FA-71876 / Error-correcting codes / Open access

SECDED overall parity ignores the parity bit itself · case 01

Clean words with an odd number of data/check ones are misclassified.

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

ROOT CAUSE

p is computed over r[1:] only.

VERIFIED REPAIR

Compute the overall parity over all eight bits.

Unsuccessful approach: Using r[0] alone as the parity indicator ignores the other seven bits.

Case contract

Extended Hamming (8,4) SECDED decoder. r[0] is the overall parity bit; r[1..7] are Hamming positions 1..7 with data at 3, 5, 6, 7. s is the XOR of set positions 1..7 and p the parity of all eight bits. s=0,p=0: "clean"; p=1: single error at position s (s=0 means the overall parity bit) - "corrected"; s!=0,p=0: ["double", None]. Return [status, data]. Non-binary or wrong-length input returns None.

Why this case matters

ECC DRAM controllers must distinguish correctable single-bit errors from uncorrectable double-bit errors.

1 / The failure

Exit 1

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

N = 1
observations = []
def solve(r):
    if len(r) != 8 or any(b not in (0, 1) for b in r):
        return None
    s = 0
    for pos in range(1, 8):
        if r[pos]:
            s ^= pos
    p = sum(r[1:]) % 2
    c = list(r)
    if s == 0 and p == 0:
        status = 'clean'
    elif p == 1:
        status = 'corrected'
        c[s] ^= 1
    else:
        return ['double', None]
    return [status, [c[3], c[5], c[6], c[7]]]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression [[1, 0, 1, 0, 1, 0, 1, 0]]', [[1, 0, 1, 0, 1, 0, 1, 0]], ['clean', [0, 0, 1, 0]]], ['regression [[1, 0, 1, 0, 1, 1, 1, 0]]', [[1, 0, 1, 0, 1, 1, 1, 0]], ['corrected', [0, 0, 1, 0]]], ['partial-repair [[0, 1, 0, 0, 0, 0, 0, 0]]', [[0, 1, 0, 0, 0, 0, 0, 0]], ['corrected', [0, 0, 0, 0]]], ['partial-repair [[0, 1, 1, 0, 1, 1, 0, 1]]', [[0, 1, 1, 0, 1, 1, 0, 1]], ['corrected', [0, 0, 0, 1]]], ['control [[0, 0, 0, 0, 0, 0, 0, 0]]', [[0, 0, 0, 0, 0, 0, 0, 0]], ['clean', [0, 0, 0, 