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FA-80761 / Bidirectional text layout / Open access

Isolating run sequences: first-strong isolate chaining · case 01

Text around an FSI isolate is split into separate sequences.

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

ROOT CAUSE

FSI is not recognised as an initiator when chaining runs.

THE FAILURE

FSI is not recognised as an initiator when chaining runs.

Unsuccessful approach: Dropping LRI instead breaks a different isolate type.

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') 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: first-strong isolate chaining', [['EN', 'LRI', 'L', 'RLI', 'PDI', 'ON', 'FSI', 'R', 'R', 'R', 'ON', 'PDI', 'R', 'LRI'], [0, 0, 2, 2, 2, 2, 2, 4, 5, 5, 4, 2, 2, 2], 0], [[[0, 1], 'L', 'L'], [[2, 3, 4, 5, 6, 11, 12, 13], 'L', 'L'], [[7], 'L', 'R'], [[8, 9], 'R', 'R'], [[10], 'R', 'L']]), ('regression: first-strong isolate chaining', [['EN', 'L', 'L', 'FSI', 'R', 'PDI', 'L', 'EN', 'ON', 'PDI', 'L', 'L', 'EN', 'ON'], [1, 2, 2, 1, 3, 1, 2, 2, 1, 1, 1, 1, 2, 1], 1], [[[0], 'R', 'L'], [[1, 2], 'L', 'L'], [[3, 5], 'L', 'L'], [[4], 'R', 'R'], [[6, 7], 'L', 'L'], [[8, 9, 10, 11], 'L', 'L'], [[12], 'L', 'L'], [[13], 'L', 'R']]), ('regression: first-strong isolate chaining', [['EN', 'EN', 'PDI', 'R', 'FSI', 'L', 'LRI', 'L', 'PDI', 'FSI', 'FSI', 'PDI', 'PDI'], [0, 0, 0, 0, 0, 2, 2, 4, 2, 2, 4, 4, 2], 0], [[[0, 1, 2, 3, 4], 'L', 'L'], [[5, 6, 8, 9, 12], 'L', 'L'], [[7], 'L', 'L'], [[10, 11], 'L', 'L']]), ('partial-repair probe', [['L', 'FSI', 'LRI', 'ON', 'R', 'PDI', 'LRI', 'ON'], [2, 1, 2, 4, 4, 2, 2, 4], 1], [[[0], 'L', 'L'], [[1], 'L', 'R'], [[2, 5, 6], 'L', 'L'], [[3, 4], 'L', 'L'], [[7], 'L', 'L']]), ('unmatched initiator at end', [['L', 'R', 'RLI'], [0, 1, 1], 0], [[[0], 'L', 'R'], [[1, 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']]), ('control layout', [['R', 'EN', 'L', 'L', 'R', 'R', 'PDI', 'EN', 'PDI', 'L', 'PDI', 'ON', 'ON'], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 0], [[[0], 'R', 'R'], [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], 'R', 'L']]), ('control layout', [['EN', 'R', 'RLI'], [1, 1, 1], 1], [[[0, 1, 2], 'R', 'R']])], [('regression: first-strong isolate chaining', [['FSI', 'R', 'EN', 'R', 'PDI', 'R', 'EN', 'R', 'R', 'EN', 'RLI', 'L', 'EN'], [1, 2, 2, 2, 1, 1, 1, 1, 1, 2, 1, 4, 4], 1], [[[0, 4, 5, 