FA-72156 / Error-correcting codes / Open access

Depuncturing ignores the partial final pattern period · case 01

Blocks whose length is not a multiple of the pattern period are rejected.

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

ROOT CAUSE

The kept count only counts whole pattern periods.

VERIFIED REPAIR

Add the kept positions of the leading slice of the pattern for the remainder.

Unsuccessful approach: Adding the full remainder length counts punctured positions of the tail as kept.

Case contract

Depuncture a rate-matched soft stream: the mother-code stream of length total was punctured with a cyclic 0/1 pattern starting at pattern phase 0 for every block. Reinsert LLR 0 at punctured positions and place received values at kept positions. If the number of received values differs from the number of kept positions, or the pattern keeps nothing, return None. Return the depunctured list.

Why this case matters

Rate-compatible punctured convolutional and turbo codes need exact depuncturing before decoding.

1 / The failure

Exit 1

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

N = 1
observations = []
def solve(rx, pattern, total):
    if not pattern or sum(pattern) == 0 or total < 0:
        return None
    kept = sum(pattern) * (total // len(pattern))
    if kept != len(rx):
        return None
    out, j = [], 0
    for k in range(total):
        if pattern[k % len(pattern)]:
            out.append(rx[j])
            j += 1
        else:
            out.append(0)
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression [[-5, -1, 4, 1, -3, 2, 4, 6, 1, -1], [1, 1, 0, 1], 13]', [[-5, -1, 4, 1, -3, 2, 4, 6, 1, -1], [1, 1, 0, 1], 13], [-5, -1, 0, 4, 1, -3, 0, 2, 4, 6, 0, 1, -1]], ['regression [[-1, -3, 1, 4, -3], [1, 1, 0, 1], 6]', [[-1, -3, 1, 4, -3], [1, 1, 0, 1], 6], [-1, -3, 0, 1, 4, -3]], ['partial-repair [[2, 1, -3, 6, -1, -5, -3], [1, 0, 1, 1, 1, 0], 10]', [[2, 1, -3, 6, -1, -5, -3], [1, 0, 1, 1, 1, 0], 10], [2, 0, 1, -3, 6, 0, -1, 0, -5, -3]], ['partial-repair [[-1, 4, 1, -5, -3], [1, 0, 1, 1, 1, 0], 8]', [[-1, 4, 1, -5, -3], [1, 0, 1, 1, 1, 0], 8], [-1, 0, 4, 1, -5, 0, -3, 0]], ['control [[1, -3, -5, 2, 2, -1, -3, 2, 4], [1, 1, 1, 0], 12]', [[1, -3, -5, 2, 2, -1, -3, 2, 4], [1, 1, 1, 0], 12], [1, -3, -5, 0, 2, 2, -1, 0, -3, 2, 4, 0]], ['control [[-5, -3, -1, 6, -3, -5, -5, -3], [1, 1, 0], 12]', [[-5, -3, -1, 6, -3, -5, -5, -3], [1, 1, 0], 12], [-5, -3, 0, -1, 