0]]], ['control [[0, 0, 0, 0, 0, 0, 1, 1]]', [[0, 0, 0, 0, 0, 0, 1, 1]], ['double', None]], ['control [[0, 1, 1, 0, 1, 0, 0, 1]]', [[0, 1, 1, 0, 1, 0, 0, 1]], ['clean', [0, 0, 0, 1]]], ['control [[0, 1, 0, 1, 1, 0, 0, 1]]', [[0, 1, 0, 1, 1, 0, 0, 1]], ['double', None]]], [['regression [[1, 1, 0, 0, 0, 0, 1, 1]]', [[1, 1, 0, 0, 0, 0, 1, 1]], ['clean', [0, 0, 1, 1]]], ['regression [[1, 1, 1, 0, 0, 0, 1, 1]]', [[1, 1, 1, 0, 0, 0, 1, 1]], ['corrected', [0, 0, 1, 1]]], ['partial-repair [[1, 0, 0, 1, 1, 0, 1, 0]]', [[1, 0, 0, 1, 1, 0, 1, 0]], ['double', None]], ['control [[0, 0, 1, 0, 0, 0, 1, 0]]', [[0, 0, 1, 0, 0, 0, 1, 0]], ['double', None]], ['control [[0, 0, 0, 0, 1, 1, 1, 1]]', [[0, 0, 0, 0, 1, 1, 1, 1]], ['clean', [0, 1, 1, 1]]], ['control [[0, 0, 0, 0, 0, 1, 1, 0]]', [[0, 0, 0, 0, 0, 1, 1, 0]], ['double', None]], ['control [[0, 1, 0, 1, 1, 0, 1, 0]]', [[0, 1, 0, 1, 1, 0, 1, 0]], ['clean', [1, 0, 1, 0]]], ['control [[0, 1, 1, 1, 0, 0, 1, 0]]', [[0, 1, 1, 1, 0, 0, 1, 0]], ['double', None]]], [['regression [[1, 1, 0, 0, 1, 1, 0, 0]]', [[1, 1, 0, 0, 1, 1, 0, 0]], ['clean', [0, 1, 0, 0]]], ['regression [[1, 1, 1, 0, 1, 1, 0, 0]]', [[1, 1, 1, 0, 1, 1, 0, 0]], ['corrected', [0, 1, 0, 0]]], ['partial-repair [[1, 0, 0, 0, 1, 0, 0, 0]]', [[1, 0, 0, 0, 1, 0, 0, 0]], ['double', None]], ['control [[0, 0, 1, 1, 0, 0, 1, 1]]', [[0, 0, 1, 1, 0, 0, 1, 1]], ['clean', [1, 0, 1, 1]]], ['control [[0, 0, 1, 1, 0, 1, 1, 0]]', [[0, 0, 1, 1, 0, 1, 1, 0]], ['double', None]], ['control [[0, 0, 1, 1, 1, 1, 0, 0]]', [[0, 0, 1, 1, 1, 1, 0, 0]], ['clean', [1, 1, 0, 0]]], ['control [[0, 0, 1, 0, 1, 0, 0, 0]]', [[0, 0, 1, 0, 1, 0, 0, 0]], ['double', None]], ['control [[0, 1, 0, 1, 0, 1, 0, 1]]', [[0, 1, 0, 1, 0, 1, 0, 1]], ['clean', [1, 1, 0, 1]]]], [['regression [[1, 0, 1, 0, 0, 1, 0, 1]]', [[1, 0, 1, 0, 0, 1, 0, 1]], ['clean', [0, 1, 0, 1]]], ['regression [[1, 0, 1, 0, 0, 1, 1, 1]]', [[1, 0, 1, 0, 0, 1, 1, 1]], ['corrected', [0, 1, 0, 1]]], ['partial-repair [[1, 0, 1, 1, 0, 1, 1, 1]]', [[1, 0, 1, 1, 0, 1, 1, 1]], ['double', None]], ['partial-repair [[0, 1, 1, 0, 0, 0, 1, 0]]', [[0, 1, 1, 0, 0, 0, 1, 0]], ['corrected', [0, 1, 1, 0]]], ['control [[0, 1, 1, 1, 0, 1, 0, 0]]', [[0, 1, 1, 1, 0, 1, 0, 0]], ['double', None]], ['control [[0, 1, 1, 0, 0, 0, 0, 0]]', [[0, 1, 1, 0, 0, 0, 0, 0]], ['double', None]], ['control [[0, 0, 0, 0, 0, 0, 0, 0]]', [[0, 0, 0, 0, 0, 0, 0, 0]], ['clean', [0, 0, 0, 0]]], ['control [[0, 0, 0, 0, 0, 0, 1, 1]]', [[0, 0, 0, 0, 0, 0, 1, 1]], ['double', None]]], [['regression [[1, 1, 1, 1, 0, 0, 0, 0]]', [[1, 1, 1, 1, 0, 0, 0, 0]], ['clean', [1, 0, 0, 0]]], ['regression [[1, 1, 0, 1, 0, 1, 0, 0]]', [[1, 1, 0, 1, 0, 1, 0, 0]], ['double', None]], ['partial-repair [[0, 1, 1, 1, 0, 0, 0, 0]]', [[0, 1, 1, 1, 0, 0, 0, 0]], ['corrected', [1, 0, 0, 0]]], ['control [[0, 1, 0, 1, 1, 0, 0, 1]]', [[0, 1, 0, 1, 1, 0, 0, 1]], ['double', None]], ['control [[0, 1, 1, 0, 0, 1, 1, 0]]', [[0, 1, 1, 0, 0, 1, 1, 0]], ['clean', [0, 1, 1, 0]]], ['control [[0, 0, 1, 0, 0, 0, 1, 0]]', [[0, 0, 1, 0, 0, 0, 1, 0]], ['double', None]], ['control [[0, 0, 0, 0, 1, 1, 1, 1]]', [[0, 0, 0, 0, 1, 1, 1, 1]], ['clean', [0, 1, 1, 1]]], ['control [[0, 0, 0, 0, 0, 1, 1, 0]]', [[0, 0, 0, 0, 0, 1, 1, 0]], ['double', None]]]]
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 fixture	Actual	Expected	Outcome
regression [[1, 0, 1, 0, 1, 0, 1, 0]]	`['corrected', [0, 0, 1, 0]]`	`['clean', [0, 0, 1, 0]]`	Failed
regression [[1, 0, 1, 0, 1, 1, 1, 0]]	`['double', None]`	`['corrected', [0, 0, 1, 0]]`	Failed
partial-repair [[0, 1, 0, 0, 0, 0, 0, 0]]	`['corrected', [0, 0, 0, 0]]`	`['corrected', [0, 0, 0, 0]]`	Passed
partial-repair [[0, 1, 1, 0, 1, 1, 0, 1]]	`['corrected', [0, 0, 0, 1]]`	`['corrected', [0, 0, 0, 1]]`	Passed
control [[0, 0, 0, 0, 0, 0, 0, 0]]	`['clean', [0, 0, 0, 0]]`	`['clean', [0, 0, 0, 0]]`	Passed
control [[0, 0, 0, 0, 0, 0, 1, 1]]	`['double', None]`	`['double', None]`	Passed
control [[0, 1, 1, 0, 1, 0, 0, 1]]	`['clean', [0, 0, 0, 1]]`	`['clean', [0, 0, 0, 1]]`	Passed
control [[0, 1, 0, 1, 1, 0, 0, 1]]	`['double', None]`	`['double', None]`	Passed

