash integrity['https:', '//', 'example', '.com', '/path', '/to', '/page', '.html']['https:', '//', 'example', '.com', '/path', '/to', '/page', '.html']Passed
regression: double slash integrity['http://a', '.b.org/x', '//y?q=1&r', '=2']['http://a', '.b.org', '/x//y?q=1', '&r=2']Failed
regression: double slash integrity['http://a', '.b.org/x', '//y?q=1&r', '=2']['http://a', '.b.org', '/x//y?q=1', '&r=2']Failed
double slash inside path['http://a.b', '.org/x//y', '?q=1&r=2']['http://a.b', '.org/x//y', '?q=1&r=2']Passed
break after scheme['https://', 'example', '.com', '/path/to', '/page', '.html']['https://', 'example', '.com', '/path/to', '/page', '.html']Passed
control layout['https', '://w', '.org', '/a=b', '/c&d']['https', '://w', '.org', '/a=b', '/c&d']Passed
control layout['file:///usr', '/local/share', '/doc']['file:///usr', '/local/share', '/doc']Passed

SHA-256 / 860be1427159b0c7d7f209c1d248a152a75f7ae76b23e26ae0c4420e43c269c4

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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.

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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 2026-09-29T14:49:52.806865+00:00.

Case digest / 0eb7f56b1977e16a195094bc9682f77920629de23dffc8f9ab8472be8c6f35d5