6, 0, -3, -5, 0, -5, -3, 0]], ['control [[1, 2], [1, 1, 0], 3]', [[1, 2], [1, 1, 0], 3], [1, 2, 0]], ['control [[1, 2, 3], [1, 1, 0], 3]', [[1, 2, 3], [1, 1, 0], 3], None]], [['regression [[-1, 4, 1, -5, -3], [1, 0, 1, 1, 1, 0], 8]', [[-1, 4, 1, -5, -3], [1, 0, 1, 1, 1, 0], 8], [-1, 0, 4, 1, -5, 0, -3, 0]], ['regression [[1, -1, -1, 6, 2, 4, -1, 1, 4, 6, 6], [1, 1, 1, 0], 14]', [[1, -1, -1, 6, 2, 4, -1, 1, 4, 6, 6], [1, 1, 1, 0], 14], [1, -1, -1, 0, 6, 2, 4, 0, -1, 1, 4, 0, 6, 6]], ['partial-repair [[-3, 6, 6], [0, 1, 1, 1], 5]', [[-3, 6, 6], [0, 1, 1, 1], 5], [0, -3, 6, 6, 0]], ['partial-repair [[4], [1, 0, 0], 2]', [[4], [1, 0, 0], 2], [4, 0]], ['control [[1, -3, -5, 2, 2, -1, -3, 2, 4], [1, 1, 1, 0], 12]', [[1, -3, -5, 2, 2, -1, -3, 2, 4], [1, 1, 1, 0], 12], [1, -3, -5, 0, 2, 2, -1, 0, -3, 2, 4, 0]], ['control [[-5, -3, -1, 6, -3, -5, -5, -3], [1, 1, 0], 12]', [[-5, -3, -1, 6, -3, -5, -5, -3], [1, 1, 0], 12], [-5, -3, 0, -1, 6, 0, -3, -5, 0, -5, -3, 0]], ['control [[1, 2], [1, 1, 0], 3]', [[1, 2], [1, 1, 0], 3], [1, 2, 0]], ['control [[1, 2, 3], [1, 1, 0], 3]', [[1, 2, 3], [1, 1, 0], 3], None]], [['regression [[6, 2, -1], [1, 0], 5]', [[6, 2, -1], [1, 0], 5], [6, 0, 2, 0, -1]], ['regression [[-3, 2, -3, -1, 4, 2, 1, 6, 6, -5], [1, 1, 0], 14]', [[-3, 2, -3, -1, 4, 2, 1, 6, 6, -5], [1, 1, 0], 14], [-3, 2, 0, -3, -1, 0, 4, 2, 0, 1, 6, 0, 6, -5]], ['partial-repair [[-1, 4, 1, -5, -3], [1, 0, 1, 1, 1, 0], 8]', [[-1, 4, 1, -5, -3], [1, 0, 1, 1, 1, 0], 8], [-1, 0, 4, 1, -5, 0, -3, 0]], ['partial-repair [[6, 4, 2], [0, 1, 1, 1], 5]', [[6, 4, 2], [0, 1, 1, 1], 5], [0, 6, 4, 2, 0]], ['control [[1, -3, -5, 2, 2, -1, -3, 2, 4], [1, 1, 1, 0], 12]', [[1, -3, -5, 2, 2, -1, -3, 2, 4], [1, 1, 1, 0], 12], [1, -3, -5, 0, 2, 2, -1, 0, -3, 2, 4, 0]], ['control [[-5, -3, -1, 6, -3, -5, -5, -3], [1, 1, 0], 12]', [[-5, -3, -1, 6, -3, -5, -5, -3], [1, 1, 0], 12], [-5, -3, 0, -1, 6, 0, -3, -5, 0, -5, -3, 0]], ['control [[1, 2], [1, 1, 0], 3]', [[1, 2], [1, 1, 0], 3], [1, 2, 0]], ['control [[1, 2, 3], [1, 1, 0], 3]', [[1, 2, 3], [1, 1, 0], 3], None]], [['regression [[7, 8, 9, 5], [1, 1, 0, 1], 5]', [[7, 8, 9, 5], [1, 1, 0, 1], 5], [7, 8, 0, 9, 5]], ['regression [[-5, -1, 4, 1, -3, 2, 4, 6, 1, -1], [1, 1, 0, 1], 13]', [[-5, -1, 4, 1, -3, 2, 4, 6, 1, -1], [1, 1, 0, 1], 13], [-5, -1, 0, 4, 1, -3, 0, 2, 4, 6, 0, 1, -1]], ['partial-repair [[4], [1, 0, 0], 2]', [[4], [1, 0, 0], 2], [4, 0]], ['partial-repair [[2, 1, -3, 