FAILURE MAP
← Case archive

FA-71951 / Error-correcting codes / Open access

Viterbi scores a pair mismatch as one error · case 01

Pairs with both bits wrong are penalised like a single error, so wrong paths win.

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

ROOT CAUSE

The branch metric adds (o0 != y0) or (o1 != y1) instead of the sum of both mismatches.

THE FAILURE

The branch metric adds (o0 != y0) or (o1 != y1) instead of the sum of both mismatches.

Unsuccessful approach: Weighting the first bit double is not a Hamming distance either.

Case contract

Hard-decision Viterbi decoder for the terminated K=3 (7,5) code (outputs g=7 then g=5 per step, two zero tail bits). Branch metric is the Hamming distance between the received pair and the branch output. Survivors keep the first strictly better candidate (states in ascending order, input 0 before 1). Decoding ends in state 0 and the two tail bits are removed. Return [decoded bits, final path metric]; odd or too-short input returns None.

Why this case matters

Receivers recover convolutionally coded frames by maximum-likelihood trellis search.

1 / The failure

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

N = 1
observations = []
def solve(r):
    if len(r) % 2 or len(r) < 4:
        return None
    INF = 10 ** 9
    metric = [0, INF, INF, INF]
    paths = [[], [], [], []]
    for t in range(len(r) // 2):
        y0, y1 = r[2 * t], r[2 * t + 1]
        new_m = [INF] * 4
        new_p = [None] * 4
        for st in range(4):
            if metric[st] >= INF:
                continue
            for b in (0, 1):
                reg = (b << 2) | st
                o0 = bin(reg & 7).count('1') % 2
                o1 = bin(reg & 5).count('1') % 2
                ns = reg >> 1
                m = metric[st] + ((o0 != y0) or (o1 != y1))
                if m < new_m[ns]:
                    new_m[ns] = m
                    new_p[ns] = paths[st] + [b]
        metric, paths = new_m, new_p
    return [paths[0][:-2], metric[0]]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression [[1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]]', [[1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]], [[1, 1, 0, 0, 0, 0], 2]], ['regression [[1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1]]', [[1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1]], [[1, 0, 1, 0, 0, 0, 1, 0, 1], 2]], ['partial-repair [[0, 1, 0, 1, 0, 1, 1, 1, 0, 1]]', [[0, 1, 0, 1, 0, 1, 1, 1, 0, 1]], [[1, 1, 0], 2]], ['partial-repair [[0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0]]', [[0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0]], [[0, 1, 0, 0], 2]], ['control [[1, 1, 0, 1, 0, 1, 1, 1, 0, 0]]', [[1, 1, 0, 1, 0, 1, 1, 1, 0, 0]], [[1, 1, 0], 0]], ['control [[1, 1, 0, 0, 0, 1, 1, 1, 0, 0]]', [[1, 1, 0, 0, 0, 1, 1, 1, 0, 0]], [[1, 1, 0], 1]], ['control [[1, 1, 0, 1, 0, 1, 1, 0, 0, 1]]', [[1, 1, 0, 1, 0, 1, 1, 0, 0, 1]], [[1, 1, 0], 2]], ['control [[0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0]]', [[0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0]], [[0, 1, 0, 0], 0]]], [['regression [[1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]]', [[1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]], [[1, 1, 0, 0, 0, 0], 2]], ['regression [[1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1]]', [[1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1]], [[1, 0, 1, 0, 0, 0, 1, 0, 1], 2]], ['partial-repair [[0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1]]', [[0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1]], [[0, 1, 0, 1, 1], 1]], ['control [[0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1]]', [[0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1]], [[0, 1, 0, 0], 2]], ['control [[1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0]]', [[1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0]], [[1, 0, 1, 0, 0], 0]], ['control [[1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0]]', [[1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0]], [[1, 0, 1, 0, 0], 1]], ['control [[1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1]]', [[1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1]], [[1, 0, 1, 0, 0], 2]], ['control [[1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]]', [[1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]], [[1, 1, 0, 0, 0, 0], 0]]], [['regression [[1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]]', [[1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]], [[1, 