FAILURE MAP
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FA-80356 / Bidirectional text layout / Open access

First-strong paragraph direction: numbers as strong · case 01

Paragraphs that start with a number become left-to-right.

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

ROOT CAUSE

European numbers are counted as strong left-to-right characters.

VERIFIED REPAIR

Only class L counts as strong left-to-right.

Unsuccessful approach: Counting numbers only when the default is LTR still lets digits decide.

Case contract

Input [bidi classes, default level]. Scan for the first L (level 0) or R/AL (level 1), skipping characters between an isolate initiator (LRI, RLI, FSI) and its matching PDI (nesting counted; an unmatched PDI is ignored). Embedding codes are not skipped. Return [level, index of deciding character] or [default, None].

Why this case matters

Mixed right-to-left and left-to-right text must resolve levels and visual order exactly, or words, numbers and carets land in the wrong place.

1 / The failure

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

N = 1
observations = []
def solve(x):
    classes, default = x
    depth = 0
    for i, c in enumerate(classes):
        if c in ('LRI', 'RLI', 'FSI'):
            depth += 1
        elif c == 'PDI':
            if depth > 0:
                depth -= 1
        elif depth == 0:
            if c in ('L', 'EN'):
                return [0, i]
            if c in ('R', 'AL'):
                return [1, i]
    return [default, None]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('numbers are not strong', [['EN', 'ON', 'R'], 0], [1, 2]), ('regression: numbers as strong', [['NSM', 'WS', 'EN', 'EN', 'L', 'FSI', 'ON'], 0], [0, 4]), ('regression: numbers as strong', [['LRE', 'EN', 'L'], 0], [0, 2]), ('regression: numbers as strong', [['LRE', 'EN', 'EN', 'WS', 'RLI', 'R'], 0], [0, None]), ('stray PDI before isolate', [['PDI', 'RLI', 'L', 'PDI', 'R'], 0], [1, 4]), ('nested isolates', [['LRI', 'RLI', 'R', 'PDI', 'L', 'PDI', 'R'], 0], [1, 6]), ('control layout', [['L', 'RLI', 'L'], 1], [0, 0]), ('control layout', [['FSI', 'WS', 'NSM', 'AN', 'RLI', 'RLI', 'LRE', 'ON'], 1], [1, None])], [('regression: numbers as strong', [['LRE', 'AN', 'EN'], 1], [1, None]), ('regression: numbers as strong', [['ON', 'EN', 'RLI'], 0], [0, None]), ('regression: numbers as strong', [['EN', 'AN', 'WS', 'L', 'NSM', 'ON', 'LRI', 'PDI', 'EN', 'ON'], 0], [0, 3]), ('regression: numbers as strong', [['EN', 'LRE', 'R'], 0], [1, 2]), ('stray PDI before isolate', [['PDI', 'RLI', 'L', 'PDI', 'R'], 0], [1, 