6, -1, -5, -3], [1, 0, 1, 1, 1, 0], 10]', [[2, 1, -3, 6, -1, -5, -3], [1, 0, 1, 1, 1, 0], 10], [2, 0, 1, -3, 6, 0, -1, 0, -5, -3]], ['control [[1, -3, -5, 2, 2, -1, -3, 2, 4], [1, 1, 1, 0], 12]', [[1, -3, -5, 2, 2, -1, -3, 2, 4], [1, 1, 1, 0], 12], [1, -3, -5, 0, 2, 2, -1, 0, -3, 2, 4, 0]], ['control [[-5, -3, -1, 6, -3, -5, -5, -3], [1, 1, 0], 12]', [[-5, -3, -1, 6, -3, -5, -5, -3], [1, 1, 0], 12], [-5, -3, 0, -1, 6, 0, -3, -5, 0, -5, -3, 0]], ['control [[1, 2], [1, 1, 0], 3]', [[1, 2], [1, 1, 0], 3], [1, 2, 0]], ['control [[1, 2, 3], [1, 1, 0], 3]', [[1, 2, 3], [1, 1, 0], 3], None]], [['regression [[2, 1, -3, 6, -1, -5, -3], [1, 0, 1, 1, 1, 0], 10]', [[2, 1, -3, 6, -1, -5, -3], [1, 0, 1, 1, 1, 0], 10], [2, 0, 1, -3, 6, 0, -1, 0, -5, -3]], ['regression [[-1, 4, 1, -5, -3], [1, 0, 1, 1, 1, 0], 8]', [[-1, 4, 1, -5, -3], [1, 0, 1, 1, 1, 0], 8], [-1, 0, 4, 1, -5, 0, -3, 0]], ['partial-repair [[6, 4, 2], [0, 1, 1, 1], 5]', [[6, 4, 2], [0, 1, 1, 1], 5], [0, 6, 4, 2, 0]], ['partial-repair [[-3, 6, 6], [0, 1, 1, 1], 5]', [[-3, 6, 6], [0, 1, 1, 1], 5], [0, -3, 6, 6, 0]], ['control [[1, -3, -5, 2, 2, -1, -3, 2, 4], [1, 1, 1, 0], 12]', [[1, -3, -5, 2, 2, -1, -3, 2, 4], [1, 1, 1, 0], 12], [1, -3, -5, 0, 2, 2, -1, 0, -3, 2, 4, 0]], ['control [[-5, -3, -1, 6, -3, -5, -5, -3], [1, 1, 0], 12]', [[-5, -3, -1, 6, -3, -5, -5, -3], [1, 1, 0], 12], [-5, -3, 0, -1, 6, 0, -3, -5, 0, -5, -3, 0]], ['control [[1, 2], [1, 1, 0], 3]', [[1, 2], [1, 1, 0], 3], [1, 2, 0]], ['control [[1, 2, 3], [1, 1, 0], 3]', [[1, 2, 3], [1, 1, 0], 3], 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 [[-5, -1, 4, 1, -3, 2, 4, 6, 1, -1], [1, 1, 0, 1], 13]	`None`	`[-5, -1, 0, 4, 1, -3, 0, 2, 4, 6, 0, 1, -1]`	Failed
regression [[-1, -3, 1, 4, -3], [1, 1, 0, 1], 6]	`None`	`[-1, -3, 0, 1, 4, -3]`	Failed
partial-repair [[2, 1, -3, 6, -1, -5, -3], [1, 0, 1, 1, 1, 0], 10]	`None`	`[2, 0, 1, -3, 6, 0, -1, 0, -5, -3]`	Failed
partial-repair [[-1, 4, 1, -5, -3], [1, 0, 1, 1, 1, 0], 8]	`None`	`[-1, 0, 4, 1, -5, 0, -3, 0]`	Failed
control [[1, -3, -5, 2, 2, -1, -3, 2, 4], [1, 1, 1, 0], 12]	`[1, -3, -5, 0, 2, 2, -1, 0, -3, 2, 4, 0]`	`[1, -3, -5, 0, 2, 2, -1, 0, -3, 2, 4, 0]`	Passed
control [[-5, -3, -1, 6, -3, -5, -5, -3], [1, 1, 0], 12]	`[-5, -3, 0, -1, 6, 0, -3, -5, 0, -5, -3, 0]`	`[-5, -3, 0, -1, 6, 0, -3, -5, 0, -5, -3, 0]`	Passed
control [[1, 2], [1, 1, 0], 3]	`[1, 2, 0]`	`[1, 2, 0]`	Passed
control [[1, 2, 3], [1, 1, 0], 3]	`None`	`None`	Passed