1, 0, 0, 0, 0], 2]], ['regression [[1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1]]', [[1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1]], [[1, 0, 1, 0, 0, 0, 1, 0, 1], 2]], ['partial-repair [[0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1]]', [[0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1]], [[0, 0, 0, 1, 0, 1], 1]], ['partial-repair [[0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1]]', [[0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1]], [[0, 0, 0, 1, 0, 1], 2]], ['control [[1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0]]', [[1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0]], [[1, 1, 0, 0, 0, 0], 1]], ['control [[1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1]]', [[1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1]], [[1, 1, 0, 0, 0, 0], 2]], ['control [[1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1]]', [[1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1]], [[1, 0, 0, 0, 1, 1, 1], 0]], ['control [[1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1]]', [[1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1]], [[1, 0, 0, 0, 1, 1, 1], 1]]], [['regression [[1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]]', [[1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]], [[1, 1, 0, 0, 0, 0], 2]], ['regression [[1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1]]', [[1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1]], [[1, 0, 1, 0, 0, 0, 1, 0, 1], 2]], ['partial-repair [[0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1]]', [[0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1]], [[0, 1, 0, 1], 2]], ['partial-repair [[1, 1, 1, 0]]', [[1, 1, 1, 0]], [[], 3]], ['control [[1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0]]', [[1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0]], [[1, 0, 0, 0, 1, 1, 1], 2]], ['control [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1]]', [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1]], [[0, 0, 0, 0, 0, 0, 1, 1], 0]], ['control [[0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1]]', [[0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1]], [[0, 0, 0, 0, 0, 0, 1, 1], 1]], ['control [[0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0]]', [[0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0]], [[0, 0, 0, 0, 0, 0, 1, 1], 2]]], [['regression [[1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]]', [[1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]], [[1, 1, 0, 0, 0, 0], 2]], ['regression [[1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1]]', [[1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1]], [[1, 0, 1, 0, 0, 0, 1, 0, 1], 2]], ['partial-repair [[0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0]]', [[0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0]], [[0, 1, 0, 0], 2]], ['partial-repair [[1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0]]', [[1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0]], [[1, 0, 1, 0, 0], 2]], ['control [[0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1]]', [[0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1]], [[0, 1, 0, 1, 1], 0]], ['control [[0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0]]', [[0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0]], [[0, 1, 0, 1, 1], 2]], ['control [[0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1]]', [[0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1]], [[0, 0, 0, 1, 0, 1], 0]], ['control [[0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0]]', [[0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0]], [[0, 0, 0, 1, 0, 1], 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
regression [[1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]][[1, 1, 0, 0, 0, 0], 1][[1, 1, 0, 0, 0, 0], 2]Failed
regression [[1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1]][[1, 0, 0, 0, 0, 0, 1, 0, 1], 2][[1, 0, 1, 0, 0, 0, 1, 0, 1], 2]Failed
partial-repair [[0, 1, 0, 1, 0, 1, 1, 1, 0, 1]][[1, 1, 0], 2][[1, 1, 0], 2]Passed
partial-repair [[0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0]][[0, 1, 0, 0], 2][[0, 1, 0, 0], 2]Passed
control [[1, 1, 0, 1, 0, 1, 1, 1, 0, 0]][[1, 1, 0], 0][[1, 1, 0], 0]Passed
control [[1, 1, 0, 0, 0, 1, 1, 1, 0, 0]][[1, 1, 0], 1][[1, 1, 0], 1]Passed
control [[1, 1, 0, 1, 0, 1, 1, 0, 0, 1]][[1, 1, 0], 2][[1, 1, 0], 2]Passed
control [[0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0]][[0, 1, 0, 0], 0][[0, 1, 0, 0], 0]Passed

