FAILURE MAP
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FA-80646 / Bidirectional text layout / Open access

Caret visual position: position inverse map · case 01

Carets are placed at the logical index instead of the visual slot.

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

ROOT CAUSE

The inverse map is filled as pos[v] = i, which is just the visual order again.

VERIFIED REPAIR

Map each logical index to its visual slot.

Unsuccessful approach: Mirroring the slot numbers is not the inverse permutation.

Case contract

Input [levels, logical caret offset k, affinity]. Characters are one unit wide and visually ordered by level reversal. Affinity "after" attaches the caret to the leading edge of character k (if k < n), otherwise to the trailing edge of character k-1; offset 0 always uses the leading edge of character 0. The leading edge of an LTR character is its left side, of an RTL (odd) character its right side. Return the visual x.

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):
    def reorder(lv):
        vis = list(range(len(lv)))
        odd = [l for l in lv if l % 2 == 1]
        if not odd:
            return vis
        for lev in range(max(lv), min(odd) - 1, -1):
            i = 0
            while i < len(vis):
                if lv[vis[i]] >= lev:
                    j = i
                    while j < len(vis) and lv[vis[j]] >= lev:
                        j += 1
                    vis[i:j] = vis[i:j][::-1]
                    i = j
                else:
                    i += 1
        return vis
    
    levels, k, affinity = x
    n = len(levels)
    if n == 0:
        return 0
    vis = reorder(levels)
    pos = [0] * n
    for v, i in enumerate(vis):
        pos[v] = i
    if affinity == 'after' and k < n or k == 0:
        j = k
        leading = True
    else:
        j = k - 1
        leading = False
    rtl = levels[j] % 2 == 1
    if leading:
        return pos[j] + 1 if rtl else pos[j]
    return pos[j] if rtl else pos[j] + 1
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: position inverse map', [[2, 2, 2, 4, 4, 4, 4, 1, 1], 7, 'before'], 9), ('regression: position inverse map', [[2, 2, 2, 2, 2, 2, 2, 1], 2, 'after'], 3), ('regression: position inverse map', [[2, 2, 1, 1], 0, 'after'], 2), ('regression: position inverse map', [[1, 2, 2], 1, 'after'], 0), ('caret at direction boundary', [[0, 0, 1, 1], 2, 'before'], 2), ('line start before', [[1, 1, 0], 0, 'before'], 2), ('control layout', [[3, 0, 0, 0, 2, 2, 2], 3, 'after'], 3), ('control layout', [[4], 1, 'before'], 1)], [('regression: position inverse map', [[2, 2, 2, 2, 2, 2, 2, 2, 1], 6, 'after'], 7), ('regression: position inverse map', [[1, 1, 1, 1, 1, 2, 2, 2, 2, 1], 6, 'before'], 2), ('partial-repair probe', [[0, 0, 0, 3, 1, 1, 1, 1, 1, 1], 5, 'before'], 8), ('partial-repair probe', [[1, 1, 0, 0, 0, 0, 0, 0], 5, 'before'], 5), ('caret at direction boundary', [[0, 0, 1, 1], 2, 'before'], 2), ('line end', [[1, 1, 1], 3, 'after'], 0), ('control layout', [[3], 1, 'before'], 0), ('control layout', [[1], 1, 'before'], 0)], [('regression: position inverse map', [[2, 2, 2, 2, 2, 3, 3, 2, 1], 0, 'before'], 1), ('regression: position inverse map', [[3, 3, 2, 2, 2, 2, 2, 2, 1, 1], 7, 'after'], 9), ('partial-repair probe', [[2, 2, 2, 2, 4, 2], 4, 'before'], 4), ('partial-repair probe', [[1, 1, 1, 1, 0, 0, 0, 0, 0, 2], 2, 'after'], 2), ('caret at direction boundary', [[0, 0, 1, 1], 2, 'before'], 2), ('same boundary after', [[0, 0, 1, 1], 2, 'after'], 4), ('control layout', [[1, 2, 1, 1, 3, 3, 3], 3, 'after'], 4), ('control layout', [[3], 1, 'before'], 0)], [('regression: position inverse map', [[1, 1, 1, 1, 2, 2], 5, 'before'], 1), ('regression: position inverse map', [[2, 2, 1, 1, 1, 1, 2, 2, 2], 2, 'after'], 7), ('partial-repair probe', [[3, 3, 3, 0, 0, 0, 3], 5, 'after'], 5), ('partial-repair probe', [[3, 3, 3, 3, 3, 3, 3], 0, 'before'], 7), ('line end', [[1, 1, 1], 3, 'after'], 0), ('line start before', [[1, 1, 0], 0, 'before'], 2), ('control layout', [[1], 0, 'before'], 1), ('control layout', [[2, 2, 1, 1, 1], 3, 'before'], 2)], [('regression: position inverse map', [[4, 4, 3, 3, 3, 3, 2, 2, 2], 2, 'before'], 6), ('regression: position inverse map', [[2, 2, 1, 1], 0, 'after'], 2), ('regression: position inverse map', [[1, 1, 1, 2, 2, 2, 2, 2, 2, 1], 9, 'before'], 7), ('regression: position inverse map', [[1, 1, 1, 1, 2, 2], 5, 'before'], 1), ('line end', [[1, 1, 1], 3, 'after'], 0), ('line start before', [[1, 1, 0], 0, 'before'], 2), ('control layout', [[1], 0, 'before'], 1), ('control layout', [[1, 1, 0], 1, 'before'], 1)]]
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: position inverse map59Failed
regression: position inverse map13Failed
regression: position inverse map32Failed
regression: position inverse map20Failed
caret at direction boundary22Passed
line start before22Passed
control layout33Passed
control layout11Passed