SHA-256 / 0ac9752d5d5671234dfee25adaa64e1cec365861383aa557ffe9e6d4ae5a6fc3

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(rx, pattern, total):
    if not pattern or sum(pattern) == 0 or total < 0:
        return None
    kept = sum(pattern) * (total // len(pattern)) + total % len(pattern)
    if kept != len(rx):
        return None
    out, j = [], 0
    for k in range(total):
        if pattern[k % len(pattern)]:
            out.append(rx[j])
            j += 1
        else:
            out.append(0)
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression [[-5, -1, 4, 1, -3, 2, 4, 6, 1, -1], [1, 1, 0, 1], 13]', [[-5, -1, 4, 1, -3, 2, 4, 6, 1, -1], [1, 1, 0, 1], 13], [-5, -1, 0, 4, 1, -3, 0, 2, 4, 6, 0, 1, -1]], ['regression [[-1, -3, 1, 4, -3], [1, 1, 0, 1], 6]', [[-1, -3, 1, 4, -3], [1, 1, 0, 1], 6], [-1, -3, 0, 1, 4, -3]], ['partial-repair [[2, 1, -3, 6, -1, -5, -3], [1, 0, 1, 1, 1, 0], 10]', [[2, 1, -3, 6, -1, -5, -3], [1, 0, 1, 1, 1, 0], 10], [2, 0, 1, -3, 6, 0, -1, 0, -5, -3]], ['partial-repair [[-1, 4, 1, -5, -3], [1, 0, 1, 1, 1, 0], 8]', [[-1, 4, 1, -5, -3], [1, 0, 1, 1, 1, 0], 8], [-1, 0, 4, 1, -5, 0, -3, 0]], ['control [[1, -3, -5, 2, 2, -1, -3, 2, 4], [1, 1, 1, 0], 12]', [[1, -3, -5, 2, 2, -1, -3, 2, 4], [1, 1, 1, 0], 12], [1, -3, -5, 0, 2, 2, -1, 0, -3, 2, 4, 0]], ['control [[-5, -3, -1, 6, -3, -5, -5, -3], [1, 1, 0], 12]', [[-5, -3, -1, 6, -3, -5, -5, -3], [1, 1, 0], 12], [-5, -3, 0, -1, 6, 0, -3, -5, 0, -5, -3, 0]], ['control [[1, 2], [1, 1, 0], 3]', [[1, 2], [1, 1, 0], 3], [1, 2, 0]], ['control [[1, 2, 3], [1, 1, 0], 3]', [[1, 2, 3], [1, 1, 0], 3], None]], [['regression [[-1, 4, 1, -5, -3], [1, 0, 1, 1, 1, 0], 8]', [[-1, 4, 1, -5, -3], [1, 0, 1, 1, 1, 0], 8], [-1, 0, 4, 1, -5, 0, -3, 0]], ['regression [[1, -1, -1, 6, 2, 4, -1, 1, 4, 6, 6], [1, 1, 1, 0], 14]', [[1, -1, -1, 6, 2, 4, -1, 1, 4, 6, 6], [1, 1, 1, 0], 14], [1, -1, -1, 0, 6, 2, 4, 0, -1, 1, 4, 0, 6, 6]], ['partial-repair [[-3, 6, 6], [0, 1, 1, 1], 5]', [[-3, 6, 6], [0, 1, 1, 1], 5], [0, -3, 6, 6, 0]], ['partial-repair [[4], [1, 0, 0], 2]', [[4], [1, 0, 0], 2], [4, 0]], ['control [[1, -3, -5, 2, 2, -1, -3, 2, 4], [1, 1, 1, 0], 12]', [[1, -3, -5, 2, 2, -1, -3, 2, 4], [1, 1, 1, 0], 12], [1, -3, -5, 0, 2, 2, -1, 0, -3, 2, 4, 0]], ['control [[-5, -3, -1, 6, -3, -5, -5, -3], [1, 1, 0], 12]', [[-5, -3, -1, 6, -3, -5, -5, -3], [1, 1, 0], 12], [-5, -3, 0, -1, 6, 0, -3, -5, 0, -5, -3, 0]], ['control [[1, 2], [1, 1, 0], 3]', [[1, 2], [1, 1, 0], 3], [1, 2, 0]], ['control [[1, 2, 3], [1, 1, 0], 3]', [[1, 2, 3], [1, 1, 0], 3], None]], [['regression [[6, 2, -1], [1, 0], 5]', [[6, 2, -1], [1, 0], 5], [6, 0, 2, 0, -1]], ['regression [[-3, 2, -3, -1, 4, 2, 1, 6, 6, -5], [1, 1, 0], 14]', [[-3, 2, -3, -1, 4, 2, 1, 6, 6, -5], [1, 1, 0], 14], [-3, 2, 0, -3, -1, 0, 4, 2, 0, 1, 6, 0, 6, -5]], ['partial-repair [[-1, 4, 1, -5, -3], [1, 0, 1, 1, 1, 0], 8]', [[-1, 4, 1, -5, -3], [1, 0, 1, 1, 1, 0], 8], [-1, 0, 4, 1, -5, 0, -3, 0]], ['partial-repair [[6, 4, 2], [0, 1, 1, 1], 5]', [[6, 4, 2], [0, 1, 1, 1], 5], [0, 6, 4, 2, 0]], ['control [[1, -3, -5, 2, 2, -1, -3, 2, 4], [1, 1, 1, 0], 12]', [[1, -3, -5, 2, 2, -1, -3, 2, 4], [1, 1, 1, 0], 12], [1, -3, -5, 0, 2, 2, -1, 