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FA-80346 / Bidirectional text layout / Open access

First-strong paragraph direction: unmatched PDI · case 01

A stray PDI hides the rest of the paragraph from direction detection.

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

ROOT CAUSE

Every PDI decrements the isolate depth, driving it negative.

VERIFIED REPAIR

Only decrement when an isolate is open.

Unsuccessful approach: Resetting depth to zero closes all nested isolates at once.

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':
            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 = [[('stray PDI before isolate', [['PDI', 'RLI', 'L', 'PDI', 'R'], 0], [1, 4]), ('regression: unmatched PDI', [['LRE', 'PDI', 'AL', 'PDI', 'AN', 'RLI', 'WS', 'AL', 'R', 'EN'], 1], [1, 2]), ('partial-repair probe', [['ON', 'RLI', 'ON', 'LRI', 'AL', 'PDI', 'L', 'NSM'], 0], [0, None]), ('partial-repair probe', [['LRI', 'ON', 'RLI', 'L', 'PDI', 'AL', 'R', 'WS'], 0], [0, None]), ('FSI content skipped', [['FSI', 'R', 'PDI', 'L'], 1], [0, 3]), ('numbers are not strong', [['EN', 'ON', 'R'], 0], [1, 2]), ('control layout', [['AL', 'PDI', 'L', 'WS', 'EN', 'L', 'ES', 'ON'], 0], [1, 0]), ('control layout', [['WS', 'L', 'PDI', 'WS', 'AL'], 1], [0, 1])], [('regression: unmatched PDI', [['PDI', 'PDI', 'L', 'ON', 'L', 'EN', 'ON', 'RLI'], 0], [0, 2]), ('regression: unmatched PDI', [['PDI', 'LRI', 'AL', 'ON'], 1], [1, None]), ('partial-repair probe', [['LRI', 'WS', 'RLI', 'AN', 'PDI', 'AN', 'R', 'LRE', 'ES', 'L'], 1], [1, None]), ('partial-repair probe', [['LRI', 'EN', 'AN', 'LRI', 'RLI', 'AL', 'R', 'AN', 'PDI', 'R'], 1], [1, None]), ('numbers are not strong', [['EN', 'ON', 'R'], 0], [1, 2]), ('nested isolates', [['LRI', 'RLI', 'R', 'PDI', 'L', 'PDI', 'R'], 0], [1, 6]), ('control layout', [['LRI', 'AL', 'L', 'ON', 'AL', 'L', 'WS'], 1], [1, None]), ('control layout', [['RLI', 'WS', 'ON', 'ON', 'ON', 'L', 'R', 'LRI'], 0], [0, None])], [('regression: unmatched PDI', [['PDI', 'FSI', 'L', 'NSM', 'R', 'NSM', 'L', 'EN', 'WS', 'R'], 1], [1, None]), ('regression: unmatched PDI', [['PDI', 'AL', 'ON', 'PDI', 'L', 'WS', 'FSI', 'PDI', 'ON', 'LRI'], 0], [1, 1]), ('partial-repair probe', [['ON', 'RLI', 'ON', 'LRI', 'AL', 'PDI', 'L', 'NSM'], 0], [0, None]), ('partial-repair probe', [['LRI', 'EN', 'AN', 'LRI', 'RLI', 'AL', 'R', 'AN', 'PDI', 'R'], 1], [1, None]), ('FSI content skipped', [['FSI', 'R', 'PDI', 'L'], 1], [0, 3]), ('nested isolates', [['LRI', 'RLI', 'R', 'PDI', 'L', 'PDI', 'R'], 0], [1, 6]), ('control layout', [['WS'], 1], [1, None]), ('control layout', [['LRE', 'WS', 'LRI'], 0], [0, None])], [('regression: unmatched PDI', [['ON', 'PDI', 'LRE', 'L', 'AN', 'R', 'AL'], 1], [0, 3]), ('regression: unmatched PDI', [['EN', 'PDI', 'L', 'EN', 'FSI'], 1], [0, 2]), ('partial-repair probe', [['ON', 'RLI', 'ON', 'LRI', 'AL', 'PDI', 'L', 'NSM'], 0], [0, None]), ('partial-repair probe', [['WS', 'LRI', 'FSI', 'PDI', 'R', 'LRE'], 1], [1, None]), ('nested isolates', [['LRI', 'RLI', 'R', 'PDI', 'L', 'PDI', 'R'], 0], [1, 6]), ('Arabic letter decides', [['ON', 'AL', 'L'], 0], [1, 1]), ('control layout', [['EN', 'FSI', 'FSI', 'FSI', 'R', 'FSI', 'L'], 0], [0, None]), ('control layout', [['NSM', 'AN'], 1], [1, None])], [('regression: unmatched PDI', [['PDI', 'PDI', 'LRI', 'WS', 'LRI', 'PDI', 'LRI', 'R', 'EN', 'L'], 1], [1, None]), ('regression: unmatched PDI', [['PDI', 'AN', 'R', 'FSI', 'ES', 'EN'], 0], [1, 2]), ('partial-repair probe', [['EN', 'ES', 'LRI', 'WS', 'WS', 'FSI', 'PDI', 'AL'], 1], [1, None]), ('partial-repair probe', [['LRI', 'WS', 'RLI', 'AN', 'PDI', 'AN', 'R', 'LRE', 'ES', 'L'], 1], [1, None]), ('nested isolates', [['LRI', 'RLI', 'R', 'PDI', 'L', 'PDI', 'R'], 0], [1, 6]), ('Arabic letter decides', [['ON', 'AL', 'L'], 0], [1, 1]), ('control layout', [['WS', 'AN', 'R', 'WS', 'EN', 'WS', 'PDI'], 1], [1, 2]), ('control layout', [['AN'], 1], [1, 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 fixtureActualExpectedOutcome
stray PDI before isolate[0, 2][1, 4]Failed
regression: unmatched PDI[1, None][1, 2]Failed
partial-repair probe[0, None][0, None]Passed
partial-repair probe[0, None][0, None]Passed
FSI content skipped[0, 3][0, 3]Passed
numbers are not strong[1, 2][1, 2]Passed
control layout[1, 0][1, 0]Passed
control layout[0, 1][0, 1]Passed

