FAILURE MAP
← Case archive

FA-80776 / Bidirectional text layout / Open access

Isolating run sequences: sos level comparison · case 01

Sequence start types follow the run level only.

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

ROOT CAUSE

sos uses the run level instead of the higher of the two levels.

VERIFIED REPAIR

Take the parity of the higher level.

Unsuccessful approach: Taking the lower level is the opposite error.

Case contract

Input [classes, levels, paragraph level]. Split into maximal level runs; chain a run ending in a matched isolate initiator (LRI/RLI/FSI) with the run starting at its matching PDI (stack matching; unmatched PDI ignored). For each sequence sos = parity of max(level of first char, level of preceding char or paragraph level); eos = parity of max(level of last char, level of following char or paragraph level), using the paragraph level when the last char is an isolate initiator. Return [[indices, sos, eos]].

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, levels, para = x
    n = len(classes)
    match = {}
    stack = []
    for i, c in enumerate(classes):
        if c in ('LRI', 'RLI', 'FSI'):
            stack.append(i)
        elif c == 'PDI' and stack:
            match[stack.pop()] = i
    runs = []
    for i in range(n):
        if runs and levels[i] == levels[runs[-1][-1]]:
            runs[-1].append(i)
        else:
            runs.append([i])
    start_of = {r[0]: r for r in runs}
    seqs = []
    used = set()
    for r in runs:
        if r[0] in used:
            continue
        seq = list(r)
        used.add(r[0])
        while True:
            tail = seq[-1]
            if classes[tail] not in ('LRI', 'RLI', 'FSI') or tail not in match:
                break
            nxt = start_of.get(match[tail])
            if nxt is None:
                break
            seq.extend(nxt)
            used.add(nxt[0])
        seqs.append(seq)
    out = []
    for seq in seqs:
        first, last = seq[0], seq[-1]
        lv = levels[first]
        prev = levels[first - 1] if first > 0 else para
        sos = 'R' if lv % 2 else 'L'
        if classes[last] in ('LRI', 'RLI', 'FSI'):
            nxt_lv = para
        else:
            nxt_lv = levels[last + 1] if last + 1 < n else para
        eos = 'R' if max(levels[last], nxt_lv) % 2 else 'L'
        out.append([seq, sos, eos])
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: sos level comparison', [['L', 'FSI', 'EN', 'PDI', 'EN', 'EN', 'ON', 'EN', 'PDI', 'L', 'FSI', 'FSI', 'ON', 'ON'], [2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 2, 4, 4], 1], [[[0], 'L', 'L'], [[1, 3, 4], 'L', 'L'], [[2], 'L', 'L'], [[5], 'L', 'L'], [[6], 'L', 'L'], [[7], 'L', 'L'], [[8, 9, 10], 'L', 'R'], [[11], 'L', 'L'], [[12, 13], 'L', 'L']]), ('regression: sos level comparison', [['L', 'PDI', 'PDI', 'LRI', 'ON', 'FSI', 'ON', 'PDI'], [2, 1, 1, 1, 2, 2, 4, 2], 1], [[[0], 'L', 'L'], [[1, 2, 3], 'L', 'R'], [[4, 5, 7], 'L', 'L'], [[6], 'L', 'L']]), ('partial-repair probe', [['ON', 'RLI', 'L', 'LRI'], [0, 0, 1, 1], 0], [[[0, 1], 'L', 'L'], [[2, 3], 'R', 'R']]), ('partial-repair probe', [['PDI', 'R', 'R'], [0, 0, 1], 0], [[[0, 1], 'L', 'R'], [[2], 'R', 'R']]), ('isolate joins outer run', [['L', 'RLI', 'R', 'PDI', 'L'], [0, 0, 1, 0, 0], 0], [[[0, 1, 3, 4], 'L', 'L'], [[2], 'R', 'R']]), ('unmatched initiator at end', [['L', 'R', 'RLI'], [0, 1, 1], 0], [[[0], 'L', 'R'], [[1, 2], 