6, 7, 8], 'R', 'L'], [[1, 2, 3], 'L', 'L'], [[9], 'L', 'L'], [[10], 'L', 'R'], [[11, 12], 'L', 'L']]), ('regression: first-strong isolate chaining', [['L', 'FSI', 'EN', 'FSI', 'PDI', 'PDI', 'ON', 'ON', 'RLI', 'EN', 'RLI', 'L'], [0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 1, 4], 0], [[[0, 1, 5, 6, 7, 8], 'L', 'L'], [[2, 3, 4], 'L', 'L'], [[9], 'L', 'L'], [[10], 'L', 'R'], [[11], 'L', 'L']]), ('regression: first-strong isolate chaining', [['ON', 'PDI', 'EN', 'FSI', 'L', 'R', 'LRI', 'L', 'PDI', 'PDI', 'PDI', 'EN', 'PDI'], [1, 1, 1, 1, 2, 3, 2, 4, 2, 1, 1, 2, 1], 1], [[[0, 1, 2, 3, 9, 10], 'R', 'L'], [[4], 'L', 'R'], [[5], 'R', 'R'], [[6, 8], 'R', 'L'], [[7], 'L', 'L'], [[11], 'L', 'L'], [[12], 'L', 'R']]), ('partial-repair probe', [['LRI', 'L', 'EN', 'R', 'PDI', 'EN'], [1, 2, 2, 2, 1, 2], 1], [[[0, 4], 'R', 'L'], [[1, 2, 3], 'L', 'L'], [[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', [['L', 'L', 'R', 'PDI', 'PDI', 'L', 'ON', 'L', 'PDI'], [0, 0, 1, 0, 0, 0, 0, 0, 0], 0], [[[0, 1], 'L', 'R'], [[2], 'R', 'R'], [[3, 4, 5, 6, 7, 8], 'R', 'L']]), ('control layout', [['L', 'ON', 'R'], [0, 0, 0], 0], [[[0, 1, 2], 'L', 'L']])], [('regression: first-strong isolate chaining', [['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: first-strong isolate chaining', [['FSI', 'L', 'FSI', 'RLI', 'EN', 'ON', 'ON', 'R', 'PDI', 'L', 'PDI'], [0, 2, 2, 4, 6, 5, 5, 5, 4, 4, 2], 0], [[[0], 'L', 'L'], [[1, 2, 10], 'L', 'L'], [[3, 8, 9], 'L', 'L'], [[4], 'L', 'L'], [[5, 6, 7], 'L', 'R']]), ('partial-repair probe', [['FSI', 'RLI', 'EN', 'R', 'LRI', 'EN', 'ON', 'R', 'L', 'L', 'PDI', 'L', 'RLI'], [1, 2, 4, 3, 3, 4, 4, 4, 4, 4, 3, 4, 3], 1], [[[0], 'R', 'R'], [[1], 'L', 'L'], [[2], 'L', 'L'], [[3, 4, 10], 'L', 'L'], [[5, 6, 7, 8, 9], 'L', 'L'], [[11], 'L', 'L'], [[12], 'L', 'R']]), ('partial-repair probe', [['L', 'LRI', 'LRI', 'LRI', 'EN', 'PDI', 'R', 'FSI', 'EN', 'R', 'ON'], [2, 1, 2, 4, 6, 4, 4, 4, 6, 7, 6], 1], [[[0], 'L', 'L'], [[1], 'L', 'R'], [[2], 'L', 'L'], [[3, 5, 6, 7], 'L', 'L'], [[4], 'L', 'L'], [[8], 'L', 'R'], [[9], 'R', 'R'], [[10], 'R', 'L']]), ('isolate joins outer run', [['L', 'RLI', 'R', 'PDI', 'L'], [0, 0, 1, 0, 0], 0], [[[0, 1, 3, 4], 'L', 'L'], [[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']]), ('control layout', [['L', 'L', 'EN', 'PDI', 'R', 'EN', 'LRI', 'PDI', 'ON', 'ON', 'FSI', 'ON'], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2], 