{"abstract":"Decoding needs more iterations or fails where parallel flipping succeeds.","category":"Error-correcting codes","checks":8,"contract":"Parallel Gallager bit-flipping decoder. H lists the variable indices of each parity check. In each iteration: if every check is satisfied stop with success; otherwise count, per bit, the unsatisfied checks it joins and flip all bits that reach the maximum count. At most max_iter flipping iterations are performed and the syndrome is checked after the last one. Return [bits, iterations performed, success].","contract_signature":"H, r, max_iter","evaluation_group":"w2-error_correcting_codes-ldpc-bit-flipping","failed_approach":"Flipping every bit in any unsatisfied check overcorrects.","family":"w2-error_correcting_codes-ldpc-bit-flipping-flip-set","id":"FA-72111","implementations":{"attempt":{"sha256":"a22b196101d81f765b1e68f5ce22852590c568bc097b4765efa71ab39644ffe4","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(H, r, max_iter):\n    c = list(r)\n    for it in range(max_iter + 1):\n        unsat = [chk for chk in H if sum(c[v] for v in chk) % 2]\n        if not unsat:\n            return [c, it, True]\n        if it == max_iter:\n            break\n        cnt = [0] * len(c)\n        for chk in unsat:\n            for v in chk:\n                cnt[v] += 1\n        top = max(cnt)\n        c = [b ^ 1 if cnt[k] >= 1 else b for k, b in enumerate(c)]\n    return [c, max_iter, False]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['regression [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 1, 0], 3]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 1, 0], 3], [[0, 0, 0, 0, 0, 0, 0], 2, True]], ['regression [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 1, 0, 0, 1], 4]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 1, 0, 0, 1], 4], [[0, 0, 1, 1, 0, 0, 1], 2, True]], ['control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 2]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 2], [[0, 0, 0, 0, 0, 0, 0], 0, True]], ['control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 0]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 0], [[0, 0, 0, 0, 0, 0, 0], 0, True]], ['control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 3]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 3], [[0, 0, 0, 0, 0, 0, 0], 0, True]], ['control [[[0, 1, 3], [1, 2, 4], [0, 2, 5], [3, 4, 5]], [0, 0, 0, 0, 0, 0], 1]', [[[0, 1, 3], [1, 2, 4], [0, 2, 5], [3, 4, 5]], [0, 0, 0, 0, 0, 0], 1], [[0, 0, 0, 0, 0, 0], 0, True]], ['control [[[0, 1, 3], [1, 2, 4], [0, 2, 5], [3, 4, 5]], [0, 0, 0, 0, 0, 0], 4]', [[[0, 1, 3], [1, 2, 4], [0, 2, 5], [3, 4, 5]], [0, 0, 0, 0, 0, 0], 4], [[0, 0, 0, 0, 0, 0], 0, True]], ['control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 1, 1, 0, 0, 1, 1], 3]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 1, 1, 0, 0, 1, 1], 3], [[0, 1, 1, 0, 0, 1, 1], 0, True]]], [['regression [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 1, 0], 2]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 1, 0], 2], [[0, 0, 0, 0, 0, 0, 0], 2, True]], ['regression [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 1, 0, 0, 0, 0, 1], 2]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 1, 0, 0, 0, 0, 1], 2], [[0, 1, 0, 0, 1, 0, 1], 2, True]], ['partial-repair [[[0, 1, 3], [1, 2, 4], [0, 2, 5], [3, 4, 5]], [0, 0, 0, 0, 1, 1], 2]', [[[0, 1, 3], [1, 2, 4], [0, 2, 5], [3, 4, 5]], [0, 0, 0, 0, 1, 1], 2], [[0, 0, 1, 0, 1, 1], 1, True]], ['control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 1, 1, 0, 0, 1, 1], 3]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 1, 1, 0, 0, 1, 1], 3], [[0, 1, 1, 0, 0, 1, 1], 0, True]], ['control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 1, 1, 0, 1, 1, 1], 0]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 1, 1, 0, 1, 1, 1], 0], [[0, 1, 1, 0, 1, 1, 1], 0, False]], ['control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [1, 1, 1, 0, 0, 0, 0], 2]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [1, 