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FA-80531 / Bidirectional text layout / Open access

Explicit embedding stack: maximum depth bound · case 01

Embeddings exactly at the maximum depth are rejected.

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

ROOT CAUSE

The depth check uses < max_depth.

THE FAILURE

The depth check uses < max_depth.

Unsuccessful approach: Checking the current level lets pushes exceed the maximum.

Case contract

Input [classes, paragraph level, max depth]. RLE/RLO push the next odd level, LRE/LRO the next even level (RLO/LRO set an R/L override, RLE/LRE clear it) if the level <= max depth and no overflow is pending, else count an overflow. PDF first cancels an overflow, else pops if above the base. Codes get level "x" and class BN; other characters take the top level and the override class if any. Return [levels, classes].

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, para, max_depth = x
    stack = [(para, None)]
    overflow = 0
    levels = []
    types = []
    for c in classes:
        if c in ('RLE', 'LRE', 'RLO', 'LRO'):
            cur = stack[-1][0]
            if c in ('RLE', 'RLO'):
                new = cur + 1 if cur % 2 == 0 else cur + 2
            else:
                new = cur + 2 if cur % 2 == 0 else cur + 1
            if new < max_depth and overflow == 0:
                ovr = None if c in ('RLE', 'LRE') else ('R' if c == 'RLO' else 'L')
                stack.append((new, ovr))
            else:
                overflow += 1
            levels.append('x')
            types.append('BN')
        elif c == 'PDF':
            if overflow > 0:
                overflow -= 1
            elif len(stack) > 1:
                stack.pop()
            levels.append('x')
            types.append('BN')
        else:
            lv, ovr = stack[-1]
            levels.append(lv)
            types.append(ovr if ovr else c)
    return [levels, types]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('depth limit exactly reached', [['RLE', 'LRE', 'L', 'PDF', 'L'], 0, 2], [['x', 'x', 2, 'x', 1], ['BN', 'BN', 'L', 'BN', 'L']]), ('regression: maximum depth bound', [['LRE', 'RLE', 'L', 'LRO', 'RLE', 'ON', 'LRO', 'PDF'], 1, 5], [['x', 'x', 3, 'x', 'x', 5, 'x', 'x'], ['BN', 'BN', 'L', 'BN', 'BN', 'ON', 'BN', 'BN']]), ('partial-repair probe', [['L', 'PDF', 'LRO', 'R', 'R', 'LRE', 'WS', 'L'], 0, 3], [[0, 'x', 'x', 2, 2, 'x', 2, 2], ['L', 'BN', 'BN', 'L', 'L', 'BN', 'L', 