0], [[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], 'L', 'L'], [[11], 'L', 'L']]), ('control layout', [['RLI', 'EN', 'EN', 'L', 'ON'], [1, 3, 3, 4, 3], 1], [[[0], 'R', 'R'], [[1, 2], 'R', 'L'], [[3], 'L', 'L'], [[4], 'L', 'R']])], [('regression: first-strong isolate chaining', [['EN', 'FSI', 'ON', 'ON', 'PDI'], [2, 1, 2, 2, 1], 1], [[[0], 'L', 'L'], [[1, 4], 'L', 'R'], [[2, 3], 'L', 'L']]), ('regression: first-strong isolate chaining', [['PDI', 'RLI', 'FSI', 'ON', 'PDI', 'EN', 'PDI', 'R', 'EN', 'L', 'L', 'R', 'L', 'PDI'], [1, 1, 3, 4, 3, 4, 1, 1, 1, 1, 2, 1, 2, 1], 1], [[[0, 1, 6, 7, 8, 9], 'R', 'L'], [[2, 4], 'R', 'L'], [[3], 'L', 'L'], [[5], 'L', 'L'], [[10], 'L', 'L'], [[11], 'L', 'L'], [[12], 'L', 'L'], [[13], 'L', 'R']]), ('partial-repair probe', [['RLI', 'ON', 'LRI', 'L', 'L', 'R', 'ON', 'L', 'EN', 'PDI', 'ON'], [0, 1, 1, 2, 2, 3, 2, 2, 2, 1, 1], 0], [[[0], 'L', 'L'], [[1, 2, 9, 10], 'R', 'R'], [[3, 4], 'L', 'R'], [[5], 'R', 'R'], [[6, 7, 8], 'R', 'L']]), ('partial-repair probe', [['PDI', 'R', 'R', 'ON', 'L', 'L', 'LRI', 'R', 'L', 'PDI', 'PDI', 'EN', 'PDI', 'ON'], [0, 0, 0, 0, 0, 0, 0, 3, 2, 0, 0, 0, 0, 0], 0], [[[0, 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 13], 'L', 'L'], [[7], 'R', 'R'], [[8], 'R', 'L']]), ('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', [['PDI', 'PDI', 'L', 'ON', 'ON', 'L', 'ON', 'ON', 'EN', 'PDI'], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 0], [[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 'L', 'L']]), ('control layout', [['ON', 'PDI', 'RLI', 'L'], [0, 0, 0, 2], 0], [[[0, 1, 2], 'L', 'L'], [[3], 'L', 'L']])], [('regression: first-strong isolate chaining', [['EN', 'L', 'L', 'FSI', 'R', 'PDI', 'L', 'EN', 'ON', 'PDI', 'L', 'L', 'EN', 'ON'], [1, 2, 2, 1, 3, 1, 2, 2, 1, 1, 1, 1, 2, 1], 1], [[[0], 'R', 'L'], [[1, 2], 'L', 'L'], [[3, 5], 'L', 'L'], [[4], 'R', 'R'], [[6, 7], 'L', 'L'], [[8, 9, 10, 11], 'L', 'L'], [[12], 'L', 'L'], [[13], 'L', 'R']]), ('regression: first-strong isolate chaining', [['PDI', 'R', 'PDI', 'R', 'EN', 'FSI', 'L', 'ON', 'EN', 'PDI'], [1, 1, 1, 1, 1, 1, 2, 2, 2, 1], 1], [[[0, 1, 2, 3, 4, 5, 9], 'R', 'R'], [[6, 7, 8], 'L', 'L']]), ('regression: first-strong isolate chaining', [['LRI', 'ON', 'FSI', 'R', 'RLI', 'PDI', 'RLI', 'ON', 'PDI', 'ON', 'EN', 'PDI', 'PDI'], [1, 2, 2, 5, 4, 4, 4, 5, 4, 4, 4, 2, 1], 1], [[[0, 12], 'R', 