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FA-80521 / Bidirectional text layout / Open access

Explicit embedding stack: next odd level · case 01

RLE inside an RTL embedding produces an even level.

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

ROOT CAUSE

The next odd level is always computed as current + 1.

VERIFIED REPAIR

Use +1 from even levels and +2 from odd levels.

Unsuccessful approach: Applying the LTR increments to RLE still lands on the wrong parity.

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
            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 = [[('RLE from odd level', [['RLE', 'RLE', 'L'], 0, 6], [['x', 'x', 3], ['BN', 'BN', 'L']]), ('regression: next odd level', [['L', 'L', 'ON', 'PDF', 'RLE', 'L', 'RLO', 'R'], 0, 4], [[0, 0, 0, 'x', 'x', 1, 'x', 3], ['L', 'L', 'ON', 'BN', 'BN', 'L', 'BN', 'R']]), ('partial-repair probe', [['RLE', 'LRE', 'PDF', 'ON', 'R', 'RLO'], 0, 4], [['x', 'x', 'x', 1, 1, 'x'], ['BN', 'BN', 'BN', 'ON', 'R', 'BN']]), ('partial-repair probe', [['R', 'RLO', 'PDF', 'R', 'L', 'RLE', 'LRE', 'ON', 'R', 'RLE', 'ON', 'LRE', 'R'], 0, 4], [[0, 'x', 'x', 0, 0, 'x', 'x', 2, 2, 'x', 3, 'x', 4], ['R', 'BN', 'BN', 'R', 'L', 'BN', 'BN', 'ON', 'R', 'BN', 'ON', 'BN', 'R']]), ('LRE from odd level', [['LRE', 'R'], 1, 6], [['x', 2], ['BN', 'R']]), ('override on neutrals', [['RLO', 'ON', 'L', 'WS'], 0, 6], [['x', 1, 1, 1], ['BN', 'R', 'R', 'R']]), ('control layout', [['PDF', 'LRO', 'R', 'EN', 'LRE', 'L', 'L', 'L', 'RLE', 'R', 'L', 'LRO'], 1, 3], [['x', 'x', 2, 2, 'x', 2, 2, 2, 'x', 2, 2, 'x'], ['BN', 'BN', 'L', 'L', 'BN', 'L', 'L', 'L', 'BN', 'L', 'L', 'BN']]), ('control layout', [['R', 'LRO'], 0, 4], [[0, 'x'], ['R', 'BN']])], [('regression: next odd level', [['PDF', 'RLO', 'RLE', 'LRE', 'LRO', 'PDF', 'PDF', 'EN', 'PDF', 'R', 'L', 'EN', 'L'], 1, 5], [['x', 'x', 'x', 'x', 'x', 'x', 'x', 5, 'x', 3, 3, 3, 3], ['BN', 'BN', 'BN', 'BN', 'BN', 'BN', 'BN', 'EN', 'BN', 'R', 'R', 'R', 'R']]), ('regression: next odd level', [['WS', 'PDF', 'RLE', 'RLE', 'L'], 1, 5], [[1, 'x', 'x', 'x', 5], ['WS', 'BN', 'BN', 'BN', 'L']]), ('partial-repair probe', [['R', 'RLO', 'RLE', 'PDF', 'R', 'LRE', 'L', 'ON', 'R', 'ON', 'RLO'], 0, 3], [[0, 'x', 'x', 'x', 1, 'x', 2, 2, 2, 2, 'x'], ['R', 'BN', 'BN', 'BN', 'R', 'BN', 'L', 'ON', 'R', 'ON', 'BN']]), ('regression: next odd level', [['ON', 'L', 'EN', 'PDF', 'RLE', 'R', 'RLO', 'L', 'PDF'], 0, 5], [[0, 0, 0, 'x', 'x', 1, 'x', 3, 'x'], ['ON', 'L', 'EN', 'BN', 'BN', 'R', 'BN', 'R', 'BN']]), ('depth limit exactly reached', [['RLE', 'LRE', 'L', 'PDF', 'L'], 0, 2], [['x', 'x', 2, 'x', 