4]), ('nested isolates', [['LRI', 'RLI', 'R', 'PDI', 'L', 'PDI', 'R'], 0], [1, 6]), ('control layout', [['AN'], 1], [1, None]), ('control layout', [['FSI'], 0], [0, None])], [('regression: numbers as strong', [['ON', 'AN', 'ON', 'EN'], 0], [0, None]), ('regression: numbers as strong', [['AN', 'NSM', 'ON', 'EN', 'AN', 'NSM', 'L', 'WS', 'ON', 'ES'], 1], [0, 6]), ('regression: numbers as strong', [['EN', 'L', 'FSI', 'LRI', 'ON', 'R', 'EN', 'ON', 'ON', 'AL'], 0], [0, 1]), ('regression: numbers as strong', [['EN', 'PDI', 'RLI', 'FSI', 'RLI', 'WS', 'PDI', 'ON', 'EN', 'LRI'], 0], [0, None]), ('nested isolates', [['LRI', 'RLI', 'R', 'PDI', 'L', 'PDI', 'R'], 0], [1, 6]), ('numbers are not strong', [['EN', 'ON', 'R'], 0], [1, 2]), ('control layout', [['WS', 'WS', 'R', 'NSM'], 0], [1, 2]), ('control layout', [['WS', 'LRI', 'FSI', 'PDI', 'R', 'LRE'], 1], [1, None])], [('regression: numbers as strong', [['EN', 'EN', 'R', 'ON', 'PDI', 'L', 'FSI', 'ON', 'L'], 1], [1, 2]), ('regression: numbers as strong', [['EN', 'ON', 'R', 'AN', 'L', 'FSI'], 0], [1, 2]), ('regression: numbers as strong', [['EN', 'PDI', 'R', 'AL', 'LRE', 'WS', 'PDI', 'LRE', 'PDI'], 0], [1, 2]), ('regression: numbers as strong', [['EN', 'EN', 'WS', 'EN'], 0], [0, None]), ('nested isolates', [['LRI', 'RLI', 'R', 'PDI', 'L', 'PDI', 'R'], 0], [1, 6]), ('stray PDI before isolate', [['PDI', 'RLI', 'L', 'PDI', 'R'], 0], [1, 4]), ('control layout', [['PDI', 'PDI', 'LRI', 'WS', 'LRI', 'PDI', 'LRI', 'R', 'EN', 'L'], 1], [1, None]), ('control layout', [['AL', 'EN', 'L', 'WS', 'LRE', 'PDI'], 0], [1, 0])], [('regression: numbers as strong', [['PDI', 'EN', 'ON', 'EN', 'ON', 'RLI', 'LRI', 'L', 'WS'], 1], [1, None]), ('regression: numbers as strong', [['EN', 'AN', 'ES', 'RLI', 'AL', 'AL', 'ON', 'FSI'], 1], [1, None]), ('regression: numbers as strong', [['EN', 'PDI', 'FSI', 'EN', 'ES', 'AN', 'WS', 'PDI', 'ES'], 0], [0, None]), ('regression: numbers as strong', [['LRE', 'LRE', 'PDI', 'EN', 'PDI', 'L', 'ON', 'EN'], 0], [0, 5]), ('FSI content skipped', [['FSI', 'R', 'PDI', 'L'], 1], [0, 3]), ('Arabic letter decides', [['ON', 'AL', 'L'], 0], [1, 1]), ('control layout', [['LRI'], 0], [0, None]), ('control layout', [['AN', 'R'], 1], [1, 1])]]
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
numbers are not strong[0, 0][1, 2]Failed
regression: numbers as strong[0, 2][0, 4]Failed
regression: numbers as strong[0, 1][0, 2]Failed
regression: numbers as strong[0, 1][0, None]Failed
stray PDI before isolate[1, 4][1, 4]Passed
nested isolates[1, 6][1, 6]Passed
control layout[0, 0][0, 0]Passed
control layout[1, None][1, None]Passed

