FAILURE MAP
← Case archive

FA-72296 / Error-correcting codes / Open access

Weight distribution takes the minimum row weight as the distance · case 01

Minimum distance is overstated when a combination of rows is lighter than every row.

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

ROOT CAUSE

dmin is computed from the generator rows rather than from all nonzero codewords.

THE FAILURE

dmin is computed from the generator rows rather than from all nonzero codewords.

Unsuccessful approach: Including weight 0 in the search always reports distance 0.

Case contract

Weight distribution of the binary linear code spanned by the rows of generator matrix G (rows may be dependent). Enumerate all 2^k messages including the zero message, form codewords as XOR combinations of rows, and histogram their Hamming weights (index 0..n). dmin is the smallest nonzero weight present (0 if the code is only the zero word). Return [histogram, dmin].

Why this case matters

Code designers use weight enumerators to estimate undetected-error probability and minimum distance.

1 / The failure

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

N = 1
observations = []
def solve(G):
    k, n = len(G), len(G[0])
    hist = [0] * (n + 1)
    for msg in range(2 ** k):
        c = [0] * n
        for i in range(k):
            if msg >> i & 1:
                c = [a ^ b for a, b in zip(c, G[i])]
        hist[sum(c)] += 1
    dmin = min(sum(row) for row in G)
    return [hist, dmin]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression [[[1, 1, 0, 0, 0], [1, 1, 0, 0, 1], [0, 0, 1, 1, 1], [1, 1, 0, 0, 1]]]', [[[1, 1, 0, 0, 0], [1, 1, 0, 0, 1], [0, 0, 1, 1, 1], [1, 1, 0, 0, 1]]], [[2, 2, 4, 4, 2, 2], 1]], ['regression [[[0, 0, 0, 1, 0, 1, 1], [1, 0, 0, 1, 1, 1, 0], [0, 0, 0, 1, 1, 0, ...', [[[0, 0, 0, 1, 0, 1, 1], [1, 0, 0, 1, 1, 1, 0], [0, 0, 0, 1, 1, 0, 1], [0, 0, 0, 1, 1, 0, 0]]], [[1, 1, 6, 6, 1, 1, 0, 0], 1]], ['partial-repair [[[1, 0, 0, 0, 1, 1, 0], [0, 1, 0, 0, 1, 0, 1], [0, 