1], ['BN', 'BN', 'L', 'BN', 'L']]), ('LRE from odd level', [['LRE', 'R'], 1, 6], [['x', 2], ['BN', 'R']]), ('control layout', [['EN', 'R'], 0, 5], [[0, 0], ['EN', 'R']]), ('control layout', [['L', 'R', 'ON', 'R', 'PDF', 'ON', 'ON'], 1, 4], [[1, 1, 1, 1, 'x', 1, 1], ['L', 'R', 'ON', 'R', 'BN', 'ON', 'ON']])], [('regression: next odd level', [['PDF', 'PDF', 'R', 'L', 'RLO', 'ON', 'R', 'ON'], 1, 2], [['x', 'x', 1, 1, 'x', 1, 1, 1], ['BN', 'BN', 'R', 'L', 'BN', 'ON', 'R', 'ON']]), ('regression: next odd level', [['RLO', 'EN', 'R', 'ON', 'EN', 'L', 'ON', 'R', 'RLO', 'RLE', 'LRE', 'PDF', 'EN', 'LRE'], 1, 3], [['x', 3, 3, 3, 3, 3, 3, 3, 'x', 'x', 'x', 'x', 3, 'x'], ['BN', 'R', 'R', 'R', 'R', 'R', 'R', 'R', 'BN', 'BN', 'BN', 'BN', 'R', 'BN']]), ('regression: next odd level', [['ON', 'L', 'PDF', 'RLO', 'R'], 1, 4], [[1, 1, 'x', 'x', 3], ['ON', 'L', 'BN', 'BN', 'R']]), ('partial-repair probe', [['WS', 'L', 'L', 'RLE', 'R', 'RLO'], 0, 5], [[0, 0, 0, 'x', 1, 'x'], ['WS', 'L', 'L', 'BN', 'R', 'BN']]), ('depth limit exactly reached', [['RLE', 'LRE', 'L', 'PDF', 'L'], 0, 2], [['x', 'x', 2, 'x', 1], ['BN', 'BN', 'L', 'BN', 'L']]), ('override on neutrals', [['RLO', 'ON', 'L', 'WS'], 0, 6], [['x', 1, 1, 1], ['BN', 'R', 'R', 'R']]), ('control layout', [['ON', 'ON', 'L', 'EN', 'WS'], 1, 4], [[1, 1, 1, 1, 1], ['ON', 'ON', 'L', 'EN', 'WS']]), ('control layout', [['L', 'R', 'WS', 'ON', 'RLE', 'LRE'], 0, 5], [[0, 0, 0, 0, 'x', 'x'], ['L', 'R', 'WS', 'ON', 'BN', 'BN']])], [('regression: next odd level', [['PDF', 'PDF', 'R', 'L', 'RLO', 'ON', 'R', 'ON'], 1, 2], [['x', 'x', 1, 1, 'x', 1, 1, 1], ['BN', 'BN', 'R', 'L', 'BN', 'ON', 'R', 'ON']]), ('regression: next odd level', [['RLE', 'RLO', 'EN', 'L', 'EN', 'PDF', 'L', 'LRE', 'EN', 'LRO', 'R', 'WS', 'LRE'], 1, 3], [['x', 'x', 3, 3, 3, 'x', 3, 'x', 3, 'x', 3, 3, 'x'], ['BN', 'BN', 'EN', 'L', 'EN', 'BN', 'L', 'BN', 'EN', 'BN', 'R', 'WS', 'BN']]), ('regression: next odd level', [['RLO', 'R'], 1, 3], [['x', 3], ['BN', 'R']]), ('partial-repair probe', [['R', 'L', 'RLE', 'WS', 'R', 'LRE', 'ON', 'PDF', 'RLE'], 0, 4], [[0, 0, 'x', 1, 1, 'x', 2, 'x', 'x'], ['R', 'L', 'BN', 'WS', 'R', 'BN', 'ON', 'BN', 'BN']]), ('LRE from odd level', [['LRE', 'R'], 1, 6], [['x', 2], ['BN', 'R']]), ('override on neutrals', [['RLO', 'ON', 'L', 'WS'], 0, 6], [['x', 1, 1, 1], ['BN', 'R', 'R', 'R']]), ('control layout', [['EN', 'LRO', 'LRO', 'LRE', 'RLO', 'EN', 'PDF', 'RLE'], 0, 3], [[0, 'x', 'x', 'x', 'x', 2, 'x', 'x'], ['EN', 'BN', 'BN', 'BN', 'BN', 'L', 'BN', 'BN']]), ('control layout', [['ON', 'RLE', 'LRE', 'RLE', 'LRE', 'R', 'L', 'LRO', 'EN', 'PDF', 'L', 'L', 'LRE', 