'R', 'R']]), ('control layout', [['L', 'ON', 'R', 'RLI', 'PDI', 'LRI', 'L', 'FSI', 'ON', 'LRI'], [0, 0, 0, 0, 0, 0, 2, 2, 4, 4], 0], [[[0, 1, 2, 3, 4, 5], 'L', 'L'], [[6, 7], 'L', 'L'], [[8, 9], 'L', 'L']]), ('control layout', [['R', 'PDI', 'R', 'FSI'], [1, 1, 1, 1], 1], [[[0, 1, 2, 3], 'R', 'R']])], [('regression: sos level comparison', [['L', 'RLI', 'RLI', 'RLI', 'ON', 'PDI', 'ON', 'L', 'ON'], [2, 1, 3, 5, 7, 5, 5, 5, 5], 1], [[[0], 'L', 'L'], [[1], 'L', 'R'], [[2], 'R', 'R'], [[3, 5, 6, 7, 8], 'R', 'R'], [[4], 'R', 'R']]), ('regression: sos level comparison', [['L', 'R', 'LRI', 'PDI'], [2, 1, 1, 1], 1], [[[0], 'L', 'L'], [[1, 2, 3], 'L', 'R']]), ('partial-repair probe', [['PDI', 'RLI', 'ON'], [0, 0, 1], 0], [[[0, 1], 'L', 'L'], [[2], 'R', 'R']]), ('regression: sos level comparison', [['R', 'PDI', 'ON', 'R', 'R', 'RLI', 'L', 'L', 'LRI', 'R', 'LRI', 'L', 'EN'], [1, 1, 1, 1, 1, 1, 3, 4, 3, 5, 4, 6, 6], 1], [[[0, 1, 2, 3, 4, 5], 'R', 'R'], [[6], 'R', 'L'], [[7], 'L', 'L'], [[8], 'L', 'R'], [[9], 'R', 'R'], [[10], 'R', 'L'], [[11, 12], 'L', 'L']]), ('nested isolates', [['R', 'LRI', 'L', 'RLI', 'R', 'PDI', 'PDI', 'R'], [1, 1, 2, 2, 3, 2, 1, 1], 1], [[[0, 1, 6, 7], 'R', 'R'], [[2, 3, 5], 'L', 'L'], [[4], 'R', 'R']]), ('isolate joins outer run', [['L', 'RLI', 'R', 'PDI', 'L'], [0, 0, 1, 0, 0], 0], [[[0, 1, 3, 4], 'L', 'L'], [[2], 'R', 'R']]), ('control layout', [['L', 'L', 'ON'], [1, 1, 1], 1], [[[0, 1, 2], 'R', 'R']]), ('control layout', [['EN', 'L', 'EN', 'L', 'FSI', 'EN', 'L', 'PDI', 'L', 'ON', 'L', 'LRI', 'EN'], [0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2], 0], [[[0, 1, 2, 3, 4, 7, 8, 9, 10, 11], 'L', 'L'], [[5, 6], 'L', 'L'], [[12], 'L', 'L']])], [('regression: sos level comparison', [['R', 'EN', 'L', 'FSI', 'PDI', 'PDI', 'PDI', 'EN', 'L', 'RLI', 'ON', 'RLI'], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], 0], [[[0], 'R', 'R'], [[1, 2, 3, 4, 5, 6, 7, 8, 9], 'R', 'L'], [[10, 11], 'R', 'R']]), ('regression: sos level comparison', [['L', 'PDI', 'FSI', 'EN', 'R', 'R', 'ON', 'EN', 'PDI', 'L'], [2, 1, 1, 2, 3, 2, 2, 2, 1, 1], 1], [[[0], 'L', 'L'], [[1, 2, 8, 9], 'L', 'R'], [[3], 'L', 'R'], [[4], 'R', 'R'], [[5, 6, 7], 'R', 'L']]), ('partial-repair probe', [['FSI', 'EN', 'R', 'RLI', 'L', 'PDI', 'L'], [1, 2, 2, 2, 4, 2, 2], 1], [[[0], 'R', 'R'], [[1, 2, 3, 5, 6], 'L', 'L'], [[4], 'L', 'L']]), ('partial-repair probe', [['RLI', 'RLI', 'R', 'PDI', 'EN', 'R', 'ON', 'PDI', 'L', 'L', 'EN', 'L', 'L'], [0, 1, 3, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0], 0], [[[0, 7, 8, 9, 10, 11, 12], 'L', 'L'], [[1, 3, 4, 5, 6], 'R', 'R'], [[2], 'R', 'R']]), ('nested isolates', [['R', 'LRI', 'L', 'RLI', 'R', 'PDI', 'PDI', 'R'], [1, 1, 2, 2, 3, 2, 1, 1], 1], [[[0, 1, 6, 7], 'R', 'R'], [[2, 3, 5], 'L', 'L'], [[4], 'R', 'R']]), ('isolate joins outer run', [['L', 'RLI', 'R', 'PDI', 'L'], [0, 0, 1, 0, 0], 0], [[[0, 1, 3, 4], 'L', 'L'], [[2], 'R', 'R']]), ('control layout', [['ON', 'PDI', 'L', 'LRI'], [0, 0, 0, 0], 0], [[[0, 1, 2, 3], 'L', 'L']]), ('control layout', [['LRI', 'PDI', 'FSI'], [0, 0, 0], 0], [[[0, 1, 2], 'L', 'L']])], [('regression: sos level comparison', [['RLI', 'EN', 'ON'], [1, 4, 3], 1], [[[0], 'R', 'R'], [[1], 'L', 'L'], [[2], 'L', 'R']]), ('regression: sos level comparison', [['R', 'L', 'EN', 'L', 'PDI'], [1, 0, 0, 0, 0], 0], [[[0], 'R', 'R'], [[1, 2, 3, 4], 'R', 'L']]), ('regression: sos level comparison', [['PDI', 'R', 'L', 'ON', 'R', 'L', 'EN', 'L'], [0, 