0, 1, 0, 0, 1, ...', [[[1, 0, 0, 0, 1, 1, 0], [0, 1, 0, 0, 1, 0, 1], [0, 0, 1, 0, 0, 1, 1], [0, 0, 0, 1, 1, 1, 1]]], [[1, 0, 0, 7, 7, 0, 0, 1], 3]], ['partial-repair [[[1, 1, 1]]]', [[[1, 1, 1]]], [[1, 0, 0, 1], 3]], ['control [[[0, 0, 0]]]', [[[0, 0, 0]]], [[2, 0, 0, 0], 0]], ['control [[[1, 1, 0, 0], [0, 1, 1, 0], [0, 0, 1, 1]]]', [[[1, 1, 0, 0], [0, 1, 1, 0], [0, 0, 1, 1]]], [[1, 0, 6, 0, 1], 2]], ['control [[[1, 0, 1, 1, 0], [0, 1, 1, 1, 1]]]', [[[1, 0, 1, 1, 0], [0, 1, 1, 1, 1]]], [[1, 0, 0, 2, 1, 0], 3]], ['control [[[1, 1, 0], [1, 1, 0]]]', [[[1, 1, 0], [1, 1, 0]]], [[2, 0, 2, 0], 2]]], [['regression [[[0, 0, 1, 0, 1, 1, 1], [0, 1, 0, 1, 0, 1, 1], [1, 1, 1, 0, 1, 1, ...', [[[0, 0, 1, 0, 1, 1, 1], [0, 1, 0, 1, 0, 1, 1], [1, 1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0, 1]]], [[1, 1, 1, 4, 5, 3, 1, 0], 1]], ['regression [[[0, 1, 1, 1, 1, 0, 0], [0, 1, 1, 0, 1, 1, 1], [1, 0, 0, 0, 1, 1, ...', [[[0, 1, 1, 1, 1, 0, 0], [0, 1, 1, 0, 1, 1, 1], [1, 0, 0, 0, 1, 1, 1]]], [[1, 0, 0, 3, 2, 1, 1, 0], 3]], ['partial-repair [[[1, 0, 1, 1, 0], [0, 1, 1, 1, 1]]]', [[[1, 0, 1, 1, 0], [0, 1, 1, 1, 1]]], [[1, 0, 0, 2, 1, 0], 3]], ['partial-repair [[[1, 1, 0], [1, 1, 0]]]', [[[1, 1, 0], [1, 1, 0]]], [[2, 0, 2, 0], 2]], ['control [[[0, 0, 0]]]', [[[0, 0, 0]]], [[2, 0, 0, 0], 0]], ['control [[[1, 1, 0, 0, 0], [1, 1, 0, 0, 1], [0, 0, 1, 1, 1], [1, 1, 0, 0, 1]]]', [[[1, 1, 0, 0, 0], [1, 1, 0, 0, 1], [0, 0, 1, 1, 1], [1, 1, 0, 0, 1]]], [[2, 2, 4, 4, 2, 2], 1]], ['control [[[0, 0, 0, 1, 0, 1, 1], [1, 0, 0, 1, 1, 1, 0], [0, 0, 0, 1, 1, 0, ...', [[[0, 0, 0, 1, 0, 1, 1], [1, 0, 0, 1, 1, 1, 0], [0, 0, 0, 1, 1, 0, 1], [0, 0, 0, 1, 1, 0, 0]]], [[1, 1, 6, 6, 1, 1, 0, 0], 1]], ['control [[[1, 1, 1, 1, 1, 1, 1], [1, 0, 1, 1, 1, 0, 0], [0, 1, 1, 0, 0, 0, ...', [[[1, 1, 1, 1, 1, 1, 1], [1, 0, 1, 1, 1, 0, 0], [0, 1, 1, 0, 0, 0, 0], [1, 1, 1, 0, 0, 1, 0]]], [[1, 0, 2, 5, 5, 2, 0, 1], 2]]], [['regression [[[0, 0, 0, 1, 0, 1, 1], [1, 0, 0, 1, 1, 1, 0], [0, 0, 0, 1, 1, 0, ...', [[[0, 0, 0, 1, 0, 