'R'], [[1, 2, 11], 'L', 'L'], [[3], 'R', 'R'], [[4, 5, 6, 8, 9, 10], 'R', 'L'], [[7], 'R', 'R']]), ('partial-repair probe', [['PDI', 'LRI', 'EN', 'LRI', 'R', 'EN', 'ON', 'R', 'PDI', 'PDI'], [0, 0, 2, 2, 5, 4, 4, 4, 2, 0], 0], [[[0, 1, 9], 'L', 'L'], [[2, 3, 8], 'L', 'L'], [[4], 'R', 'R'], [[5, 6, 7], 'R', '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', 'EN', 'PDI', 'FSI', 'L', 'R'], [0, 0, 0, 0, 2, 3], 0], [[[0, 1, 2, 3], 'L', 'L'], [[4], 'L', 'R'], [[5], 'R', 'R']]), ('control layout', [['ON', 'EN', 'ON', 'EN', 'EN', 'LRI', 'RLI', 'EN', 'EN', 'EN', 'R', 'R', 'PDI'], [1, 1, 1, 1, 2, 1, 2, 3, 4, 3, 3, 3, 2], 1], [[[0, 1, 2, 3], 'R', 'L'], [[4], 'L', 'L'], [[5], 'L', 'R'], [[6, 12], 'L', 'L'], [[7], 'R', 'L'], [[8], 'L', 'L'], [[9, 10, 11], 'L', '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
regression: first-strong isolate chaining[[[0, 1], 'L', 'L'], [[2, 3, 4, 5, 6], 'L', 'L'], [[7], 'L', 'R'], [[8, 9], 'R', 'R'], [[10], 'R', 'L'], [[11, 12, 13], 'L', 'L']][[[0, 1], 'L', 'L'], [[2, 3, 4, 5, 6, 11, 12, 13], 'L', 'L'], [[7], 'L', 'R'], [[8, 9], 'R', 'R'], [[10], 'R', 'L']]Failed
regression: first-strong isolate chaining[[[0], 'R', 'L'], [[1, 2], 'L', 'L'], [[3], 'L', 'R'], [[4], 'R', 'R'], [[5], 'R', 'L'], [[6, 7], 'L', 'L'], [[8, 9, 10, 11], 'L', 'L'], [[12], 'L', 'L'], [[13], 'L', 'R']][[[0], 'R', 'L'], [[1, 2], 'L', 'L'], [[3, 5], 'L', 'L'], [[4], 'R', 'R'], [[6, 7], 'L', 'L'], [[8, 9, 10, 11], 'L', 'L'], [[12], 'L', 'L'], [[13], 'L', 'R']]Failed
regression: first-strong isolate chaining[[[0, 1, 2, 3, 4], 'L', 'L'], [[5, 6, 8, 9], 'L', 'L'], [[7], 'L', 'L'], [[10, 11], 'L', 'L'], [[12], 'L', 'L']][[[0, 1, 2, 3, 4], 'L', 'L'], [[5, 6, 8, 9, 12], 'L', 'L'], [[7], 'L', 'L'], [[10, 11], 'L', 'L']]Failed
partial-repair probe[[[0], 'L', 'L'], [[1], 'L', 'R'], [[2, 5, 6], 'L', 'L'], [[3, 4], 'L', 'L'], [[7], 'L', 'L']][[[0], 'L', 'L'], [[1], 'L', 'R'], [[2, 5, 6], 'L', 'L'], [[3, 4], 'L', 'L'], [[7], 'L', 'L']]Passed
unmatched initiator at end[[[0], 'L', 'R'], [[1, 2], 'R', 'R']][[[0], 'L', 'R'], [[1, 2], 'R', 'R']]Passed
nested isolates[[[0, 1, 6, 7], 'R', 'R'], [[2, 3, 5], 'L', 'L'], [[4], 'R', 'R']][[[0, 1, 6, 7], 'R', 'R'], [[2, 3, 5], 'L', 'L'], [[4], 'R', 'R']]Passed
control layout[[[0], 'R', 'R'], [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], 'R', 'L']][[[0], 'R', 'R'], [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], 'R', 'L']]Passed