'L']]), ('partial-repair probe', [['RLO', 'LRO', 'EN', 'LRE', 'LRE', 'L', 'L', 'RLE', 'ON', 'EN', 'L', 'ON'], 1, 5], [['x', 'x', 4, 'x', 'x', 4, 4, 'x', 4, 4, 4, 4], ['BN', 'BN', 'L', 'BN', 'BN', 'L', 'L', 'BN', 'L', 'L', 'L', 'L']]), ('override on neutrals', [['RLO', 'ON', 'L', 'WS'], 0, 6], [['x', 1, 1, 1], ['BN', 'R', 'R', 'R']]), ('RLE from odd level', [['RLE', 'RLE', 'L'], 0, 6], [['x', 'x', 3], ['BN', 'BN', 'L']]), ('control layout', [['R', 'R', 'LRE', 'L', 'L', 'LRE', 'WS', 'R', 'RLE', 'WS', 'PDF', 'EN', 'LRO'], 1, 6], [[1, 1, 'x', 2, 2, 'x', 4, 4, 'x', 5, 'x', 4, 'x'], ['R', 'R', 'BN', 'L', 'L', 'BN', 'WS', 'R', 'BN', 'WS', 'BN', 'EN', 'BN']]), ('control layout', [['L', 'WS', 'LRE', 'RLE', 'LRE', 'EN', 'R', 'L', 'RLE'], 0, 5], [[0, 0, 'x', 'x', 'x', 4, 4, 4, 'x'], ['L', 'WS', 'BN', 'BN', 'BN', 'EN', 'R', 'L', 'BN']])], [('regression: maximum depth bound', [['ON', 'LRO', 'EN'], 1, 2], [[1, 'x', 2], ['ON', 'BN', 'L']]), ('regression: maximum depth bound', [['RLE', 'L', 'LRO', 'RLE', 'L', 'R', 'L', 'R', 'RLE', 'L', 'LRO', 'L'], 0, 3], [['x', 1, 'x', 'x', 3, 3, 3, 3, 'x', 3, 'x', 3], ['BN', 'L', 'BN', 'BN', 'L', 'R', 'L', 'R', 'BN', 'L', 'BN', 'L']]), ('partial-repair probe', [['L', 'PDF', 'EN', 'LRE', 'R', 'LRE', 'RLE', 'PDF', 'WS', 'RLO', 'ON', 'L', 'R', 'R'], 1, 3], [[1, 'x', 1, 'x', 2, 'x', 'x', 'x', 2, 'x', 2, 2, 2, 2], ['L', 'BN', 'EN', 'BN', 'R', 'BN', 'BN', 'BN', 'WS', 'BN', 'ON', 'L', 'R', 'R']]), ('partial-repair probe', [['RLO', 'ON', 'RLE', 'RLE', 'L', 'R'], 0, 4], [['x', 1, 'x', 'x', 3, 3], ['BN', 'R', 'BN', 'BN', 'L', 'R']]), ('LRE from odd level', [['LRE', 'R'], 1, 6], [['x', 2], ['BN', 'R']]), ('depth limit exactly reached', [['RLE', 'LRE', 'L', 'PDF', 'L'], 0, 2], [['x', 'x', 2, 'x', 1], ['BN', 'BN', 'L', 'BN', 'L']]), ('control layout', [['R', 'EN', 'RLO', 'PDF', 'R', 'PDF', 'L', 'LRO'], 0, 6], [[0, 0, 'x', 'x', 0, 'x', 0, 'x'], ['R', 'EN', 'BN', 'BN', 'R', 'BN', 'L', 'BN']]), ('control layout', [['ON', 'RLE', 'L', 'ON', 'R'], 0, 2], [[0, 'x', 1, 1, 1], ['ON', 'BN', 'L', 'ON', 'R']])], [('regression: maximum depth bound', [['R', 'R', 'R', 'RLO', 'R', 'LRE', 'LRE', 'ON', 'RLE', 'PDF', 'RLE', 'L'], 0, 5], [[0, 0, 0, 'x', 1, 'x', 'x', 4, 'x', 'x', 'x', 5], ['R', 'R', 'R', 'BN', 'R', 'BN', 'BN', 'ON', 'BN', 'BN', 'BN', 'L']]), ('regression: maximum depth bound', [['RLE', 'L', 'LRO', 'RLE', 'L', 'R', 'L', 'R', 'RLE', 'L', 'LRO', 'L'], 0, 3], [['x', 1, 'x', 'x', 3, 3, 3, 3, 'x', 3, 'x', 3], ['BN', 'L', 'BN', 'BN', 'L', 