1, 1], [1, 0, 0, 1, 1, 1, 0], [0, 0, 0, 1, 1, 0, 1], [0, 0, 0, 1, 1, 0, 0]]], [[1, 1, 6, 6, 1, 1, 0, 0], 1]], ['regression [[[1, 0, 0, 1, 1, 0], [1, 1, 1, 0, 0, 0], [1, 0, 1, 1, 1, 0]]]', [[[1, 0, 0, 1, 1, 0], [1, 1, 1, 0, 0, 0], [1, 0, 1, 1, 1, 0]]], [[1, 1, 1, 3, 2, 0, 0], 1]], ['partial-repair [[[1, 1, 1, 1, 1, 1, 1], [1, 0, 1, 1, 1, 0, 0], [0, 1, 1, 0, 0, 0, ...', [[[1, 1, 1, 1, 1, 1, 1], [1, 0, 1, 1, 1, 0, 0], [0, 1, 1, 0, 0, 0, 0], [1, 1, 1, 0, 0, 1, 0]]], [[1, 0, 2, 5, 5, 2, 0, 1], 2]], ['control [[[0, 0, 0]]]', [[[0, 0, 0]]], [[2, 0, 0, 0], 0]], ['control [[[1, 1, 1, 0, 0, 0, 1]]]', [[[1, 1, 1, 0, 0, 0, 1]]], [[1, 0, 0, 0, 1, 0, 0, 0], 4]], ['control [[[1, 0, 1, 1], [0, 0, 0, 1]]]', [[[1, 0, 1, 1], [0, 0, 0, 1]]], [[1, 1, 1, 1, 0], 1]], ['control [[[1, 0]]]', [[[1, 0]]], [[1, 1, 0], 1]], ['control [[[0, 0, 1, 0, 1, 1, 1], [0, 1, 0, 1, 0, 1, 1], [1, 1, 1, 0, 1, 1, ...', [[[0, 0, 1, 0, 1, 1, 1], [0, 1, 0, 1, 0, 1, 1], [1, 1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0, 1]]], [[1, 1, 1, 4, 5, 3, 1, 0], 1]]], [['regression [[[0, 1, 1, 1, 1, 0, 0], [0, 1, 1, 0, 1, 1, 1], [1, 0, 0, 0, 1, 1, ...', [[[0, 1, 1, 1, 1, 0, 0], [0, 1, 1, 0, 1, 1, 1], [1, 0, 0, 0, 1, 1, 1]]], [[1, 0, 0, 3, 2, 1, 1, 0], 3]], ['regression [[[1, 1, 0, 0, 0], [1, 1, 0, 0, 1], [0, 0, 1, 1, 1], [1, 1, 0, 0, 1]]]', [[[1, 1, 0, 0, 0], [1, 1, 0, 0, 1], [0, 0, 1, 1, 1], [1, 1, 0, 0, 1]]], [[2, 2, 4, 4, 2, 2], 1]], ['partial-repair [[[1, 0, 0, 1, 1, 0], [1, 1, 1, 0, 0, 0], [1, 0, 1, 1, 1, 0]]]', [[[1, 0, 0, 1, 1, 0], [1, 1, 1, 0, 0, 0], [1, 0, 1, 1, 1, 0]]], [[1, 1, 1, 3, 2, 0, 0], 1]], ['partial-repair [[[1, 1, 1, 0, 0, 0, 1]]]', [[[1, 1, 1, 0, 0, 0, 1]]], [[1, 0, 0, 0, 1, 0, 0, 0], 4]], ['control [[[0, 0, 0]]]', [[[0, 0, 0]]], [[2, 0, 0, 0], 0]], ['control [[[0, 1, 0, 0, 1, 0, 0], [1, 1, 1, 0, 1, 1, 0], [1, 1, 0, 1, 1, 1, ...', [[[0, 1, 0, 0, 1, 0, 0], [1, 1, 1, 0, 1, 1, 0], [1, 1, 0, 1, 1, 1, 0]]], [[1, 0, 2, 2, 1, 2, 0, 0], 2]], ['control [[[0, 0, 1], [1, 1, 0]]]', [[[0, 0, 1], [1, 1, 0]]], [[1, 