control layout[[[0, 1, 2], 'R', 'R']][[[0, 1, 2], 'R', 'R']]Passed

SHA-256 / b82dae52ff6ad1fe36982b111d71da7c5feb3339c30db8f1f16088d621b52792

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 ('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: first-strong isolate chaining', [['EN', 'LRI', 'L', 'RLI', 'PDI', 'ON', 'FSI', 'R', 'R', 'R', 'ON', 'PDI', 'R', 'LRI'], [0, 0, 2, 2, 2, 2, 2, 4, 5, 5, 4, 2, 2, 2], 0], [[[0, 1], 'L', 'L'], [[2, 3, 4, 5, 6, 11, 12, 13], 'L', 'L'], [[7], 'L', 'R'], [[8, 9], 'R', 'R'], [[10], 'R', 'L']]), ('regression: first-strong isolate chaining', [['EN', 'L', 'L', 'FSI', 'R', 'PDI', 'L', 'EN', 'ON', 'PDI', 'L', 'L', 'EN', 'ON'], [1, 2, 2, 1, 3, 1, 2, 2, 1, 1, 1, 1, 2, 1], 1], [[[0], 'R', 'L'], [[1, 2], 'L', 'L'], [[3, 5], 'L', 'L'], [[4], 'R', 'R'], [[6, 7], 'L', 'L'], [[8, 9, 10, 11], 'L', 'L'], [[12], 'L', 'L'], [[13], 'L', 'R']]), ('regression: first-strong isolate chaining', [['EN', 'EN', 'PDI', 'R', 'FSI', 'L', 'LRI', 'L', 'PDI', 'FSI', 'FSI', 'PDI', 'PDI'], [0, 0, 0, 0, 0, 2, 2, 4, 2, 2, 4, 4, 2], 0], [[[0, 1, 2, 3, 4], 'L', 'L'], [[5, 6, 8, 9, 12], 'L', 'L'], [[7], 'L', 'L'], [[10, 11], 'L', 'L']]), ('partial-repair probe', [['L', 'FSI', 'LRI', 'ON', 'R', 'PDI', 'LRI', 'ON'], [2, 1, 2, 4, 4, 2, 2, 4], 1], [[[0], 'L', 'L'], [[1], 'L', 'R'], [[2, 5, 6], 'L', 'L'], [[3, 4], 'L', 'L'], [[7], 'L', 'L']]), ('unmatched initiator at end', [['L', 'R', 'RLI'], [0, 1, 1], 0], [[[0], 'L', 'R'], [[1, 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']]), ('control layout', [['R', 'EN', 'L', 'L', 'R', 'R', 'PDI', 'EN', 'PDI', 'L', 'PDI', 'ON', 'ON'], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 0], [[[0], 'R', 'R'], [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], 'R', 'L']]), ('control layout', [['EN', 'R', 'RLI'], [1, 1, 1], 1], [[[0, 1, 2], 'R', 'R']])], [('regression: first-strong isolate chaining', [['FSI', 'R', 'EN', 'R', 'PDI', 'R', 'EN', 'R', 'R', 'EN', 'RLI', 'L', 'EN'], [1, 2, 2, 2, 1, 1, 1, 1, 1, 2, 1, 4, 4], 1], [[[0, 4, 5, 6, 7, 8], 'R', 'L'], [[1, 2, 3], 'L', 'L'], [[9], 'L', 'L'], [[10], 'L', 'R'], [[11, 12], 'L', 'L']]), ('regression: first-strong isolate chaining', [['L', 'FSI', 'EN', 'FSI', 'PDI', 'PDI', 'ON', 'ON', 'RLI', 'EN', 'RLI', 'L'], [0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 1, 4], 0], [[[0, 1, 5, 6, 7, 8], 'L', 'L'], [[2, 3, 4], 