1, 1, 0, 0, 0, 0], 2], [[1, 1, 1, 0, 0, 0, 0], 0, True]], ['control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 2]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 2], [[0, 0, 0, 0, 0, 0, 0], 0, True]], ['control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 0]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 0], [[0, 0, 0, 0, 0, 0, 0], 0, True]]], [['regression [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 1, 0], 3]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 1, 0], 3], [[0, 0, 0, 0, 0, 0, 0], 2, True]], ['regression [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 1, 0, 0, 1], 4]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 1, 0, 0, 1], 4], [[0, 0, 1, 1, 0, 0, 1], 2, True]], ['partial-repair [[[0, 1, 3], [1, 2, 4], [0, 2, 5], [3, 4, 5]], [1, 1, 0, 0, 0, 0], 4]', [[[0, 1, 3], [1, 2, 4], [0, 2, 5], [3, 4, 5]], [1, 1, 0, 0, 0, 0], 4], [[1, 1, 1, 0, 0, 0], 1, True]], ['partial-repair [[[0, 1, 3], [1, 2, 4], [0, 2, 5], [3, 4, 5]], [0, 0, 0, 1, 0, 0], 1]', [[[0, 1, 3], [1, 2, 4], [0, 2, 5], [3, 4, 5]], [0, 0, 0, 1, 0, 0], 1], [[0, 0, 0, 0, 0, 0], 1, True]], ['control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 3]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 3], [[0, 0, 0, 0, 0, 0, 0], 0, True]], ['control [[[0, 1, 3], [1, 2, 4], [0, 2, 5], [3, 4, 5]], [0, 0, 0, 0, 0, 0], 1]', [[[0, 1, 3], [1, 2, 4], [0, 2, 5], [3, 4, 5]], [0, 0, 0, 0, 0, 0], 1], [[0, 0, 0, 0, 0, 0], 0, True]], ['control [[[0, 1, 3], [1, 2, 4], [0, 2, 5], [3, 4, 5]], [0, 0, 0, 0, 0, 0], 4]', [[[0, 1, 3], [1, 2, 4], [0, 2, 5], [3, 4, 5]], [0, 0, 0, 0, 0, 0], 4], [[0, 0, 0, 0, 0, 0], 0, True]], ['control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 1, 1, 0, 0, 1, 1], 3]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 1, 1, 0, 0, 1, 1], 3], [[0, 1, 1, 0, 0, 1, 1], 0, True]]], [['regression [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 1, 0], 2]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 1, 0], 2], [[0, 0, 0, 0, 0, 0, 0], 2, True]], ['regression [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 1, 0, 0, 0, 0, 1], 2]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 1, 0, 0, 0, 0, 1], 2], [[0, 1, 0, 0, 1, 0, 1], 2, True]], ['partial-repair [[[0, 1, 3], [1, 2, 4], [0, 2, 5], [3, 4, 5]], [0, 0, 0, 1, 0, 0], 2]', [[[0, 1, 3], [1, 2, 4], [0, 2, 5], [3, 4, 5]], [0, 0, 0, 1, 0, 0], 2], [[0, 0, 0, 0, 0, 0], 1, True]], ['partial-repair [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 1, 1, 0, 1, 1, 1], 1]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 1, 1, 0, 1, 1, 1], 1], [[0, 1, 1, 0, 0, 1, 0], 1, False]], ['control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [1, 1, 1, 0, 0, 0, 0], 2]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [1, 1, 1, 0, 0, 0, 0], 2], [[1, 1, 1, 0, 0, 0, 0], 0, True]], ['control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 2]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 2], [[0, 0, 0, 0, 0, 0, 0], 0, True]], ['control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 0]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 0], [[0, 0, 0, 0, 0, 0, 0], 0, True]], ['control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 3]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 3], [[0, 0, 0, 0, 0, 0, 0], 0, True]]], [['regression [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 1, 0], 3]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 1, 0], 3], [[0, 0, 0, 0, 0, 0, 0], 2, True]], ['regression [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 1, 0, 0, 1], 4]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 1, 0, 0, 1], 4], [[0, 0, 1, 1, 0, 0, 1], 2, True]], ['control [[[0, 1, 3], [1, 2, 4], [0, 2, 5], [3, 4, 5]], [0, 0, 0, 0, 0, 0], 4]', [[[0, 1, 3], [1, 2, 4], [0, 2, 5], [3, 4, 5]], [0, 0, 0, 0, 0, 0], 4], [[0, 0, 0, 0, 0, 0], 0, True]], ['control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 1, 1, 0, 0, 1, 1], 3]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 1, 1, 0, 0, 1, 