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FA-80446 / Bidirectional text layout / Open access

Implicit level runs: number raise at even level · case 01

Numbers in LTR text collapse into the surrounding RTL run.

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

ROOT CAUSE

EN/AN at even levels are raised by one instead of two.

THE FAILURE

EN/AN at even levels are raised by one instead of two.

Unsuccessful approach: Raising only AN by two leaves European numbers at the base level.

Case contract

Input [resolved classes L/R/EN/AN, embedding levels]. At even levels R goes up one and AN/EN up two; at odd levels L, EN and AN go up one. Return level runs [start, end exclusive, level] of equal final levels.

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):
    types, levels = x
    out = []
    for c, lv in zip(types, levels):
        if lv % 2 == 0:
            if c == 'R':
                out.append(lv + 1)
            elif c in ('AN', 'EN'):
                out.append(lv + 1)
            else:
                out.append(lv)
        else:
            if c in ('L', 'EN', 'AN'):
                out.append(lv + 1)
            else:
                out.append(lv)
    runs = []
    for i, lv in enumerate(out):
        if runs and runs[-1][2] == lv:
            runs[-1][1] = i + 1
        else:
            runs.append([i, i + 1, lv])
    return runs
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('number in LTR text', [['L', 'EN', 'L'], [0, 0, 0]], [[0, 1, 0], [1, 2, 2], [2, 3, 0]]), ('regression: number raise at even level', [['L', 'R', 'L', 'R', 'R', 'EN', 'EN', 'EN'], [1, 1, 3, 3, 3, 2, 2, 3]], [[0, 1, 2], [1, 2, 1], [2, 3, 4], [3, 5, 3], [5, 8, 4]]), ('regression: number raise at even level', [['EN', 'AN', 'R', 'R', 'EN', 'AN', 'R', 'R', 'AN', 'AN', 'EN'], [3, 3, 3, 2, 2, 2, 2, 3, 3, 3, 3]], [[0, 2, 4], [2, 4, 3], [4, 6, 4], [6, 8, 3], [8, 11, 4]]), ('regression: number raise at even level', [['AN', 'AN', 'R', 'EN'], [4, 4, 4, 4]], [[0, 2, 6], [2, 3, 5], [3, 4, 6]]), ('level two embedding', [['R', 'L'], [2, 2]], [[0, 1, 3], [1, 2, 2]]), ('number in RTL text', [['R', 'AN', 'R'], [1, 1, 1]], [[0, 1, 1], [1, 2, 2], [2, 3, 1]]), ('control layout', [['R', 'L'], [2, 1]], [[0, 1, 3], [1, 2, 2]]), ('control layout', [['L', 'R', 'R'], [1, 1, 1]], [[0, 1, 2], [1, 3, 1]])], [('regression: number raise at even level', [['AN', 'EN', 'EN', 'AN', 'AN'], [2, 1, 3, 1, 2]], [[0, 1, 4], [1, 2, 2], [2, 3, 4], [3, 4, 2], [4, 5, 4]]), ('regression: number raise at even level', [['R', 'AN', 'AN', 'R'], [0, 0, 0, 0]], [[0, 1, 1], [1, 3, 2], [3, 4, 1]]), ('regression: number raise at even level', [['L', 'AN', 'EN', 'AN', 'R', 'AN', 'EN', 'EN', 'R', 'R'], [2, 1, 1, 1, 2, 2, 2, 4, 4, 4]], [[0, 4, 2], [4, 5, 3], [5, 7, 4], [7, 8, 6], [8, 10, 5]]), ('regression: number raise at even level', [['R', 'L', 'EN', 'EN', 'R', 'R'], [2, 2, 2, 2, 2, 2]], [[0, 1, 3], [1, 2, 2], [2, 4, 4], [4, 6, 3]]), ('level two embedding', [['R', 'L'], [2, 2]], [[0, 1, 3], [1, 2, 2]]), ('number in LTR text', [['L', 'EN', 'L'], [0, 0, 0]], [[0, 1, 0], [1, 2, 2], [2, 3, 0]]), ('control layout', [['L'], [1]], [[0, 1, 2]]), ('control layout', [['L', 'L'], [2, 2]], [[0, 2, 2]])], [('regression: number raise at even level', [['AN', 'L', 'EN', 'EN', 'EN', 'AN', 'L'], [1, 1, 1, 1, 2, 2, 2]], [[0, 4, 2], [4, 6, 4], [6, 7, 2]]), ('regression: number raise at even level', [['EN', 'L', 'L', 'EN', 'EN', 'EN', 'R', 'AN', 'EN', 'AN', 'R', 'AN'], [1, 1, 1, 2, 2, 2, 3, 3, 1, 1, 3, 3]], [[0, 3, 2], [3, 6, 4], [6, 7, 3], [7, 8, 4], [8, 10, 2], [10, 11, 