SHA-256 / a4960082dc6c87f7dc4c219912b51048046409895fc6a70f9e7cad99084b6e97

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(r):
    if len(r) % 2 or len(r) < 4:
        return None
    INF = 10 ** 9
    metric = [0, INF, INF, INF]
    paths = [[], [], [], []]
    for t in range(len(r) // 2):
        y0, y1 = r[2 * t], r[2 * t + 1]
        new_m = [INF] * 4
        new_p = [None] * 4
        for st in range(4):
            if metric[st] >= INF:
                continue
            for b in (0, 1):
                reg = (b << 2) | st
                o0 = bin(reg & 7).count('1') % 2
                o1 = bin(reg & 5).count('1') % 2
                ns = reg >> 1
                m = metric[st] + 2 * (o0 != y0) + (o1 != y1)
                if m < new_m[ns]:
                    new_m[ns] = m
                    new_p[ns] = paths[st] + [b]
        metric, paths = new_m, new_p
    return [paths[0][:-2], metric[0]]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression [[1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]]', [[1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]], [[1, 1, 0, 0, 0, 0], 2]], ['regression [[1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1]]', [[1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1]], [[1, 0, 1, 0, 0, 0, 1, 0, 1], 2]], ['partial-repair [[0, 1, 0, 1, 0, 1, 1, 1, 0, 1]]', [[0, 1, 0, 1, 0, 1, 1, 1, 0, 1]], [[1, 1, 0], 2]], ['partial-repair [[0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0]]', [[0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0]], [[0, 1, 0, 0], 2]], ['control [[1, 1, 0, 1, 0, 1, 1, 1, 0, 0]]', [[1, 1, 0, 1, 0, 1, 1, 1, 0, 0]], [[1, 1, 0], 0]], ['control [[1, 1, 0, 0, 0, 1, 1, 1, 0, 0]]', [[1, 1, 0, 0, 0, 1, 1, 1, 0, 0]], [[1, 1, 0], 1]], ['control [[1, 1, 0, 1, 0, 1, 1, 0, 0, 1]]', [[1, 1, 0, 1, 0, 1, 1, 0, 0, 1]], [[1, 1, 0], 2]], ['control [[0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0]]', [[0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0]], [[0, 1, 0, 0], 0]]], [['regression [[1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]]', [[1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]], [[1, 1, 0, 0, 0, 0], 2]], ['regression [[1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1]]', [[1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1]], [[1, 0, 1, 0, 0, 0, 1, 0, 1], 2]], ['partial-repair [[0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1]]', [[0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1]], [[0, 1, 0, 1, 1], 1]], ['control [[0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1]]', [[0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1]], [[0, 1, 0, 0], 2]], ['control [[1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0]]', [[1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0]], [[1, 0, 1, 0, 0], 0]], ['control [[1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0]]', [[1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0]], [[1, 0, 1, 0, 0], 1]], ['control [[1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1]]', [[1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1]], [[1, 0, 1, 0, 0], 2]], ['control [[1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]]', [[1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]], [[1, 1, 0, 0, 0, 0], 0]]], [['regression [[1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]]', [[1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]], [[1, 1, 0, 0, 0, 0], 2]], ['regression [[1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1]]', [[1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1]], [[1, 0, 1, 0, 0, 0, 1, 0, 1], 2]], ['partial-repair [[0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1]]', [[0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1]], [[0, 0, 0, 1, 0, 1], 1]], ['partial-repair [[0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1]]', [[0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1]], [[0, 0, 0, 1, 0, 1], 2]], ['control [[1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0]]', [[1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0]], [[1, 1, 0, 0, 0, 0], 1]], ['control [[1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1]]', [[1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1]], [[1, 1, 0, 0, 0, 0], 2]], ['control [[1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1]]', [[1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1]], [[1, 0, 0, 0, 1, 1, 1], 0]], ['control [[1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1]]', [[1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1]], [[1, 0, 0, 0, 1, 1, 1], 1]]], [['regression [[1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]]', [[1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]], [[1, 1, 0, 0, 0, 0], 2]], ['regression [[1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1]]', [[1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1]], [[1, 0, 1, 0, 0, 0, 1, 0, 1], 2]], ['partial-repair [[0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1]]', [[0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1]], [[0, 1, 0, 1], 2]], ['partial-repair [[1, 1, 1, 0]]', [[1, 1, 1, 0]], [[], 3]], ['control [[1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0]]', [[1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0]], [[1, 0, 0, 0, 1, 1, 1], 2]], ['control [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1]]', [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1]], [[0, 0, 0, 0, 0, 0, 1, 1], 0]], ['control [[0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1]]', [[0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1]], [[0, 0, 0, 0, 0, 0, 1, 1], 1]], ['control [[0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0]]', [[0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0]], [[0, 0, 0, 0, 0, 0, 1, 1], 2]]], [['regression [[1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]]', [[1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]], [[1, 1, 0, 0, 0, 0], 2]], ['regression [[1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1]]', [[1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1]], [[1, 0, 1, 0, 0, 0, 1, 0, 1], 2]], ['partial-repair [[0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0]]', [[0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0]], [[0, 1, 0, 0], 2]], ['partial-repair [[1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0]]', [[1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0]], [[1, 0, 1, 0, 0], 2]], ['control [[0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1]]', [[0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1]], [[0, 1, 0, 1, 1], 0]], ['control [[0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0]]', [[0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0]], [[0, 1, 0, 1, 1], 2]], ['control [[0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1]]', [[0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1]], [[0, 0, 0, 1, 0, 1], 0]], ['control [[0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0]]', [[0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0]], [[0, 0, 0, 1, 0, 1], 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
regression [[1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]][[1, 1, 0, 0, 0, 0], 3][[1, 1, 0, 0, 0, 0], 2]Failed
regression [[1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1]][[1, 0, 1, 0, 0, 0, 1, 0, 1], 3][[1, 0, 1, 0, 0, 0, 1, 0, 1], 2]Failed
partial-repair [[0, 1, 0, 1, 0, 1, 1, 1, 0, 1]][[1, 1, 0], 3][[1, 1, 0], 2]Failed
partial-repair [[0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0]][[0, 1, 0, 0], 3][[0, 1, 0, 0], 2]Failed
control [[1, 1, 0, 1, 0, 1, 1, 1, 0, 0]][[1, 1, 0], 0][[1, 1, 0], 0]Passed
control [[1, 1, 0, 0, 0, 1, 1, 1, 0, 0]][[1, 1, 0], 1][[1, 1, 0], 1]Passed
control [[1, 1, 0, 1, 0, 1, 1, 0, 0, 1]][[1, 1, 0], 2][[1, 1, 0], 2]Passed
control [[0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0]][[0, 1, 0, 0], 0][[0, 1, 0, 0], 0]Passed

SHA-256 / 58cddef372a9ac9a3dbc5310ec18ac3dcf3bf908c0560cffc3ad20bfddfa3554

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.

Member access is invitation-based. Sign in with your invited account to inspect the repair.

Sign in to the archive ↗

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 2026-09-29T14:48:34.187353+00:00.

Case digest / 4cf14c9ec15a6e968924477c9c128f2f40435fd8bbc5b62d297d26dc488fc7e1