0, 0, 0, 1, 0, 0, 0], 0], [[[0, 1, 2, 3], 'L', 'R'], [[4], 'R', 'R'], [[5, 6, 7], 'R', 'L']]), ('regression: sos level comparison', [['R', 'EN', 'FSI', 'FSI', 'PDI', 'L', 'PDI'], [1, 2, 1, 2, 2, 2, 1], 1], [[[0], 'R', 'L'], [[1], 'L', 'L'], [[2, 6], 'L', 'R'], [[3, 4, 5], 'L', 'L']]), ('nested isolates', [['R', 'LRI', 'L', 'RLI', 'R', 'PDI', 'PDI', 'R'], [1, 1, 2, 2, 3, 2, 1, 1], 1], [[[0, 1, 6, 7], 'R', 'R'], [[2, 3, 5], 'L', 'L'], [[4], 'R', 'R']]), ('isolate joins outer run', [['L', 'RLI', 'R', 'PDI', 'L'], [0, 0, 1, 0, 0], 0], [[[0, 1, 3, 4], 'L', 'L'], [[2], 'R', 'R']]), ('control layout', [['PDI', 'R', 'LRI', 'PDI', 'ON', 'EN'], [0, 0, 0, 0, 0, 0], 0], [[[0, 1, 2, 3, 4, 5], 'L', 'L']]), ('control layout', [['ON', 'PDI', 'PDI', 'EN', 'R', 'L', 'L', 'ON', 'L'], [0, 0, 0, 0, 0, 0, 0, 0, 0], 0], [[[0, 1, 2, 3, 4, 5, 6, 7, 8], 'L', 'L']])], [('regression: sos level comparison', [['EN', 'RLI', 'L', 'RLI', 'ON', 'L', 'EN', 'PDI', 'EN'], [2, 1, 3, 3, 5, 6, 6, 3, 3], 1], [[[0], 'L', 'L'], [[1], 'L', 'R'], [[2, 3, 7, 8], 'R', 'R'], [[4], 'R', 'L'], [[5, 6], 'L', 'L']]), ('regression: sos level comparison', [['EN', 'ON', 'ON', 'ON'], [2, 1, 1, 1], 1], [[[0], 'L', 'L'], [[1, 2, 3], 'L', 'R']]), ('regression: sos level comparison', [['ON', 'R', 'PDI', 'R'], [0, 1, 0, 1], 0], [[[0], 'L', 'R'], [[1], 'R', 'R'], [[2], 'R', 'R'], [[3], 'R', 'R']]), ('regression: sos level comparison', [['PDI', 'PDI', 'EN', 'R', 'ON', 'L', 'R', 'R', 'L', 'L', 'R', 'R'], [1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1], 1], [[[0, 1, 2, 3, 4], 'R', 'L'], [[5], 'L', 'L'], [[6, 7, 8, 9, 10, 11], 'L', 'R']]), ('unmatched initiator at end', [['L', 'R', 'RLI'], [0, 1, 1], 0], [[[0], 'L', 'R'], [[1, 2], 'R', 'R']]), ('isolate joins outer run', [['L', 'RLI', 'R', 'PDI', 'L'], [0, 0, 1, 0, 0], 0], [[[0, 1, 3, 4], 'L', 'L'], [[2], 'R', 'R']]), ('control layout', [['L', 'FSI', 'PDI', 'PDI', 'L', 'LRI', 'ON', 'L', 'EN', 'ON'], [0, 0, 0, 0, 0, 0, 2, 2, 2, 2], 0], [[[0, 1, 2, 3, 4, 5], 'L', 'L'], [[6, 7, 8, 9], 'L', 'L']]), ('control layout', [['PDI', 'PDI', 'L', 'EN', 'EN'], [0, 0, 0, 0, 0], 0], [[[0, 1, 2, 3, 4], 'L', '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
regression: sos level comparison[[[0], 'L', 'L'], [[1, 3, 4], 'R', 'L'], [[2], 'L', 'L'], [[5], 'L', 'L'], [[6], 'R', 'L'], [[7], 'L', 'L'], [[8, 9, 10], 'R', 'R'], [[11], 'L', 'L'], [[12, 13], 'L', 'L']][[[0], 'L', 'L'], [[1, 3, 4], 'L', 'L'], [[2], 'L', 'L'], [[5], 'L', 'L'], [[6], 'L', 'L'], [[7], 'L', 'L'], [[8, 9, 10], 'L', 'R'], [[11], 'L', 'L'], [[12, 13], 'L', 'L']]Failed
regression: sos level comparison[[[0], 'L', 'L'], [[1, 2, 3], 'R', 'R'], [[4, 5, 7], 'L', 'L'], [[6], 'L', 'L']][[[0], 'L', 'L'], [[1, 2, 3], 'L', 'R'], [[4, 5, 7], 'L', 'L'], [[6], 'L', 'L']]Failed
partial-repair probe[[[0, 1], 'L', 'L'], [[2, 3], 'R', 'R']][[[0, 1], 'L', 'L'], [[2, 3], 'R', 'R']]Passed
partial-repair probe[[[0, 1], 'L', 'R'], [[2], 'R', 'R']][[[0, 1], 'L', 'R'], [[2], 'R', 'R']]Passed
isolate joins outer run[[[0, 1, 3, 4], 'L', 'L'], [[2], 'R', 'R']][[[0, 1, 3, 4], 'L', 'L'], [[2], 'R', 'R']]Passed
unmatched initiator at end[[[0], 'L', 'R'], [[1, 2], 'R', 'R']][[[0], 'L', 'R'], [[1, 2], 'R', 'R']]Passed
control layout[[[0, 1, 2, 3, 4, 5], 'L', 'L'], [[6, 7], 'L', 'L'], [[8, 9], 'L', 'L']][[[0, 1, 2, 3, 4, 5], 'L', 'L'], [[6, 7], 'L', 'L'], [[8, 9], 'L', 'L']]Passed
control layout[[[0, 1, 2, 3], 'R', 'R']][[[0, 1, 2, 3], 'R', 'R']]Passed