3], [11, 12, 4]]), ('regression: number raise at even level', [['AN', 'EN', 'AN', 'L', 'AN', 'AN', 'L', 'R', 'EN', 'EN', 'EN', 'R'], [2, 1, 1, 1, 1, 0, 0, 0, 0, 2, 2, 2]], [[0, 1, 4], [1, 6, 2], [6, 7, 0], [7, 8, 1], [8, 9, 2], [9, 11, 4], [11, 12, 3]]), ('regression: number raise at even level', [['L', 'EN', 'AN', 'R', 'AN', 'L', 'R', 'EN'], [4, 4, 4, 2, 2, 1, 1, 1]], [[0, 1, 4], [1, 3, 6], [3, 4, 3], [4, 5, 4], [5, 6, 2], [6, 7, 1], [7, 8, 2]]), ('number in RTL text', [['R', 'AN', 'R'], [1, 1, 1]], [[0, 1, 1], [1, 2, 2], [2, 3, 1]]), ('number in LTR text', [['L', 'EN', 'L'], [0, 0, 0]], [[0, 1, 0], [1, 2, 2], [2, 3, 0]]), ('control layout', [['L', 'R', 'R', 'EN', 'EN', 'L'], [1, 1, 1, 1, 1, 3]], [[0, 1, 2], [1, 3, 1], [3, 5, 2], [5, 6, 4]]), ('control layout', [['EN', 'AN', 'R', 'EN'], [1, 1, 1, 1]], [[0, 2, 2], [2, 3, 1], [3, 4, 2]])], [('regression: number raise at even level', [['L', 'L', 'L', 'R', 'R', 'AN', 'L', 'EN', 'R', 'AN', 'EN'], [2, 2, 2, 4, 4, 4, 4, 4, 4, 2, 2]], [[0, 3, 2], [3, 5, 5], [5, 6, 6], [6, 7, 4], [7, 8, 6], [8, 9, 5], [9, 11, 4]]), ('regression: number raise at even level', [['EN', 'EN', 'R', 'AN', 'L'], [3, 3, 2, 2, 2]], [[0, 2, 4], [2, 3, 3], [3, 4, 4], [4, 5, 2]]), ('regression: number raise at even level', [['EN', 'R', 'AN', 'R'], [0, 0, 0, 0]], [[0, 1, 2], [1, 2, 1], [2, 3, 2], [3, 4, 1]]), ('regression: number raise at even level', [['L', 'AN', 'EN', 'AN', 'R', 'AN', 'EN', 'EN', 'R', 'R'], [2, 1, 1, 1, 2, 2, 2, 4, 4, 4]], [[0, 4, 2], [4, 5, 3], [5, 7, 4], [7, 8, 6], [8, 10, 5]]), ('number in LTR text', [['L', 'EN', 'L'], [0, 0, 0]], [[0, 1, 0], [1, 2, 2], [2, 3, 0]]), ('level two embedding', [['R', 'L'], [2, 2]], [[0, 1, 3], [1, 2, 2]]), ('control layout', [['AN', 'L'], [3, 3]], [[0, 2, 4]]), ('control layout', [['L', 'R'], [3, 0]], [[0, 1, 4], [1, 2, 1]])], [('regression: number raise at even level', [['R', 'AN', 'L', 'AN', 'L', 'AN', 'AN', 'EN', 'EN', 'AN'], [0, 0, 0, 0, 3, 3, 1, 1, 1, 1]], [[0, 1, 1], [1, 2, 2], [2, 3, 0], [3, 4, 2], [4, 6, 4], [6, 10, 2]]), ('regression: number raise at even level', [['L', 'AN', 'L', 'AN', 'R', 'EN', 'AN', 'R', 'R', 'AN'], [1, 1, 1, 1, 0, 0, 0, 0, 1, 1]], [[0, 4, 2], [4, 5, 1], [5, 7, 2], [7, 9, 1], [9, 10, 2]]), ('regression: number raise at even level', [['EN'], [4]], [[0, 1, 6]]), ('regression: number raise at even level', [['L', 'EN', 'EN', 'R'], [1, 1, 4, 4]], [[0, 2, 2], [2, 3, 6], [3, 4, 5]]), ('number in LTR text', [['L', 'EN', 'L'], [0, 0, 0]], [[0, 1, 0], [1, 2, 2], [2, 3, 0]]), ('number in RTL text', [['R', 'AN', 'R'], [1, 1, 1]], [[0, 1, 1], [1, 2, 2], [2, 3, 1]]), ('control layout', [['EN', 'AN', 'L', 'AN'], [1, 1, 1, 1]], [[0, 4, 2]]), ('control layout', [['R', 'L', 'L', 'L', 'L', 'AN'], [2, 1, 1, 1, 1, 1]], [[0, 1, 3], [1, 6, 2]])]]
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 in LTR text[[0, 1, 0], [1, 2, 1], [2, 3, 0]][[0, 1, 0], [1, 2, 2], [2, 3, 0]]Failed
regression: number raise at even level[[0, 1, 2], [1, 2, 1], [2, 3, 4], [3, 7, 3], [7, 8, 4]][[0, 1, 2], [1, 2, 1], [2, 3, 4], [3, 5, 3], [5, 8, 4]]Failed
regression: number raise at even level[[0, 2, 4], [2, 8, 3], [8, 11, 4]][[0, 2, 4], [2, 4, 3], [4, 6, 4], [6, 8, 3], [8, 11, 4]]Failed
regression: number raise at even level[[0, 4, 5]][[0, 2, 6], [2, 3, 5], [3, 4, 6]]Failed
level two embedding[[0, 1, 3], [1, 2, 2]][[0, 1, 3], [1, 2, 2]]Passed
number in RTL text[[0, 1, 1], [1, 2, 2], [2, 3, 1]][[0, 1, 1], [1, 2, 2], [2, 3, 1]]Passed
control layout[[0, 1, 3], [1, 2, 2]][[0, 1, 3], [1, 2, 2]]Passed
control layout[[0, 1, 2], [1, 3, 1]][[0, 1, 2], [1, 3, 1]]Passed