SHA-256 / ba058e82e8a94bffa730e091743c4ec1ad93beecd5c586f717364c9c7bc49396

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) != 8 or any(b not in (0, 1) for b in r):
        return None
    s = 0
    for pos in range(1, 8):
        if r[pos]:
            s ^= pos
    p = r[0]
    c = list(r)
    if s == 0 and p == 0:
        status = 'clean'
    elif p == 1:
        status = 'corrected'
        c[s] ^= 1
    else:
        return ['double', None]
    return [status, [c[3], c[5], c[6], c[7]]]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression [[1, 0, 1, 0, 1, 0, 1, 0]]', [[1, 0, 1, 0, 1, 0, 1, 0]], ['clean', [0, 0, 1, 0]]], ['regression [[1, 0, 1, 0, 1, 1, 1, 0]]', [[1, 0, 1, 0, 1, 1, 1, 0]], ['corrected', [0, 0, 1, 0]]], ['partial-repair [[0, 1, 0, 0, 0, 0, 0, 0]]', [[0, 1, 0, 0, 0, 0, 0, 0]], ['corrected', [0, 0, 0, 0]]], ['partial-repair [[0, 1, 1, 0, 1, 1, 0, 1]]', [[0, 1, 1, 0, 1, 1, 0, 1]], ['corrected', [0, 0, 0, 1]]], ['control [[0, 0, 0, 0, 0, 0, 0, 0]]', [[0, 0, 0, 0, 0, 0, 0, 0]], ['clean', [0, 0, 0, 0]]], ['control [[0, 0, 0, 0, 0, 0, 1, 1]]', [[0, 0, 0, 0, 0, 0, 1, 1]], ['double', None]], ['control [[0, 1, 1, 0, 1, 0, 0, 1]]', [[0, 1, 1, 0, 1, 0, 0, 1]], ['clean', [0, 0, 0, 1]]], ['control [[0, 1, 0, 1, 1, 0, 0, 1]]', [[0, 1, 0, 1, 1, 0, 0, 1]], ['double', None]]], [['regression [[1, 1, 0, 0, 0, 0, 1, 1]]', [[1, 1, 0, 0, 0, 0, 1, 1]], ['clean', [0, 0, 1, 1]]], ['regression [[1, 1, 1, 0, 0, 0, 1, 1]]', [[1, 1, 1, 0, 0, 0, 1, 1]], ['corrected', [0, 0, 1, 1]]], ['partial-repair [[1, 0, 0, 1, 1, 0, 1, 0]]', [[1, 0, 0, 1, 1, 0, 1, 0]], ['double', None]], ['control [[0, 0, 1, 0, 0, 0, 1, 0]]', [[0, 0, 1, 0, 0, 0, 1, 0]], ['double', None]], ['control [[0, 0, 0, 0, 1, 1, 1, 1]]', [[0, 0, 0, 0, 1, 1, 1, 1]], ['clean', [0, 1, 1, 1]]], ['control [[0, 0, 0, 0, 0, 1, 1, 0]]', [[0, 0, 0, 0, 0, 1, 1, 0]], ['double', None]], ['control [[0, 1, 0, 1, 1, 0, 1, 0]]', [[0, 1, 0, 1, 1, 0, 1, 0]], ['clean', [1, 0, 1, 0]]], ['control [[0, 1, 1, 1, 0, 0, 1, 0]]', [[0, 1, 1, 1, 0, 0, 1, 0]], ['double', None]]], [['regression [[1, 1, 0, 0, 1, 1, 0, 0]]', [[1, 1, 0, 0, 1, 1, 0, 0]], ['clean', [0, 1, 0, 0]]], ['regression [[1, 1, 1, 0, 1, 1, 0, 0]]', [[1, 1, 1, 0, 1, 1, 0, 0]], ['corrected', [0, 1, 0, 0]]], ['partial-repair [[1, 0, 0, 0, 1, 0, 0, 0]]', [[1, 0, 0, 0, 1, 0, 0, 0]], ['double', None]], ['control [[0, 0, 1, 1, 0, 0, 1, 1]]', [[0, 0, 1, 1, 0, 0, 1, 1]], ['clean', [1, 0, 1, 1]]], ['control [[0, 0, 1, 1, 0, 1, 1, 0]]', [[0, 0, 1, 1, 0, 1, 1, 0]], ['double', None]], ['control [[0, 0, 1, 1, 1, 1, 0, 