SHA-256 / 1d78b5f01acc9cfb8958a039a50b9cddeebb06f5dcb69a825de2d8246c707308

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(x):
    classes, levels, para = x
    n = len(classes)
    match = {}
    stack = []
    for i, c in enumerate(classes):
        if c in ('LRI', 'RLI', 'FSI'):
            stack.append(i)
        elif c == 'PDI' and stack:
            match[stack.pop()] = i
    runs = []
    for i in range(n):
        if runs and levels[i] == levels[runs[-1][-1]]:
            runs[-1].append(i)
        else:
            runs.append([i])
    start_of = {r[0]: r for r in runs}
    seqs = []
    used = set()
    for r in runs:
        if r[0] in used:
            continue
        seq = list(r)
        used.add(r[0])
        while True:
            tail = seq[-1]
            if classes[tail] not in ('LRI', 'RLI', 'FSI') or tail not in match:
                break
            nxt = start_of.get(match[tail])
            if nxt is None:
                break
            seq.extend(nxt)
            used.add(nxt[0])
        seqs.append(seq)
    out = []
    for seq in seqs:
        first, last = seq[0], seq[-1]
        lv = levels[first]
        prev = levels[first - 1] if first > 0 else para
        sos = 'R' if min(lv, prev) % 2 else 'L'
        if classes[last] in ('LRI', 'RLI', 'FSI'):
            nxt_lv = para
        else:
            nxt_lv = levels[last + 1] if last + 1 < n else para
        eos = 'R' if max(levels[last], nxt_lv) % 2 else 'L'
        out.append([seq, sos, eos])
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: sos level comparison', [['L', 'FSI', 'EN', 'PDI', 'EN', 'EN', 'ON', 'EN', 'PDI', 'L', 'FSI', 'FSI', 'ON', 'ON'], [2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 2, 4, 4], 1], [[[0], 'L', 'L'], [[1, 3, 4], 'L', 'L'], [[2], 'L', 'L'], [[5], 'L', 'L'], [[6], 'L', 'L'], [[7], 'L', 'L'], [[8, 9, 10], 'L', 'R'], [[11], 'L', 'L'], [[12, 13], 'L', 'L']]), ('regression: sos level comparison', [['L', 'PDI', 'PDI', 'LRI', 'ON', 'FSI', 'ON', 'PDI'], [2, 1, 1, 1, 2, 2, 4, 2], 1], [[[0], 'L', 'L'], [[1, 2, 3], 'L', 'R'], [[4, 5, 7], 'L', 'L'], [[6], 'L', 'L']]), ('partial-repair probe', [['ON', 'RLI', 'L', 'LRI'], [0, 0, 1, 1], 0], [[[0, 1], 'L', 'L'], [[2, 3], 'R', 'R']]), ('partial-repair probe', [['PDI', 'R', 'R'], [0, 0, 1], 0], [[[0, 1], 'L', 'R'], [[2], 'R', 'R']]), ('isolate joins outer run', [['L', 'RLI', 'R', 'PDI', 'L'], [0, 0, 1, 0, 0], 0], [[[0, 1, 3, 4], 'L', 'L'], [[2], 'R', 'R']]), ('unmatched initiator at end', [['L', 'R', 'RLI'], [0, 1, 1], 0], [[[0], 'L', 'R'], [[1, 2], 'R', 'R']]), ('control layout', [['L', 'ON', 'R', 'RLI', 'PDI', 'LRI', 'L', 'FSI', 'ON', 'LRI'], [0, 0, 0, 0, 0, 0, 2, 2, 4, 4], 0], [[[0, 1, 2, 3, 4, 5], 'L', 'L'], [[6, 7], 'L', 'L'], [[8, 9], 'L', 'L']]), ('control layout', [['R', 'PDI', 'R', 'FSI'], [1, 1, 1, 1], 1], [[[0, 1, 2, 3], 'R', 'R']])], [('regression: sos level comparison', [['L', 'RLI', 'RLI', 'RLI', 'ON', 'PDI', 'ON', 'L', 'ON'], [2, 1, 3, 5, 7, 5, 5, 5, 5], 1], [[[0], 'L', 'L'], [[1], 'L', 'R'], [[2], 'R', 'R'], [[3, 5, 6, 7, 8], 'R', 'R'], [[4], 'R', 'R']]), ('regression: sos level comparison', [['L', 'R', 'LRI', 'PDI'], [2, 1, 1, 1], 1], [[[0], 'L', 'L'], [[1, 2, 3], 'L', 'R']]), ('partial-repair probe', [['PDI', 'RLI', 'ON'], [0, 0, 1], 0], [[[0, 1], 'L', 'L'], [[2], 'R', 'R']]), ('regression: sos level comparison', [['R', 'PDI', 'ON', 'R', 'R', 'RLI', 'L', 'L', 'LRI', 'R', 'LRI', 'L', 'EN'], [1, 1, 1, 1, 1, 1, 3, 4, 3, 5, 4, 6, 6], 1], [[[0, 1, 2, 3, 4, 5], 'R', 'R'], [[6], 'R', 'L'], [[7], 'L', 'L'], [[8], 'L', 'R'], [[9], 'R', 'R'], [[10], 'R', 'L'], [[11, 12], 'L', 'L']]), ('nested isolates', [['R', 'LRI', 'L', 'RLI', 'R', 'PDI', 'PDI', 'R'], [1, 1, 2, 2, 3, 2, 1, 1], 1], [[[0, 1, 6, 7], 'R', 'R'], [[2, 3, 5], 'L', 'L'], [[4], 'R', 'R']]), ('isolate joins outer run', [['L', 'RLI', 'R', 'PDI', 'L'], [0, 0, 1, 0, 0], 0], [[[0, 1, 3, 4], 'L', 'L'], [[2], 'R', 'R']]), ('control layout', [['L', 'L', 'ON'], [1, 1, 1], 1], [[[0, 1, 2], 'R', 'R']]), ('control layout', [['EN', 'L', 'EN', 'L', 'FSI', 'EN', 'L', 'PDI', 'L', 'ON', 'L', 'LRI', 'EN'], [0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2], 0], [[[0, 1, 2, 3, 4, 7, 8, 9, 10, 11], 'L', 'L'], [[5, 6], 'L', 'L'], [[12], 'L', 'L']])], [('regression: sos level comparison', [['R', 'EN', 'L', 'FSI', 'PDI', 'PDI', 'PDI', 'EN', 'L', 'RLI', 'ON', 'RLI'], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], 0], [[[0], 'R', 'R'], [[1, 2, 3, 4, 5, 6, 7, 8, 9], 'R', 'L'], [[10, 11], 'R', 'R']]), ('regression: sos level comparison', [['L', 'PDI', 'FSI', 'EN', 'R', 'R', 'ON', 'EN', 'PDI', 'L'], [2, 1, 1, 2, 3, 2, 2, 2, 1, 1], 1], [[[0], 'L', 'L'], [[1, 2, 8, 9], 'L', 'R'], [[3], 'L', 'R'], [[4], 