SHA-256 / 3de908dce8e55435b600d4f15fde2827e356c890a472542c8c3eb3d5c314ddf0

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(x):
    classes, default = x
    depth = 0
    for i, c in enumerate(classes):
        if c in ('LRI', 'RLI', 'FSI'):
            depth += 1
        elif c == 'PDI':
            if depth > 0:
                depth -= 1
        elif depth == 0:
            if c == 'L' or c == 'EN' and default == 0:
                return [0, i]
            if c in ('R', 'AL'):
                return [1, i]
    return [default, None]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('numbers are not strong', [['EN', 'ON', 'R'], 0], [1, 2]), ('regression: numbers as strong', [['NSM', 'WS', 'EN', 'EN', 'L', 'FSI', 'ON'], 0], [0, 4]), ('regression: numbers as strong', [['LRE', 'EN', 'L'], 0], [0, 2]), ('regression: numbers as strong', [['LRE', 'EN', 'EN', 'WS', 'RLI', 'R'], 0], [0, None]), ('stray PDI before isolate', [['PDI', 'RLI', 'L', 'PDI', 'R'], 0], [1, 4]), ('nested isolates', [['LRI', 'RLI', 'R', 'PDI', 'L', 'PDI', 'R'], 0], [1, 6]), ('control layout', [['L', 'RLI', 'L'], 1], [0, 0]), ('control layout', [['FSI', 'WS', 'NSM', 'AN', 'RLI', 'RLI', 'LRE', 'ON'], 1], [1, None])], [('regression: numbers as strong', [['LRE', 'AN', 'EN'], 1], [1, None]), ('regression: numbers as strong', [['ON', 'EN', 'RLI'], 0], [0, None]), ('regression: numbers as strong', [['EN', 'AN', 'WS', 'L', 'NSM', 'ON', 'LRI', 'PDI', 'EN', 'ON'], 0], [0, 3]), ('regression: numbers as strong', [['EN', 'LRE', 'R'], 0], [1, 2]), ('stray PDI before isolate', [['PDI', 'RLI', 'L', 'PDI', 'R'], 0], [1, 4]), ('nested isolates', [['LRI', 'RLI', 'R', 'PDI', 'L', 'PDI', 'R'], 0], [1, 6]), ('control layout', [['AN'], 1], [1, None]), ('control layout', [['FSI'], 0], [0, None])], [('regression: numbers as strong', [['ON', 'AN', 'ON', 'EN'], 0], [0, None]), ('regression: numbers as strong', [['AN', 'NSM', 'ON', 'EN', 'AN', 'NSM', 'L', 'WS', 'ON', 'ES'], 1], [0, 6]), ('regression: numbers as strong', [['EN', 'L', 'FSI', 'LRI', 'ON', 'R', 'EN', 'ON', 'ON', 'AL'], 0], [0, 1]), ('regression: numbers as strong', [['EN', 'PDI', 'RLI', 'FSI', 'RLI', 'WS', 'PDI', 'ON', 'EN', 'LRI'], 0], [0, None]), ('nested isolates', [['LRI', 'RLI', 'R', 'PDI', 'L', 'PDI', 'R'], 0], [1, 6]), ('numbers are not strong', [['EN', 'ON', 'R'], 0], [1, 2]), ('control layout', [['WS', 'WS', 'R', 'NSM'], 0], [1, 2]), ('control layout', [['WS', 'LRI', 'FSI', 'PDI', 'R', 'LRE'], 1], [1, None])], [('regression: numbers as strong', [['EN', 'EN', 'R', 'ON', 'PDI', 'L', 'FSI', 'ON', 'L'], 1], [1, 2]), ('regression: numbers as strong', [['EN', 'ON', 'R', 'AN', 'L', 'FSI'], 0], [1, 2]), ('regression: numbers as strong', [['EN', 'PDI', 'R', 'AL', 'LRE', 'WS', 'PDI', 'LRE', 'PDI'], 0], [1, 2]), ('regression: numbers as strong', [['EN', 'EN', 'WS', 'EN'], 0], [0, None]), ('nested isolates', [['LRI', 'RLI', 'R', 'PDI', 'L', 'PDI', 'R'], 0], [1, 6]), ('stray PDI before isolate', [['PDI', 'RLI', 'L', 'PDI', 'R'], 0], [1, 4]), ('control layout', [['PDI', 'PDI', 'LRI', 'WS', 'LRI', 'PDI', 'LRI', 'R', 'EN', 'L'], 1], [1, None]), ('control layout', [['AL', 'EN', 'L', 'WS', 'LRE', 'PDI'], 0], [1, 0])], [('regression: numbers as strong', [['PDI', 'EN', 'ON', 'EN', 'ON', 'RLI', 'LRI', 'L', 'WS'], 1], [1, None]), ('regression: numbers as strong', [['EN', 'AN', 'ES', 'RLI', 'AL', 'AL', 'ON', 'FSI'], 1], [1, None]), ('regression: numbers as strong', [['EN', 'PDI', 'FSI', 'EN', 'ES', 'AN', 'WS', 'PDI', 'ES'], 0], [0, None]), ('regression: numbers as strong', [['LRE', 'LRE', 'PDI', 'EN', 'PDI', 'L', 'ON', 'EN'], 0], [0, 5]), ('FSI content skipped', [['FSI', 'R', 'PDI', 'L'], 1], [0, 3]), ('Arabic letter decides', [['ON', 'AL', 'L'], 0], [1, 1]), ('control layout', [['LRI'], 0], [0, None]), ('control layout', [['AN', 'R'], 1], [1, 1])]]
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
numbers are not strong[0, 0][1, 2]Failed
regression: numbers as strong[0, 2][0, 4]Failed
regression: numbers as strong[0, 1][0, 2]Failed
regression: numbers as strong[0, 1][0, None]Failed
stray PDI before isolate[1, 4][1, 4]Passed
nested isolates[1, 6][1, 6]Passed
control layout[0, 0][0, 0]Passed
control layout[1, None][1, None]Passed