'L', 'L'], [[9], 'L', 'L'], [[10], 'L', 'R'], [[11], 'L', 'L']]), ('regression: first-strong isolate chaining', [['ON', 'PDI', 'EN', 'FSI', 'L', 'R', 'LRI', 'L', 'PDI', 'PDI', 'PDI', 'EN', 'PDI'], [1, 1, 1, 1, 2, 3, 2, 4, 2, 1, 1, 2, 1], 1], [[[0, 1, 2, 3, 9, 10], 'R', 'L'], [[4], 'L', 'R'], [[5], 'R', 'R'], [[6, 8], 'R', 'L'], [[7], 'L', 'L'], [[11], 'L', 'L'], [[12], 'L', 'R']]), ('partial-repair probe', [['LRI', 'L', 'EN', 'R', 'PDI', 'EN'], [1, 2, 2, 2, 1, 2], 1], [[[0, 4], 'R', 'L'], [[1, 2, 3], 'L', 'L'], [[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', [['L', 'L', 'R', 'PDI', 'PDI', 'L', 'ON', 'L', 'PDI'], [0, 0, 1, 0, 0, 0, 0, 0, 0], 0], [[[0, 1], 'L', 'R'], [[2], 'R', 'R'], [[3, 4, 5, 6, 7, 8], 'R', 'L']]), ('control layout', [['L', 'ON', 'R'], [0, 0, 0], 0], [[[0, 1, 2], 'L', 'L']])], [('regression: first-strong isolate chaining', [['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: first-strong isolate chaining', [['FSI', 'L', 'FSI', 'RLI', 'EN', 'ON', 'ON', 'R', 'PDI', 'L', 'PDI'], [0, 2, 2, 4, 6, 5, 5, 5, 4, 4, 2], 0], [[[0], 'L', 'L'], [[1, 2, 10], 'L', 'L'], [[3, 8, 9], 'L', 'L'], [[4], 'L', 'L'], [[5, 6, 7], 'L', 'R']]), ('partial-repair probe', [['FSI', 'RLI', 'EN', 'R', 'LRI', 'EN', 'ON', 'R', 'L', 'L', 'PDI', 'L', 'RLI'], [1, 2, 4, 3, 3, 4, 4, 4, 4, 4, 3, 4, 3], 1], [[[0], 'R', 'R'], [[1], 'L', 'L'], [[2], 'L', 'L'], [[3, 4, 10], 'L', 'L'], [[5, 6, 7, 8, 9], 'L', 'L'], [[11], 'L', 'L'], [[12], 'L', 'R']]), ('partial-repair probe', [['L', 'LRI', 'LRI', 'LRI', 'EN', 'PDI', 'R', 'FSI', 'EN', 'R', 'ON'], [2, 1, 2, 4, 6, 4, 4, 4, 6, 7, 6], 1], [[[0], 'L', 'L'], [[1], 'L', 'R'], [[2], 'L', 'L'], [[3, 5, 6, 7], 'L', 'L'], [[4], 'L', 'L'], [[8], 'L', 'R'], [[9], 'R', 'R'], [[10], 'R', 'L']]), ('isolate joins outer run', [['L', 'RLI', 'R', 'PDI', 'L'], [0, 0, 1, 0, 0], 0], [[[0, 1, 3, 4], 'L', 'L'], [[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']]), ('control layout', [['L', 'L', 'EN', 'PDI', 'R', 'EN', 'LRI', 'PDI', 'ON', 'ON', 'FSI', 'ON'], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2], 0], [[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], 'L', 'L'], [[11], 'L', 'L']]), ('control layout', [['RLI', 'EN', 'EN', 'L', 'ON'], [1, 3, 3, 4, 3], 1], [[[0], 'R', 'R'], [[1, 2], 'R', 'L'], [[3], 'L', 'L'], [[4], 'L', 'R']])], [('regression: first-strong isolate chaining', [['EN', 'FSI', 'ON', 'ON', 