'R', 'R'], [[5, 6, 7], 'R', 'L']]), ('partial-repair probe', [['FSI', 'EN', 'R', 'RLI', 'L', 'PDI', 'L'], [1, 2, 2, 2, 4, 2, 2], 1], [[[0], 'R', 'R'], [[1, 2, 3, 5, 6], 'L', 'L'], [[4], 'L', 'L']]), ('partial-repair probe', [['RLI', 'RLI', 'R', 'PDI', 'EN', 'R', 'ON', 'PDI', 'L', 'L', 'EN', 'L', 'L'], [0, 1, 3, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0], 0], [[[0, 7, 8, 9, 10, 11, 12], 'L', 'L'], [[1, 3, 4, 5, 6], 'R', 'R'], [[2], 'R', 'R']]), ('nested isolates', [['R', 'LRI', 'L', 'RLI', 'R', 'PDI', 'PDI', 'R'], [1, 1, 2, 2, 3, 2, 1, 1], 1], [[[0, 1, 6, 7], 'R', 'R'], [[2, 3, 5], 'L', 'L'], [[4], 'R', 'R']]), ('isolate joins outer run', [['L', 'RLI', 'R', 'PDI', 'L'], [0, 0, 1, 0, 0], 0], [[[0, 1, 3, 4], 'L', 'L'], [[2], 'R', 'R']]), ('control layout', [['ON', 'PDI', 'L', 'LRI'], [0, 0, 0, 0], 0], [[[0, 1, 2, 3], 'L', 'L']]), ('control layout', [['LRI', 'PDI', 'FSI'], [0, 0, 0], 0], [[[0, 1, 2], 'L', 'L']])], [('regression: sos level comparison', [['RLI', 'EN', 'ON'], [1, 4, 3], 1], [[[0], 'R', 'R'], [[1], 'L', 'L'], [[2], 'L', 'R']]), ('regression: sos level comparison', [['R', 'L', 'EN', 'L', 'PDI'], [1, 0, 0, 0, 0], 0], [[[0], 'R', 'R'], [[1, 2, 3, 4], 'R', 'L']]), ('regression: sos level comparison', [['PDI', 'R', 'L', 'ON', 'R', 'L', 'EN', 'L'], [0, 0, 0, 0, 1, 0, 0, 0], 0], [[[0, 1, 2, 3], 'L', 'R'], [[4], 'R', 'R'], [[5, 6, 7], 'R', 'L']]), ('regression: sos level comparison', [['R', 'EN', 'FSI', 'FSI', 'PDI', 'L', 'PDI'], [1, 2, 1, 2, 2, 2, 1], 1], [[[0], 'R', 'L'], [[1], 'L', 'L'], [[2, 6], 'L', 'R'], [[3, 4, 5], 'L', 'L']]), ('nested isolates', [['R', 'LRI', 'L', 'RLI', 'R', 'PDI', 'PDI', 'R'], [1, 1, 2, 2, 3, 2, 1, 1], 1], [[[0, 1, 6, 7], 'R', 'R'], [[2, 3, 5], 'L', 'L'], [[4], 'R', 'R']]), ('isolate joins outer run', [['L', 'RLI', 'R', 'PDI', 'L'], [0, 0, 1, 0, 0], 0], [[[0, 1, 3, 4], 'L', 'L'], [[2], 'R', 'R']]), ('control layout', [['PDI', 'R', 'LRI', 'PDI', 'ON', 'EN'], [0, 0, 0, 0, 0, 0], 0], [[[0, 1, 2, 3, 4, 5], 'L', 'L']]), ('control layout', [['ON', 'PDI', 'PDI', 'EN', 'R', 'L', 'L', 'ON', 'L'], [0, 0, 0, 0, 0, 0, 0, 0, 0], 0], [[[0, 1, 2, 3, 4, 5, 6, 7, 8], 'L', 'L']])], [('regression: sos level comparison', [['EN', 'RLI', 'L', 'RLI', 'ON', 'L', 'EN', 'PDI', 'EN'], [2, 1, 3, 3, 5, 6, 6, 3, 3], 1], [[[0], 'L', 'L'], [[1], 'L', 'R'], [[2, 3, 7, 8], 'R', 'R'], [[4], 'R', 'L'], [[5, 6], 'L', 'L']]), ('regression: sos level comparison', [['EN', 'ON', 'ON', 'ON'], [2, 1, 1, 1], 1], [[[0], 'L', 'L'], [[1, 2, 3], 'L', 'R']]), ('regression: sos level comparison', [['ON', 'R', 'PDI', 'R'], [0, 1, 0, 1], 0], [[[0], 'L', 'R'], [[1], 'R', 'R'], [[2], 'R', 'R'], [[3], 'R', 'R']]), ('regression: sos level comparison', [['PDI', 'PDI', 'EN', 'R', 'ON', 'L', 'R', 'R', 'L', 'L', 'R', 'R'], [1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1], 1], [[[0, 1, 2, 3, 4], 'R', 'L'], [[5], 'L', 'L'], [[6, 7, 8, 9, 10, 11], 'L', 'R']]), ('unmatched initiator at end', [['L', 'R', 'RLI'], [0, 1, 1], 0], [[[0], 'L', 'R'], [[1, 2], 'R', 'R']]), ('isolate joins outer run', [['L', 'RLI', 'R', 'PDI', 'L'], [0, 0, 1, 0, 0], 0], [[[0, 1, 3, 4], 'L', 'L'], [[2], 'R', 'R']]), ('control layout', [['L', 'FSI', 'PDI', 'PDI', 'L', 'LRI', 'ON', 'L', 'EN', 'ON'], [0, 0, 0, 0, 0, 0, 2, 2, 2, 2], 0], [[[0, 1, 2, 3, 4, 5], 'L', 'L'], [[6, 7, 8, 9], 'L', 'L']]), ('control layout', [['PDI', 'PDI', 'L', 'EN', 'EN'], [0, 0, 0, 0, 0], 0], [[[0, 1, 2, 3, 4], 'L', '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
regression: sos level comparison[[[0], 'R', 'L'], [[1, 3, 4], 'R', 'L'], [[2], 'R', 'L'], [[5], 'R', 'L'], [[6], 'R', 'L'], [[7], 'R', 'L'], [[8, 9, 10], 'R', 'R'], [[11], 'R', 'L'], [[12, 13], 'L', 'L']][[[0], 'L', 'L'], [[1, 3, 4], 'L', 'L'], [[2], 'L', 'L'], [[5], 'L', 'L'], [[6], 'L', 'L'], [[7], 'L', 'L'], [[8, 9, 10], 'L', 'R'], [[11], 'L', 'L'], [[12, 13], 'L', 'L']]Failed
regression: sos level comparison[[[0], 'R', 'L'], [[1, 2, 3], 'R', 'R'], [[4, 5, 7], 'R', 'L'], [[6], 'L', 'L']][[[0], 'L', 'L'], [[1, 2, 3], 'L', 'R'], [[4, 5, 7], 'L', 'L'], [[6], 'L', 'L']]Failed
partial-repair probe[[[0, 1], 'L', 'L'], [[2, 3], 'L', 'R']][[[0, 1], 'L', 'L'], [[2, 3], 'R', 'R']]Failed
partial-repair probe[[[0, 1], 'L', 'R'], [[2], 'L', 'R']][[[0, 1], 'L', 'R'], [[2], 'R', 'R']]Failed
isolate joins outer run[[[0, 1, 3, 4], 'L', 'L'], [[2], 'L', 'R']][[[0, 1, 3, 4], 'L', 'L'], [[2], 'R', 'R']]Failed
unmatched initiator at end[[[0], 'L', 'R'], [[1, 2], 'L', 'R']][[[0], 'L', 'R'], [[1, 2], 'R', 'R']]Failed
control layout[[[0, 1, 2, 3, 4, 5], 'L', 'L'], [[6, 7], 'L', 'L'], [[8, 9], 'L', 'L']][[[0, 1, 2, 3, 4, 5], 'L', 'L'], [[6, 7], 'L', 'L'], [[8, 9], 'L', 'L']]Passed
control layout[[[0, 1, 2, 3], 'R', 'R']][[[0, 1, 2, 3], 'R', 'R']]Passed