'R', 'L', 'R', 'BN', 'L', 'BN', 'L']]), ('partial-repair probe', [['L', 'RLO', 'ON', 'RLE', 'RLE', 'WS', 'LRE', 'L', 'PDF', 'R', 'RLE', 'L'], 1, 2], [[1, 'x', 1, 'x', 'x', 1, 'x', 1, 'x', 1, 'x', 1], ['L', 'BN', 'ON', 'BN', 'BN', 'WS', 'BN', 'L', 'BN', 'R', 'BN', 'L']]), ('partial-repair probe', [['RLO', 'ON', 'RLE', 'RLE', 'L', 'R'], 0, 4], [['x', 1, 'x', 'x', 3, 3], ['BN', 'R', 'BN', 'BN', 'L', 'R']]), ('RLE from odd level', [['RLE', 'RLE', 'L'], 0, 6], [['x', 'x', 3], ['BN', 'BN', 'L']]), ('override on neutrals', [['RLO', 'ON', 'L', 'WS'], 0, 6], [['x', 1, 1, 1], ['BN', 'R', 'R', 'R']]), ('control layout', [['PDF', 'LRO'], 0, 5], [['x', 'x'], ['BN', 'BN']]), ('control layout', [['PDF', 'L', 'R', 'RLE'], 0, 5], [['x', 0, 0, 'x'], ['BN', 'L', 'R', 'BN']])], [('regression: maximum depth bound', [['LRE', 'ON', 'R', 'R', 'RLO', 'LRO'], 1, 2], [['x', 2, 2, 2, 'x', 'x'], ['BN', 'ON', 'R', 'R', 'BN', 'BN']]), ('regression: maximum depth bound', [['LRE', 'L', 'R', 'PDF', 'RLE'], 1, 2], [['x', 2, 2, 'x', 'x'], ['BN', 'L', 'R', 'BN', 'BN']]), ('regression: maximum depth bound', [['ON', 'RLE', 'L', 'EN', 'R', 'LRE', 'R', 'ON', 'WS', 'RLE', 'L', 'PDF', 'LRE', 'R'], 0, 3], [[0, 'x', 1, 1, 1, 'x', 2, 2, 2, 'x', 3, 'x', 'x', 2], ['ON', 'BN', 'L', 'EN', 'R', 'BN', 'R', 'ON', 'WS', 'BN', 'L', 'BN', 'BN', 'R']]), ('partial-repair probe', [['R', 'R', 'EN', 'RLE', 'EN', 'RLE', 'ON', 'PDF', 'LRO'], 1, 2], [[1, 1, 1, 'x', 1, 'x', 1, 'x', 'x'], ['R', 'R', 'EN', 'BN', 'EN', 'BN', 'ON', 'BN', 'BN']]), ('LRE from odd level', [['LRE', 'R'], 1, 6], [['x', 2], ['BN', 'R']]), ('depth limit exactly reached', [['RLE', 'LRE', 'L', 'PDF', 'L'], 0, 2], [['x', 'x', 2, 'x', 1], ['BN', 'BN', 'L', 'BN', 'L']]), ('control layout', [['L', 'EN', 'ON', 'L', 'EN', 'L', 'PDF', 'R', 'L', 'RLE', 'PDF', 'LRE'], 0, 3], [[0, 0, 0, 0, 0, 0, 'x', 0, 0, 'x', 'x', 'x'], ['L', 'EN', 'ON', 'L', 'EN', 'L', 'BN', 'R', 'L', 'BN', 'BN', 'BN']]), ('control layout', [['ON', 'R', 'RLE'], 1, 2], [[1, 1, 'x'], ['ON', 'R', 'BN']])], [('regression: maximum depth bound', [['L', 'ON', 'ON', 'ON', 'RLO', 'PDF', 'R', 'LRO', 'EN', 'PDF', 'PDF'], 1, 2], [[1, 1, 1, 1, 'x', 'x', 1, 'x', 2, 'x', 'x'], ['L', 'ON', 'ON', 'ON', 'BN', 'BN', 'R', 'BN', 'L', 'BN', 'BN']]), ('regression: maximum depth bound', [['LRO', 'EN', 'RLO', 'RLE', 'LRE'], 1, 2], [['x', 2, 'x', 'x', 'x'], ['BN', 'L', 'BN', 'BN', 'BN']]), ('partial-repair probe', [['L', 'RLO', 'ON', 'RLE', 'RLE', 'WS', 'LRE', 'L', 'PDF', 'R', 'RLE', 'L'], 