1], 3], [[0, 1, 1, 0, 0, 1, 1], 0, True]], ['control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 1, 1, 0, 1, 1, 1], 0]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 1, 1, 0, 1, 1, 1], 0], [[0, 1, 1, 0, 1, 1, 1], 0, False]], ['control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [1, 1, 1, 0, 0, 0, 0], 2]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [1, 1, 1, 0, 0, 0, 0], 2], [[1, 1, 1, 0, 0, 0, 0], 0, True]], ['control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 2]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 2], [[0, 0, 0, 0, 0, 0, 0], 0, True]], ['control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 0]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 0], [[0, 0, 0, 0, 0, 0, 0], 0, True]]]]\nfor label, args, expected in fixtures[N - 1]:\n    check(label, solve(*args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"broken":{"sha256":"a9514862e724bd473cc4de0e46ae2ba7f9a636661931af79f0a327a4f8e8e7c4","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(H, r, max_iter):\n    c = list(r)\n    for it in range(max_iter + 1):\n        unsat = [chk for chk in H if sum(c[v] for v in chk) % 2]\n        if not unsat:\n            return [c, it, True]\n        if it == max_iter:\n            break\n        cnt = [0] * len(c)\n        for chk in unsat:\n            for v in chk:\n                cnt[v] += 1\n        top = max(cnt)\n        c = [b ^ 1 if k == cnt.index(top) else b for k, b in enumerate(c)]\n    return [c, max_iter, False]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['regression [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 1, 0], 3]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 1, 0], 3], [[0, 0, 0, 0, 0, 0, 0], 2, True]], ['regression [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 1, 0, 0, 1], 4]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 1, 0, 0, 1], 4], [[0, 0, 1, 1, 0, 0, 1], 2, True]], ['control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 2]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 2], [[0, 0, 0, 0, 0, 0, 0], 0, True]], ['control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 0]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 0], [[0, 0, 0, 0, 0, 0, 0], 0, True]], ['control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 3]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 3], [[0, 0, 0, 0, 0, 0, 0], 0, True]], ['control [[[0, 1, 3], [1, 2, 4], [0, 2, 5], [3, 4, 5]], [0, 0, 0, 0, 0, 0], 1]', [[[0, 1, 3], [1, 2, 4], [0, 2, 5], [3, 4, 5]], [0, 0, 0, 0, 0, 0], 1], [[0, 0, 0, 0, 0, 0], 0, True]], ['control [[[0, 1, 3], [1, 2, 4], [0, 2, 5], [3, 4, 5]], [0, 0, 0, 0, 0, 0], 4]', [[[0, 1, 3], [1, 2, 4], [0, 2, 5], [3, 4, 5]], [0, 0, 0, 0, 0, 0], 4], [[0, 0, 0, 0, 0, 0], 0, True]], ['control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 1, 1, 0, 0, 1, 1], 3]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 1, 1, 0, 0, 1, 1], 3], [[0, 1, 1, 0, 0, 1, 1], 0, True]]], [['regression [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 1, 0], 2]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 1, 0], 2], [[0, 0, 0, 0, 0, 0, 0], 2, True]], ['regression [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 1, 0, 0, 0, 0, 1], 2]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 1, 0, 0, 0, 0, 1], 2], [[0, 1, 0, 0, 1, 0, 1], 2, True]], ['partial-repair [[[0, 1, 3], [1, 2, 4], [0, 2, 5], [3, 4, 5]], [0, 0, 0, 0, 1, 1], 2]', [[[0, 1, 3], [1, 2, 4], [0, 2, 5], [3, 4, 5]], [0, 0, 0, 0, 1, 1], 2], [[0, 0, 1, 0, 1, 1], 1, True]], ['control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 1, 1, 0, 0, 1, 1], 3]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 1, 1, 0, 0, 1, 1], 3], [[0, 1, 1, 0, 0, 1, 1], 0, True]], ['control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 1, 1, 0, 1, 1, 1], 0]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 1, 1, 0, 1, 1, 1], 0], [[0, 1, 1, 0, 1, 1, 1], 0, False]], ['control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [1, 1, 1, 0, 0, 