SHA-256 / 99e62454db0ff94fe96d8dd121b4f5fb87510b7b432dccbec4717fa702783905

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(x):
    types, levels = x
    out = []
    for c, lv in zip(types, levels):
        if lv % 2 == 0:
            if c == 'R':
                out.append(lv + 1)
            elif c == 'AN':
                out.append(lv + 2)
            else:
                out.append(lv)
        else:
            if c in ('L', 'EN', 'AN'):
                out.append(lv + 1)
            else:
                out.append(lv)
    runs = []
    for i, lv in enumerate(out):
        if runs and runs[-1][2] == lv:
            runs[-1][1] = i + 1
        else:
            runs.append([i, i + 1, lv])
    return runs
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('number in LTR text', [['L', 'EN', 'L'], [0, 0, 0]], [[0, 1, 0], [1, 2, 2], [2, 3, 0]]), ('regression: number raise at even level', [['L', 'R', 'L', 'R', 'R', 'EN', 'EN', 'EN'], [1, 1, 3, 3, 3, 2, 2, 3]], [[0, 1, 2], [1, 2, 1], [2, 3, 4], [3, 5, 3], [5, 8, 4]]), ('regression: number raise at even level', [['EN', 'AN', 'R', 'R', 'EN', 'AN', 'R', 'R', 'AN', 'AN', 'EN'], [3, 3, 3, 2, 2, 2, 2, 3, 3, 3, 3]], [[0, 2, 4], [2, 4, 3], [4, 6, 4], [6, 8, 3], [8, 11, 4]]), ('regression: number raise at even level', [['AN', 'AN', 'R', 'EN'], [4, 4, 4, 4]], [[0, 2, 6], [2, 3, 5], [3, 4, 6]]), ('level two embedding', [['R', 'L'], [2, 2]], [[0, 1, 3], [1, 2, 2]]), ('number in RTL text', [['R', 'AN', 'R'], [1, 1, 1]], [[0, 1, 1], [1, 2, 2], [2, 3, 1]]), ('control layout', [['R', 'L'], [2, 1]], [[0, 1, 3], [1, 2, 2]]), ('control layout', [['L', 'R', 'R'], [1, 1, 1]], [[0, 1, 2], [1, 3, 1]])], [('regression: number raise at even level', [['AN', 'EN', 'EN', 'AN', 'AN'], [2, 1, 3, 1, 2]], [[0, 1, 4], [1, 2, 2], [2, 3, 4], [3, 4, 2], [4, 5, 4]]), ('regression: number raise at even level', [['R', 'AN', 'AN', 'R'], [0, 0, 0, 0]], [[0, 1, 1], [1, 3, 2], [3, 4, 1]]), ('regression: number raise at even level', [['L', 'AN', 'EN', 'AN', 'R', 'AN', 'EN', 'EN', 'R', 'R'], [2, 1, 1, 1, 2, 2, 2, 4, 4, 4]], [[0, 4, 2], [4, 5, 3], [5, 7, 4], [7, 8, 6], [8, 10, 5]]), ('regression: number raise at even level', [['R', 'L', 'EN', 'EN', 'R', 'R'], [2, 2, 2, 2, 2, 2]], [[0, 1, 3], [1, 2, 2], [2, 4, 4], [4, 6, 3]]), ('level two embedding', [['R', 'L'], [2, 2]], [[0, 1, 3], [1, 2, 2]]), ('number in LTR text', [['L', 'EN', 'L'], [0, 0, 0]], [[0, 1, 0], [1, 