0, -3, 2, 4, 0]], ['control [[-5, -3, -1, 6, -3, -5, -5, -3], [1, 1, 0], 12]', [[-5, -3, -1, 6, -3, -5, -5, -3], [1, 1, 0], 12], [-5, -3, 0, -1, 6, 0, -3, -5, 0, -5, -3, 0]], ['control [[1, 2], [1, 1, 0], 3]', [[1, 2], [1, 1, 0], 3], [1, 2, 0]], ['control [[1, 2, 3], [1, 1, 0], 3]', [[1, 2, 3], [1, 1, 0], 3], None]], [['regression [[7, 8, 9, 5], [1, 1, 0, 1], 5]', [[7, 8, 9, 5], [1, 1, 0, 1], 5], [7, 8, 0, 9, 5]], ['regression [[-5, -1, 4, 1, -3, 2, 4, 6, 1, -1], [1, 1, 0, 1], 13]', [[-5, -1, 4, 1, -3, 2, 4, 6, 1, -1], [1, 1, 0, 1], 13], [-5, -1, 0, 4, 1, -3, 0, 2, 4, 6, 0, 1, -1]], ['partial-repair [[4], [1, 0, 0], 2]', [[4], [1, 0, 0], 2], [4, 0]], ['partial-repair [[2, 1, -3, 6, -1, -5, -3], [1, 0, 1, 1, 1, 0], 10]', [[2, 1, -3, 6, -1, -5, -3], [1, 0, 1, 1, 1, 0], 10], [2, 0, 1, -3, 6, 0, -1, 0, -5, -3]], ['control [[1, -3, -5, 2, 2, -1, -3, 2, 4], [1, 1, 1, 0], 12]', [[1, -3, -5, 2, 2, -1, -3, 2, 4], [1, 1, 1, 0], 12], [1, -3, -5, 0, 2, 2, -1, 0, -3, 2, 4, 0]], ['control [[-5, -3, -1, 6, -3, -5, -5, -3], [1, 1, 0], 12]', [[-5, -3, -1, 6, -3, -5, -5, -3], [1, 1, 0], 12], [-5, -3, 0, -1, 6, 0, -3, -5, 0, -5, -3, 0]], ['control [[1, 2], [1, 1, 0], 3]', [[1, 2], [1, 1, 0], 3], [1, 2, 0]], ['control [[1, 2, 3], [1, 1, 0], 3]', [[1, 2, 3], [1, 1, 0], 3], None]], [['regression [[2, 1, -3, 6, -1, -5, -3], [1, 0, 1, 1, 1, 0], 10]', [[2, 1, -3, 6, -1, -5, -3], [1, 0, 1, 1, 1, 0], 10], [2, 0, 1, -3, 6, 0, -1, 0, -5, -3]], ['regression [[-1, 4, 1, -5, -3], [1, 0, 1, 1, 1, 0], 8]', [[-1, 4, 1, -5, -3], [1, 0, 1, 1, 1, 0], 8], [-1, 0, 4, 1, -5, 0, -3, 0]], ['partial-repair [[6, 4, 2], [0, 1, 1, 1], 5]', [[6, 4, 2], [0, 1, 1, 1], 5], [0, 6, 4, 2, 0]], ['partial-repair [[-3, 6, 6], [0, 1, 1, 1], 5]', [[-3, 6, 6], [0, 1, 1, 1], 5], [0, -3, 6, 6, 0]], ['control [[1, -3, -5, 2, 2, -1, -3, 2, 4], [1, 1, 1, 0], 12]', [[1, -3, -5, 2, 2, -1, -3, 2, 4], [1, 1, 1, 0], 12], [1, -3, -5, 0, 2, 2, -1, 0, -3, 2, 4, 0]], ['control [[-5, -3, -1, 6, -3, -5, -5, -3], [1, 1, 0], 12]', [[-5, -3, -1, 6, -3, -5, -5, -3], [1, 1, 0], 12], [-5, -3, 0, -1, 6, 0, -3, -5, 0, -5, -3, 0]], ['control [[1, 2], [1, 1, 0], 3]', [[1, 2], [1, 1, 0], 3], [1, 2, 0]], ['control [[1, 2, 3], [1, 1, 0], 3]', [[1, 2, 3], [1, 1, 0], 3], 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 [[-5, -1, 4, 1, -3, 2, 4, 6, 1, -1], [1, 1, 0, 1], 13]	`[-5, -1, 0, 4, 1, -3, 0, 2, 4, 6, 0, 1, -1]`	`[-5, -1, 0, 4, 1, -3, 0, 2, 4, 6, 0, 1, -1]`	Passed
regression [[-1, -3, 1, 4, -3], [1, 1, 0, 1], 6]	`[-1, -3, 0, 1, 4, -3]`	`[-1, -3, 0, 1, 4, -3]`	Passed
partial-repair [[2, 1, -3, 6, -1, -5, -3], [1, 0, 1, 1, 1, 0], 10]	`None`	`[2, 0, 1, -3, 6, 0, -1, 0, -5, -3]`	Failed
partial-repair [[-1, 4, 1, -5, -3], [1, 0, 1, 1, 1, 0], 8]	`None`	`[-1, 0, 4, 1, -5, 0, -3, 0]`	Failed
control [[1, -3, -5, 2, 2, -1, -3, 2, 4], [1, 1, 1, 0], 12]	`[1, -3, -5, 0, 2, 2, -1, 0, -3, 2, 4, 0]`	`[1, -3, -5, 0, 2, 2, -1, 0, -3, 2, 4, 0]`	Passed
control [[-5, -3, -1, 6, -3, -5, -5, -3], [1, 1, 0], 12]	`[-5, -3, 0, -1, 6, 0, -3, -5, 0, -5, -3, 0]`	`[-5, -3, 0, -1, 6, 0, -3, -5, 0, -5, -3, 0]`	Passed
control [[1, 2], [1, 1, 0], 3]	`[1, 2, 0]`	`[1, 2, 0]`	Passed
control [[1, 2, 3], [1, 1, 0], 3]	`None`	`None`	Passed