SHA-256 / 5e3a3489d27acfc99d44255c2bef33308ab1d8608e8d05b5ba72133235ffecd9

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':
            depth = 0
        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 = [[('stray PDI before isolate', [['PDI', 'RLI', 'L', 'PDI', 'R'], 0], [1, 4]), ('regression: unmatched PDI', [['LRE', 'PDI', 'AL', 'PDI', 'AN', 'RLI', 'WS', 'AL', 'R', 'EN'], 1], [1, 2]), ('partial-repair probe', [['ON', 'RLI', 'ON', 'LRI', 'AL', 'PDI', 'L', 'NSM'], 0], [0, None]), ('partial-repair probe', [['LRI', 'ON', 'RLI', 'L', 'PDI', 'AL', 'R', 'WS'], 0], [0, None]), ('FSI content skipped', [['FSI', 'R', 'PDI', 'L'], 1], [0, 3]), ('numbers are not strong', [['EN', 'ON', 'R'], 0], [1, 2]), ('control layout', [['AL', 'PDI', 'L', 'WS', 'EN', 'L', 'ES', 'ON'], 0], [1, 0]), ('control layout', [['WS', 'L', 'PDI', 'WS', 'AL'], 1], [0, 1])], [('regression: unmatched PDI', [['PDI', 'PDI', 'L', 'ON', 'L', 'EN', 'ON', 'RLI'], 0], [0, 2]), ('regression: unmatched PDI', [['PDI', 'LRI', 'AL', 'ON'], 1], [1, None]), ('partial-repair probe', [['LRI', 'WS', 'RLI', 'AN', 'PDI', 'AN', 'R', 'LRE', 'ES', 'L'], 1], [1, None]), ('partial-repair probe', [['LRI', 'EN', 'AN', 'LRI', 'RLI', 'AL', 'R', 'AN', 'PDI', 'R'], 1], [1, None]), ('numbers are not strong', [['EN', 'ON', 'R'], 0], [1, 2]), ('nested isolates', [['LRI', 'RLI', 'R', 'PDI', 'L', 'PDI', 'R'], 0], [1, 6]), ('control layout', [['LRI', 'AL', 'L', 'ON', 'AL', 'L', 'WS'], 1], [1, None]), ('control layout', [['RLI', 'WS', 'ON', 'ON', 'ON', 'L', 'R', 'LRI'], 0], [0, None])], [('regression: unmatched PDI', [['PDI', 'FSI', 'L', 'NSM', 'R', 'NSM', 'L', 'EN', 'WS', 'R'], 1], [1, None]), ('regression: unmatched PDI', [['PDI', 'AL', 'ON', 'PDI', 'L', 'WS', 'FSI', 'PDI', 'ON', 'LRI'], 0], [1, 1]), ('partial-repair probe', [['ON', 'RLI', 'ON', 'LRI', 'AL', 'PDI', 'L', 'NSM'], 0], [0, None]), ('partial-repair probe', [['LRI', 'EN', 'AN', 'LRI', 'RLI', 'AL', 'R', 'AN', 'PDI', 'R'], 1], [1, None]), ('FSI content skipped', [['FSI', 'R', 'PDI', 'L'], 1], [0, 3]), ('nested isolates', [['LRI', 'RLI', 'R', 'PDI', 'L', 'PDI', 'R'], 0], [1, 6]), ('control layout', [['WS'], 1], [1, None]), ('control layout', [['LRE', 'WS', 'LRI'], 0], [0, None])], [('regression: unmatched PDI', [['ON', 'PDI', 'LRE', 'L', 'AN', 'R', 'AL'], 1], [0, 3]), ('regression: unmatched PDI', [['EN', 'PDI', 'L', 'EN', 'FSI'], 1], [0, 2]), ('partial-repair probe', [['ON', 'RLI', 'ON', 'LRI', 'AL', 'PDI', 'L', 'NSM'], 0], [0, None]), ('partial-repair probe', [['WS', 'LRI', 'FSI', 'PDI', 'R', 'LRE'], 1], [1, None]), ('nested isolates', [['LRI', 'RLI', 'R', 'PDI', 'L', 'PDI', 'R'], 0], [1, 6]), ('Arabic letter decides', [['ON', 'AL', 'L'], 0], [1, 1]), ('control layout', [['EN', 'FSI', 'FSI', 'FSI', 'R', 'FSI', 'L'], 0], [0, None]), ('control layout', [['NSM', 'AN'], 1], [1, None])], [('regression: unmatched PDI', [['PDI', 'PDI', 'LRI', 'WS', 'LRI', 'PDI', 'LRI', 'R', 'EN', 'L'], 1], [1, None]), ('regression: unmatched PDI', [['PDI', 'AN', 'R', 'FSI', 'ES', 'EN'], 0], [1, 2]), ('partial-repair probe', [['EN', 'ES', 'LRI', 'WS', 'WS', 'FSI', 'PDI', 'AL'], 1], [1, None]), ('partial-repair probe', [['LRI', 'WS', 'RLI', 'AN', 'PDI', 'AN', 'R', 'LRE', 'ES', 'L'], 1], [1, None]), ('nested isolates', [['LRI', 'RLI', 'R', 'PDI', 'L', 'PDI', 'R'], 0], [1, 6]), ('Arabic letter decides', [['ON', 'AL', 'L'], 0], [1, 1]), ('control layout', [['WS', 'AN', 'R', 'WS', 'EN', 'WS', 'PDI'], 1], [1, 2]), ('control layout', [['AN'], 1], [1, 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 fixtureActualExpectedOutcome
stray PDI before isolate[1, 4][1, 4]Passed
regression: unmatched PDI[1, 2][1, 2]Passed
partial-repair probe[0, 6][0, None]Failed
partial-repair probe[1, 5][0, None]Failed
FSI content skipped[0, 3][0, 3]Passed
numbers are not strong[1, 2][1, 2]Passed
control layout[1, 0][1, 0]Passed
control layout[0, 1][0, 1]Passed

