FA-80341 / Bidirectional text layout / Open access

First-strong paragraph direction: Arabic letter strength · case 01

Paragraphs starting with Arabic letters default to left-to-right.

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

ROOT CAUSE

Only class R is treated as a right-to-left strong character; AL is skipped.

VERIFIED REPAIR

Treat both R and AL as strong right-to-left.

Unsuccessful approach: Adding AN instead of AL makes Arabic digits decide the direction.

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 == 'L':
                return [0, i]
            if c == 'R':
                return [1, i]
    return [default, None]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('Arabic letter decides', [['ON', 'AL', 'L'], 0], [1, 1]), ('regression: Arabic letter strength', [['AL'], 0], [1, 0]), ('regression: Arabic letter strength', [['AL', 'EN'], 1], [1, 0]), ('partial-repair probe', [['AN', 'R', 'L', 'ON', 'L'], 1], [1, 1]), ('numbers are not strong', [['EN', 'ON', 'R'], 0], [1, 2]), ('stray PDI before isolate', [['PDI', 'RLI', 'L', 'PDI', 'R'], 0], [1, 4]), ('control layout', [['WS', 'FSI'], 0], [0, None]), ('control layout', [['EN', 'R'], 0], [1, 1])], [('regression: Arabic letter strength', [['AL', 'ON', 'PDI', 'AL', 'WS'], 1], [1, 0]), ('regression: Arabic letter strength', [['WS', 'WS', 'AL', 'AN', 'WS', 'PDI'], 0], [1, 2]), ('regression: Arabic letter strength', [['AL', 'RLI', 'PDI', 'WS', 'FSI', 'ON', 'L'], 1], [1, 0]), ('partial-repair probe', [['AN', 'ES', 'L', 'L', 'WS', 'L', 'AL', 'R'], 0], [0, 2]), ('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', 'FSI', 'L', 'NSM', 'ON', 'R'], 1], [1, None]), ('control layout', [['R', 'WS', 'ON', 'AN', 'RLI', 'RLI'], 0], [1, 0])], [('regression: Arabic letter strength', [['AL', 'EN'], 1], [1, 0]), ('regression: Arabic letter strength', [['ON', 'AL', 'FSI'], 0], [1, 1]), ('regression: Arabic letter strength', [['AL', 'L', 'WS'], 0], [1, 0]), ('partial-repair probe', [['LRE', 'AN', 'L', 'AN'], 1], [0, 2]), ('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', [['EN', 'PDI', 'L', 'EN', 'FSI'], 1], [0, 2]), ('control layout', [['RLI', 'PDI', 'RLI', 'EN'], 1], [1, None])], [('regression: Arabic letter strength', [['EN', 'LRE', 'AL', 'FSI'], 1], [1, 2]), ('regression: Arabic letter strength', [['ON', 'AL', 'ES', 'L', 'PDI', 'AN', 'NSM', 'LRI', 'ON'], 0], [1, 1]), ('partial-repair probe', [['ON', 'AN', 'RLI', 'RLI', 'R', 'R', 'EN', 'EN', 'L'], 1], [1, None]), ('regression: Arabic letter strength', [['AL', 'R', 'ON', 'AN', 'AL', 'EN', 'L', 'PDI', 'PDI', 'L'], 0], [1, 0]), ('FSI content skipped', [['FSI', 'R', 'PDI', 'L'], 1], [0, 3]), ('numbers are not strong', [['EN', 'ON', 'R'], 0], [1, 2]), ('control layout', [['L', 'R', 'R', 'NSM', 'L', 'PDI', 'PDI', 'EN'], 1], [0, 0]), ('control layout', [['LRI', 'ES'], 0], [0, None])], [('regression: Arabic letter strength', [['AL', 'PDI'], 1], [1, 0]), ('regression: Arabic letter strength', [['AL', 'RLI', 'PDI', 'WS', 'FSI', 'ON', 'L'], 1], [1, 0]), ('regression: Arabic letter strength', [['NSM', 'AL', 'PDI', 'ON', 'AN', 'WS'], 0], [1, 1]), ('regression: Arabic letter strength', [['ON', 'AL'], 1], [1, 1]), ('FSI content skipped', [['FSI', 'R', 'PDI', 'L'], 1], [0, 3]), ('numbers are not strong', [['EN', 'ON', 'R'], 0], [1, 2]), ('control layout', [['WS'], 0], [0, None]), ('control layout', [['EN'], 0], [0, None])]]
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 fixture	Actual	Expected	Outcome
Arabic letter decides	`[0, 2]`	`[1, 1]`	Failed
regression: Arabic letter strength	`[0, None]`	`[1, 0]`	Failed
regression: Arabic letter strength	`[1, None]`	`[1, 0]`	Failed
partial-repair probe	`[1, 1]`	`[1, 1]`	Passed
numbers are not strong	`[1, 2]`	`[1, 2]`	Passed
stray PDI before isolate	`[1, 4]`	`[1, 4]`	Passed
control layout	`[0, None]`	`[0, None]`	Passed
control layout	`[1, 1]`	`[1, 1]`	Passed

