FAILURE MAP
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FA-80471 / Bidirectional text layout / Open access

Visual reordering by levels: highest level start · case 01

Numbers embedded at an even level inside RTL text read backwards.

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

ROOT CAUSE

The reversal passes start at the highest odd level, skipping a higher even level.

VERIFIED REPAIR

Start the passes at the highest level on the line, odd or even.

Unsuccessful approach: Starting one below the maximum level also skips the top pass.

Case contract

Input resolved levels of one line. From the highest level down to the lowest odd level on the line, reverse every maximal visual run of characters at that level or higher. Return logical indices in visual order (identity when no odd level).

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):
    levels = x
    order = list(range(len(levels)))
    odd = [l for l in levels if l % 2 == 1]
    if not odd:
        return order
    hi = max(odd)
    lo = min(odd)
    vis = [[lv, i] for i, lv in enumerate(levels)]
    for lev in range(hi, lo - 1, -1):
        i = 0
        while i < len(vis):
            if vis[i][0] >= lev:
                j = i
                while j < len(vis) and vis[j][0] >= lev:
                    j += 1
                vis[i:j] = vis[i:j][::-1]
                i = j
            else:
                i += 1
    return [p[1] for p in vis]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('number inside RTL', [1, 1, 2, 2, 1], [4, 2, 3, 1, 0]), ('regression: highest level start', [1, 1, 2, 2, 2, 2, 2], [2, 3, 4, 5, 6, 1, 0]), ('partial-repair probe', [0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0], [0, 1, 2, 3, 4, 5, 6, 8, 7, 9, 10]), ('regression: highest level start', [3, 3, 4, 4, 4, 2, 2, 2, 2, 4], [2, 3, 4, 1, 0, 5, 6, 7, 8, 9]), ('all even levels', [0, 2, 2, 0], [0, 1, 2, 3]), ('lowest odd is three', [2, 3, 3, 2], [0, 2, 1, 3]), ('control layout', [2, 2, 2], [0, 1, 2]), ('control layout', [2, 2, 2, 2], [0, 1, 2, 3])], [('regression: highest level start', [1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2], [9, 10, 11, 8, 7, 6, 5, 4, 3, 2, 1, 0]), ('regression: highest level start', [1, 1, 1, 1, 2, 2, 1, 0], [6, 4, 5, 3, 2, 1, 0, 7]), ('partial-repair probe', [1, 1, 1, 1, 1, 1, 1, 1, 1], [8, 7, 6, 5, 4, 3, 2, 1, 0]), ('partial-repair probe', [1, 1], [1, 0]), ('lowest odd is three', [2, 3, 3, 2], [0, 2, 1, 3]), ('all even