1, 1, 1], 1]], ['control [[[0, 0, 1, 0]]]', [[[0, 0, 1, 0]]], [[1, 1, 0, 0, 0], 1]]], [['regression [[[1, 0, 0, 1, 1, 0], [1, 1, 1, 0, 0, 0], [1, 0, 1, 1, 1, 0]]]', [[[1, 0, 0, 1, 1, 0], [1, 1, 1, 0, 0, 0], [1, 0, 1, 1, 1, 0]]], [[1, 1, 1, 3, 2, 0, 0], 1]], ['regression [[[0, 0, 1, 0, 1, 1, 1], [0, 1, 0, 1, 0, 1, 1], [1, 1, 1, 0, 1, 1, ...', [[[0, 0, 1, 0, 1, 1, 1], [0, 1, 0, 1, 0, 1, 1], [1, 1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0, 1]]], [[1, 1, 1, 4, 5, 3, 1, 0], 1]], ['partial-repair [[[1, 0]]]', [[[1, 0]]], [[1, 1, 0], 1]], ['control [[[0, 0, 0]]]', [[[0, 0, 0]]], [[2, 0, 0, 0], 0]], ['control [[[1, 0, 0, 0, 1, 1, 0], [0, 1, 0, 0, 1, 0, 1], [0, 0, 1, 0, 0, 1, ...', [[[1, 0, 0, 0, 1, 1, 0], [0, 1, 0, 0, 1, 0, 1], [0, 0, 1, 0, 0, 1, 1], [0, 0, 0, 1, 1, 1, 1]]], [[1, 0, 0, 7, 7, 0, 0, 1], 3]], ['control [[[1, 1, 1]]]', [[[1, 1, 1]]], [[1, 0, 0, 1], 3]], ['control [[[1, 1, 0, 0], [0, 1, 1, 0], [0, 0, 1, 1]]]', [[[1, 1, 0, 0], [0, 1, 1, 0], [0, 0, 1, 1]]], [[1, 0, 6, 0, 1], 2]], ['control [[[1, 0, 1, 1, 0], [0, 1, 1, 1, 1]]]', [[[1, 0, 1, 1, 0], [0, 1, 1, 1, 1]]], [[1, 0, 0, 2, 1, 0], 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
regression [[[1, 1, 0, 0, 0], [1, 1, 0, 0, 1], [0, 0, 1, 1, 1], [1, 1, 0, 0, 1]]][[2, 2, 4, 4, 2, 2], 2][[2, 2, 4, 4, 2, 2], 1]Failed
regression [[[0, 0, 0, 1, 0, 1, 1], [1, 0, 0, 1, 1, 1, 0], [0, 0, 0, 1, 1, 0, ...[[1, 1, 6, 6, 1, 1, 0, 0], 2][[1, 1, 6, 6, 1, 1, 0, 0], 1]Failed
partial-repair [[[1, 0, 0, 0, 1, 1, 0], [0, 1, 0, 0, 1, 0, 1], [0, 0, 1, 0, 0, 1, ...[[1, 0, 0, 7, 7, 0, 0, 1], 3][[1, 0, 0, 7, 7, 0, 0, 1], 3]Passed
partial-repair [[[1, 1, 1]]][[1, 0, 0, 1], 3][[1, 0, 0, 1], 3]Passed
control [[[0, 0, 0]]][[2, 0, 0, 0], 0][[2, 0, 0, 0], 0]Passed
control [[[1, 1, 0, 0], [0, 1, 1, 0], [0, 0, 1, 1]]][[1, 0, 6, 0, 1], 2][[1, 0, 6, 0, 1], 2]Passed
control [[[1, 0, 1, 1, 0], [0, 1, 1, 1, 1]]][[1, 0, 0, 2, 1, 0], 3][[1, 0, 0, 2, 1, 0], 3]Passed
control [[[1, 1, 0], [1, 1, 0]]][[2, 0, 2, 0], 2][[2, 0, 2, 0], 2]Passed