SHA-256 / 98094899587eabc07b3598b0915c80ce0078206b53d8a797ff491828d7e6e320

3 / The verified repair

Exit 0

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

N = 1
observations = []
def solve(rx, pattern, total):
    if not pattern or sum(pattern) == 0 or total < 0:
        return None
    kept = sum(pattern) * (total // len(pattern)) + sum(pattern[:total % len(pattern)])
    if kept != len(rx):
        return None
    out, j = [], 0
    for k in range(total):
        if pattern[k % len(pattern)]:
            out.append(rx[j])
            j += 1
        else:
            out.append(0)
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression [[-5, -1, 4, 1, -3, 2, 4, 6, 1, -1], [1, 1, 0, 1], 13]', [[-5, -1, 4, 1, -3, 2, 4, 6, 1, -1], [1, 1, 0, 1], 13], [-5, -1, 0, 4, 1, -3, 0, 2, 4, 6, 0, 1, -1]], ['regression [[-1, -3, 1, 4, -3], [1, 1, 0, 1], 6]', [[-1, -3, 1, 4, -3], [1, 1, 0, 1], 6], [-1, -3, 0, 1, 4, -3]], ['partial-repair [[2, 1, -3, 6, -1, -5, -3], [1, 0, 1, 1, 1, 0], 10]', [[2, 1, -3, 6, -1, -5, -3], [1, 0, 1, 1, 1, 0], 10], [2, 0, 1, -3, 6, 0, -1, 0, -5, -3]], ['partial-repair [[-1, 4, 1, -5, -3], [1, 0, 1, 1, 1, 0], 8]', [[-1, 4, 1, -5, -3], [1, 0, 1, 1, 1, 0], 8], [-1, 0, 4, 1, -5, 0, -3, 0]], ['control [[1, -3, -5, 2, 2, -1, -3, 2, 4], [1, 1, 1, 0], 12]', [[1, -3, -5, 2, 2, -1, -3, 2, 4], [1, 1, 1, 0], 12], [1, -3, -5, 0, 2, 2, -1, 0, -3, 2, 4, 0]], ['control [[-5, -3, -1, 6, -3, -5, -5, -3], [1, 1, 0], 12]', [[-5, -3, -1, 6, -3, -5, -5, -3], [1, 1, 0], 12], [-5, -3, 0, -1, 6, 0, -3, -5, 0, -5, -3, 0]], ['control [[1, 2], [1, 1, 0], 3]', [[1, 2], [1, 1, 0], 3], [1, 2, 0]], ['control [[1, 2, 3], [1, 1, 0], 3]', [[1, 2, 3], [1, 1, 0], 3], None]], [['regression [[-1, 4, 1, -5, -3], [1, 0, 1, 1, 1, 0], 8]', [[-1, 4, 1, -5, -3], [1, 0, 1, 1, 1, 0], 8], [-1, 0, 4, 1, -5, 0, -3, 0]], ['regression [[1, -1, -1, 6, 2, 4, -1, 1, 4, 6, 6], [1, 1, 1, 0], 14]', [[1, -1, -1, 6, 2, 4, -1, 1, 4, 6, 6], [1, 1, 1, 0], 14], [1, -1, -1, 0, 6, 2, 4, 0, -1, 1, 4, 0, 6, 6]], ['partial-repair [[-3, 6, 6], [0, 1, 1, 1], 5]', [[-3, 6, 6], [0, 1, 1, 1], 5], [0, -3, 6, 6, 0]], ['partial-repair [[4], [1, 0, 0], 2]', [[4], [1, 0, 0], 2], [4, 0]], ['control [[1, -3, -5, 2, 2, -1, -3, 2, 4], [1, 1, 1, 0], 12]', [[1, -3, -5, 