1, 2], [[1, 'x', 1, 'x', 'x', 1, 'x', 1, 'x', 1, 'x', 1], ['L', 'BN', 'ON', 'BN', 'BN', 'WS', 'BN', 'L', 'BN', 'R', 'BN', 'L']]), ('partial-repair probe', [['RLE', 'L', 'R', 'L', 'WS', 'ON', 'PDF', 'LRO', 'RLO', 'RLO', 'R', 'ON', 'EN', 'L'], 1, 4], [['x', 3, 3, 3, 3, 3, 'x', 'x', 'x', 'x', 3, 3, 3, 3], ['BN', 'L', 'R', 'L', 'WS', 'ON', 'BN', 'BN', 'BN', 'BN', 'R', 'R', 'R', 'R']]), ('RLE from odd level', [['RLE', 'RLE', 'L'], 0, 6], [['x', 'x', 3], ['BN', 'BN', 'L']]), ('depth limit exactly reached', [['RLE', 'LRE', 'L', 'PDF', 'L'], 0, 2], [['x', 'x', 2, 'x', 1], ['BN', 'BN', 'L', 'BN', 'L']]), ('control layout', [['ON', 'R', 'L', 'R', 'EN', 'R', 'PDF'], 1, 3], [[1, 1, 1, 1, 1, 1, 'x'], ['ON', 'R', 'L', 'R', 'EN', 'R', 'BN']]), ('control layout', [['PDF', 'R', 'ON', 'L', 'ON', 'EN', 'PDF', 'L', 'RLO', 'PDF', 'R', 'R'], 1, 6], [['x', 1, 1, 1, 1, 1, 'x', 1, 'x', 'x', 1, 1], ['BN', 'R', 'ON', 'L', 'ON', 'EN', 'BN', 'L', 'BN', 'BN', 'R', 'R']])]]
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
depth limit exactly reached[['x', 'x', 1, 'x', 1], ['BN', 'BN', 'L', 'BN', 'L']][['x', 'x', 2, 'x', 1], ['BN', 'BN', 'L', 'BN', 'L']]Failed
regression: maximum depth bound[['x', 'x', 3, 'x', 'x', 4, 'x', 'x'], ['BN', 'BN', 'L', 'BN', 'BN', 'L', 'BN', 'BN']][['x', 'x', 3, 'x', 'x', 5, 'x', 'x'], ['BN', 'BN', 'L', 'BN', 'BN', 'ON', 'BN', 'BN']]Failed
partial-repair probe[[0, 'x', 'x', 2, 2, 'x', 2, 2], ['L', 'BN', 'BN', 'L', 'L', 'BN', 'L', 'L']][[0, 'x', 'x', 2, 2, 'x', 2, 2], ['L', 'BN', 'BN', 'L', 'L', 'BN', 'L', 'L']]Passed
partial-repair probe[['x', 'x', 4, 'x', 'x', 4, 4, 'x', 4, 4, 4, 4], ['BN', 'BN', 'L', 'BN', 'BN', 'L', 'L', 'BN', 'L', 'L', 'L', 'L']][['x', 'x', 4, 'x', 'x', 4, 4, 'x', 4, 4, 4, 4], ['BN', 'BN', 'L', 'BN', 'BN', 'L', 'L', 'BN', 'L', 'L', 'L', 'L']]Passed
override on neutrals[['x', 1, 1, 1], ['BN', 'R', 'R', 'R']][['x', 1, 1, 1], ['BN', 'R', 'R', 'R']]Passed
RLE from odd level[['x', 'x', 3], ['BN', 'BN', 'L']][['x', 'x', 3], ['BN', 'BN', 'L']]Passed
control layout[[1, 1, 'x', 2, 2, 'x', 4, 4, 'x', 5, 'x', 4, 'x'], ['R', 'R', 'BN', 'L', 'L', 'BN', 'WS', 'R', 'BN', 'WS', 'BN', 'EN', 'BN']][[1, 1, 'x', 2, 2, 'x', 4, 4, 'x', 5, 'x', 4, 'x'], ['R', 'R', 'BN', 'L', 'L', 'BN', 'WS', 'R', 'BN', 'WS', 'BN', 'EN', 'BN']]Passed
control layout[[0, 0, 'x', 'x', 'x', 4, 4, 4, 'x'], ['L', 'WS', 'BN', 'BN', 'BN', 'EN', 'R', 'L', 'BN']][[0, 0, 'x', 'x', 'x', 4, 4, 4, 'x'], ['L', 'WS', 'BN', 'BN', 'BN', 'EN', 'R', 'L', 'BN']]Passed