2, 2], [2, 3, 0]]), ('control layout', [['L'], [1]], [[0, 1, 2]]), ('control layout', [['L', 'L'], [2, 2]], [[0, 2, 2]])], [('regression: number raise at even level', [['AN', 'L', 'EN', 'EN', 'EN', 'AN', 'L'], [1, 1, 1, 1, 2, 2, 2]], [[0, 4, 2], [4, 6, 4], [6, 7, 2]]), ('regression: number raise at even level', [['EN', 'L', 'L', 'EN', 'EN', 'EN', 'R', 'AN', 'EN', 'AN', 'R', 'AN'], [1, 1, 1, 2, 2, 2, 3, 3, 1, 1, 3, 3]], [[0, 3, 2], [3, 6, 4], [6, 7, 3], [7, 8, 4], [8, 10, 2], [10, 11, 3], [11, 12, 4]]), ('regression: number raise at even level', [['AN', 'EN', 'AN', 'L', 'AN', 'AN', 'L', 'R', 'EN', 'EN', 'EN', 'R'], [2, 1, 1, 1, 1, 0, 0, 0, 0, 2, 2, 2]], [[0, 1, 4], [1, 6, 2], [6, 7, 0], [7, 8, 1], [8, 9, 2], [9, 11, 4], [11, 12, 3]]), ('regression: number raise at even level', [['L', 'EN', 'AN', 'R', 'AN', 'L', 'R', 'EN'], [4, 4, 4, 2, 2, 1, 1, 1]], [[0, 1, 4], [1, 3, 6], [3, 4, 3], [4, 5, 4], [5, 6, 2], [6, 7, 1], [7, 8, 2]]), ('number in RTL text', [['R', 'AN', 'R'], [1, 1, 1]], [[0, 1, 1], [1, 2, 2], [2, 3, 1]]), ('number in LTR text', [['L', 'EN', 'L'], [0, 0, 0]], [[0, 1, 0], [1, 2, 2], [2, 3, 0]]), ('control layout', [['L', 'R', 'R', 'EN', 'EN', 'L'], [1, 1, 1, 1, 1, 3]], [[0, 1, 2], [1, 3, 1], [3, 5, 2], [5, 6, 4]]), ('control layout', [['EN', 'AN', 'R', 'EN'], [1, 1, 1, 1]], [[0, 2, 2], [2, 3, 1], [3, 4, 2]])], [('regression: number raise at even level', [['L', 'L', 'L', 'R', 'R', 'AN', 'L', 'EN', 'R', 'AN', 'EN'], [2, 2, 2, 4, 4, 4, 4, 4, 4, 2, 2]], [[0, 3, 2], [3, 5, 5], [5, 6, 6], [6, 7, 4], [7, 8, 6], [8, 9, 5], [9, 11, 4]]), ('regression: number raise at even level', [['EN', 'EN', 'R', 'AN', 'L'], [3, 3, 2, 2, 2]], [[0, 2, 4], [2, 3, 3], [3, 4, 4], [4, 5, 2]]), ('regression: number raise at even level', [['EN', 'R', 'AN', 'R'], [0, 0, 0, 0]], [[0, 1, 2], [1, 2, 1], [2, 3, 2], [3, 4, 1]]), ('regression: number raise at even level', [['L', 'AN', 'EN', 'AN', 'R', 'AN', 'EN', 'EN', 'R', 'R'], [2, 1, 1, 1, 2, 2, 2, 4, 4, 4]], [[0, 4, 2], [4, 5, 3], [5, 7, 4], [7, 8, 6], [8, 10, 5]]), ('number in LTR text', [['L', 'EN', 'L'], [0, 0, 0]], [[0, 1, 0], [1, 2, 2], [2, 3, 0]]), ('level two embedding', [['R', 'L'], [2, 2]], [[0, 1, 3], [1, 2, 2]]), ('control layout', [['AN', 'L'], [3, 3]], [[0, 2, 4]]), ('control layout', [['L', 'R'], [3, 0]], [[0, 1, 4], [1, 2, 1]])], [('regression: number raise at even level', [['R', 'AN', 'L', 'AN', 'L', 'AN', 'AN', 'EN', 'EN', 'AN'], [0, 0, 0, 