2, 2, -1, -3, 2, 4], [1, 1, 1, 0], 12], [1, -3, -5, 0, 2, 2, -1, 0, -3, 2, 4, 0]], ['control [[-5, -3, -1, 6, -3, -5, -5, -3], [1, 1, 0], 12]', [[-5, -3, -1, 6, -3, -5, -5, -3], [1, 1, 0], 12], [-5, -3, 0, -1, 6, 0, -3, -5, 0, -5, -3, 0]], ['control [[1, 2], [1, 1, 0], 3]', [[1, 2], [1, 1, 0], 3], [1, 2, 0]], ['control [[1, 2, 3], [1, 1, 0], 3]', [[1, 2, 3], [1, 1, 0], 3], None]], [['regression [[6, 2, -1], [1, 0], 5]', [[6, 2, -1], [1, 0], 5], [6, 0, 2, 0, -1]], ['regression [[-3, 2, -3, -1, 4, 2, 1, 6, 6, -5], [1, 1, 0], 14]', [[-3, 2, -3, -1, 4, 2, 1, 6, 6, -5], [1, 1, 0], 14], [-3, 2, 0, -3, -1, 0, 4, 2, 0, 1, 6, 0, 6, -5]], ['partial-repair [[-1, 4, 1, -5, -3], [1, 0, 1, 1, 1, 0], 8]', [[-1, 4, 1, -5, -3], [1, 0, 1, 1, 1, 0], 8], [-1, 0, 4, 1, -5, 0, -3, 0]], ['partial-repair [[6, 4, 2], [0, 1, 1, 1], 5]', [[6, 4, 2], [0, 1, 1, 1], 5], [0, 6, 4, 2, 0]], ['control [[1, -3, -5, 2, 2, -1, -3, 2, 4], [1, 1, 1, 0], 12]', [[1, -3, -5, 2, 2, -1, -3, 2, 4], [1, 1, 1, 0], 12], [1, -3, -5, 0, 2, 2, -1, 0, -3, 2, 4, 0]], ['control [[-5, -3, -1, 6, -3, -5, -5, -3], [1, 1, 0], 12]', [[-5, -3, -1, 6, -3, -5, -5, -3], [1, 1, 0], 12], [-5, -3, 0, -1, 6, 0, -3, -5, 0, -5, -3, 0]], ['control [[1, 2], [1, 1, 0], 3]', [[1, 2], [1, 1, 0], 3], [1, 2, 0]], ['control [[1, 2, 3], [1, 1, 0], 3]', [[1, 2, 3], [1, 1, 0], 3], None]], [['regression [[7, 8, 9, 5], [1, 1, 0, 1], 5]', [[7, 8, 9, 5], [1, 1, 0, 1], 5], [7, 8, 0, 9, 5]], ['regression [[-5, -1, 4, 1, -3, 2, 4, 6, 1, -1], [1, 1, 0, 1], 13]', [[-5, -1, 4, 1, -3, 2, 4, 6, 1, -1], [1, 1, 0, 1], 13], [-5, -1, 0, 4, 1, -3, 0, 2, 4, 6, 0, 1, -1]], ['partial-repair [[4], [1, 0, 0], 2]', [[4], [1, 0, 0], 2], [4, 0]], ['partial-repair [[2, 1, -3, 6, -1, -5, -3], [1, 0, 1, 1, 1, 0], 10]', [[2, 1, -3, 6, -1, -5, -3], [1, 0, 1, 1, 1, 0], 10], [2, 0, 1, -3, 6, 0, -1, 0, -5, -3]], ['control [[1, -3, -5, 2, 2, -1, -3, 2, 4], [1, 1, 1, 0], 12]', [[1, -3, -5, 2, 2, -1, -3, 2, 4], [1, 1, 1, 0], 12], [1, -3, -5, 0, 2, 2, -1, 0, -3, 2, 4, 0]], ['control [[-5, -3, -1, 6, -3, -5, -5, -3], [1, 1, 0], 12]', [[-5, -3, -1, 6, -3, -5, -5, -3], [1, 1, 0], 12], [-5, -3, 0, -1, 6, 0, -3, -5, 0, -5, -3, 0]], ['control [[1, 2], [1, 1, 0], 3]', [[1, 2], [1, 1, 0], 3], [1, 2, 0]], ['control [[1, 2, 