SHA-256 / fd3556d99b3b49741414121648609584b7f9fc8c6dbe6af56ea37d89186e5e9f

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(x):
    classes, para, max_depth = x
    stack = [(para, None)]
    overflow = 0
    levels = []
    types = []
    for c in classes:
        if c in ('RLE', 'LRE', 'RLO', 'LRO'):
            cur = stack[-1][0]
            if c in ('RLE', 'RLO'):
                new = cur + 1 if cur % 2 == 0 else cur + 2
            else:
                new = cur + 2 if cur % 2 == 0 else cur + 1
            if cur < max_depth and overflow == 0:
                ovr = None if c in ('RLE', 'LRE') else ('R' if c == 'RLO' else 'L')
                stack.append((new, ovr))
            else:
                overflow += 1
            levels.append('x')
            types.append('BN')
        elif c == 'PDF':
            if overflow > 0:
                overflow -= 1
            elif len(stack) > 1:
                stack.pop()
            levels.append('x')
            types.append('BN')
        else:
            lv, ovr = stack[-1]
            levels.append(lv)
            types.append(ovr if ovr else c)
    return [levels, types]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('depth limit exactly reached', [['RLE', 'LRE', 'L', 'PDF', 'L'], 0, 2], [['x', 'x', 2, 'x', 1], ['BN', 'BN', 'L', 'BN', 'L']]), ('regression: maximum depth bound', [['LRE', 'RLE', 'L', 'LRO', 'RLE', 'ON', 'LRO', 'PDF'], 1, 5], [['x', 'x', 3, 'x', 'x', 5, 'x', 'x'], ['BN', 'BN', 'L', 'BN', 'BN', 'ON', 'BN', 'BN']]), ('partial-repair probe', [['L', 'PDF', 'LRO', 'R', 'R', 'LRE', 'WS', 'L'], 0, 3], [[0, 'x', 'x', 2, 2, 'x', 2, 2], ['L', 'BN', 'BN', 'L', 'L', 'BN', 'L', 'L']]), ('partial-repair probe', [['RLO', 'LRO', 'EN', 'LRE', 'LRE', 'L', 'L', 'RLE', 'ON', 'EN', 'L', 'ON'], 1, 5], [['x', 'x', 4, 'x', 'x', 4, 4, 'x', 4, 4, 4, 4], ['BN', 'BN', 'L', 'BN', 'BN', 'L', 'L', 'BN', 'L', 'L', 'L', 'L']]), ('override on neutrals', [['RLO', 'ON', 'L', 'WS'], 0, 6], [['x', 1, 1, 1], ['BN', 'R', 'R', 'R']]), ('RLE from odd level', [['RLE', 'RLE', 'L'], 0, 6], [['x', 'x', 3], ['BN', 'BN', 'L']]), ('control layout', [['R', 'R', 'LRE', 'L', 'L', 'LRE', 'WS', 'R', 'RLE', 'WS', 'PDF', 'EN', 'LRO'], 1, 6], [[1, 1, 'x', 2, 2, 'x', 4, 4, 'x', 5, 'x', 4, 'x'], ['R', 'R', 'BN', 'L', 'L', 'BN', 'WS', 'R', 'BN', 'WS', 'BN', 'EN', 'BN']]), ('control layout', [['L', 'WS', 'LRE', 'RLE', 'LRE', 