0]]', [[0, 0, 1, 1, 1, 1, 0, 0]], ['clean', [1, 1, 0, 0]]], ['control [[0, 0, 1, 0, 1, 0, 0, 0]]', [[0, 0, 1, 0, 1, 0, 0, 0]], ['double', None]], ['control [[0, 1, 0, 1, 0, 1, 0, 1]]', [[0, 1, 0, 1, 0, 1, 0, 1]], ['clean', [1, 1, 0, 1]]]], [['regression [[1, 0, 1, 0, 0, 1, 0, 1]]', [[1, 0, 1, 0, 0, 1, 0, 1]], ['clean', [0, 1, 0, 1]]], ['regression [[1, 0, 1, 0, 0, 1, 1, 1]]', [[1, 0, 1, 0, 0, 1, 1, 1]], ['corrected', [0, 1, 0, 1]]], ['partial-repair [[1, 0, 1, 1, 0, 1, 1, 1]]', [[1, 0, 1, 1, 0, 1, 1, 1]], ['double', None]], ['partial-repair [[0, 1, 1, 0, 0, 0, 1, 0]]', [[0, 1, 1, 0, 0, 0, 1, 0]], ['corrected', [0, 1, 1, 0]]], ['control [[0, 1, 1, 1, 0, 1, 0, 0]]', [[0, 1, 1, 1, 0, 1, 0, 0]], ['double', None]], ['control [[0, 1, 1, 0, 0, 0, 0, 0]]', [[0, 1, 1, 0, 0, 0, 0, 0]], ['double', None]], ['control [[0, 0, 0, 0, 0, 0, 0, 0]]', [[0, 0, 0, 0, 0, 0, 0, 0]], ['clean', [0, 0, 0, 0]]], ['control [[0, 0, 0, 0, 0, 0, 1, 1]]', [[0, 0, 0, 0, 0, 0, 1, 1]], ['double', None]]], [['regression [[1, 1, 1, 1, 0, 0, 0, 0]]', [[1, 1, 1, 1, 0, 0, 0, 0]], ['clean', [1, 0, 0, 0]]], ['regression [[1, 1, 0, 1, 0, 1, 0, 0]]', [[1, 1, 0, 1, 0, 1, 0, 0]], ['double', None]], ['partial-repair [[0, 1, 1, 1, 0, 0, 0, 0]]', [[0, 1, 1, 1, 0, 0, 0, 0]], ['corrected', [1, 0, 0, 0]]], ['control [[0, 1, 0, 1, 1, 0, 0, 1]]', [[0, 1, 0, 1, 1, 0, 0, 1]], ['double', None]], ['control [[0, 1, 1, 0, 0, 1, 1, 0]]', [[0, 1, 1, 0, 0, 1, 1, 0]], ['clean', [0, 1, 1, 0]]], ['control [[0, 0, 1, 0, 0, 0, 1, 0]]', [[0, 0, 1, 0, 0, 0, 1, 0]], ['double', None]], ['control [[0, 0, 0, 0, 1, 1, 1, 1]]', [[0, 0, 0, 0, 1, 1, 1, 1]], ['clean', [0, 1, 1, 1]]], ['control [[0, 0, 0, 0, 0, 1, 1, 0]]', [[0, 0, 0, 0, 0, 1, 1, 0]], ['double', None]]]]
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 fixture	Actual	Expected	Outcome
regression [[1, 0, 1, 0, 1, 0, 1, 0]]	`['corrected', [0, 0, 1, 0]]`	`['clean', [0, 0, 1, 0]]`	Failed
regression [[1, 0, 1, 0, 1, 1, 1, 0]]	`['corrected', [0, 0, 1, 0]]`	`['corrected', [0, 0, 1, 0]]`	Passed
partial-repair [[0, 1, 0, 0, 0, 0, 0, 0]]	`['double', None]`	`['corrected', [0, 0, 0, 0]]`	Failed
partial-repair [[0, 1, 1, 0, 1, 1, 0, 1]]	`['double', None]`	`['corrected', [0, 0, 0, 1]]`	Failed
control [[0, 0, 0, 0, 0, 0, 0, 0]]	`['clean', [0, 0, 0, 0]]`	`['clean', [0, 0, 0, 0]]`	Passed
control [[0, 0, 0, 0, 0, 0, 1, 1]]	`['double', None]`	`['double', None]`	Passed
control [[0, 1, 1, 0, 1, 0, 0, 1]]	`['clean', [0, 0, 0, 1]]`	`['clean', [0, 0, 0, 1]]`	Passed
control [[0, 1, 0, 1, 1, 0, 0, 1]]	`['double', None]`	`['double', None]`	Passed