SHA-256 / 7418cc3e62934522aca00556eb2408f1a100f2347795c03c9c8a1d93fbf38509

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(G):
    k, n = len(G), len(G[0])
    hist = [0] * (n + 1)
    for msg in range(2 ** k):
        c = [0] * n
        for i in range(k):
            if msg >> i & 1:
                c = [a ^ b for a, b in zip(c, G[i])]
        hist[sum(c)] += 1
    dmin = min(w for w in range(0, n + 1) if hist[w]) if any(hist[1:]) else 0
    return [hist, dmin]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression [[[1, 1, 0, 0, 0], [1, 1, 0, 0, 1], [0, 0, 1, 1, 1], [1, 1, 0, 0, 1]]]', [[[1, 1, 0, 0, 0], [1, 1, 0, 0, 1], [0, 0, 1, 1, 1], [1, 1, 0, 0, 1]]], [[2, 2, 4, 4, 2, 2], 1]], ['regression [[[0, 0, 0, 1, 0, 1, 1], [1, 0, 0, 1, 1, 1, 0], [0, 0, 0, 1, 1, 0, ...', [[[0, 0, 0, 1, 0, 1, 1], [1, 0, 0, 1, 1, 1, 0], [0, 0, 0, 1, 1, 0, 1], [0, 0, 0, 1, 1, 0, 0]]], [[1, 1, 6, 6, 1, 1, 0, 0], 1]], ['partial-repair [[[1, 0, 0, 0, 1, 1, 0], [0, 1, 0, 0, 1, 0, 1], [0, 0, 1, 0, 0, 1, ...', [[[1, 0, 0, 0, 1, 1, 0], [0, 1, 0, 0, 1, 0, 1], [0, 0, 1, 0, 0, 1, 1], [0, 0, 0, 1, 1, 1, 1]]], [[1, 0, 0, 7, 7, 0, 0, 1], 3]], ['partial-repair [[[1, 1, 1]]]', [[[1, 1, 1]]], [[1, 0, 0, 1], 3]], ['control [[[0, 0, 0]]]', [[[0, 0, 0]]], [[2, 0, 0, 0], 0]], ['control [[[1, 1, 0, 0], [0, 1, 1, 0], [0, 0, 1, 1]]]', [[[1, 1, 0, 0], [0, 1, 1, 0], [0, 0, 1, 1]]], [[1, 0, 6, 0, 1], 2]], ['control [[[1, 0, 1, 1, 0], [0, 1, 1, 1, 1]]]', [[[1, 0, 1, 1, 0], [0, 1, 1, 1, 1]]], [[1, 0, 0, 2, 1, 0], 3]], ['control [[[1, 1, 0], [1, 1, 0]]]', [[[1, 1, 0], [1, 1, 0]]], [[2, 0, 2, 0], 2]]], [['regression [[[0, 0, 1, 0, 1, 1, 1], [0, 1, 0, 1, 0, 1, 1], [1, 1, 1, 0, 1, 1, ...', [[[0, 0, 1, 0, 1, 1, 1], [0, 1, 0, 1, 0, 1, 1], [1, 1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0, 1]]], [[1, 1, 1, 4, 5, 3, 1, 0], 1]], ['regression [[[0, 1, 1, 1, 1, 0, 0], [0, 1, 1, 0, 1, 1, 1], [1, 0, 0, 0, 1, 1, ...', [[[0, 1, 1, 1, 1, 0, 0], [0, 1, 1, 0, 1, 1, 1], [1, 0, 0, 0, 1, 1, 1]]], [[1, 0, 0, 3, 2, 1, 1, 0], 3]], ['partial-repair [[[1, 0, 1, 1, 0], [0, 1, 1, 1, 1]]]', [[[1, 0, 1, 1, 0], [0, 1, 1, 1, 1]]], [[1, 0, 0, 2, 1, 0], 3]], ['partial-repair [[[1, 1, 0], [1, 1, 0]]]', [[[1, 1, 0], [1, 1, 0]]], [[2, 0, 2, 0], 2]], ['control [[[0, 0, 0]]]', [[[0, 0, 0]]], [[2, 0, 0, 0], 0]], ['control [[[1, 1, 0, 0, 0], [1, 1, 0, 0, 1], [0, 0, 1, 1, 1], [1, 1, 0, 0, 1]]]', [[[1, 1, 0, 0, 0], [1, 1, 0, 0, 1], [0, 0, 1, 1, 1], [1, 1, 0, 0, 1]]], [[2, 2, 4, 4, 2, 2], 