levels', [0, 2, 2, 0], [0, 1, 2, 3]), ('control layout', [0, 0, 2, 1, 1, 1, 1], [0, 1, 6, 5, 4, 3, 2]), ('control layout', [1, 3, 2, 2, 2], [1, 2, 3, 4, 0])], [('regression: highest level start', [2, 2, 2, 1, 1, 1, 1, 1, 4, 4, 4], [8, 9, 10, 7, 6, 5, 4, 3, 0, 1, 2]), ('regression: highest level start', [4, 4, 1, 1, 1, 2, 2, 3, 3], [5, 6, 8, 7, 4, 3, 2, 0, 1]), ('regression: highest level start', [2, 2, 2, 1, 1, 0, 0, 1, 1, 1, 1, 1], [4, 3, 0, 1, 2, 5, 6, 11, 10, 9, 8, 7]), ('regression: highest level start', [4, 4, 4, 4, 2, 1], [5, 0, 1, 2, 3, 4]), ('number inside RTL', [1, 1, 2, 2, 1], [4, 2, 3, 1, 0]), ('all even levels', [0, 2, 2, 0], [0, 1, 2, 3]), ('control layout', [4, 4, 4, 4, 4], [0, 1, 2, 3, 4]), ('control layout', [2, 0, 0, 0, 1], [0, 1, 2, 3, 4])], [('regression: highest level start', [2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2], [8, 9, 10, 11, 7, 6, 5, 4, 0, 1, 2, 3]), ('regression: highest level start', [2, 2, 1, 1, 1, 1, 4, 4, 2, 2, 2], [6, 7, 8, 9, 10, 5, 4, 3, 2, 0, 1]), ('partial-repair probe', [3, 3, 2], [1, 0, 2]), ('regression: highest level start', [2, 2, 2, 2, 2, 1, 1, 1], [7, 6, 5, 0, 1, 2, 3, 4]), ('number inside RTL', [1, 1, 2, 2, 1], [4, 2, 3, 1, 0]), ('all even levels', [0, 2, 2, 0], [0, 1, 2, 3]), ('control layout', [2, 0, 0, 0, 0, 0], [0, 1, 2, 3, 4, 5]), ('control layout', [3, 1, 1], [2, 1, 0])], [('regression: highest level start', [4, 4, 2, 3, 1, 2, 2, 2, 2, 1, 1, 1], [11, 10, 9, 5, 6, 7, 8, 4, 0, 1, 2, 3]), ('regression: highest level start', [1, 2, 2, 4, 4, 2], [1, 2, 3, 4, 5, 0]), ('partial-repair probe', [3, 3, 3, 3, 3, 0, 3, 3, 3], [4, 3, 2, 1, 0, 5, 8, 7, 6]), ('partial-repair probe', [1, 1, 1, 3, 3, 2, 3, 3, 1, 1, 1], [10, 9, 8, 4, 3, 5, 7, 6, 2, 1, 0]), ('all even levels', [0, 2, 2, 0], [0, 1, 2, 3]), ('lowest odd is three', [2, 3, 3, 2], [0, 2, 1, 3]), ('control layout', [3], [0]), ('control layout', [2, 2, 2, 2], [0, 1, 2, 3])]]
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
number inside RTL[4, 3, 2, 1, 0][4, 2, 3, 1, 0]Failed
regression: highest level start[6, 5, 4, 3, 2, 1, 0][2, 3, 4, 5, 6, 1, 0]Failed
partial-repair probe[0, 1, 2, 3, 4, 5, 6, 8, 7, 9, 10][0, 1, 2, 3, 4, 5, 6, 8, 7, 9, 10]Passed
regression: highest level start[4, 3, 2, 1, 0, 5, 6, 7, 8, 9][2, 3, 4, 1, 0, 5, 6, 7, 8, 9]Failed
all even levels[0, 1, 2, 3][0, 1, 2, 3]Passed
lowest odd is three[0, 2, 1, 3][0, 2, 1, 3]Passed
control layout[0, 1, 2][0, 1, 2]Passed
control layout[0, 1, 2, 3][0, 1, 2, 3]Passed