SHA-256 / 537a7935061a0883465f1be745304525e9c735d238d402ffdb29efbebfd58c1c

3 / The verified repair

Exit 0

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

N = 1
observations = []
def solve(r):
    if len(r) != 8 or any(b not in (0, 1) for b in r):
        return None
    s = 0
    for pos in range(1, 8):
        if r[pos]:
            s ^= pos
    p = sum(r) % 2
    c = list(r)
    if s == 0 and p == 0:
        status = 'clean'
    elif p == 1:
        status = 'corrected'
        c[s] ^= 1
    else:
        return ['double', None]
    return [status, [c[3], c[5], c[6], c[7]]]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression [[1, 0, 1, 0, 1, 0, 1, 0]]', [[1, 0, 1, 0, 1, 0, 1, 0]], ['clean', [0, 0, 1, 0]]], ['regression [[1, 0, 1, 0, 1, 1, 1, 0]]', [[1, 0, 1, 0, 1, 1, 1, 0]], ['corrected', [0, 0, 1, 0]]], ['partial-repair [[0, 1, 0, 0, 0, 0, 0, 0]]', [[0, 1, 0, 0, 0, 0, 0, 0]], ['corrected', [0, 0, 0, 0]]], ['partial-repair [[0, 1, 1, 0, 1, 1, 0, 1]]', [[0, 1, 1, 0, 1, 1, 0, 1]], ['corrected', [0, 0, 0, 1]]], ['control [[0, 0, 0, 0, 0, 0, 0, 0]]', [[0, 0, 0, 0, 0, 0, 0, 0]], ['clean', [0, 0, 0, 0]]], ['control [[0, 0, 0, 0, 0, 0, 1, 1]]', [[0, 0, 0, 0, 0, 0, 1, 1]], ['double', None]], ['control [[0, 1, 1, 0, 1, 0, 0, 1]]', [[0, 1, 1, 0, 1, 0, 0, 1]], ['clean', [0, 0, 0, 1]]], ['control [[0, 1, 0, 1, 1, 0, 0, 1]]', [[0, 1, 0, 1, 1, 0, 0, 1]], ['double', None]]], [['regression [[1, 1, 0, 0, 0, 0, 1, 1]]', [[1, 1, 0, 0, 0, 0, 1, 1]], ['clean', [0, 0, 1, 1]]], ['regression [[1, 1, 1, 0, 0, 0, 1, 1]]', [[1, 1, 1, 0, 0, 0, 1, 1]], ['corrected', [0, 0, 1, 1]]], ['partial-repair [[1, 0, 0, 1, 1, 0, 1, 0]]', [[1, 0, 0, 1, 1, 0, 1, 0]], ['double', None]], ['control [[0, 0, 1, 0, 0, 0, 1, 0]]', [[0, 0, 1, 0, 0, 0, 1, 0]], ['double', None]], ['control [[0, 0, 0, 0, 1, 1, 1, 1]]', [[0, 0, 0, 0, 1, 1, 1, 1]], ['clean', [0, 1, 1, 1]]], ['control [[0, 0, 0, 0, 0, 1, 1, 0]]', [[0, 0, 0, 0, 0, 1, 1, 0]], ['double', None]], ['control [[0, 1, 0, 1, 1, 0, 1, 0]]', [[0, 1, 0, 1, 1, 0, 1, 0]], ['clean', [1, 0, 1, 0]]], ['control [[0, 1, 1, 1, 0, 0, 1, 0]]', [[0, 1, 1, 1, 0, 0, 1, 0]], ['double', None]]], [['regression [[1, 1, 0, 0, 1, 1, 0, 0]]', [[1, 1, 0, 0, 1, 1, 0, 0]], ['clean', [0, 1, 0, 0]]], ['regression [[1, 1, 1, 0, 1, 1, 0, 0]]', [[1, 1, 1, 0, 1, 1, 0, 0]], ['corrected', [0, 1, 0, 0]]], ['partial-repair [[1, 0, 0, 0, 1, 0, 0, 0]]', [[1, 0, 0, 0, 1, 0, 0, 0]], ['double', None]], ['control [[0, 0, 1, 1, 0, 0, 1, 1]]', [[0, 0, 1, 1, 0, 0, 1, 1]], ['clean', [1, 0, 1, 1]]], ['control [[0, 0, 1, 1, 0, 1, 1, 0]]', [[0, 0, 1, 1, 0, 1, 1, 0]], ['double', None]], ['control [[0, 0, 1, 1, 1, 1, 0, 0]]', [[0, 0, 1, 1, 1, 1, 0, 0]], ['clean', [1, 1, 0, 0]]], ['control [[0, 0, 1, 0, 1, 0, 