SHA-256 / 47c6474a5317fab57e5e2f26110aa16bf901dd55915304e5563e716f62e3ff5e

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':
                return [0, i]
            if c in ('R', 'AN'):
                return [1, i]
    return [default, None]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('Arabic letter decides', [['ON', 'AL', 'L'], 0], [1, 1]), ('regression: Arabic letter strength', [['AL'], 0], [1, 0]), ('regression: Arabic letter strength', [['AL', 'EN'], 1], [1, 0]), ('partial-repair probe', [['AN', 'R', 'L', 'ON', 'L'], 1], [1, 1]), ('numbers are not strong', [['EN', 'ON', 'R'], 0], [1, 2]), ('stray PDI before isolate', [['PDI', 'RLI', 'L', 'PDI', 'R'], 0], [1, 4]), ('control layout', [['WS', 'FSI'], 0], [0, None]), ('control layout', [['EN', 'R'], 0], [1, 1])], [('regression: Arabic letter strength', [['AL', 'ON', 'PDI', 'AL', 'WS'], 1], [1, 0]), ('regression: Arabic letter strength', [['WS', 'WS', 'AL', 'AN', 'WS', 'PDI'], 0], [1, 2]), ('regression: Arabic letter strength', [['AL', 'RLI', 'PDI', 'WS', 'FSI', 'ON', 'L'], 1], [1, 0]), ('partial-repair probe', [['AN', 'ES', 'L', 'L', 'WS', 'L', 'AL', 'R'], 0], [0, 2]), ('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', 'FSI', 'L', 'NSM', 'ON', 'R'], 1], [1, None]), ('control layout', [['R', 'WS', 'ON', 'AN', 'RLI', 'RLI'], 0], [1, 0])], [('regression: Arabic letter strength', [['AL', 'EN'], 1], [1, 0]), ('regression: Arabic letter strength', [['ON', 'AL', 'FSI'], 0], [1, 1]), ('regression: Arabic letter strength', [['AL', 'L', 'WS'], 0], [1, 0]), ('partial-repair probe', [['LRE', 'AN', 'L', 'AN'], 1], [0, 2]), ('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', [['EN', 'PDI', 'L', 'EN', 'FSI'], 1], [0, 2]), ('control layout', [['RLI', 'PDI', 'RLI', 'EN'], 1], [1, None])], [('regression: Arabic letter strength', [['EN', 'LRE', 'AL', 'FSI'], 1], [1, 2]), ('regression: Arabic letter strength', [['ON', 'AL', 'ES', 'L', 'PDI', 'AN', 'NSM', 'LRI', 'ON'], 0], [1, 1]), ('partial-repair probe', [['ON', 'AN', 'RLI', 'RLI', 'R', 'R', 'EN', 'EN', 'L'], 1], [1, None]), ('regression: Arabic letter strength', [['AL', 'R', 'ON', 'AN', 'AL', 'EN', 'L', 'PDI', 'PDI', 'L'], 0], [1, 0]), ('FSI content skipped', [['FSI', 'R', 'PDI', 'L'], 1], [0, 3]), ('numbers are not strong', [['EN', 'ON', 'R'], 0], [1, 2]), ('control layout', [['L', 'R', 'R', 'NSM', 'L', 'PDI', 'PDI', 'EN'], 1], [0, 0]), ('control layout', [['LRI', 'ES'], 0], [0, None])], [('regression: Arabic letter strength', [['AL', 'PDI'], 1], [1, 0]), ('regression: Arabic letter strength', [['AL', 'RLI', 'PDI', 'WS', 'FSI', 'ON', 'L'], 1], [1, 0]), ('regression: Arabic letter strength', [['NSM', 'AL', 'PDI', 'ON', 'AN', 'WS'], 0], [1, 1]), ('regression: Arabic letter strength', [['ON', 'AL'], 1], [1, 1]), ('FSI content skipped', [['FSI', 'R', 'PDI', 'L'], 1], [0, 3]), ('numbers are not strong', [['EN', 'ON', 'R'], 0], [1, 2]), ('control layout', [['WS'], 0], [0, None]), ('control layout', [['EN'], 0], [0, None])]]
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 fixture	Actual	Expected	Outcome
Arabic letter decides	`[0, 2]`	`[1, 1]`	Failed
regression: Arabic letter strength	`[0, None]`	`[1, 0]`	Failed
regression: Arabic letter strength	`[1, None]`	`[1, 0]`	Failed
partial-repair probe	`[1, 0]`	`[1, 1]`	Failed
numbers are not strong	`[1, 2]`	`[1, 2]`	Passed
stray PDI before isolate	`[1, 4]`	`[1, 4]`	Passed
control layout	`[0, None]`	`[0, None]`	Passed
control layout	`[1, 1]`	`[1, 1]`	Passed