SHA-256 / b72d9f307fba658feb57d882dacecd250ab7e843e1644f9da49150fff9371f7b

3 / The verified repair

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

N = 1
observations = []
def solve(x):
    classes, levels, para = x
    n = len(classes)
    match = {}
    stack = []
    for i, c in enumerate(classes):
        if c in ('LRI', 'RLI', 'FSI'):
            stack.append(i)
        elif c == 'PDI' and stack:
            match[stack.pop()] = i
    runs = []
    for i in range(n):
        if runs and levels[i] == levels[runs[-1][-1]]:
            runs[-1].append(i)
        else:
            runs.append([i])
    start_of = {r[0]: r for r in runs}
    seqs = []
    used = set()
    for r in runs:
        if r[0] in used:
            continue
        seq = list(r)
        used.add(r[0])
        while True:
            tail = seq[-1]
            if classes[tail] not in ('LRI', 'RLI', 'FSI') or tail not in match:
                break
            nxt = start_of.get(match[tail])
            if nxt is None:
                break
            seq.extend(nxt)
            used.add(nxt[0])
        seqs.append(seq)
    out = []
    for seq in seqs:
        first, last = seq[0], seq[-1]
        lv = levels[first]
        prev = levels[first - 1] if first > 0 else para
        sos = 'R' if max(lv, prev) % 2 else 'L'
        if classes[last] in ('LRI', 'RLI', 'FSI'):
            nxt_lv = para
        else:
            nxt_lv = levels[last + 1] if last + 1 < n else para
        eos = 'R' if max(levels[last], nxt_lv) % 2 else 'L'
        out.append([seq, sos, eos])
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: sos level comparison', [['L', 'FSI', 'EN', 'PDI', 'EN', 'EN', 'ON', 'EN', 'PDI', 'L', 'FSI', 'FSI', 'ON', 'ON'], [2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 2, 4, 4], 1], [[[0], 'L', 'L'], [[1, 3, 4], 'L', 'L'], [[2], 'L', 'L'], [[5], 'L', 'L'], [[6], 'L', 'L'], [[7], 'L', 'L'], [[8, 9, 10], 'L', 'R'], [[11], 'L', 'L'], [[12, 13], 'L', 'L']]), ('regression: sos level comparison', [['L', 'PDI', 'PDI', 'LRI', 'ON', 'FSI', 'ON', 'PDI'], [2, 1, 1, 1, 2, 2, 4, 2], 1], [[[0], 'L', 'L'], [[1, 2, 3], 'L', 'R'], [[4, 5, 7], 'L', 'L'], [[6], 'L', 'L']]), ('partial-repair probe', [['ON', 'RLI', 'L', 'LRI'], [0, 0, 1, 1], 0], [[[0, 1], 'L', 'L'], [[2, 3], 'R', 'R']]), ('partial-repair probe', [['PDI', 'R', 'R'], [0, 0, 1], 0], [[[0, 1], 'L', 'R'], [[2], 'R', 'R']]), ('isolate joins outer run', [['L', 'RLI', 'R', 'PDI', 'L'], [0, 0, 1, 0, 0], 0], [[[0, 1, 3, 4], 'L', 'L'], [[2], 'R', 'R']]), ('unmatched initiator at end', [['L', 'R', 'RLI'], [0, 1, 1], 0], [[[0], 'L', 'R'], [[1, 2], 'R', 'R']]), ('control layout', [['L', 'ON', 'R', 'RLI', 'PDI', 'LRI', 'L', 'FSI', 'ON', 'LRI'], [0, 0, 0, 0, 0, 0, 2, 2, 4, 4], 0], [[[0, 1, 2, 3, 4, 5], 'L', 'L'], [[6, 7], 'L', 'L'], [[8, 9], 'L', 'L']]), ('control layout', [['R', 'PDI', 'R', 'FSI'], [1, 1, 1, 1], 1], [[[0, 1, 2, 3], 'R', 'R']])], [('regression: sos level comparison', [['L', 'RLI', 'RLI', 'RLI', 'ON', 'PDI', 'ON', 'L', 'ON'], [2, 1, 3, 5, 7, 5, 5, 5, 5], 1], [[[0], 'L', 'L'], [[1], 'L', 'R'], [[2], 'R', 'R'], [[3, 5, 6, 7, 8], 'R', 'R'], [[4], 'R', 'R']]), ('regression: sos level comparison', [['L', 'R', 'LRI', 'PDI'], [2, 1, 1, 1], 1], [[[0], 