3], [1, 1, 0], 3]', [[1, 2, 3], [1, 1, 0], 3], None]], [['regression [[2, 1, -3, 6, -1, -5, -3], [1, 0, 1, 1, 1, 0], 10]', [[2, 1, -3, 6, -1, -5, -3], [1, 0, 1, 1, 1, 0], 10], [2, 0, 1, -3, 6, 0, -1, 0, -5, -3]], ['regression [[-1, 4, 1, -5, -3], [1, 0, 1, 1, 1, 0], 8]', [[-1, 4, 1, -5, -3], [1, 0, 1, 1, 1, 0], 8], [-1, 0, 4, 1, -5, 0, -3, 0]], ['partial-repair [[6, 4, 2], [0, 1, 1, 1], 5]', [[6, 4, 2], [0, 1, 1, 1], 5], [0, 6, 4, 2, 0]], ['partial-repair [[-3, 6, 6], [0, 1, 1, 1], 5]', [[-3, 6, 6], [0, 1, 1, 1], 5], [0, -3, 6, 6, 0]], ['control [[1, -3, -5, 2, 2, -1, -3, 2, 4], [1, 1, 1, 0], 12]', [[1, -3, -5, 2, 2, -1, -3, 2, 4], [1, 1, 1, 0], 12], [1, -3, -5, 0, 2, 2, -1, 0, -3, 2, 4, 0]], ['control [[-5, -3, -1, 6, -3, -5, -5, -3], [1, 1, 0], 12]', [[-5, -3, -1, 6, -3, -5, -5, -3], [1, 1, 0], 12], [-5, -3, 0, -1, 6, 0, -3, -5, 0, -5, -3, 0]], ['control [[1, 2], [1, 1, 0], 3]', [[1, 2], [1, 1, 0], 3], [1, 2, 0]], ['control [[1, 2, 3], [1, 1, 0], 3]', [[1, 2, 3], [1, 1, 0], 3], 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 [[-5, -1, 4, 1, -3, 2, 4, 6, 1, -1], [1, 1, 0, 1], 13]	`[-5, -1, 0, 4, 1, -3, 0, 2, 4, 6, 0, 1, -1]`	`[-5, -1, 0, 4, 1, -3, 0, 2, 4, 6, 0, 1, -1]`	Passed
regression [[-1, -3, 1, 4, -3], [1, 1, 0, 1], 6]	`[-1, -3, 0, 1, 4, -3]`	`[-1, -3, 0, 1, 4, -3]`	Passed
partial-repair [[2, 1, -3, 6, -1, -5, -3], [1, 0, 1, 1, 1, 0], 10]	`[2, 0, 1, -3, 6, 0, -1, 0, -5, -3]`	`[2, 0, 1, -3, 6, 0, -1, 0, -5, -3]`	Passed
partial-repair [[-1, 4, 1, -5, -3], [1, 0, 1, 1, 1, 0], 8]	`[-1, 0, 4, 1, -5, 0, -3, 0]`	`[-1, 0, 4, 1, -5, 0, -3, 0]`	Passed
control [[1, -3, -5, 2, 2, -1, -3, 2, 4], [1, 1, 1, 0], 12]	`[1, -3, -5, 0, 2, 2, -1, 0, -3, 2, 4, 0]`	`[1, -3, -5, 0, 2, 2, -1, 0, -3, 2, 4, 0]`	Passed
control [[-5, -3, -1, 6, -3, -5, -5, -3], [1, 1, 0], 12]	`[-5, -3, 0, -1, 6, 0, -3, -5, 0, -5, -3, 0]`	`[-5, -3, 0, -1, 6, 0, -3, -5, 0, -5, -3, 0]`	Passed
control [[1, 2], [1, 1, 0], 3]	`[1, 2, 0]`	`[1, 2, 0]`	Passed
control [[1, 2, 3], [1, 1, 0], 3]	`None`	`None`	Passed

SHA-256 / 9bcac2248cd1399d60ffd642ba1d42cafaaecd4cf78609eaa4b8196cba270383

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 2026-09-29T14:48:35.995382+00:00.

Case digest / 76fc0f99bc8277b6cf73329a11f7a08c6d9b46e1d5742530d272258df4330a03