SHA-256 / c4121b9c166492151b40b51ea4edd51e849c7e574e73250b7733810b8029efa1

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(x):
    levels = x
    order = list(range(len(levels)))
    odd = [l for l in levels if l % 2 == 1]
    if not odd:
        return order
    hi = max(levels) - 1
    lo = min(odd)
    vis = [[lv, i] for i, lv in enumerate(levels)]
    for lev in range(hi, lo - 1, -1):
        i = 0
        while i < len(vis):
            if vis[i][0] >= lev:
                j = i
                while j < len(vis) and vis[j][0] >= lev:
                    j += 1
                vis[i:j] = vis[i:j][::-1]
                i = j
            else:
                i += 1
    return [p[1] for p in vis]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('number inside RTL', [1, 1, 2, 2, 1], [4, 2, 3, 1, 0]), ('regression: highest level start', [1, 1, 2, 2, 2, 2, 2], [2, 3, 4, 5, 6, 1, 0]), ('partial-repair probe', [0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0], [0, 1, 2, 3, 4, 5, 6, 8, 7, 9, 10]), ('regression: highest level start', [3, 3, 4, 4, 4, 2, 2, 2, 2, 4], [2, 3, 4, 1, 0, 5, 6, 7, 8, 9]), ('all even levels', [0, 2, 2, 0], [0, 1, 2, 3]), ('lowest odd is three', [2, 3, 3, 2], [0, 2, 1, 3]), ('control layout', [2, 2, 2], [0, 1, 2]), ('control layout', [2, 2, 2, 2], [0, 1, 2, 3])], [('regression: highest level start', [1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2], [9, 10, 11, 8, 7, 6, 5, 4, 3, 2, 1, 0]), ('regression: highest level start', [1, 1, 1, 1, 2, 2, 1, 0], [6, 4, 5, 3, 2, 1, 0, 7]), ('partial-repair probe', [1, 1, 1, 1, 1, 1, 1, 1, 1], [8, 7, 6, 5, 4, 3, 2, 1, 0]), ('partial-repair probe', [1, 1], [1, 0]), ('lowest odd is three', [2, 3, 3, 2], [0, 2, 1, 3]), ('all even levels', [0, 2, 2, 0], [0, 1, 2, 3]), ('control layout', [0, 0, 2, 1, 1, 1, 1], [0, 1, 6, 5, 4, 3, 2]), ('control layout', [1, 3, 2, 2, 2], [1, 2, 3, 4, 0])], [('regression: highest level start', [2, 2, 2, 1, 1, 1, 1, 1, 4, 4, 4], [8, 9, 10, 7, 6, 5, 4, 3, 0, 1, 2]), ('regression: highest level start', [4, 4, 1, 1, 1, 2, 2, 3, 3], [5, 6, 8, 7, 4, 3, 2, 0, 1]), ('regression: highest level start', [2, 2, 2, 1, 1, 0, 0, 1, 1, 1, 1, 1], [4, 3, 0, 1, 2, 5, 6, 11, 10, 9, 8, 7]), ('regression: highest level start', [4, 4, 4, 4, 2, 1], [5, 0, 1, 2, 3, 4]), ('number inside RTL', [1, 1, 2, 2, 1], [4, 2, 3, 1, 0]), ('all even levels', [0, 2, 2, 0], [0, 1, 2, 3]), ('control layout', [4, 4, 4, 4, 4], [0, 1, 2, 3, 4]), ('control layout', [2, 0, 0, 0, 1], [0, 1, 2, 3, 4])], [('regression: highest level start', [2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2], [8, 9, 10, 11, 7, 6, 5, 4, 0, 1, 2, 3]), ('regression: highest level start', [2, 2, 1, 1, 1, 1, 4, 4, 2, 2, 2], [6, 7, 8, 9, 10, 5, 4, 3, 2, 0, 1]), ('partial-repair probe', [3, 3, 2], [1, 0, 2]), ('regression: highest level start', [2, 2, 2, 2, 2, 1, 1, 1], [7, 6, 5, 0, 1, 2, 3, 4]), ('number inside RTL', [1, 1, 2, 2, 1], [4, 2, 3, 1, 0]), ('all even levels', [0, 2, 2, 0], [0, 1, 2, 3]), ('control layout', [2, 0, 0, 0, 0, 0], [0, 1, 2, 3, 4, 5]), ('control layout', [3, 1, 1], [2, 1, 0])], [('regression: highest level start', [4, 4, 2, 3, 1, 2, 2, 2, 2, 1, 1, 1], [11, 10, 9, 5, 6, 7, 8, 4, 0, 1, 2, 3]), ('regression: highest level start', [1, 2, 2, 4, 4, 2], [1, 2, 3, 4, 5, 0]), ('partial-repair probe', [3, 3, 3, 3, 3, 0, 3, 3, 3], [4, 3, 2, 1, 0, 5, 8, 7, 6]), ('partial-repair probe', [1, 1, 1, 3, 3, 2, 3, 3, 1, 1, 1], [10, 9, 8, 4, 3, 5, 7, 6, 2, 1, 0]), ('all even levels', [0, 2, 2, 0], [0, 1, 2, 3]), ('lowest odd is three', [2, 3, 3, 2], [0, 2, 1, 3]), ('control layout', [3], [0]), ('control layout', [2, 2, 2, 2], [0, 1, 2, 3])]]
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
number inside RTL[4, 3, 2, 1, 0][4, 2, 3, 1, 0]Failed
regression: highest level start[6, 5, 4, 3, 2, 1, 0][2, 3, 4, 5, 6, 1, 0]Failed
partial-repair probe[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10][0, 1, 2, 3, 4, 5, 6, 8, 7, 9, 10]Failed
regression: highest level start[4, 3, 2, 1, 0, 5, 6, 7, 8, 9][2, 3, 4, 1, 0, 5, 6, 7, 8, 9]Failed
all even levels[0, 1, 2, 3][0, 1, 2, 3]Passed
lowest odd is three[0, 1, 2, 3][0, 2, 1, 3]Failed
control layout[0, 1, 2][0, 1, 2]Passed
control layout[0, 1, 2, 3][0, 1, 2, 3]Passed