'PDF'], 0, 4], [[0, 'x', 'x', 'x', 'x', 4, 4, 'x', 4, 'x', 4, 4, 'x', 'x'], ['ON', 'BN', 'BN', 'BN', 'BN', 'R', 'L', 'BN', 'EN', 'BN', 'L', 'L', 'BN', 'BN']])], [('regression: next odd level', [['RLO', 'ON', 'EN', 'EN', 'ON', 'R'], 1, 2], [['x', 1, 1, 1, 1, 1], ['BN', 'ON', 'EN', 'EN', 'ON', 'R']]), ('regression: next odd level', [['RLE', 'RLO', 'EN', 'L', 'EN', 'PDF', 'L', 'LRE', 'EN', 'LRO', 'R', 'WS', 'LRE'], 1, 3], [['x', 'x', 3, 3, 3, 'x', 3, 'x', 3, 'x', 3, 3, 'x'], ['BN', 'BN', 'EN', 'L', 'EN', 'BN', 'L', 'BN', 'EN', 'BN', 'R', 'WS', 'BN']]), ('regression: next odd level', [['RLO', 'R'], 1, 3], [['x', 3], ['BN', 'R']]), ('regression: next odd level', [['L', 'L', 'RLO', 'RLO', 'L', 'R', 'RLE', 'RLE', 'R', 'R', 'L', 'LRE', 'EN'], 1, 6], [[1, 1, 'x', 'x', 5, 5, 'x', 'x', 5, 5, 5, 'x', 5], ['L', 'L', 'BN', 'BN', 'R', 'R', 'BN', 'BN', 'R', 'R', 'R', 'BN', 'R']]), ('override on neutrals', [['RLO', 'ON', 'L', 'WS'], 0, 6], [['x', 1, 1, 1], ['BN', 'R', 'R', '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', 'L', 'LRE', 'LRO', 'RLE'], 1, 3], [[1, 1, 'x', 'x', 'x'], ['R', 'L', 'BN', 'BN', 'BN']]), ('control layout', [['ON', 'L', 'LRO', 'RLO', 'PDF', 'PDF', 'R', 'R', 'ON', 'L', 'ON', 'L'], 1, 3], [[1, 1, 'x', 'x', 'x', 'x', 1, 1, 1, 1, 1, 1], ['ON', 'L', 'BN', 'BN', 'BN', 'BN', 'R', 'R', 'ON', 'L', 'ON', 'L']])]]
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
RLE from odd level[['x', 'x', 2], ['BN', 'BN', 'L']][['x', 'x', 3], ['BN', 'BN', 'L']]Failed
regression: next odd level[[0, 0, 0, 'x', 'x', 1, 'x', 2], ['L', 'L', 'ON', 'BN', 'BN', 'L', 'BN', 'R']][[0, 0, 0, 'x', 'x', 1, 'x', 3], ['L', 'L', 'ON', 'BN', 'BN', 'L', 'BN', 'R']]Failed
partial-repair probe[['x', 'x', 'x', 1, 1, 'x'], ['BN', 'BN', 'BN', 'ON', 'R', 'BN']][['x', 'x', 'x', 1, 1, 'x'], ['BN', 'BN', 'BN', 'ON', 'R', 'BN']]Passed
partial-repair probe[[0, 'x', 'x', 0, 0, 'x', 'x', 2, 2, 'x', 3, 'x', 4], ['R', 'BN', 'BN', 'R', 'L', 'BN', 'BN', 'ON', 'R', 'BN', 'ON', 'BN', 'R']][[0, 'x', 'x', 0, 0, 'x', 'x', 2, 2, 'x', 3, 'x', 4], ['R', 'BN', 'BN', 'R', 'L', 'BN', 'BN', 'ON', 'R', 'BN', 'ON', 'BN', 'R']]Passed
LRE from odd level[['x', 2], ['BN', 'R']][['x', 2], ['BN', 'R']]Passed
override on neutrals[['x', 1, 1, 1], ['BN', 'R', 'R', 'R']][['x', 1, 1, 1], ['BN', 'R', 'R', 'R']]Passed
control layout[['x', 'x', 2, 2, 'x', 2, 2, 2, 'x', 2, 2, 'x'], ['BN', 'BN', 'L', 'L', 'BN', 'L', 'L', 'L', 'BN', 'L', 'L', 'BN']][['x', 'x', 2, 2, 'x', 2, 2, 2, 'x', 2, 2, 'x'], ['BN', 'BN', 'L', 'L', 'BN', 'L', 'L', 'L', 'BN', 'L', 'L', 'BN']]Passed
control layout[[0, 'x'], ['R', 'BN']][[0, 'x'], ['R', 'BN']]Passed