'EN', 'R', 'L', 'RLE'], 0, 5], [[0, 0, 'x', 'x', 'x', 4, 4, 4, 'x'], ['L', 'WS', 'BN', 'BN', 'BN', 'EN', 'R', 'L', 'BN']])], [('regression: maximum depth bound', [['ON', 'LRO', 'EN'], 1, 2], [[1, 'x', 2], ['ON', 'BN', 'L']]), ('regression: maximum depth bound', [['RLE', 'L', 'LRO', 'RLE', 'L', 'R', 'L', 'R', 'RLE', 'L', 'LRO', 'L'], 0, 3], [['x', 1, 'x', 'x', 3, 3, 3, 3, 'x', 3, 'x', 3], ['BN', 'L', 'BN', 'BN', 'L', 'R', 'L', 'R', 'BN', 'L', 'BN', 'L']]), ('partial-repair probe', [['L', 'PDF', 'EN', 'LRE', 'R', 'LRE', 'RLE', 'PDF', 'WS', 'RLO', 'ON', 'L', 'R', 'R'], 1, 3], [[1, 'x', 1, 'x', 2, 'x', 'x', 'x', 2, 'x', 2, 2, 2, 2], ['L', 'BN', 'EN', 'BN', 'R', 'BN', 'BN', 'BN', 'WS', 'BN', 'ON', 'L', 'R', 'R']]), ('partial-repair probe', [['RLO', 'ON', 'RLE', 'RLE', 'L', 'R'], 0, 4], [['x', 1, 'x', 'x', 3, 3], ['BN', 'R', 'BN', 'BN', 'L', 'R']]), ('LRE from odd level', [['LRE', 'R'], 1, 6], [['x', 2], ['BN', 'R']]), ('depth limit exactly reached', [['RLE', 'LRE', 'L', 'PDF', 'L'], 0, 2], [['x', 'x', 2, 'x', 1], ['BN', 'BN', 'L', 'BN', 'L']]), ('control layout', [['R', 'EN', 'RLO', 'PDF', 'R', 'PDF', 'L', 'LRO'], 0, 6], [[0, 0, 'x', 'x', 0, 'x', 0, 'x'], ['R', 'EN', 'BN', 'BN', 'R', 'BN', 'L', 'BN']]), ('control layout', [['ON', 'RLE', 'L', 'ON', 'R'], 0, 2], [[0, 'x', 1, 1, 1], ['ON', 'BN', 'L', 'ON', 'R']])], [('regression: maximum depth bound', [['R', 'R', 'R', 'RLO', 'R', 'LRE', 'LRE', 'ON', 'RLE', 'PDF', 'RLE', 'L'], 0, 5], [[0, 0, 0, 'x', 1, 'x', 'x', 4, 'x', 'x', 'x', 5], ['R', 'R', 'R', 'BN', 'R', 'BN', 'BN', 'ON', 'BN', 'BN', 'BN', 'L']]), ('regression: maximum depth bound', [['RLE', 'L', 'LRO', 'RLE', 'L', 'R', 'L', 'R', 'RLE', 'L', 'LRO', 'L'], 0, 3], [['x', 1, 'x', 'x', 3, 3, 3, 3, 'x', 3, 'x', 3], ['BN', 'L', 'BN', 'BN', 'L', 'R', 'L', 'R', 'BN', 'L', 'BN', 'L']]), ('partial-repair probe', [['L', 'RLO', 'ON', 'RLE', 'RLE', 'WS', 'LRE', 'L', 'PDF', 'R', 'RLE', 'L'], 1, 2], [[1, 'x', 1, 'x', 'x', 1, 'x', 1, 'x', 1, 'x', 1], ['L', 'BN', 'ON', 'BN', 'BN', 'WS', 'BN', 'L', 'BN', 'R', 'BN', 'L']]), ('partial-repair probe', [['RLO', 'ON', 'RLE', 'RLE', 'L', 'R'], 0, 4], [['x', 1, 'x', 'x', 3, 3], ['BN', 'R', 'BN', 'BN', 'L', 'R']]), ('RLE from odd level', [['RLE', 'RLE', 'L'], 0, 6], [['x', 'x', 3], ['BN', 'BN', 'L']]), ('override on neutrals', [['RLO', 'ON', 'L', 'WS'], 0, 6], [['x', 1, 1, 1], ['BN', 'R', 'R', 'R']]), ('control layout', [['PDF', 