SHA-256 / c869fbd23d099c1a72a2efbcfa1c55b6da413ab88dff5fd2dd2d53581616c92f

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 = [[('stray PDI before isolate', [['PDI', 'RLI', 'L', 'PDI', 'R'], 0], [1, 4]), ('regression: unmatched PDI', [['LRE', 'PDI', 'AL', 'PDI', 'AN', 'RLI', 'WS', 'AL', 'R', 'EN'], 1], [1, 2]), ('partial-repair probe', [['ON', 'RLI', 'ON', 'LRI', 'AL', 'PDI', 'L', 'NSM'], 0], [0, None]), ('partial-repair probe', [['LRI', 'ON', 'RLI', 'L', 'PDI', 'AL', 'R', 'WS'], 0], [0, None]), ('FSI content skipped', [['FSI', 'R', 'PDI', 'L'], 1], [0, 3]), ('numbers are not strong', [['EN', 'ON', 'R'], 0], [1, 2]), ('control layout', [['AL', 'PDI', 'L', 'WS', 'EN', 'L', 'ES', 'ON'], 0], [1, 0]), ('control layout', [['WS', 'L', 'PDI', 'WS', 'AL'], 1], [0, 1])], [('regression: unmatched PDI', [['PDI', 'PDI', 'L', 'ON', 'L', 'EN', 'ON', 'RLI'], 0], [0, 2]), ('regression: unmatched PDI', [['PDI', 'LRI', 'AL', 'ON'], 1], [1, None]), ('partial-repair probe', [['LRI', 'WS', 'RLI', 'AN', 'PDI', 'AN', 'R', 'LRE', 'ES', 'L'], 1], [1, None]), ('partial-repair probe', [['LRI', 'EN', 'AN', 'LRI', 'RLI', 'AL', 'R', 'AN', 'PDI', 'R'], 1], [1, None]), ('numbers are not strong', [['EN', 'ON', 'R'], 0], [1, 2]), ('nested isolates', [['LRI', 'RLI', 'R', 'PDI', 'L', 'PDI', 'R'], 0], [1, 6]), ('control layout', [['LRI', 'AL', 'L', 'ON', 'AL', 'L', 'WS'], 1], [1, None]), ('control layout', [['RLI', 'WS', 'ON', 'ON', 'ON', 'L', 'R', 'LRI'], 0], [0, None])], [('regression: unmatched PDI', [['PDI', 'FSI', 'L', 'NSM', 'R', 'NSM', 'L', 'EN', 'WS', 'R'], 1], [1, None]), ('regression: unmatched PDI', [['PDI', 'AL', 'ON', 'PDI', 'L', 'WS', 'FSI', 'PDI', 'ON', 'LRI'], 0], [1, 1]), ('partial-repair probe', [['ON', 'RLI', 'ON', 'LRI', 'AL', 'PDI', 'L', 'NSM'], 0], [0, None]), ('partial-repair probe', [['LRI', 'EN', 'AN', 'LRI', 'RLI', 'AL', 'R', 'AN', 'PDI', 'R'], 1], [1, None]), ('FSI content skipped', [['FSI', 'R', 'PDI', 'L'], 1], [0, 3]), ('nested isolates', [['LRI', 'RLI', 'R', 'PDI', 'L', 'PDI', 'R'], 0], [1, 