'L', 'L'], [[1, 2, 3], 'L', 'R']]), ('partial-repair probe', [['PDI', 'RLI', 'ON'], [0, 0, 1], 0], [[[0, 1], 'L', 'L'], [[2], 'R', 'R']]), ('regression: sos level comparison', [['R', 'PDI', 'ON', 'R', 'R', 'RLI', 'L', 'L', 'LRI', 'R', 'LRI', 'L', 'EN'], [1, 1, 1, 1, 1, 1, 3, 4, 3, 5, 4, 6, 6], 1], [[[0, 1, 2, 3, 4, 5], 'R', 'R'], [[6], 'R', 'L'], [[7], 'L', 'L'], [[8], 'L', 'R'], [[9], 'R', 'R'], [[10], 'R', 'L'], [[11, 12], 'L', 'L']]), ('nested isolates', [['R', 'LRI', 'L', 'RLI', 'R', 'PDI', 'PDI', 'R'], [1, 1, 2, 2, 3, 2, 1, 1], 1], [[[0, 1, 6, 7], 'R', 'R'], [[2, 3, 5], 'L', 'L'], [[4], 'R', 'R']]), ('isolate joins outer run', [['L', 'RLI', 'R', 'PDI', 'L'], [0, 0, 1, 0, 0], 0], [[[0, 1, 3, 4], 'L', 'L'], [[2], 'R', 'R']]), ('control layout', [['L', 'L', 'ON'], [1, 1, 1], 1], [[[0, 1, 2], 'R', 'R']]), ('control layout', [['EN', 'L', 'EN', 'L', 'FSI', 'EN', 'L', 'PDI', 'L', 'ON', 'L', 'LRI', 'EN'], [0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2], 0], [[[0, 1, 2, 3, 4, 7, 8, 9, 10, 11], 'L', 'L'], [[5, 6], 'L', 'L'], [[12], 'L', 'L']])], [('regression: sos level comparison', [['R', 'EN', 'L', 'FSI', 'PDI', 'PDI', 'PDI', 'EN', 'L', 'RLI', 'ON', 'RLI'], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], 0], [[[0], 'R', 'R'], [[1, 2, 3, 4, 5, 6, 7, 8, 9], 'R', 'L'], [[10, 11], 'R', 'R']]), ('regression: sos level comparison', [['L', 'PDI', 'FSI', 'EN', 'R', 'R', 'ON', 'EN', 'PDI', 'L'], [2, 1, 1, 2, 3, 2, 2, 2, 1, 1], 1], [[[0], 'L', 'L'], [[1, 2, 8, 9], 'L', 'R'], [[3], 'L', 'R'], [[4], 'R', 'R'], [[5, 6, 7], 'R', 'L']]), ('partial-repair probe', [['FSI', 'EN', 'R', 'RLI', 'L', 'PDI', 'L'], [1, 2, 2, 2, 4, 2, 2], 1], [[[0], 'R', 'R'], [[1, 2, 3, 5, 6], 'L', 'L'], [[4], 'L', 'L']]), ('partial-repair probe', [['RLI', 'RLI', 'R', 'PDI', 'EN', 'R', 'ON', 'PDI', 'L', 'L', 'EN', 'L', 'L'], [0, 1, 3, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0], 0], [[[0, 7, 8, 9, 10, 11, 12], 'L', 'L'], [[1, 3, 4, 5, 6], 'R', 'R'], [[2], 'R', 'R']]), ('nested isolates', [['R', 'LRI', 'L', 'RLI', 'R', 'PDI', 'PDI', 'R'], [1, 1, 2, 2, 3, 2, 1, 1], 1], [[[0, 1, 6, 7], 'R', 'R'], [[2, 3, 5], 'L', 'L'], [[4], 'R', 'R']]), ('isolate joins outer run', [['L', 'RLI', 'R', 'PDI', 'L'], [0, 0, 1, 0, 0], 0], [[[0, 1, 3, 4], 'L', 'L'], [[2], 'R', 'R']]), ('control layout', [['ON', 'PDI', 'L', 'LRI'], [0, 0, 0, 0], 0], [[[0, 1, 2, 3], 'L', 'L']]), ('control layout', [['LRI', 'PDI', 'FSI'], [0, 0, 0], 0], [[[0, 1, 2], 'L', 'L']])], [('regression: sos level comparison', [['RLI', 'EN', 'ON'], [1, 4, 3], 1], [[[0], 'R', 'R'], [[1], 'L', 'L'], [[2], 'L', 'R']]), ('regression: sos level comparison', [['R', 'L', 'EN', 'L', 'PDI'], [1, 0, 0, 0, 0], 0], [[[0], 'R', 'R'], [[1, 2, 3, 4], 'R', 'L']]), ('regression: sos level comparison', [['PDI', 'R', 'L', 'ON', 'R', 'L', 'EN', 'L'], [0, 0, 0, 0, 1, 0, 0, 0], 0], [[[0, 1, 2, 3], 'L', 'R'], [[4], 'R', 'R'], [[5, 6, 7], 'R', 'L']]), ('regression: sos level comparison', [['R', 'EN', 'FSI', 'FSI', 'PDI', 'L', 'PDI'], [1, 2, 1, 2, 2, 2, 1], 1], [[[0], 'R', 'L'], [[1], 'L', 'L'], [[2, 6], 'L', 'R'], [[3, 4, 5], 'L', 'L']]), ('nested isolates', [['R', 'LRI', 'L', 'RLI', 'R', 'PDI', 'PDI', 'R'], [1, 1, 2, 2, 3, 2, 1, 1], 1], [[[0, 1, 6, 7], 'R', 'R'], [[2, 3, 5], 