1]], ['control [[[0, 0, 0, 1, 0, 1, 1], [1, 0, 0, 1, 1, 1, 0], [0, 0, 0, 1, 1, 0, ...', [[[0, 0, 0, 1, 0, 1, 1], [1, 0, 0, 1, 1, 1, 0], [0, 0, 0, 1, 1, 0, 1], [0, 0, 0, 1, 1, 0, 0]]], [[1, 1, 6, 6, 1, 1, 0, 0], 1]], ['control [[[1, 1, 1, 1, 1, 1, 1], [1, 0, 1, 1, 1, 0, 0], [0, 1, 1, 0, 0, 0, ...', [[[1, 1, 1, 1, 1, 1, 1], [1, 0, 1, 1, 1, 0, 0], [0, 1, 1, 0, 0, 0, 0], [1, 1, 1, 0, 0, 1, 0]]], [[1, 0, 2, 5, 5, 2, 0, 1], 2]]], [['regression [[[0, 0, 0, 1, 0, 1, 1], [1, 0, 0, 1, 1, 1, 0], [0, 0, 0, 1, 1, 0, ...', [[[0, 0, 0, 1, 0, 1, 1], [1, 0, 0, 1, 1, 1, 0], [0, 0, 0, 1, 1, 0, 1], [0, 0, 0, 1, 1, 0, 0]]], [[1, 1, 6, 6, 1, 1, 0, 0], 1]], ['regression [[[1, 0, 0, 1, 1, 0], [1, 1, 1, 0, 0, 0], [1, 0, 1, 1, 1, 0]]]', [[[1, 0, 0, 1, 1, 0], [1, 1, 1, 0, 0, 0], [1, 0, 1, 1, 1, 0]]], [[1, 1, 1, 3, 2, 0, 0], 1]], ['partial-repair [[[1, 1, 1, 1, 1, 1, 1], [1, 0, 1, 1, 1, 0, 0], [0, 1, 1, 0, 0, 0, ...', [[[1, 1, 1, 1, 1, 1, 1], [1, 0, 1, 1, 1, 0, 0], [0, 1, 1, 0, 0, 0, 0], [1, 1, 1, 0, 0, 1, 0]]], [[1, 0, 2, 5, 5, 2, 0, 1], 2]], ['control [[[0, 0, 0]]]', [[[0, 0, 0]]], [[2, 0, 0, 0], 0]], ['control [[[1, 1, 1, 0, 0, 0, 1]]]', [[[1, 1, 1, 0, 0, 0, 1]]], [[1, 0, 0, 0, 1, 0, 0, 0], 4]], ['control [[[1, 0, 1, 1], [0, 0, 0, 1]]]', [[[1, 0, 1, 1], [0, 0, 0, 1]]], [[1, 1, 1, 1, 0], 1]], ['control [[[1, 0]]]', [[[1, 0]]], [[1, 1, 0], 1]], ['control [[[0, 0, 1, 0, 1, 1, 1], [0, 1, 0, 1, 0, 1, 1], [1, 1, 1, 0, 1, 1, ...', [[[0, 0, 1, 0, 1, 1, 1], [0, 1, 0, 1, 0, 1, 1], [1, 1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0, 1]]], [[1, 1, 1, 4, 5, 3, 1, 0], 1]]], [['regression [[[0, 1, 1, 1, 1, 0, 0], [0, 1, 1, 0, 1, 1, 1], [1, 0, 0, 0, 1, 1, ...', [[[0, 1, 1, 1, 1, 0, 0], [0, 1, 1, 0, 1, 1, 1], [1, 0, 0, 0, 1, 1, 1]]], [[1, 0, 0, 3, 2, 1, 1, 0], 3]], ['regression [[[1, 1, 0, 0, 0], [1, 1, 0, 0, 1], [0, 0, 1, 1, 1], [1, 1, 0, 0, 1]]]', [[[1, 1, 0, 0, 0], [1, 1, 0, 0, 1], [0, 0, 1, 1, 1], [1, 1, 0, 0, 1]]], [[2, 2, 4, 4, 2, 2], 1]], ['partial-repair [[[1, 0, 0, 1, 1, 0], [1, 1, 1, 0, 0, 0], [1, 0, 1, 1, 1, 0]]]', [[[1, 0, 0, 1, 1, 0], [1, 1, 1, 0, 0, 0], [1, 0, 1, 1, 1, 0]]], [[1, 1, 1, 3, 2, 0, 0], 1]], ['partial-repair [[[1, 1, 1, 0, 0, 0, 1]]]', [[[1, 1, 1, 0, 0, 0, 1]]], [[1, 0, 0, 0, 1, 0, 0, 0], 4]], ['control [[[0, 0, 0]]]', [[[0, 0, 0]]], [[2, 0, 0, 0], 0]], ['control [[[0, 1, 0, 0, 1, 0, 0], [1, 1, 1, 0, 1, 1, 0], [1, 1, 0, 1, 1, 1, ...', [[[0, 1, 0, 0, 1, 0, 0], [1, 1, 1, 0, 1, 1, 0], [1, 1, 0, 1, 1, 1, 0]]], [[1, 0, 2, 2, 1, 2, 0, 0], 