0, 3, 3, 1, 1, 1, 1]], [[0, 1, 1], [1, 2, 2], [2, 3, 0], [3, 4, 2], [4, 6, 4], [6, 10, 2]]), ('regression: number raise at even level', [['L', 'AN', 'L', 'AN', 'R', 'EN', 'AN', 'R', 'R', 'AN'], [1, 1, 1, 1, 0, 0, 0, 0, 1, 1]], [[0, 4, 2], [4, 5, 1], [5, 7, 2], [7, 9, 1], [9, 10, 2]]), ('regression: number raise at even level', [['EN'], [4]], [[0, 1, 6]]), ('regression: number raise at even level', [['L', 'EN', 'EN', 'R'], [1, 1, 4, 4]], [[0, 2, 2], [2, 3, 6], [3, 4, 5]]), ('number in LTR text', [['L', 'EN', 'L'], [0, 0, 0]], [[0, 1, 0], [1, 2, 2], [2, 3, 0]]), ('number in RTL text', [['R', 'AN', 'R'], [1, 1, 1]], [[0, 1, 1], [1, 2, 2], [2, 3, 1]]), ('control layout', [['EN', 'AN', 'L', 'AN'], [1, 1, 1, 1]], [[0, 4, 2]]), ('control layout', [['R', 'L', 'L', 'L', 'L', 'AN'], [2, 1, 1, 1, 1, 1]], [[0, 1, 3], [1, 6, 2]])]]
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 in LTR text[[0, 3, 0]][[0, 1, 0], [1, 2, 2], [2, 3, 0]]Failed
regression: number raise at even level[[0, 1, 2], [1, 2, 1], [2, 3, 4], [3, 5, 3], [5, 7, 2], [7, 8, 4]][[0, 1, 2], [1, 2, 1], [2, 3, 4], [3, 5, 3], [5, 8, 4]]Failed
regression: number raise at even level[[0, 2, 4], [2, 4, 3], [4, 5, 2], [5, 6, 4], [6, 8, 3], [8, 11, 4]][[0, 2, 4], [2, 4, 3], [4, 6, 4], [6, 8, 3], [8, 11, 4]]Failed
regression: number raise at even level[[0, 2, 6], [2, 3, 5], [3, 4, 4]][[0, 2, 6], [2, 3, 5], [3, 4, 6]]Failed
level two embedding[[0, 1, 3], [1, 2, 2]][[0, 1, 3], [1, 2, 2]]Passed
number in RTL text[[0, 1, 1], [1, 2, 2], [2, 3, 1]][[0, 1, 1], [1, 2, 2], [2, 3, 1]]Passed
control layout[[0, 1, 3], [1, 2, 2]][[0, 1, 3], [1, 2, 2]]Passed
control layout[[0, 1, 2], [1, 3, 1]][[0, 1, 2], [1, 3, 1]]Passed

SHA-256 / 7243cdc3c7ac9292381a1e5dc10148ace35a3b246d17a2dadf2989c4e3413c7f

HELD IN THE MEMBER ARCHIVE

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

This mechanism has 8 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

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

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Verification & scope

A deterministic toy bidi model over stipulated class labels and integer levels; it is inspired by, but does not claim conformance to, any published algorithm. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.

Observations recorded using Python 3.12.14 at 2026-09-29T14:49:54.094267+00:00.

Case digest / 87b46d4b502924760eff9771df76713488f9022b53d2dd23bde5eaed626471bc