SHA-256 / c7d52a93c980942b7406465d2319b97ebdf97682b2baba809697e269a64504fb

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 == 1 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 = [[('RLE from odd level', [['RLE', 'RLE', 'L'], 0, 6], [['x', 'x', 3], ['BN', 'BN', 'L']]), ('regression: next odd level', [['L', 'L', 'ON', 'PDF', 'RLE', 'L', 'RLO', 'R'], 0, 4], [[0, 0, 0, 'x', 'x', 1, 'x', 3], ['L', 'L', 'ON', 'BN', 'BN', 'L', 'BN', 'R']]), ('partial-repair probe', [['RLE', 'LRE', 'PDF', 'ON', 'R', 'RLO'], 0, 4], [['x', 'x', 'x', 1, 1, 'x'], ['BN', 'BN', 'BN', 'ON', 'R', 'BN']]), ('partial-repair probe', [['R', 'RLO', 'PDF', 'R', 'L', 'RLE', 'LRE', 'ON', 'R', 'RLE', 'ON', 'LRE', 'R'], 0, 4], [[0, 'x', 'x', 0, 0, 'x', 'x', 2, 2, 'x', 3, 'x', 4], ['R', 'BN', 'BN', 'R', 'L', 'BN', 'BN', 'ON', 'R', 'BN', 'ON', 'BN', 'R']]), ('LRE from odd level', [['LRE', 'R'], 1, 6], [['x', 2], ['BN', 'R']]), ('override on neutrals', [['RLO', 'ON', 'L', 'WS'], 0, 6], [['x', 1, 1, 1], ['BN', 'R', 'R', 'R']]), ('control layout', [['PDF', 'LRO', 'R', 'EN', 'LRE', 'L', 'L', 'L', 'RLE', 'R', 'L', 'LRO'], 1, 3], [['x', 'x', 2, 2, 'x', 2, 2, 2, 'x', 2, 2, 'x'], ['BN', 'BN', 'L', 'L', 'BN', 'L', 'L', 'L', 'BN', 'L', 'L', 'BN']]), ('control layout', [['R', 'LRO'], 0, 4], [[0, 'x'], ['R', 'BN']])], [('regression: next odd level', [['PDF', 'RLO', 'RLE', 'LRE', 'LRO', 'PDF', 'PDF', 'EN', 'PDF', 'R', 'L', 'EN', 'L'], 1, 5], [['x', 'x', 'x', 'x', 'x', 'x', 'x', 5, 'x', 3, 3, 3, 3], ['BN', 'BN', 'BN', 'BN', 'BN', 'BN', 'BN', 'EN', 'BN', 'R', 'R', 'R', 'R']]), ('regression: next odd level', [['WS', 'PDF', 'RLE', 'RLE', 'L'], 1, 5], [[1, 'x', 'x', 'x', 5], ['WS', 'BN', 'BN', 'BN', 'L']]), ('partial-repair probe', [['R', 'RLO', 'RLE', 'PDF', 'R', 'LRE', 'L', 'ON', 'R', 'ON', 'RLO'], 0, 3], [[0, 'x', 'x', 'x', 1, 'x', 2, 2, 2, 2, 'x'], ['R', 'BN', 'BN', 'BN', 'R', 'BN', 'L', 'ON', 'R', 'ON', 'BN']]), ('regression: next odd level', [['ON', 'L', 'EN', 'PDF', 'RLE', 'R', 'RLO', 'L', 'PDF'], 0, 5], [[0, 0, 0, 'x', 'x', 1, 'x', 3, 'x'], ['ON', 'L', 'EN', 'BN', 'BN', 'R', 'BN', 'R', 'BN']]), ('depth limit exactly reached', [['RLE', 'LRE', 'L', 'PDF', 'L'], 0, 2], [['x', 'x', 2, 'x', 1], ['BN', 'BN', 'L', 'BN', 'L']]), ('LRE from odd level', [['LRE', 'R'], 1, 6], [['x', 2], ['BN', 'R']]), ('control layout', [['EN', 'R'], 0, 5], [[0, 0], ['EN', 'R']]), ('control layout', [['L', 'R', 'ON', 'R', 'PDF', 'ON', 'ON'], 1, 4], [[1, 1, 1, 1, 'x', 1, 1], ['L', 'R', 'ON', 'R', 'BN', 'ON', 'ON']])], [('regression: next odd level', [['PDF', 'PDF', 'R', 'L', 'RLO', 'ON', 'R', 'ON'], 1, 2], [['x', 'x', 1, 1, 'x', 1, 1, 1], ['BN', 'BN', 'R', 'L', 'BN', 'ON', 'R', 'ON']]), ('regression: next odd level', [['RLO', 'EN', 'R', 'ON', 'EN', 'L', 'ON', 'R', 'RLO', 'RLE', 'LRE', 'PDF', 'EN', 'LRE'], 1, 3], [['x', 3, 3, 3, 3, 3, 3, 3, 'x', 'x', 'x', 'x', 3, 'x'], ['BN', 'R', 'R', 'R', 'R', 'R', 'R', 'R', 'BN', 'BN', 'BN', 'BN', 'R', 'BN']]), ('regression: next odd level', [['ON', 'L', 'PDF', 'RLO', 'R'], 1, 4], [[1, 1, 'x', 'x', 3], ['ON', 'L', 'BN', 'BN', 'R']]), ('partial-repair probe', [['WS', 'L', 'L', 'RLE', 'R', 'RLO'], 0, 5], [[0, 0, 0, 'x', 1, 'x'], ['WS', 'L', 'L', 'BN', 'R', 'BN']]), ('depth limit exactly reached', [['RLE', 'LRE', 'L', 'PDF', 'L'], 0, 2], [['x', 'x', 2, 'x', 1], ['BN', 'BN', 'L', 'BN', 'L']]), ('override on neutrals', [['RLO', 'ON', 'L', 'WS'], 0, 6], [['x', 1, 1, 1], ['BN', 'R', 'R', 'R']]), ('control layout', [['ON', 'ON', 'L', 'EN', 'WS'], 1, 4], [[1, 1, 1, 1, 1], ['ON', 'ON', 'L', 'EN', 'WS']]), ('control layout', [['L', 'R', 'WS', 'ON', 'RLE', 'LRE'], 0, 5], [[0, 0, 0, 0, 'x', 'x'], ['L', 'R', 'WS', 'ON', 'BN', 'BN']])], [('regression: next odd level', [['PDF', 