SHA-256 / fd2deafab27671e4260a43557d4a15ec6c8868e28f147f5530ce9f45b1157847

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(x):
    def reorder(lv):
        vis = list(range(len(lv)))
        odd = [l for l in lv if l % 2 == 1]
        if not odd:
            return vis
        for lev in range(max(lv), min(odd) - 1, -1):
            i = 0
            while i < len(vis):
                if lv[vis[i]] >= lev:
                    j = i
                    while j < len(vis) and lv[vis[j]] >= lev:
                        j += 1
                    vis[i:j] = vis[i:j][::-1]
                    i = j
                else:
                    i += 1
        return vis
    
    levels, k, affinity = x
    n = len(levels)
    if n == 0:
        return 0
    vis = reorder(levels)
    pos = [0] * n
    for v, i in enumerate(vis):
        pos[i] = n - 1 - v
    if affinity == 'after' and k < n or k == 0:
        j = k
        leading = True
    else:
        j = k - 1
        leading = False
    rtl = levels[j] % 2 == 1
    if leading:
        return pos[j] + 1 if rtl else pos[j]
    return pos[j] if rtl else pos[j] + 1
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: position inverse map', [[2, 2, 2, 4, 4, 4, 4, 1, 1], 7, 'before'], 9), ('regression: position inverse map', [[2, 2, 2, 2, 2, 2, 2, 1], 2, 'after'], 3), ('regression: position inverse map', [[2, 2, 1, 1], 0, 'after'], 2), ('regression: position inverse map', [[1, 2, 2], 1, 'after'], 0), ('caret at direction boundary', [[0, 0, 1, 1], 2, 'before'], 2), ('line start before', [[1, 1, 0], 0, 'before'], 2), ('control layout', [[3, 0, 0, 0, 2, 2, 2], 3, 'after'], 3), ('control layout', [[4], 1, 'before'], 1)], [('regression: position inverse map', [[2, 2, 2, 2, 2, 2, 2, 2, 1], 6, 'after'], 7), ('regression: position inverse map', [[1, 1, 1, 1, 1, 2, 2, 2, 2, 1], 6, 'before'], 2), ('partial-repair probe', [[0, 0, 0, 3, 1, 1, 1, 1, 1, 1], 5, 'before'], 8), ('partial-repair probe', [[1, 1, 0, 0, 0, 0, 0, 0], 5, 'before'], 5), ('caret at direction boundary', [[0, 0, 1, 1], 2, 'before'], 2), ('line end', [[1, 1, 1], 3, 'after'], 0), ('control layout', [[3], 1, 'before'], 0), ('control layout', [[1], 1, 'before'], 0)], [('regression: position inverse map', [[2, 2, 2, 2, 2, 3, 3, 2, 1], 0, 'before'], 1), ('regression: position inverse map', [[3, 3, 2, 2, 2, 2, 2, 2, 1, 1], 7, 'after'], 9), ('partial-repair