'L', 'L'], [[4], 'R', 'R']]), ('isolate joins outer run', [['L', 'RLI', 'R', 'PDI', 'L'], [0, 0, 1, 0, 0], 0], [[[0, 1, 3, 4], 'L', 'L'], [[2], 'R', 'R']]), ('control layout', [['PDI', 'R', 'LRI', 'PDI', 'ON', 'EN'], [0, 0, 0, 0, 0, 0], 0], [[[0, 1, 2, 3, 4, 5], 'L', 'L']]), ('control layout', [['ON', 'PDI', 'PDI', 'EN', 'R', 'L', 'L', 'ON', 'L'], [0, 0, 0, 0, 0, 0, 0, 0, 0], 0], [[[0, 1, 2, 3, 4, 5, 6, 7, 8], 'L', 'L']])], [('regression: sos level comparison', [['EN', 'RLI', 'L', 'RLI', 'ON', 'L', 'EN', 'PDI', 'EN'], [2, 1, 3, 3, 5, 6, 6, 3, 3], 1], [[[0], 'L', 'L'], [[1], 'L', 'R'], [[2, 3, 7, 8], 'R', 'R'], [[4], 'R', 'L'], [[5, 6], 'L', 'L']]), ('regression: sos level comparison', [['EN', 'ON', 'ON', 'ON'], [2, 1, 1, 1], 1], [[[0], 'L', 'L'], [[1, 2, 3], 'L', 'R']]), ('regression: sos level comparison', [['ON', 'R', 'PDI', 'R'], [0, 1, 0, 1], 0], [[[0], 'L', 'R'], [[1], 'R', 'R'], [[2], 'R', 'R'], [[3], 'R', 'R']]), ('regression: sos level comparison', [['PDI', 'PDI', 'EN', 'R', 'ON', 'L', 'R', 'R', 'L', 'L', 'R', 'R'], [1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1], 1], [[[0, 1, 2, 3, 4], 'R', 'L'], [[5], 'L', 'L'], [[6, 7, 8, 9, 10, 11], 'L', 'R']]), ('unmatched initiator at end', [['L', 'R', 'RLI'], [0, 1, 1], 0], [[[0], 'L', 'R'], [[1, 2], 'R', 'R']]), ('isolate joins outer run', [['L', 'RLI', 'R', 'PDI', 'L'], [0, 0, 1, 0, 0], 0], [[[0, 1, 3, 4], 'L', 'L'], [[2], 'R', 'R']]), ('control layout', [['L', 'FSI', 'PDI', 'PDI', 'L', 'LRI', 'ON', 'L', 'EN', 'ON'], [0, 0, 0, 0, 0, 0, 2, 2, 2, 2], 0], [[[0, 1, 2, 3, 4, 5], 'L', 'L'], [[6, 7, 8, 9], 'L', 'L']]), ('control layout', [['PDI', 'PDI', 'L', 'EN', 'EN'], [0, 0, 0, 0, 0], 0], [[[0, 1, 2, 3, 4], 'L', '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
regression: sos level comparison[[[0], 'L', 'L'], [[1, 3, 4], 'L', 'L'], [[2], 'L', 'L'], [[5], 'L', 'L'], [[6], 'L', 'L'], [[7], 'L', 'L'], [[8, 9, 10], 'L', 'R'], [[11], 'L', 'L'], [[12, 13], 'L', 'L']][[[0], 'L', 'L'], [[1, 3, 4], 'L', 'L'], [[2], 'L', 'L'], [[5], 'L', 'L'], [[6], 'L', 'L'], [[7], 'L', 'L'], [[8, 9, 10], 'L', 'R'], [[11], 'L', 'L'], [[12, 13], 'L', 'L']]Passed
regression: sos level comparison[[[0], 'L', 'L'], [[1, 2, 3], 'L', 'R'], [[4, 5, 7], 'L', 'L'], [[6], 'L', 'L']][[[0], 'L', 'L'], [[1, 2, 3], 'L', 'R'], [[4, 5, 7], 'L', 'L'], [[6], 'L', 'L']]Passed
partial-repair probe[[[0, 1], 'L', 'L'], [[2, 3], 'R', 'R']][[[0, 1], 'L', 'L'], [[2, 3], 'R', 'R']]Passed
partial-repair probe[[[0, 1], 'L', 'R'], [[2], 'R', 'R']][[[0, 1], 'L', 'R'], [[2], 'R', 'R']]Passed
isolate joins outer run[[[0, 1, 3, 4], 'L', 'L'], [[2], 'R', 'R']][[[0, 1, 3, 4], 'L', 'L'], [[2], 'R', 'R']]Passed
unmatched initiator at end[[[0], 'L', 'R'], [[1, 2], 'R', 'R']][[[0], 'L', 'R'], [[1, 2], 'R', 'R']]Passed
control layout[[[0, 1, 2, 3, 4, 5], 'L', 'L'], [[6, 7], 'L', 'L'], [[8, 9], 'L', 'L']][[[0, 1, 2, 3, 4, 5], 'L', 'L'], [[6, 7], 'L', 'L'], [[8, 9], 'L', 'L']]Passed
control layout[[[0, 1, 2, 3], 'R', 'R']][[[0, 1, 2, 3], 'R', 'R']]Passed

SHA-256 / 206955c6e04586eb70f9824752a55f3b166a17944415135b793b58b207000e93

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 2026-09-29T14:49:56.793940+00:00.

Case digest / f520902ba4e5ea879018b6425f78b1796d48dd931161c7bcc50944088ea81bf0