0, 0], 2]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [1, 1, 1, 0, 0, 0, 0], 2], [[1, 1, 1, 0, 0, 0, 0], 0, True]], ['control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 2]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 2], [[0, 0, 0, 0, 0, 0, 0], 0, True]], ['control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 0]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 0], [[0, 0, 0, 0, 0, 0, 0], 0, True]]], [['regression [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 1, 0], 3]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 1, 0], 3], [[0, 0, 0, 0, 0, 0, 0], 2, True]], ['regression [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 1, 0, 0, 1], 4]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 1, 0, 0, 1], 4], [[0, 0, 1, 1, 0, 0, 1], 2, True]], ['partial-repair [[[0, 1, 3], [1, 2, 4], [0, 2, 5], [3, 4, 5]], [1, 1, 0, 0, 0, 0], 4]', [[[0, 1, 3], [1, 2, 4], [0, 2, 5], [3, 4, 5]], [1, 1, 0, 0, 0, 0], 4], [[1, 1, 1, 0, 0, 0], 1, True]], ['partial-repair [[[0, 1, 3], [1, 2, 4], [0, 2, 5], [3, 4, 5]], [0, 0, 0, 1, 0, 0], 1]', [[[0, 1, 3], [1, 2, 4], [0, 2, 5], [3, 4, 5]], [0, 0, 0, 1, 0, 0], 1], [[0, 0, 0, 0, 0, 0], 1, True]], ['control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 3]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 3], [[0, 0, 0, 0, 0, 0, 0], 0, True]], ['control [[[0, 1, 3], [1, 2, 4], [0, 2, 5], [3, 4, 5]], [0, 0, 0, 0, 0, 0], 1]', [[[0, 1, 3], [1, 2, 4], [0, 2, 5], [3, 4, 5]], [0, 0, 0, 0, 0, 0], 1], [[0, 0, 0, 0, 0, 0], 0, True]], ['control [[[0, 1, 3], [1, 2, 4], [0, 2, 5], [3, 4, 5]], [0, 0, 0, 0, 0, 0], 4]', [[[0, 1, 3], [1, 2, 4], [0, 2, 5], [3, 4, 5]], [0, 0, 0, 0, 0, 0], 4], [[0, 0, 0, 0, 0, 0], 0, True]], ['control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 1, 1, 0, 0, 1, 1], 3]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 1, 1, 0, 0, 1, 1], 3], [[0, 1, 1, 0, 0, 1, 1], 0, True]]], [['regression [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 1, 0], 2]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 1, 0], 2], [[0, 0, 0, 0, 0, 0, 0], 2, True]], ['regression [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 1, 0, 0, 0, 0, 1], 2]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 1, 0, 0, 0, 0, 1], 2], [[0, 1, 0, 0, 1, 0, 1], 2, True]], ['partial-repair [[[0, 1, 3], [1, 2, 4], [0, 2, 5], [3, 4, 5]], [0, 0, 0, 1, 0, 0], 2]', [[[0, 1, 3], [1, 2, 4], [0, 2, 5], [3, 4, 5]], [0, 0, 0, 1, 0, 0], 2], [[0, 0, 0, 0, 0, 0], 1, True]], ['partial-repair [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 1, 1, 0, 1, 1, 1], 1]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 1, 1, 0, 1, 1, 1], 1], [[0, 1, 1, 0, 0, 1, 0], 1, False]], ['control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [1, 1, 1, 0, 0, 0, 0], 2]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [1, 1, 1, 0, 0, 0, 0], 2], [[1, 1, 1, 0, 0, 0, 0], 0, True]], ['control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 2]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 2], [[0, 0, 0, 0, 0, 0, 0], 0, True]], ['control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 0]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 0], [[0, 0, 0, 0, 0, 0, 0], 0, True]], ['control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 3]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 3], [[0, 0, 0, 0, 0, 0, 0], 0, True]]], [['regression [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 1, 0], 3]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 1, 0], 3], [[0, 0, 0, 0, 0, 0, 0], 2, True]], ['regression [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 1, 0, 0, 1], 4]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 1, 0, 0, 1], 4], [[0, 0, 1, 1, 0, 0, 1], 2, True]], ['control [[[0, 1, 3], [1, 2, 4], [0, 2, 5], [3, 4, 5]], [0, 0, 0, 0, 0, 0], 4]', [[[0, 1, 3], [1, 2, 4], [0, 2, 5], [3, 4, 5]], [0, 0, 0, 0, 0, 0], 4], [[0, 0, 0, 0, 0, 0], 0, True]], ['control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 1, 1, 0, 0, 1, 1], 