probe', [[2, 2, 2, 2, 4, 2], 4, 'before'], 4), ('partial-repair probe', [[1, 1, 1, 1, 0, 0, 0, 0, 0, 2], 2, 'after'], 2), ('caret at direction boundary', [[0, 0, 1, 1], 2, 'before'], 2), ('same boundary after', [[0, 0, 1, 1], 2, 'after'], 4), ('control layout', [[1, 2, 1, 1, 3, 3, 3], 3, 'after'], 4), ('control layout', [[3], 1, 'before'], 0)], [('regression: position inverse map', [[1, 1, 1, 1, 2, 2], 5, 'before'], 1), ('regression: position inverse map', [[2, 2, 1, 1, 1, 1, 2, 2, 2], 2, 'after'], 7), ('partial-repair probe', [[3, 3, 3, 0, 0, 0, 3], 5, 'after'], 5), ('partial-repair probe', [[3, 3, 3, 3, 3, 3, 3], 0, 'before'], 7), ('line end', [[1, 1, 1], 3, 'after'], 0), ('line start before', [[1, 1, 0], 0, 'before'], 2), ('control layout', [[1], 0, 'before'], 1), ('control layout', [[2, 2, 1, 1, 1], 3, 'before'], 2)], [('regression: position inverse map', [[4, 4, 3, 3, 3, 3, 2, 2, 2], 2, 'before'], 6), ('regression: position inverse map', [[2, 2, 1, 1], 0, 'after'], 2), ('regression: position inverse map', [[1, 1, 1, 2, 2, 2, 2, 2, 2, 1], 9, 'before'], 7), ('regression: position inverse map', [[1, 1, 1, 1, 2, 2], 5, 'before'], 1), ('line end', [[1, 1, 1], 3, 'after'], 0), ('line start before', [[1, 1, 0], 0, 'before'], 2), ('control layout', [[1], 0, 'before'], 1), ('control layout', [[1, 1, 0], 1, 'before'], 1)]]
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: position inverse map19Failed
regression: position inverse map43Failed
regression: position inverse map12Failed
regression: position inverse map20Failed
caret at direction boundary32Failed
line start before22Passed
control layout33Passed
control layout11Passed

SHA-256 / c7fcf18668a8ab663404974354aa02323807159a8e385bf325875ec3b540cf86

3 / The verified repair

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

N = 1
observations = []
def solve(x):
    def reorder(lv):
        vis = list(range(len(lv)))
        odd = [l for l in lv if l % 2 == 1]
        if not odd:
            return vis
        for lev in range(max(lv), min(odd) - 1, -1):
            i = 0
            while i < len(vis):
                if lv[vis[i]] >= lev:
                    j = i
                    while j < len(vis) and lv[vis[j]] >= lev:
                        j += 1
                    vis[i:j] = vis[i:j][::-1]
                    i = j
                else:
                    i += 1
        return vis
    