'PDI'], [2, 1, 2, 2, 1], 1], [[[0], 'L', 'L'], [[1, 4], 'L', 'R'], [[2, 3], 'L', 'L']]), ('regression: first-strong isolate chaining', [['PDI', 'RLI', 'FSI', 'ON', 'PDI', 'EN', 'PDI', 'R', 'EN', 'L', 'L', 'R', 'L', 'PDI'], [1, 1, 3, 4, 3, 4, 1, 1, 1, 1, 2, 1, 2, 1], 1], [[[0, 1, 6, 7, 8, 9], 'R', 'L'], [[2, 4], 'R', 'L'], [[3], 'L', 'L'], [[5], 'L', 'L'], [[10], 'L', 'L'], [[11], 'L', 'L'], [[12], 'L', 'L'], [[13], 'L', 'R']]), ('partial-repair probe', [['RLI', 'ON', 'LRI', 'L', 'L', 'R', 'ON', 'L', 'EN', 'PDI', 'ON'], [0, 1, 1, 2, 2, 3, 2, 2, 2, 1, 1], 0], [[[0], 'L', 'L'], [[1, 2, 9, 10], 'R', 'R'], [[3, 4], 'L', 'R'], [[5], 'R', 'R'], [[6, 7, 8], 'R', 'L']]), ('partial-repair probe', [['PDI', 'R', 'R', 'ON', 'L', 'L', 'LRI', 'R', 'L', 'PDI', 'PDI', 'EN', 'PDI', 'ON'], [0, 0, 0, 0, 0, 0, 0, 3, 2, 0, 0, 0, 0, 0], 0], [[[0, 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 13], 'L', 'L'], [[7], 'R', 'R'], [[8], 'R', 'L']]), ('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', [['PDI', 'PDI', 'L', 'ON', 'ON', 'L', 'ON', 'ON', 'EN', 'PDI'], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 0], [[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 'L', 'L']]), ('control layout', [['ON', 'PDI', 'RLI', 'L'], [0, 0, 0, 2], 0], [[[0, 1, 2], 'L', 'L'], [[3], 'L', 'L']])], [('regression: first-strong isolate chaining', [['EN', 'L', 'L', 'FSI', 'R', 'PDI', 'L', 'EN', 'ON', 'PDI', 'L', 'L', 'EN', 'ON'], [1, 2, 2, 1, 3, 1, 2, 2, 1, 1, 1, 1, 2, 1], 1], [[[0], 'R', 'L'], [[1, 2], 'L', 'L'], [[3, 5], 'L', 'L'], [[4], 'R', 'R'], [[6, 7], 'L', 'L'], [[8, 9, 10, 11], 'L', 'L'], [[12], 'L', 'L'], [[13], 'L', 'R']]), ('regression: first-strong isolate chaining', [['PDI', 'R', 'PDI', 'R', 'EN', 'FSI', 'L', 'ON', 'EN', 'PDI'], [1, 1, 1, 1, 1, 1, 2, 2, 2, 1], 1], [[[0, 1, 2, 3, 4, 5, 9], 'R', 'R'], [[6, 7, 8], 'L', 'L']]), ('regression: first-strong isolate chaining', [['LRI', 'ON', 'FSI', 'R', 'RLI', 'PDI', 'RLI', 'ON', 'PDI', 'ON', 'EN', 'PDI', 'PDI'], [1, 2, 2, 5, 4, 4, 4, 5, 4, 4, 4, 2, 1], 1], [[[0, 12], 'R', 'R'], [[1, 2, 11], 'L', 'L'], [[3], 'R', 'R'], [[4, 5, 6, 8, 9, 10], 'R', 'L'], [[7], 'R', 'R']]), ('partial-repair probe', [['PDI', 'LRI', 'EN', 'LRI', 'R', 'EN', 'ON', 'R', 'PDI', 'PDI'], [0, 0, 2, 2, 5, 4, 4, 4, 2, 0], 0], [[[0, 1, 9], 'L', 'L'], [[2, 3, 8], 'L', 'L'], [[4], 'R', 'R'], [[5, 6, 7], 'R', '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', 