SHA-256 / 0a60d3b37c31323b10ee3cf646740964650953839c124c4217232105f91a21a8

3 / The verified repair

Exit 0
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(x):
    classes, default = x
    depth = 0
    for i, c in enumerate(classes):
        if c in ('LRI', 'RLI', 'FSI'):
            depth += 1
        elif c == 'PDI':
            if depth > 0:
                depth -= 1
        elif depth == 0:
            if c == 'L':
                return [0, i]
            if c in ('R', 'AL'):
                return [1, i]
    return [default, None]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('numbers are not strong', [['EN', 'ON', 'R'], 0], [1, 2]), ('regression: numbers as strong', [['NSM', 'WS', 'EN', 'EN', 'L', 'FSI', 'ON'], 0], [0, 4]), ('regression: numbers as strong', [['LRE', 'EN', 'L'], 0], [0, 2]), ('regression: numbers as strong', [['LRE', 'EN', 'EN', 'WS', 'RLI', 'R'], 0], [0, None]), ('stray PDI before isolate', [['PDI', 'RLI', 'L', 'PDI', 'R'], 0], [1, 4]), ('nested isolates', [['LRI', 'RLI', 'R', 'PDI', 'L', 'PDI', 'R'], 0], [1, 6]), ('control layout', [['L', 'RLI', 'L'], 1], [0, 0]), ('control layout', [['FSI', 'WS', 'NSM', 'AN', 'RLI', 'RLI', 'LRE', 'ON'], 1], [1, None])], [('regression: numbers as strong', [['LRE', 'AN', 'EN'], 1], [1, None]), ('regression: numbers as strong', [['ON', 'EN', 'RLI'], 0], [0, None]), ('regression: numbers as strong', [['EN', 'AN', 'WS', 'L', 'NSM', 'ON', 'LRI', 'PDI', 'EN', 'ON'], 0], [0, 3]), ('regression: numbers as strong', [['EN', 'LRE', 'R'], 0], [1, 2]), ('stray PDI before isolate', [['PDI', 'RLI', 'L', 'PDI', 'R'], 0], [1, 4]), ('nested isolates', [['LRI', 'RLI', 'R', 'PDI', 'L', 'PDI', 'R'], 0], [1, 6]), ('control layout', [['AN'], 1], [1, None]), ('control layout', [['FSI'], 0], [0, None])], [('regression: numbers as strong', [['ON', 'AN', 'ON', 'EN'], 0], [0, None]), ('regression: numbers as strong', [['AN', 'NSM', 'ON', 'EN', 'AN', 'NSM', 'L', 'WS', 'ON', 'ES'], 1], [0, 6]), ('regression: numbers as strong', [['EN', 'L', 'FSI', 'LRI', 'ON', 'R', 'EN', 'ON', 'ON', 'AL'], 0], [0, 1]), ('regression: numbers as strong', [['EN', 'PDI', 'RLI', 'FSI', 'RLI', 'WS', 'PDI', 'ON', 'EN', 'LRI'], 0], [0, None]), ('nested isolates', [['LRI', 'RLI', 'R', 'PDI', 'L', 'PDI', 'R'], 0], [1, 6]), ('numbers are not strong', [['EN', 'ON', 