3]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 1, 1, 0, 0, 1, 1], 3], [[0, 1, 1, 0, 0, 1, 1], 0, True]], ['control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 1, 1, 0, 1, 1, 1], 0]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 1, 1, 0, 1, 1, 1], 0], [[0, 1, 1, 0, 1, 1, 1], 0, False]], ['control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [1, 1, 1, 0, 0, 0, 0], 2]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [1, 1, 1, 0, 0, 0, 0], 2], [[1, 1, 1, 0, 0, 0, 0], 0, True]], ['control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 2]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 2], [[0, 0, 0, 0, 0, 0, 0], 0, True]], ['control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 0]', [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 0], [[0, 0, 0, 0, 0, 0, 0], 0, True]]]]\nfor label, args, expected in fixtures[N - 1]:\n    check(label, solve(*args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"}},"limitations":"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.","method":"Deterministic executable model with adversarial boundary fixtures.","provenance":{"created_by":"Failure Map","dependencies":"Python standard library","family":"w2-error_correcting_codes-ldpc-bit-flipping-flip-set","generated_at":"2026-09-29T14:48:35.594544+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Hard-decision LDPC decoders in flash controllers use bit flipping as a low-power first pass.","root_cause":"Only the first bit with the maximum unsatisfied count is flipped.","sha256":"1d30bfe7f0a4141daf6f2e02687b177b1e65fd79e3c521c0bc7d1c613d8c0f2d","title":"Bit flipping flips only the first most-suspect bit · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verified":true,"visibility":"public","verification":{"attempt":{"elapsed_ms":40.253,"exit_code":1,"observations":[{"actual":[[0,1,1,1,1,0,1],3,false],"check":"regression [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 1, 0], 3]","expected":[[0,0,0,0,0,0,0],2,true],"passed":false},{"actual":[[0,0,0,0,0,0,1],4,false],"check":"regression [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 1, 0, 0, 1], 4]","expected":[[0,0,1,1,0,0,1],2,true],"passed":false},{"actual":[[0,0,0,0,0,0,0],0,true],"check":"control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 2]","expected":[[0,0,0,0,0,0,0],0,true],"passed":true},{"actual":[[0,0,0,0,0,0,0],0,true],"check":"control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 0]","expected":[[0,0,0,0,0,0,0],0,true],"passed":true},{"actual":[[0,0,0,0,0,0,0],0,true],"check":"control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 3]","expected":[[0,0,0,0,0,0,0],0,true],"passed":true},{"actual":[[0,0,0,0,0,0],0,true],"check":"control [[[0, 1, 3], [1, 2, 4], [0, 2, 5], [3, 4, 5]], [0, 0, 0, 0, 0, 0], 1]","expected":[[0,0,0,0,0,0],0,true],"passed":true},{"actual":[[0,0,0,0,0,0],0,true],"check":"control [[[0, 1, 3], [1, 2, 4], [0, 2, 5], [3, 4, 5]], [0, 0, 0, 0, 0, 0], 4]","expected":[[0,0,0,0,0,0],0,true],"passed":true},{"actual":[[0,1,1,0,0,1,1],0,true],"check":"control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 1, 1, 0, 0, 1, 1], 3]","expected":[[0,1,1,0,0,1,1],0,true],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 1, 0], 3]\", \"actual\": [[0, 1, 1, 1, 1, 0, 1], 3, false], \"expected\": [[0, 0, 0, 0, 0, 0, 0], 2, true], \"passed\": false}, {\"check\": \"regression [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 1, 0, 0, 1], 4]\", \"actual\": [[0, 0, 0, 0, 0, 0, 1], 4, false], \"expected\": [[0, 0, 1, 1, 0, 0, 1], 2, true], \"passed\": false}, {\"check\": \"control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 2]\", \"actual\": [[0, 0, 0, 0, 0, 0, 0], 0, true], \"expected\": [[0, 0, 0, 0, 0, 0, 0], 0, true], \"passed\": true}, {\"check\": \"control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 0]\", \"actual\": [[0, 0, 0, 0, 0, 0, 0], 0, true], \"expected\": [[0, 0, 0, 0, 0, 0, 0], 0, true], \"passed\": true}, {\"check\": \"control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 