'EN', 'PDI', 'FSI', 'L', 'R'], [0, 0, 0, 0, 2, 3], 0], [[[0, 1, 2, 3], 'L', 'L'], [[4], 'L', 'R'], [[5], 'R', 'R']]), ('control layout', [['ON', 'EN', 'ON', 'EN', 'EN', 'LRI', 'RLI', 'EN', 'EN', 'EN', 'R', 'R', 'PDI'], [1, 1, 1, 1, 2, 1, 2, 3, 4, 3, 3, 3, 2], 1], [[[0, 1, 2, 3], 'R', 'L'], [[4], 'L', 'L'], [[5], 'L', 'R'], [[6, 12], 'L', 'L'], [[7], 'R', 'L'], [[8], 'L', 'L'], [[9, 10, 11], 'L', '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
regression: first-strong isolate chaining[[[0, 1], 'L', 'L'], [[2, 3, 4, 5, 6, 11, 12, 13], 'L', 'L'], [[7], 'L', 'R'], [[8, 9], 'R', 'R'], [[10], 'R', 'L']][[[0, 1], 'L', 'L'], [[2, 3, 4, 5, 6, 11, 12, 13], 'L', 'L'], [[7], 'L', 'R'], [[8, 9], 'R', 'R'], [[10], 'R', 'L']]Passed
regression: first-strong isolate chaining[[[0], 'R', 'L'], [[1, 2], 'L', 'L'], [[3, 5], 'L', 'L'], [[4], 'R', 'R'], [[6, 7], 'L', 'L'], [[8, 9, 10, 11], 'L', 'L'], [[12], 'L', 'L'], [[13], 'L', 'R']][[[0], 'R', 'L'], [[1, 2], 'L', 'L'], [[3, 5], 'L', 'L'], [[4], 'R', 'R'], [[6, 7], 'L', 'L'], [[8, 9, 10, 11], 'L', 'L'], [[12], 'L', 'L'], [[13], 'L', 'R']]Passed
regression: first-strong isolate chaining[[[0, 1, 2, 3, 4], 'L', 'L'], [[5, 6], 'L', 'L'], [[7], 'L', 'L'], [[8, 9, 12], 'L', 'L'], [[10, 11], 'L', 'L']][[[0, 1, 2, 3, 4], 'L', 'L'], [[5, 6, 8, 9, 12], 'L', 'L'], [[7], 'L', 'L'], [[10, 11], 'L', 'L']]Failed
partial-repair probe[[[0], 'L', 'L'], [[1], 'L', 'R'], [[2], 'L', 'L'], [[3, 4], 'L', 'L'], [[5, 6], 'L', 'L'], [[7], 'L', 'L']][[[0], 'L', 'L'], [[1], 'L', 'R'], [[2, 5, 6], 'L', 'L'], [[3, 4], 'L', 'L'], [[7], 'L', 'L']]Failed
unmatched initiator at end[[[0], 'L', 'R'], [[1, 2], 'R', 'R']][[[0], 'L', 'R'], [[1, 2], 'R', 'R']]Passed
nested isolates[[[0, 1], 'R', 'R'], [[2, 3, 5], 'L', 'L'], [[4], 'R', 'R'], [[6, 7], 'L', 'R']][[[0, 1, 6, 7], 'R', 'R'], [[2, 3, 5], 'L', 'L'], [[4], 'R', 'R']]Failed
control layout[[[0], 'R', 'R'], [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], 'R', 'L']][[[0], 'R', 'R'], [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], 'R', 'L']]Passed
control layout[[[0, 1, 2], 'R', 'R']][[[0, 1, 2], 'R', 'R']]Passed

SHA-256 / 49ee0f14b4d21f608b6b09725ae891cd2781ce208e36f01409dedcbc8a1e758b

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 2026-09-29T14:49:56.758997+00:00.

Case digest / deb33e52aa8a2c8428b9eddc39f3b45d8f3f04b0b253688610e4d951d68a7b97