'R'], 0], [1, 2]), ('control layout', [['WS', 'WS', 'R', 'NSM'], 0], [1, 2]), ('control layout', [['WS', 'LRI', 'FSI', 'PDI', 'R', 'LRE'], 1], [1, None])], [('regression: numbers as strong', [['EN', 'EN', 'R', 'ON', 'PDI', 'L', 'FSI', 'ON', 'L'], 1], [1, 2]), ('regression: numbers as strong', [['EN', 'ON', 'R', 'AN', 'L', 'FSI'], 0], [1, 2]), ('regression: numbers as strong', [['EN', 'PDI', 'R', 'AL', 'LRE', 'WS', 'PDI', 'LRE', 'PDI'], 0], [1, 2]), ('regression: numbers as strong', [['EN', 'EN', 'WS', 'EN'], 0], [0, None]), ('nested isolates', [['LRI', 'RLI', 'R', 'PDI', 'L', 'PDI', 'R'], 0], [1, 6]), ('stray PDI before isolate', [['PDI', 'RLI', 'L', 'PDI', 'R'], 0], [1, 4]), ('control layout', [['PDI', 'PDI', 'LRI', 'WS', 'LRI', 'PDI', 'LRI', 'R', 'EN', 'L'], 1], [1, None]), ('control layout', [['AL', 'EN', 'L', 'WS', 'LRE', 'PDI'], 0], [1, 0])], [('regression: numbers as strong', [['PDI', 'EN', 'ON', 'EN', 'ON', 'RLI', 'LRI', 'L', 'WS'], 1], [1, None]), ('regression: numbers as strong', [['EN', 'AN', 'ES', 'RLI', 'AL', 'AL', 'ON', 'FSI'], 1], [1, None]), ('regression: numbers as strong', [['EN', 'PDI', 'FSI', 'EN', 'ES', 'AN', 'WS', 'PDI', 'ES'], 0], [0, None]), ('regression: numbers as strong', [['LRE', 'LRE', 'PDI', 'EN', 'PDI', 'L', 'ON', 'EN'], 0], [0, 5]), ('FSI content skipped', [['FSI', 'R', 'PDI', 'L'], 1], [0, 3]), ('Arabic letter decides', [['ON', 'AL', 'L'], 0], [1, 1]), ('control layout', [['LRI'], 0], [0, None]), ('control layout', [['AN', 'R'], 1], [1, 1])]]
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
numbers are not strong[1, 2][1, 2]Passed
regression: numbers as strong[0, 4][0, 4]Passed
regression: numbers as strong[0, 2][0, 2]Passed
regression: numbers as strong[0, None][0, None]Passed
stray PDI before isolate[1, 4][1, 4]Passed
nested isolates[1, 6][1, 6]Passed
control layout[0, 0][0, 0]Passed
control layout[1, None][1, None]Passed

SHA-256 / f53ba4caea2e6ab2b4d1b515f89ebdc1c97b964ee3eef0dcbafb88d838e4eebe

Verification & scope

A deterministic toy bidi model over stipulated class labels and integer levels; it is inspired by, but does not claim conformance to, any published algorithm. 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 2026-09-29T14:49:52.936432+00:00.

Case digest / bc5be712de917eddd80df8ef4905238dfe95d99456dd1a002a580e5f03503c99