6]), ('control layout', [['WS'], 1], [1, None]), ('control layout', [['LRE', 'WS', 'LRI'], 0], [0, None])], [('regression: unmatched PDI', [['ON', 'PDI', 'LRE', 'L', 'AN', 'R', 'AL'], 1], [0, 3]), ('regression: unmatched PDI', [['EN', 'PDI', 'L', 'EN', 'FSI'], 1], [0, 2]), ('partial-repair probe', [['ON', 'RLI', 'ON', 'LRI', 'AL', 'PDI', 'L', 'NSM'], 0], [0, None]), ('partial-repair probe', [['WS', 'LRI', 'FSI', 'PDI', 'R', 'LRE'], 1], [1, None]), ('nested isolates', [['LRI', 'RLI', 'R', 'PDI', 'L', 'PDI', 'R'], 0], [1, 6]), ('Arabic letter decides', [['ON', 'AL', 'L'], 0], [1, 1]), ('control layout', [['EN', 'FSI', 'FSI', 'FSI', 'R', 'FSI', 'L'], 0], [0, None]), ('control layout', [['NSM', 'AN'], 1], [1, None])], [('regression: unmatched PDI', [['PDI', 'PDI', 'LRI', 'WS', 'LRI', 'PDI', 'LRI', 'R', 'EN', 'L'], 1], [1, None]), ('regression: unmatched PDI', [['PDI', 'AN', 'R', 'FSI', 'ES', 'EN'], 0], [1, 2]), ('partial-repair probe', [['EN', 'ES', 'LRI', 'WS', 'WS', 'FSI', 'PDI', 'AL'], 1], [1, None]), ('partial-repair probe', [['LRI', 'WS', 'RLI', 'AN', 'PDI', 'AN', 'R', 'LRE', 'ES', 'L'], 1], [1, None]), ('nested isolates', [['LRI', 'RLI', 'R', 'PDI', 'L', 'PDI', 'R'], 0], [1, 6]), ('Arabic letter decides', [['ON', 'AL', 'L'], 0], [1, 1]), ('control layout', [['WS', 'AN', 'R', 'WS', 'EN', 'WS', 'PDI'], 1], [1, 2]), ('control layout', [['AN'], 1], [1, 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 fixtureActualExpectedOutcome
stray PDI before isolate[1, 4][1, 4]Passed
regression: unmatched PDI[1, 2][1, 2]Passed
partial-repair probe[0, None][0, None]Passed
partial-repair probe[0, None][0, None]Passed
FSI content skipped[0, 3][0, 3]Passed
numbers are not strong[1, 2][1, 2]Passed
control layout[1, 0][1, 0]Passed
control layout[0, 1][0, 1]Passed

SHA-256 / bde639bcb37bf4facc107d0771e22ebef4b725669763ab5a7ce7623940db6ebd

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 2026-09-29T14:49:52.940037+00:00.

Case digest / c42031017dd5513a527ab8c86a9ba907357037de6f582f16d14cbac3fb58aeff