2]], ['control [[[0, 0, 1], [1, 1, 0]]]', [[[0, 0, 1], [1, 1, 0]]], [[1, 1, 1, 1], 1]], ['control [[[0, 0, 1, 0]]]', [[[0, 0, 1, 0]]], [[1, 1, 0, 0, 0], 1]]], [['regression [[[1, 0, 0, 1, 1, 0], [1, 1, 1, 0, 0, 0], [1, 0, 1, 1, 1, 0]]]', [[[1, 0, 0, 1, 1, 0], [1, 1, 1, 0, 0, 0], [1, 0, 1, 1, 1, 0]]], [[1, 1, 1, 3, 2, 0, 0], 1]], ['regression [[[0, 0, 1, 0, 1, 1, 1], [0, 1, 0, 1, 0, 1, 1], [1, 1, 1, 0, 1, 1, ...', [[[0, 0, 1, 0, 1, 1, 1], [0, 1, 0, 1, 0, 1, 1], [1, 1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0, 1]]], [[1, 1, 1, 4, 5, 3, 1, 0], 1]], ['partial-repair [[[1, 0]]]', [[[1, 0]]], [[1, 1, 0], 1]], ['control [[[0, 0, 0]]]', [[[0, 0, 0]]], [[2, 0, 0, 0], 0]], ['control [[[1, 0, 0, 0, 1, 1, 0], [0, 1, 0, 0, 1, 0, 1], [0, 0, 1, 0, 0, 1, ...', [[[1, 0, 0, 0, 1, 1, 0], [0, 1, 0, 0, 1, 0, 1], [0, 0, 1, 0, 0, 1, 1], [0, 0, 0, 1, 1, 1, 1]]], [[1, 0, 0, 7, 7, 0, 0, 1], 3]], ['control [[[1, 1, 1]]]', [[[1, 1, 1]]], [[1, 0, 0, 1], 3]], ['control [[[1, 1, 0, 0], [0, 1, 1, 0], [0, 0, 1, 1]]]', [[[1, 1, 0, 0], [0, 1, 1, 0], [0, 0, 1, 1]]], [[1, 0, 6, 0, 1], 2]], ['control [[[1, 0, 1, 1, 0], [0, 1, 1, 1, 1]]]', [[[1, 0, 1, 1, 0], [0, 1, 1, 1, 1]]], [[1, 0, 0, 2, 1, 0], 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
regression [[[1, 1, 0, 0, 0], [1, 1, 0, 0, 1], [0, 0, 1, 1, 1], [1, 1, 0, 0, 1]]][[2, 2, 4, 4, 2, 2], 0][[2, 2, 4, 4, 2, 2], 1]Failed
regression [[[0, 0, 0, 1, 0, 1, 1], [1, 0, 0, 1, 1, 1, 0], [0, 0, 0, 1, 1, 0, ...[[1, 1, 6, 6, 1, 1, 0, 0], 0][[1, 1, 6, 6, 1, 1, 0, 0], 1]Failed
partial-repair [[[1, 0, 0, 0, 1, 1, 0], [0, 1, 0, 0, 1, 0, 1], [0, 0, 1, 0, 0, 1, ...[[1, 0, 0, 7, 7, 0, 0, 1], 0][[1, 0, 0, 7, 7, 0, 0, 1], 3]Failed
partial-repair [[[1, 1, 1]]][[1, 0, 0, 1], 0][[1, 0, 0, 1], 3]Failed
control [[[0, 0, 0]]][[2, 0, 0, 0], 0][[2, 0, 0, 0], 0]Passed
control [[[1, 1, 0, 0], [0, 1, 1, 0], [0, 0, 1, 1]]][[1, 0, 6, 0, 1], 0][[1, 0, 6, 0, 1], 2]Failed
control [[[1, 0, 1, 1, 0], [0, 1, 1, 1, 1]]][[1, 0, 0, 2, 1, 0], 0][[1, 0, 0, 2, 1, 0], 3]Failed
control [[[1, 1, 0], [1, 1, 0]]][[2, 0, 2, 0], 0][[2, 0, 2, 0], 2]Failed

SHA-256 / 6373818cfdafff9294471df28800dfb34617b6247be96faeef441b4df1cd0eea

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, bounded teaching model of the named code under the stated contract; not a production codec. 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 2026-09-29T14:48:37.279988+00:00.

Case digest / 24965b26dc003731a3011afbef3be0ff95703277a824b7395a6d79472d8a0047