'PDF', 'R', 'L', 'RLO', 'ON', 'R', 'ON'], 1, 2], [['x', 'x', 1, 1, 'x', 1, 1, 1], ['BN', 'BN', 'R', 'L', 'BN', 'ON', 'R', 'ON']]), ('regression: next odd level', [['RLE', 'RLO', 'EN', 'L', 'EN', 'PDF', 'L', 'LRE', 'EN', 'LRO', 'R', 'WS', 'LRE'], 1, 3], [['x', 'x', 3, 3, 3, 'x', 3, 'x', 3, 'x', 3, 3, 'x'], ['BN', 'BN', 'EN', 'L', 'EN', 'BN', 'L', 'BN', 'EN', 'BN', 'R', 'WS', 'BN']]), ('regression: next odd level', [['RLO', 'R'], 1, 3], [['x', 3], ['BN', 'R']]), ('partial-repair probe', [['R', 'L', 'RLE', 'WS', 'R', 'LRE', 'ON', 'PDF', 'RLE'], 0, 4], [[0, 0, 'x', 1, 1, 'x', 2, 'x', 'x'], ['R', 'L', 'BN', 'WS', 'R', 'BN', 'ON', 'BN', 'BN']]), ('LRE from odd level', [['LRE', 'R'], 1, 6], [['x', 2], ['BN', 'R']]), ('override on neutrals', [['RLO', 'ON', 'L', 'WS'], 0, 6], [['x', 1, 1, 1], ['BN', 'R', 'R', 'R']]), ('control layout', [['EN', 'LRO', 'LRO', 'LRE', 'RLO', 'EN', 'PDF', 'RLE'], 0, 3], [[0, 'x', 'x', 'x', 'x', 2, 'x', 'x'], ['EN', 'BN', 'BN', 'BN', 'BN', 'L', 'BN', 'BN']]), ('control layout', [['ON', 'RLE', 'LRE', 'RLE', 'LRE', 'R', 'L', 'LRO', 'EN', 'PDF', 'L', 'L', 'LRE', 'PDF'], 0, 4], [[0, 'x', 'x', 'x', 'x', 4, 4, 'x', 4, 'x', 4, 4, 'x', 'x'], ['ON', 'BN', 'BN', 'BN', 'BN', 'R', 'L', 'BN', 'EN', 'BN', 'L', 'L', 'BN', 'BN']])], [('regression: next odd level', [['RLO', 'ON', 'EN', 'EN', 'ON', 'R'], 1, 2], [['x', 1, 1, 1, 1, 1], ['BN', 'ON', 'EN', 'EN', 'ON', 'R']]), ('regression: next odd level', [['RLE', 'RLO', 'EN', 'L', 'EN', 'PDF', 'L', 'LRE', 'EN', 'LRO', 'R', 'WS', 'LRE'], 1, 3], [['x', 'x', 3, 3, 3, 'x', 3, 'x', 3, 'x', 3, 3, 'x'], ['BN', 'BN', 'EN', 'L', 'EN', 'BN', 'L', 'BN', 'EN', 'BN', 'R', 'WS', 'BN']]), ('regression: next odd level', [['RLO', 'R'], 1, 3], [['x', 3], ['BN', 'R']]), ('regression: next odd level', [['L', 'L', 'RLO', 'RLO', 'L', 'R', 'RLE', 'RLE', 'R', 'R', 'L', 'LRE', 'EN'], 1, 6], [[1, 1, 'x', 'x', 5, 5, 'x', 'x', 5, 5, 5, 'x', 5], ['L', 'L', 'BN', 'BN', 'R', 'R', 'BN', 'BN', 'R', 'R', 'R', 'BN', 'R']]), ('override on neutrals', [['RLO', 'ON', 'L', 'WS'], 0, 6], [['x', 1, 1, 1], ['BN', 'R', 'R', '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', 'L', 'LRE', 'LRO', 'RLE'], 1, 3], [[1, 1, 'x', 'x', 'x'], ['R', 'L', 'BN', 'BN', 'BN']]), ('control layout', [['ON', 'L', 'LRO', 'RLO', 'PDF', 'PDF', 'R', 'R', 'ON', 'L', 'ON', 'L'], 1, 3], [[1, 1, 'x', 'x', 'x', 'x', 1, 1, 1, 1, 1, 1], ['ON', 'L', 'BN', 'BN', 'BN', 'BN', 'R', 'R', 'ON', 'L', 'ON', 'L']])]]
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
RLE from odd level[['x', 'x', 4], ['BN', 'BN', 'L']][['x', 'x', 3], ['BN', 'BN', 'L']]Failed
regression: next odd level[[0, 0, 0, 'x', 'x', 2, 'x', 4], ['L', 'L', 'ON', 'BN', 'BN', 'L', 'BN', 'R']][[0, 0, 0, 'x', 'x', 1, 'x', 3], ['L', 'L', 'ON', 'BN', 'BN', 'L', 'BN', 'R']]Failed
partial-repair probe[['x', 'x', 'x', 2, 2, 'x'], ['BN', 'BN', 'BN', 'ON', 'R', 'BN']][['x', 'x', 'x', 1, 1, 'x'], ['BN', 'BN', 'BN', 'ON', 'R', 'BN']]Failed
partial-repair probe[[0, 'x', 'x', 0, 0, 'x', 'x', 4, 4, 'x', 4, 'x', 4], ['R', 'BN', 'BN', 'R', 'L', 'BN', 'BN', 'ON', 'R', 'BN', 'ON', 'BN', 'R']][[0, 'x', 'x', 0, 0, 'x', 'x', 2, 2, 'x', 3, 'x', 4], ['R', 'BN', 'BN', 'R', 'L', 'BN', 'BN', 'ON', 'R', 'BN', 'ON', 'BN', 'R']]Failed
LRE from odd level[['x', 2], ['BN', 'R']][['x', 2], ['BN', 'R']]Passed
override on neutrals[['x', 2, 2, 2], ['BN', 'R', 'R', 'R']][['x', 1, 1, 1], ['BN', 'R', 'R', 'R']]Failed
control layout[['x', 'x', 2, 2, 'x', 2, 2, 2, 'x', 2, 2, 'x'], ['BN', 'BN', 'L', 'L', 'BN', 'L', 'L', 'L', 'BN', 'L', 'L', 'BN']][['x', 'x', 2, 2, 'x', 2, 2, 2, 'x', 2, 2, 'x'], ['BN', 'BN', 'L', 'L', 'BN', 'L', 'L', 'L', 'BN', 'L', 'L', 'BN']]Passed
control layout[[0, 'x'], ['R', 'BN']][[0, 'x'], ['R', 'BN']]Passed