'LRO'], 0, 5], [['x', 'x'], ['BN', 'BN']]), ('control layout', [['PDF', 'L', 'R', 'RLE'], 0, 5], [['x', 0, 0, 'x'], ['BN', 'L', 'R', 'BN']])], [('regression: maximum depth bound', [['LRE', 'ON', 'R', 'R', 'RLO', 'LRO'], 1, 2], [['x', 2, 2, 2, 'x', 'x'], ['BN', 'ON', 'R', 'R', 'BN', 'BN']]), ('regression: maximum depth bound', [['LRE', 'L', 'R', 'PDF', 'RLE'], 1, 2], [['x', 2, 2, 'x', 'x'], ['BN', 'L', 'R', 'BN', 'BN']]), ('regression: maximum depth bound', [['ON', 'RLE', 'L', 'EN', 'R', 'LRE', 'R', 'ON', 'WS', 'RLE', 'L', 'PDF', 'LRE', 'R'], 0, 3], [[0, 'x', 1, 1, 1, 'x', 2, 2, 2, 'x', 3, 'x', 'x', 2], ['ON', 'BN', 'L', 'EN', 'R', 'BN', 'R', 'ON', 'WS', 'BN', 'L', 'BN', 'BN', 'R']]), ('partial-repair probe', [['R', 'R', 'EN', 'RLE', 'EN', 'RLE', 'ON', 'PDF', 'LRO'], 1, 2], [[1, 1, 1, 'x', 1, 'x', 1, 'x', 'x'], ['R', 'R', 'EN', 'BN', 'EN', 'BN', 'ON', 'BN', 'BN']]), ('LRE from odd level', [['LRE', 'R'], 1, 6], [['x', 2], ['BN', 'R']]), ('depth limit exactly reached', [['RLE', 'LRE', 'L', 'PDF', 'L'], 0, 2], [['x', 'x', 2, 'x', 1], ['BN', 'BN', 'L', 'BN', 'L']]), ('control layout', [['L', 'EN', 'ON', 'L', 'EN', 'L', 'PDF', 'R', 'L', 'RLE', 'PDF', 'LRE'], 0, 3], [[0, 0, 0, 0, 0, 0, 'x', 0, 0, 'x', 'x', 'x'], ['L', 'EN', 'ON', 'L', 'EN', 'L', 'BN', 'R', 'L', 'BN', 'BN', 'BN']]), ('control layout', [['ON', 'R', 'RLE'], 1, 2], [[1, 1, 'x'], ['ON', 'R', 'BN']])], [('regression: maximum depth bound', [['L', 'ON', 'ON', 'ON', 'RLO', 'PDF', 'R', 'LRO', 'EN', 'PDF', 'PDF'], 1, 2], [[1, 1, 1, 1, 'x', 'x', 1, 'x', 2, 'x', 'x'], ['L', 'ON', 'ON', 'ON', 'BN', 'BN', 'R', 'BN', 'L', 'BN', 'BN']]), ('regression: maximum depth bound', [['LRO', 'EN', 'RLO', 'RLE', 'LRE'], 1, 2], [['x', 2, 'x', 'x', 'x'], ['BN', 'L', 'BN', 'BN', 'BN']]), ('partial-repair probe', [['L', 'RLO', 'ON', 'RLE', 'RLE', 'WS', 'LRE', 'L', 'PDF', 'R', 'RLE', 'L'], 1, 2], [[1, 'x', 1, 'x', 'x', 1, 'x', 1, 'x', 1, 'x', 1], ['L', 'BN', 'ON', 'BN', 'BN', 'WS', 'BN', 'L', 'BN', 'R', 'BN', 'L']]), ('partial-repair probe', [['RLE', 'L', 'R', 'L', 'WS', 'ON', 'PDF', 'LRO', 'RLO', 'RLO', 'R', 'ON', 'EN', 'L'], 1, 4], [['x', 3, 3, 3, 3, 3, 'x', 'x', 'x', 'x', 3, 3, 3, 3], ['BN', 'L', 'R', 'L', 'WS', 'ON', 'BN', 'BN', 'BN', 'BN', 'R', 'R', 'R', 'R']]), ('RLE from odd level', [['RLE', 'RLE', 'L'], 0, 6], [['x', 'x', 3], ['BN', 'BN', 'L']]), ('depth limit exactly reached', [['RLE', 'LRE', 'L', 'PDF', 'L'], 0, 