SHA-256 / ae5f2f7010a38733e32fe65ffa5e989af38cb2f5c51207d1684eb2957f934870

3 / The verified repair

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

N = 1
observations = []
def solve(x):
    levels = x
    order = list(range(len(levels)))
    odd = [l for l in levels if l % 2 == 1]
    if not odd:
        return order
    hi = max(levels)
    lo = min(odd)
    vis = [[lv, i] for i, lv in enumerate(levels)]
    for lev in range(hi, lo - 1, -1):
        i = 0
        while i < len(vis):
            if vis[i][0] >= lev:
                j = i
                while j < len(vis) and vis[j][0] >= lev:
                    j += 1
                vis[i:j] = vis[i:j][::-1]
                i = j
            else:
                i += 1
    return [p[1] for p in vis]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('number inside RTL', [1, 1, 2, 2, 1], [4, 2, 3, 1, 0]), ('regression: highest level start', [1, 1, 2, 2, 2, 2, 2], [2, 3, 4, 5, 6, 1, 0]), ('partial-repair probe', [0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0], [0, 1, 2, 3, 4, 5, 6, 8, 7, 9, 10]), ('regression: highest level start', [3, 3, 4, 4, 4, 2, 2, 2, 2, 4], [2, 3, 4, 1, 0, 5, 6, 7, 8, 9]), ('all even levels', [0, 2, 2, 0], [0, 1, 2, 3]), ('lowest odd is three', [2, 3, 3, 2], [0, 2, 1, 3]), ('control layout', [2, 2, 2], [0, 1, 2]), ('control layout', [2, 2, 2, 2], [0, 1, 2, 3])], [('regression: highest level start', [1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2], [9, 10, 11, 8, 7, 6, 5, 4, 3, 2, 1, 0]), ('regression: highest level start', [1, 1, 1, 1, 2, 2, 1, 0], [6, 4, 5, 3, 2, 1, 0, 7]), ('partial-repair probe', [1, 1, 1, 1, 1, 1, 1, 1, 1], [8, 7, 6, 5, 4, 3, 2, 1, 0]), ('partial-repair probe', [1, 1], [1, 0]), ('lowest odd is three', [2, 3, 3, 2], [0, 2, 1, 3]), ('all even levels', [0, 2, 2, 0], [0, 1, 2, 3]), ('control layout', [0, 0, 2, 1, 1, 1, 1], [0, 1, 6, 5, 4, 3, 2]), ('control layout', [1, 3, 2, 2, 2], [1, 2, 3, 4, 0])], [('regression: highest level start', [2, 2, 2, 1, 1, 1, 1, 1, 4, 4, 4], [8, 9, 10, 7, 6, 5, 4, 3, 0, 1, 2]), ('regression: highest level start', [4, 4, 1, 1, 1, 2, 2, 3, 3], [5, 6, 8, 7, 4, 3, 2, 0, 1]), ('regression: highest level start', [2, 2, 2, 1, 1, 0, 0, 1, 1, 1, 1, 1], [4, 3, 0, 1, 2, 5, 6, 11, 