SHA-256 / 3aec27957076d537c91b6f8c7ad924ccb4f57eb5af58bed4d450ae1d9dd0d363

3 / The verified repair

Exit 0
"""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 = [[('RLE from odd level', [['RLE', 'RLE', 'L'], 0, 6], [['x', 'x', 3], ['BN', 'BN', 'L']]), ('regression: next odd level', [['L', 'L', 'ON', 'PDF', 'RLE', 'L', 'RLO', 'R'], 0, 4], [[0, 0, 0, 'x', 'x', 1, 'x', 3], ['L', 'L', 'ON', 'BN', 'BN', 'L', 'BN', 'R']]), ('partial-repair probe', [['RLE', 'LRE', 'PDF', 'ON', 'R', 'RLO'], 0, 4], [['x', 'x', 'x', 1, 1, 'x'], ['BN', 'BN', 'BN', 'ON', 'R', 'BN']]), ('partial-repair probe', [['R', 'RLO', 'PDF', 'R', 'L', 'RLE', 'LRE', 'ON', 'R', 'RLE', 'ON', 'LRE', 'R'], 0, 4], [[0, 'x', 'x', 0, 0, 'x', 'x', 2, 2, 'x', 3, 'x', 4], ['R', 'BN', 'BN', 'R', 'L', 'BN', 'BN', 'ON', 'R', 'BN', 'ON', 'BN', 'R']]), ('LRE from odd level', [['LRE', 'R'], 1, 6], [['x', 2], ['BN', 'R']]), ('override on neutrals', [['RLO', 'ON', 'L', 'WS'], 0, 6], [['x', 1, 1, 1], ['BN', 'R', 'R', 'R']]), ('control layout', [['PDF', 'LRO', 'R', 'EN', 'LRE', 'L', 'L', 'L', 'RLE', 'R', 'L', 'LRO'], 1, 3], [['x', 'x', 2, 2, 'x', 2, 2, 2, 'x', 2, 2, 'x'], ['BN', 'BN', 'L', 'L', 'BN', 'L', 'L', 'L', 'BN', 'L', 'L', 'BN']]), ('control layout', [['R', 'LRO'], 0, 4], [[0, 'x'], ['R', 'BN']])], [('regression: next odd level', [['PDF', 'RLO', 'RLE', 'LRE', 'LRO', 'PDF', 'PDF', 'EN', 'PDF', 'R', 'L', 'EN', 'L'], 1, 5], [['x', 'x', 'x', 'x', 'x', 'x', 'x', 5, 'x', 3, 3, 3, 3], ['BN', 'BN', 'BN', 'BN', 'BN', 'BN', 'BN', 'EN', 'BN', 'R', 'R', 'R', 'R']]), ('regression: next odd level', [['WS', 'PDF', 'RLE', 'RLE', 'L'], 1, 5], [[1, 'x', 'x', 'x', 5], ['WS', 'BN', 'BN', 'BN', 'L']]), ('partial-repair probe', [['R', 'RLO', 'RLE', 'PDF', 'R', 'LRE', 'L', 'ON', 'R', 'ON', 'RLO'], 0, 3], [[0, 'x', 'x', 'x', 1, 'x', 2, 2, 2, 2, 'x'], ['R', 'BN', 'BN', 'BN', 'R', 'BN', 'L', 'ON', 'R', 'ON', 'BN']]), ('regression: next odd level', [['ON', 'L', 'EN', 'PDF', 'RLE', 'R', 'RLO', 'L', 'PDF'], 0, 5], [[0, 0, 0, 'x', 'x', 1, 'x', 3, 'x'], ['ON', 'L', 'EN', 'BN', 'BN', 'R', 'BN', 'R', 'BN']]), ('depth limit exactly reached', [['RLE', 'LRE', 'L', 'PDF', 'L'], 0, 2], [['x', 'x', 2, 'x', 1], ['BN', 'BN', 'L', 'BN', 'L']]), ('LRE from odd level', [['LRE', 'R'], 1, 6], [['x', 2], ['BN', 'R']]), ('control layout', [['EN', 'R'], 0, 5], [[0, 0], ['EN', 'R']]), ('control layout', [['L', 'R', 'ON', 'R', 'PDF', 'ON', 'ON'], 1, 4], [[1, 1, 1, 1, 'x', 1, 1], ['L', 'R', 'ON', 'R', 'BN', 'ON', 'ON']])], [('regression: next odd level', [['PDF', 'PDF', 'R', 'L', 'RLO', 'ON', 