    levels, k, affinity = x
    n = len(levels)
    if n == 0:
        return 0
    vis = reorder(levels)
    pos = [0] * n
    for v, i in enumerate(vis):
        pos[i] = v
    if affinity == 'after' and k < n or k == 0:
        j = k
        leading = True
    else:
        j = k - 1
        leading = False
    rtl = levels[j] % 2 == 1
    if leading:
        return pos[j] + 1 if rtl else pos[j]
    return pos[j] if rtl else pos[j] + 1
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: position inverse map', [[2, 2, 2, 4, 4, 4, 4, 1, 1], 7, 'before'], 9), ('regression: position inverse map', [[2, 2, 2, 2, 2, 2, 2, 1], 2, 'after'], 3), ('regression: position inverse map', [[2, 2, 1, 1], 0, 'after'], 2), ('regression: position inverse map', [[1, 2, 2], 1, 'after'], 0), ('caret at direction boundary', [[0, 0, 1, 1], 2, 'before'], 2), ('line start before', [[1, 1, 0], 0, 'before'], 2), ('control layout', [[3, 0, 0, 0, 2, 2, 2], 3, 'after'], 3), ('control layout', [[4], 1, 'before'], 1)], [('regression: position inverse map', [[2, 2, 2, 2, 2, 2, 2, 2, 1], 6, 'after'], 7), ('regression: position inverse map', [[1, 1, 1, 1, 1, 2, 2, 2, 2, 1], 6, 'before'], 2), ('partial-repair probe', [[0, 0, 0, 3, 1, 1, 1, 1, 1, 1], 5, 'before'], 8), ('partial-repair probe', [[1, 1, 0, 0, 0, 0, 0, 0], 5, 'before'], 5), ('caret at direction boundary', [[0, 0, 1, 1], 2, 'before'], 2), ('line end', [[1, 1, 1], 3, 'after'], 0), ('control layout', [[3], 1, 'before'], 0), ('control layout', [[1], 1, 'before'], 0)], [('regression: position inverse map', [[2, 2, 2, 2, 2, 3, 3, 2, 1], 0, 'before'], 1), ('regression: position inverse map', [[3, 3, 2, 2, 2, 2, 2, 2, 1, 1], 7, 'after'], 9), ('partial-repair probe', [[2, 2, 2, 2, 4, 2], 4, 'before'], 4), ('partial-repair probe', [[1, 1, 1, 1, 0, 0, 0, 0, 0, 2], 2, 'after'], 2), ('caret at direction boundary', [[0, 0, 1, 1], 2, 'before'], 2), ('same boundary after', [[0, 0, 1, 1], 2, 'after'], 4), ('control layout', [[1, 2, 1, 1, 3, 3, 3], 3, 'after'], 4), ('control layout', [[3], 1, 'before'], 0)], [('regression: position inverse map', [[1, 1, 1, 1, 2, 2], 5, 'before'], 1), ('regression: position inverse map', [[2, 2, 1, 1, 1, 1, 2, 2, 2], 2, 'after'], 7), ('partial-repair probe', [[3, 3, 3, 0, 0, 0, 3], 5, 'after'], 5), ('partial-repair probe', [[3, 3, 3, 3, 3, 3, 3], 0, 'before'], 7), ('line end', [[1, 1, 1], 3, 'after'], 0), ('line start before', [[1, 1, 0], 0, 'before'], 2), ('control layout', [[1], 0, 'before'], 1), ('control layout', [[2, 2, 1, 1, 1], 3, 'before'], 2)], [('regression: position inverse map', [[4, 4, 3, 3, 3, 3, 2, 2, 2], 2, 'before'], 6), ('regression: position inverse map', [[2, 2, 1, 1], 0, 'after'], 2), ('regression: position inverse map', [[1, 1, 1, 2, 2, 2, 2, 2, 2, 1], 9, 'before'], 7), ('regression: position inverse map', [[1, 1, 1, 1, 2, 2], 5, 'before'], 1), ('line end', [[1, 1, 1], 3, 'after'], 0), ('line start before', [[1, 1, 0], 0, 'before'], 2), ('control layout', [[1], 0, 'before'], 1), ('control layout', [[1, 1, 0], 1, 'before'], 1)]]
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: position inverse map99Passed
regression: position inverse map33Passed
regression: position inverse map22Passed
regression: position inverse map00Passed
caret at direction boundary22Passed
line start before22Passed
control layout33Passed
control layout11Passed

SHA-256 / d318d36ef5ebba4fd836f314caba0646020b6224154171bdb9d15131b3646422

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 2026-09-29T14:49:55.720736+00:00.

Case digest / 73df4464c2c2381ee662fcdb9f9db5f2568d306f06f33132acada9b1d0240da2