2], [['x', 'x', 2, 'x', 1], ['BN', 'BN', 'L', 'BN', 'L']]), ('control layout', [['ON', 'R', 'L', 'R', 'EN', 'R', 'PDF'], 1, 3], [[1, 1, 1, 1, 1, 1, 'x'], ['ON', 'R', 'L', 'R', 'EN', 'R', 'BN']]), ('control layout', [['PDF', 'R', 'ON', 'L', 'ON', 'EN', 'PDF', 'L', 'RLO', 'PDF', 'R', 'R'], 1, 6], [['x', 1, 1, 1, 1, 1, 'x', 1, 'x', 'x', 1, 1], ['BN', 'R', 'ON', 'L', 'ON', 'EN', 'BN', 'L', 'BN', 'BN', 'R', 'R']])]]
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
depth limit exactly reached[['x', 'x', 2, 'x', 1], ['BN', 'BN', 'L', 'BN', 'L']][['x', 'x', 2, 'x', 1], ['BN', 'BN', 'L', 'BN', 'L']]Passed
regression: maximum depth bound[['x', 'x', 3, 'x', 'x', 5, 'x', 'x'], ['BN', 'BN', 'L', 'BN', 'BN', 'ON', 'BN', 'BN']][['x', 'x', 3, 'x', 'x', 5, 'x', 'x'], ['BN', 'BN', 'L', 'BN', 'BN', 'ON', 'BN', 'BN']]Passed
partial-repair probe[[0, 'x', 'x', 2, 2, 'x', 4, 4], ['L', 'BN', 'BN', 'L', 'L', 'BN', 'WS', 'L']][[0, 'x', 'x', 2, 2, 'x', 2, 2], ['L', 'BN', 'BN', 'L', 'L', 'BN', 'L', 'L']]Failed
partial-repair probe[['x', 'x', 4, 'x', 'x', 6, 6, 'x', 6, 6, 6, 6], ['BN', 'BN', 'L', 'BN', 'BN', 'L', 'L', 'BN', 'ON', 'EN', 'L', 'ON']][['x', 'x', 4, 'x', 'x', 4, 4, 'x', 4, 4, 4, 4], ['BN', 'BN', 'L', 'BN', 'BN', 'L', 'L', 'BN', 'L', 'L', 'L', 'L']]Failed
override on neutrals[['x', 1, 1, 1], ['BN', 'R', 'R', 'R']][['x', 1, 1, 1], ['BN', 'R', 'R', 'R']]Passed
RLE from odd level[['x', 'x', 3], ['BN', 'BN', 'L']][['x', 'x', 3], ['BN', 'BN', 'L']]Passed
control layout[[1, 1, 'x', 2, 2, 'x', 4, 4, 'x', 5, 'x', 4, 'x'], ['R', 'R', 'BN', 'L', 'L', 'BN', 'WS', 'R', 'BN', 'WS', 'BN', 'EN', 'BN']][[1, 1, 'x', 2, 2, 'x', 4, 4, 'x', 5, 'x', 4, 'x'], ['R', 'R', 'BN', 'L', 'L', 'BN', 'WS', 'R', 'BN', 'WS', 'BN', 'EN', 'BN']]Passed
control layout[[0, 0, 'x', 'x', 'x', 4, 4, 4, 'x'], ['L', 'WS', 'BN', 'BN', 'BN', 'EN', 'R', 'L', 'BN']][[0, 0, 'x', 'x', 'x', 4, 4, 4, 'x'], ['L', 'WS', 'BN', 'BN', 'BN', 'EN', 'R', 'L', 'BN']]Passed

SHA-256 / e777c57d10d9b4b226345d62d4d80f1de7e7135f96271487b5e05485bf465883

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

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.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

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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 2026-09-29T14:49:54.820639+00:00.

Case digest / c61141948ac3278ee73825e0fa8b92bbfbdf557e238d7fc706cf7b8b06f80eda