10, 9, 8, 7]), ('regression: highest level start', [4, 4, 4, 4, 2, 1], [5, 0, 1, 2, 3, 4]), ('number inside RTL', [1, 1, 2, 2, 1], [4, 2, 3, 1, 0]), ('all even levels', [0, 2, 2, 0], [0, 1, 2, 3]), ('control layout', [4, 4, 4, 4, 4], [0, 1, 2, 3, 4]), ('control layout', [2, 0, 0, 0, 1], [0, 1, 2, 3, 4])], [('regression: highest level start', [2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2], [8, 9, 10, 11, 7, 6, 5, 4, 0, 1, 2, 3]), ('regression: highest level start', [2, 2, 1, 1, 1, 1, 4, 4, 2, 2, 2], [6, 7, 8, 9, 10, 5, 4, 3, 2, 0, 1]), ('partial-repair probe', [3, 3, 2], [1, 0, 2]), ('regression: highest level start', [2, 2, 2, 2, 2, 1, 1, 1], [7, 6, 5, 0, 1, 2, 3, 4]), ('number inside RTL', [1, 1, 2, 2, 1], [4, 2, 3, 1, 0]), ('all even levels', [0, 2, 2, 0], [0, 1, 2, 3]), ('control layout', [2, 0, 0, 0, 0, 0], [0, 1, 2, 3, 4, 5]), ('control layout', [3, 1, 1], [2, 1, 0])], [('regression: highest level start', [4, 4, 2, 3, 1, 2, 2, 2, 2, 1, 1, 1], [11, 10, 9, 5, 6, 7, 8, 4, 0, 1, 2, 3]), ('regression: highest level start', [1, 2, 2, 4, 4, 2], [1, 2, 3, 4, 5, 0]), ('partial-repair probe', [3, 3, 3, 3, 3, 0, 3, 3, 3], [4, 3, 2, 1, 0, 5, 8, 7, 6]), ('partial-repair probe', [1, 1, 1, 3, 3, 2, 3, 3, 1, 1, 1], [10, 9, 8, 4, 3, 5, 7, 6, 2, 1, 0]), ('all even levels', [0, 2, 2, 0], [0, 1, 2, 3]), ('lowest odd is three', [2, 3, 3, 2], [0, 2, 1, 3]), ('control layout', [3], [0]), ('control layout', [2, 2, 2, 2], [0, 1, 2, 3])]]
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
number inside RTL[4, 2, 3, 1, 0][4, 2, 3, 1, 0]Passed
regression: highest level start[2, 3, 4, 5, 6, 1, 0][2, 3, 4, 5, 6, 1, 0]Passed
partial-repair probe[0, 1, 2, 3, 4, 5, 6, 8, 7, 9, 10][0, 1, 2, 3, 4, 5, 6, 8, 7, 9, 10]Passed
regression: highest level start[2, 3, 4, 1, 0, 5, 6, 7, 8, 9][2, 3, 4, 1, 0, 5, 6, 7, 8, 9]Passed
all even levels[0, 1, 2, 3][0, 1, 2, 3]Passed
lowest odd is three[0, 2, 1, 3][0, 2, 1, 3]Passed
control layout[0, 1, 2][0, 1, 2]Passed
control layout[0, 1, 2, 3][0, 1, 2, 3]Passed

SHA-256 / cc0f2b9a9294cbb5dec6a3db9daa6adec936d4abb5f55f8c2f7f88e067d5d74e

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 2026-09-29T14:49:54.185211+00:00.

Case digest / 8815f9ba06fe08e4d30f70075f76a901faa43ae2a2d996a767dca6c9ee0dcd3c