SHA-256 / 8e236c5bef1633e0e180e388e0c3554e1f03c1efef991f5a997d97b8f25d4427

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 = [[('Arabic letter decides', [['ON', 'AL', 'L'], 0], [1, 1]), ('regression: Arabic letter strength', [['AL'], 0], [1, 0]), ('regression: Arabic letter strength', [['AL', 'EN'], 1], [1, 0]), ('partial-repair probe', [['AN', 'R', 'L', 'ON', 'L'], 1], [1, 1]), ('numbers are not strong', [['EN', 'ON', 'R'], 0], [1, 2]), ('stray PDI before isolate', [['PDI', 'RLI', 'L', 'PDI', 'R'], 0], [1, 4]), ('control layout', [['WS', 'FSI'], 0], [0, None]), ('control layout', [['EN', 'R'], 0], [1, 1])], [('regression: Arabic letter strength', [['AL', 'ON', 'PDI', 'AL', 'WS'], 1], [1, 0]), ('regression: Arabic letter strength', [['WS', 'WS', 'AL', 'AN', 'WS', 'PDI'], 0], [1, 2]), ('regression: Arabic letter strength', [['AL', 'RLI', 'PDI', 'WS', 'FSI', 'ON', 'L'], 1], [1, 0]), ('partial-repair probe', [['AN', 'ES', 'L', 'L', 'WS', 'L', 'AL', 'R'], 0], [0, 2]), ('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', 'FSI', 'L', 'NSM', 'ON', 'R'], 1], [1, None]), ('control layout', [['R', 'WS', 'ON', 'AN', 'RLI', 'RLI'], 0], [1, 0])], [('regression: Arabic letter strength', [['AL', 'EN'], 1], [1, 0]), ('regression: Arabic letter strength', [['ON', 'AL', 'FSI'], 0], [1, 1]), ('regression: Arabic letter strength', [['AL', 'L', 'WS'], 0], [1, 0]), ('partial-repair probe', [['LRE', 'AN', 'L', 'AN'], 1], [0, 2]), ('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', [['EN', 'PDI', 'L', 'EN', 'FSI'], 1], [0, 2]), ('control layout', [['RLI', 'PDI', 'RLI', 'EN'], 1], [1, None])], [('regression: Arabic letter strength', [['EN', 'LRE', 'AL', 'FSI'], 1], [1, 2]), ('regression: Arabic letter strength', [['ON', 'AL', 'ES', 'L', 'PDI', 'AN', 'NSM', 'LRI', 'ON'], 0], [1, 1]), ('partial-repair probe', [['ON', 'AN', 'RLI', 'RLI', 'R', 'R', 'EN', 'EN', 'L'], 1], [1, None]), ('regression: Arabic letter strength', [['AL', 'R', 'ON', 'AN', 'AL', 'EN', 'L', 'PDI', 'PDI', 'L'], 0], [1, 0]), ('FSI content skipped', [['FSI', 'R', 'PDI', 'L'], 1], [0, 3]), ('numbers are not strong', [['EN', 'ON', 'R'], 0], [1, 2]), ('control layout', [['L', 'R', 'R', 'NSM', 'L', 'PDI', 'PDI', 'EN'], 1], [0, 0]), ('control layout', [['LRI', 'ES'], 0], [0, None])], [('regression: Arabic letter strength', [['AL', 'PDI'], 1], [1, 0]), ('regression: Arabic letter strength', [['AL', 'RLI', 'PDI', 'WS', 'FSI', 'ON', 'L'], 1], [1, 0]), ('regression: Arabic letter strength', [['NSM', 'AL', 'PDI', 'ON', 'AN', 'WS'], 0], [1, 1]), ('regression: Arabic letter strength', [['ON', 'AL'], 1], [1, 1]), ('FSI content skipped', [['FSI', 'R', 'PDI', 'L'], 1], [0, 3]), ('numbers are not strong', [['EN', 'ON', 'R'], 0], [1, 2]), ('control layout', [['WS'], 0], [0, None]), ('control layout', [['EN'], 0], [0, None])]]
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 fixture	Actual	Expected	Outcome
Arabic letter decides	`[1, 1]`	`[1, 1]`	Passed
regression: Arabic letter strength	`[1, 0]`	`[1, 0]`	Passed
regression: Arabic letter strength	`[1, 0]`	`[1, 0]`	Passed
partial-repair probe	`[1, 1]`	`[1, 1]`	Passed
numbers are not strong	`[1, 2]`	`[1, 2]`	Passed
stray PDI before isolate	`[1, 4]`	`[1, 4]`	Passed
control layout	`[0, None]`	`[0, None]`	Passed
control layout	`[1, 1]`	`[1, 1]`	Passed

SHA-256 / 2db669c004c99f1ae0200880b5e2a283cdb2dc136f24634611584908016866e3

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 2026-09-29T14:49:52.893595+00:00.

Case digest / 7c092b15693f46f036f658bf382f2b6d654c48a95f233ac18c11438d664161a7