3]\", \"actual\": [[0, 0, 0, 0, 0, 0, 0], 0, true], \"expected\": [[0, 0, 0, 0, 0, 0, 0], 0, true], \"passed\": true}, {\"check\": \"control [[[0, 1, 3], [1, 2, 4], [0, 2, 5], [3, 4, 5]], [0, 0, 0, 0, 0, 0], 1]\", \"actual\": [[0, 0, 0, 0, 0, 0], 0, true], \"expected\": [[0, 0, 0, 0, 0, 0], 0, true], \"passed\": true}, {\"check\": \"control [[[0, 1, 3], [1, 2, 4], [0, 2, 5], [3, 4, 5]], [0, 0, 0, 0, 0, 0], 4]\", \"actual\": [[0, 0, 0, 0, 0, 0], 0, true], \"expected\": [[0, 0, 0, 0, 0, 0], 0, true], \"passed\": true}, {\"check\": \"control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 1, 1, 0, 0, 1, 1], 3]\", \"actual\": [[0, 1, 1, 0, 0, 1, 1], 0, true], \"expected\": [[0, 1, 1, 0, 0, 1, 1], 0, true], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":39.178,"exit_code":1,"observations":[{"actual":[[0,0,0,0,0,0,0],1,true],"check":"regression [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 1, 0], 3]","expected":[[0,0,0,0,0,0,0],2,true],"passed":false},{"actual":[[0,0,1,1,0,0,1],1,true],"check":"regression [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 1, 0, 0, 1], 4]","expected":[[0,0,1,1,0,0,1],2,true],"passed":false},{"actual":[[0,0,0,0,0,0,0],0,true],"check":"control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 2]","expected":[[0,0,0,0,0,0,0],0,true],"passed":true},{"actual":[[0,0,0,0,0,0,0],0,true],"check":"control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 0]","expected":[[0,0,0,0,0,0,0],0,true],"passed":true},{"actual":[[0,0,0,0,0,0,0],0,true],"check":"control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 3]","expected":[[0,0,0,0,0,0,0],0,true],"passed":true},{"actual":[[0,0,0,0,0,0],0,true],"check":"control [[[0, 1, 3], [1, 2, 4], [0, 2, 5], [3, 4, 5]], [0, 0, 0, 0, 0, 0], 1]","expected":[[0,0,0,0,0,0],0,true],"passed":true},{"actual":[[0,0,0,0,0,0],0,true],"check":"control [[[0, 1, 3], [1, 2, 4], [0, 2, 5], [3, 4, 5]], [0, 0, 0, 0, 0, 0], 4]","expected":[[0,0,0,0,0,0],0,true],"passed":true},{"actual":[[0,1,1,0,0,1,1],0,true],"check":"control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 1, 1, 0, 0, 1, 1], 3]","expected":[[0,1,1,0,0,1,1],0,true],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 1, 0], 3]\", \"actual\": [[0, 0, 0, 0, 0, 0, 0], 1, true], \"expected\": [[0, 0, 0, 0, 0, 0, 0], 2, true], \"passed\": false}, {\"check\": \"regression [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 1, 0, 0, 1], 4]\", \"actual\": [[0, 0, 1, 1, 0, 0, 1], 1, true], \"expected\": [[0, 0, 1, 1, 0, 0, 1], 2, true], \"passed\": false}, {\"check\": \"control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 2]\", \"actual\": [[0, 0, 0, 0, 0, 0, 0], 0, true], \"expected\": [[0, 0, 0, 0, 0, 0, 0], 0, true], \"passed\": true}, {\"check\": \"control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 0]\", \"actual\": [[0, 0, 0, 0, 0, 0, 0], 0, true], \"expected\": [[0, 0, 0, 0, 0, 0, 0], 0, true], \"passed\": true}, {\"check\": \"control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 0, 0], 3]\", \"actual\": [[0, 0, 0, 0, 0, 0, 0], 0, true], \"expected\": [[0, 0, 0, 0, 0, 0, 0], 0, true], \"passed\": true}, {\"check\": \"control [[[0, 1, 3], [1, 2, 4], [0, 2, 5], [3, 4, 5]], [0, 0, 0, 0, 0, 0], 1]\", \"actual\": [[0, 0, 0, 0, 0, 0], 0, true], \"expected\": [[0, 0, 0, 0, 0, 0], 0, true], \"passed\": true}, {\"check\": \"control [[[0, 1, 3], [1, 2, 4], [0, 2, 5], [3, 4, 5]], [0, 0, 0, 0, 0, 0], 4]\", \"actual\": [[0, 0, 0, 0, 0, 0], 0, true], \"expected\": [[0, 0, 0, 0, 0, 0], 0, true], \"passed\": true}, {\"check\": \"control [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 1, 1, 0, 0, 1, 1], 3]\", \"actual\": [[0, 1, 1, 0, 0, 1, 1], 0, true], \"expected\": [[0, 1, 1, 0, 0, 1, 1], 0, true], \"passed\": true}], \"passed\": false}\n"}},"member_only":{"stages":["fixed"],"fields":["implementations.fixed","verification.fixed","harness","repair"],"note":"The verified repair, its recorded checks, the repair description, and the scoring harness are available to members."}}