'R', 'ON'], 1, 2], [['x', 'x', 1, 1, 'x', 1, 1, 1], ['BN', 'BN', 'R', 'L', 'BN', 'ON', 'R', 'ON']]), ('regression: next odd level', [['RLO', 'EN', 'R', 'ON', 'EN', 'L', 'ON', 'R', 'RLO', 'RLE', 'LRE', 'PDF', 'EN', 'LRE'], 1, 3], [['x', 3, 3, 3, 3, 3, 3, 3, 'x', 'x', 'x', 'x', 3, 'x'], ['BN', 'R', 'R', 'R', 'R', 'R', 'R', 'R', 'BN', 'BN', 'BN', 'BN', 'R', 'BN']]), ('regression: next odd level', [['ON', 'L', 'PDF', 'RLO', 'R'], 1, 4], [[1, 1, 'x', 'x', 3], ['ON', 'L', 'BN', 'BN', 'R']]), ('partial-repair probe', [['WS', 'L', 'L', 'RLE', 'R', 'RLO'], 0, 5], [[0, 0, 0, 'x', 1, 'x'], ['WS', 'L', 'L', 'BN', 'R', 'BN']]), ('depth limit exactly reached', [['RLE', 'LRE', 'L', 'PDF', 'L'], 0, 2], [['x', 'x', 2, 'x', 1], ['BN', 'BN', 'L', 'BN', 'L']]), ('override on neutrals', [['RLO', 'ON', 'L', 'WS'], 0, 6], [['x', 1, 1, 1], ['BN', 'R', 'R', 'R']]), ('control layout', [['ON', 'ON', 'L', 'EN', 'WS'], 1, 4], [[1, 1, 1, 1, 1], ['ON', 'ON', 'L', 'EN', 'WS']]), ('control layout', [['L', 'R', 'WS', 'ON', 'RLE', 'LRE'], 0, 5], [[0, 0, 0, 0, 'x', 'x'], ['L', 'R', 'WS', 'ON', 'BN', 'BN']])], [('regression: next odd level', [['PDF', 'PDF', 'R', 'L', 'RLO', 'ON', 'R', 'ON'], 1, 2], [['x', 'x', 1, 1, 'x', 1, 1, 1], ['BN', 'BN', 'R', 'L', 'BN', 'ON', 'R', 'ON']]), ('regression: next odd level', [['RLE', 'RLO', 'EN', 'L', 'EN', 'PDF', 'L', 'LRE', 'EN', 'LRO', 'R', 'WS', 'LRE'], 1, 3], [['x', 'x', 3, 3, 3, 'x', 3, 'x', 3, 'x', 3, 3, 'x'], ['BN', 'BN', 'EN', 'L', 'EN', 'BN', 'L', 'BN', 'EN', 'BN', 'R', 'WS', 'BN']]), ('regression: next odd level', [['RLO', 'R'], 1, 3], [['x', 3], ['BN', 'R']]), ('partial-repair probe', [['R', 'L', 'RLE', 'WS', 'R', 'LRE', 'ON', 'PDF', 'RLE'], 0, 4], [[0, 0, 'x', 1, 1, 'x', 2, 'x', 'x'], ['R', 'L', 'BN', 'WS', 'R', 'BN', 'ON', 'BN', 'BN']]), ('LRE from odd level', [['LRE', 'R'], 1, 6], [['x', 2], ['BN', 'R']]), ('override on neutrals', [['RLO', 'ON', 'L', 'WS'], 0, 6], [['x', 1, 1, 1], ['BN', 'R', 'R', 'R']]), ('control layout', [['EN', 'LRO', 'LRO', 'LRE', 'RLO', 'EN', 'PDF', 'RLE'], 0, 3], [[0, 'x', 'x', 'x', 'x', 2, 'x', 'x'], ['EN', 'BN', 'BN', 'BN', 'BN', 'L', 'BN', 'BN']]), ('control layout', [['ON', 'RLE', 'LRE', 'RLE', 'LRE', 'R', 'L', 'LRO', 'EN', 'PDF', 'L', 'L', 'LRE', 'PDF'], 0, 4], [[0, 'x', 'x', 'x', 'x', 4, 4, 'x', 4, 'x', 4, 4, 'x', 'x'], ['ON', 'BN', 'BN', 'BN', 'BN', 'R', 'L', 'BN', 'EN', 'BN', 'L', 'L', 'BN', 'BN']])], [('regression: next odd level', [['RLO', 'ON', 'EN', 'EN', 'ON', 'R'], 1, 2], [['x', 1, 1, 1, 1, 1], ['BN', 'ON', 'EN', 'EN', 'ON', 'R']]), ('regression: next odd level', [['RLE', 'RLO', 'EN', 'L', 'EN', 'PDF', 'L', 'LRE', 'EN', 'LRO', 'R', 'WS', 'LRE'], 1, 3], [['x', 'x', 3, 3, 3, 'x', 3, 'x', 3, 'x', 3, 3, 'x'], ['BN', 'BN', 'EN', 'L', 'EN', 'BN', 'L', 'BN', 'EN', 'BN', 'R', 'WS', 'BN']]), ('regression: next odd level', [['RLO', 'R'], 1, 3], [['x', 3], ['BN', 'R']]), ('regression: next odd level', [['L', 'L', 'RLO', 'RLO', 'L', 'R', 'RLE', 'RLE', 'R', 'R', 'L', 'LRE', 'EN'], 1, 6], [[1, 1, 'x', 'x', 5, 5, 'x', 'x', 5, 5, 5, 'x', 5], ['L', 'L', 'BN', 'BN', 'R', 'R', 'BN', 'BN', 'R', 'R', 'R', 'BN', 'R']]), ('override on neutrals', [['RLO', 'ON', 'L', 'WS'], 0, 6], [['x', 1, 1, 1], ['BN', 'R', 'R', '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', 'L', 'LRE', 'LRO', 'RLE'], 1, 3], [[1, 1, 'x', 'x', 'x'], ['R', 'L', 'BN', 'BN', 'BN']]), ('control layout', [['ON', 'L', 'LRO', 'RLO', 'PDF', 'PDF', 'R', 'R', 'ON', 'L', 'ON', 'L'], 1, 3], [[1, 1, 'x', 'x', 'x', 'x', 1, 1, 1, 1, 1, 1], ['ON', 'L', 'BN', 'BN', 'BN', 'BN', 'R', 'R', 'ON', 'L', 'ON', 'L']])]]
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
RLE from odd level[['x', 'x', 3], ['BN', 'BN', 'L']][['x', 'x', 3], ['BN', 'BN', 'L']]Passed
regression: next odd level[[0, 0, 0, 'x', 'x', 1, 'x', 3], ['L', 'L', 'ON', 'BN', 'BN', 'L', 'BN', 'R']][[0, 0, 0, 'x', 'x', 1, 'x', 3], ['L', 'L', 'ON', 'BN', 'BN', 'L', 'BN', 'R']]Passed
partial-repair probe[['x', 'x', 'x', 1, 1, 'x'], ['BN', 'BN', 'BN', 'ON', 'R', 'BN']][['x', 'x', 'x', 1, 1, 'x'], ['BN', 'BN', 'BN', 'ON', 'R', 'BN']]Passed
partial-repair probe[[0, 'x', 'x', 0, 0, 'x', 'x', 2, 2, 'x', 3, 'x', 4], ['R', 'BN', 'BN', 'R', 'L', 'BN', 'BN', 'ON', 'R', 'BN', 'ON', 'BN', 'R']][[0, 'x', 'x', 0, 0, 'x', 'x', 2, 2, 'x', 3, 'x', 4], ['R', 'BN', 'BN', 'R', 'L', 'BN', 'BN', 'ON', 'R', 'BN', 'ON', 'BN', 'R']]Passed
LRE from odd level[['x', 2], ['BN', 'R']][['x', 2], ['BN', 'R']]Passed
override on neutrals[['x', 1, 1, 1], ['BN', 'R', 'R', 'R']][['x', 1, 1, 1], ['BN', 'R', 'R', 'R']]Passed
control layout[['x', 'x', 2, 2, 'x', 2, 2, 2, 'x', 2, 2, 'x'], ['BN', 'BN', 'L', 'L', 'BN', 'L', 'L', 'L', 'BN', 'L', 'L', 'BN']][['x', 'x', 2, 2, 'x', 2, 2, 2, 'x', 2, 2, 'x'], ['BN', 'BN', 'L', 'L', 'BN', 'L', 'L', 'L', 'BN', 'L', 'L', 'BN']]Passed
control layout[[0, 'x'], ['R', 'BN']][[0, 'x'], ['R', 'BN']]Passed

SHA-256 / b736ad9ea66169410ac2f3631cab43c3f94e8a1ffee41d91d32ea6a3638a0988

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 2026-09-29T14:49:54.775292+00:00.

Case digest / 242562e369ab06335168f77b7cc8fef40380fe9c97456628cccc40607401de17