0, 0]]', [[0, 0, 1, 0, 1, 0, 0, 0]], ['double', None]], ['control [[0, 1, 0, 1, 0, 1, 0, 1]]', [[0, 1, 0, 1, 0, 1, 0, 1]], ['clean', [1, 1, 0, 1]]]], [['regression [[1, 0, 1, 0, 0, 1, 0, 1]]', [[1, 0, 1, 0, 0, 1, 0, 1]], ['clean', [0, 1, 0, 1]]], ['regression [[1, 0, 1, 0, 0, 1, 1, 1]]', [[1, 0, 1, 0, 0, 1, 1, 1]], ['corrected', [0, 1, 0, 1]]], ['partial-repair [[1, 0, 1, 1, 0, 1, 1, 1]]', [[1, 0, 1, 1, 0, 1, 1, 1]], ['double', None]], ['partial-repair [[0, 1, 1, 0, 0, 0, 1, 0]]', [[0, 1, 1, 0, 0, 0, 1, 0]], ['corrected', [0, 1, 1, 0]]], ['control [[0, 1, 1, 1, 0, 1, 0, 0]]', [[0, 1, 1, 1, 0, 1, 0, 0]], ['double', None]], ['control [[0, 1, 1, 0, 0, 0, 0, 0]]', [[0, 1, 1, 0, 0, 0, 0, 0]], ['double', None]], ['control [[0, 0, 0, 0, 0, 0, 0, 0]]', [[0, 0, 0, 0, 0, 0, 0, 0]], ['clean', [0, 0, 0, 0]]], ['control [[0, 0, 0, 0, 0, 0, 1, 1]]', [[0, 0, 0, 0, 0, 0, 1, 1]], ['double', None]]], [['regression [[1, 1, 1, 1, 0, 0, 0, 0]]', [[1, 1, 1, 1, 0, 0, 0, 0]], ['clean', [1, 0, 0, 0]]], ['regression [[1, 1, 0, 1, 0, 1, 0, 0]]', [[1, 1, 0, 1, 0, 1, 0, 0]], ['double', None]], ['partial-repair [[0, 1, 1, 1, 0, 0, 0, 0]]', [[0, 1, 1, 1, 0, 0, 0, 0]], ['corrected', [1, 0, 0, 0]]], ['control [[0, 1, 0, 1, 1, 0, 0, 1]]', [[0, 1, 0, 1, 1, 0, 0, 1]], ['double', None]], ['control [[0, 1, 1, 0, 0, 1, 1, 0]]', [[0, 1, 1, 0, 0, 1, 1, 0]], ['clean', [0, 1, 1, 0]]], ['control [[0, 0, 1, 0, 0, 0, 1, 0]]', [[0, 0, 1, 0, 0, 0, 1, 0]], ['double', None]], ['control [[0, 0, 0, 0, 1, 1, 1, 1]]', [[0, 0, 0, 0, 1, 1, 1, 1]], ['clean', [0, 1, 1, 1]]], ['control [[0, 0, 0, 0, 0, 1, 1, 0]]', [[0, 0, 0, 0, 0, 1, 1, 0]], ['double', None]]]]
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 fixture	Actual	Expected	Outcome
regression [[1, 0, 1, 0, 1, 0, 1, 0]]	`['clean', [0, 0, 1, 0]]`	`['clean', [0, 0, 1, 0]]`	Passed
regression [[1, 0, 1, 0, 1, 1, 1, 0]]	`['corrected', [0, 0, 1, 0]]`	`['corrected', [0, 0, 1, 0]]`	Passed
partial-repair [[0, 1, 0, 0, 0, 0, 0, 0]]	`['corrected', [0, 0, 0, 0]]`	`['corrected', [0, 0, 0, 0]]`	Passed
partial-repair [[0, 1, 1, 0, 1, 1, 0, 1]]	`['corrected', [0, 0, 0, 1]]`	`['corrected', [0, 0, 0, 1]]`	Passed
control [[0, 0, 0, 0, 0, 0, 0, 0]]	`['clean', [0, 0, 0, 0]]`	`['clean', [0, 0, 0, 0]]`	Passed
control [[0, 0, 0, 0, 0, 0, 1, 1]]	`['double', None]`	`['double', None]`	Passed
control [[0, 1, 1, 0, 1, 0, 0, 1]]	`['clean', [0, 0, 0, 1]]`	`['clean', [0, 0, 0, 1]]`	Passed
control [[0, 1, 0, 1, 1, 0, 0, 1]]	`['double', None]`	`['double', None]`	Passed

SHA-256 / ca6cd9e352b2f88d7e56b52dbdf55f4a6f60b238bb5054d5a50598314ddfbb58

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 2026-09-29T14:48:33.534326+00:00.

Case digest / 194c543de41f19282c9a15ca5aa19b547f068a75e526f03e0e88f3f9de917d6a