{"abstract":"A surplus exactly at the threshold is not refunded.","category":"Loan amortization schedules","checks":7,"contract":"x = {'disbursements': annual amounts, 'low_point': projected lowest balance, 'cushion_months', 'refund_threshold'}. total = sum; base = round_half_up(total/12); cushion = round_half_up(total*cushion_months/12); diff = low_point - cushion; shortage = max(0, -diff) is collected over 12 months rounded up; surplus = max(0, diff) is refunded when >= refund_threshold, otherwise floor(surplus/12) is credited monthly. Return {'base', 'cushion', 'shortage', 'refund', 'monthly'}.","evaluation_group":"w2-loan-amortization-schedules-escrow-analysis","failed_approach":"Testing the low point instead of the surplus ignores the cushion.","family":"w2-loan-amortization-schedules-escrow-analysis-refund-threshold-test","id":"FA-58681","implementations":{"attempt":{"sha256":"34517b3e7fb9ae7ac2dd3a289edd0176a70a2dac034a34dc1b1b0666a55c6261","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(x):\n    def rnd(n, d):\n        q, r = divmod(n, d)\n        return q + (1 if 2 * r >= d else 0)\n    total = sum(x['disbursements'])\n    base = rnd(total, 12)\n    cushion = rnd(total * x['cushion_months'], 12)\n    diff = x['low_point'] - cushion\n    shortage = max(0, -diff)\n    surplus = max(0, diff)\n    refund = surplus if x['low_point'] >= x['refund_threshold'] else 0\n    monthly = base + (shortage + 11) // 12 - (0 if refund else surplus // 12)\n    return {'base': base, 'cushion': cushion, 'shortage': shortage, 'refund': refund, 'monthly': monthly}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['regression: surplus exactly at threshold', {'disbursements': [120000], 'low_point': 25000, 'cushion_months': 2, 'refund_threshold': 5000}, {'base': 10000, 'cushion': 20000, 'shortage': 0, 'refund': 5000, 'monthly': 10000}], ['regression: refund threshold test, partial-repair probe', {'disbursements': [7, 120000, 7], 'low_point': 40000, 'cushion_months': 2, 'refund_threshold': 20000}, {'base': 10001, 'cushion': 20002, 'shortage': 0, 'refund': 0, 'monthly': 8335}], ['control 1', {'disbursements': [120000, 36000, 99999], 'low_point': -5000, 'cushion_months': 2, 'refund_threshold': 20000}, {'base': 21333, 'cushion': 42667, 'shortage': 47667, 'refund': 0, 'monthly': 25306}], ['control 2', {'disbursements': [99999, 250000], 'low_point': 80000, 'cushion_months': 1, 'refund_threshold': 0}, {'base': 29167, 'cushion': 29167, 'shortage': 0, 'refund': 50833, 'monthly': 29167}], ['control 3', {'disbursements': [120000], 'low_point': 0, 'cushion_months': 1, 'refund_threshold': 20000}, {'base': 10000, 'cushion': 10000, 'shortage': 10000, 'refund': 0, 'monthly': 10834}], ['control 4', {'disbursements': [36000, 120000, 7], 'low_point': -5000, 'cushion_months': 2, 'refund_threshold': 20000}, {'base': 13001, 'cushion': 26001, 'shortage': 31001, 'refund': 0, 'monthly': 15585}], ['control 5', {'disbursements': [99999, 250000, 7], 'low_point': -5000, 'cushion_months': 1, 'refund_threshold': 20000}, {'base': 29167, 'cushion': 29167, 'shortage': 34167, 'refund': 0, 'monthly': 32015}]], [['regression: surplus exactly at threshold', {'disbursements': [120000], 'low_point': 25000, 'cushion_months': 2, 'refund_threshold': 5000}, {'base': 10000, 'cushion': 20000, 'shortage': 0, 'refund': 5000, 'monthly': 10000}], ['regression: refund threshold test', {'disbursements': [120000], 'low_point': 40000, 'cushion_months': 2, 'refund_threshold': 20000}, {'base': 10000, 'cushion': 20000, 'shortage': 0, 'refund': 20000, 'monthly': 10000}], ['regression: refund threshold test, partial-repair probe', {'disbursements': [36000], 'low_point': 10000, 'cushion_months': 2, 'refund_threshold': 5000}, {'base': 3000, 'cushion': 6000, 'shortage': 0, 'refund': 0, 'monthly': 2667}], ['control 1', {'disbursements': [120000, 36000], 'low_point': 80000, 'cushion_months': 1, 'refund_threshold': 0}, {'base': 13000, 'cushion': 13000, 'shortage': 0, 'refund': 67000, 'monthly': 13000}], ['control 2', {'disbursements': [7, 36000], 'low_point': 0, 'cushion_months': 0, 'refund_threshold': 0}, {'base': 3001, 'cushion': 0, 'shortage': 0, 'refund': 0, 'monthly': 3001}], ['control 3', {'disbursements': [120000, 120000], 'low_point': 40000, 'cushion_months': 2, 'refund_threshold': 5000}, {'base': 20000, 'cushion': 40000, 'shortage': 0, 'refund': 0, 'monthly': 20000}], ['control 4', {'disbursements': [250000, 99999, 120000], 'low_point': 150000, 'cushion_months': 5, 'refund_threshold': 20000}, {'base': 39167, 'cushion': 195833, 'shortage': 45833, 'refund': 0, 'monthly': 42987}]], [['regression: surplus exactly at threshold', {'disbursements': [120000], 'low_point': 25000, 'cushion_months': 2, 'refund_threshold': 5000}, {'base': 10000, 'cushion': 20000, 'shortage': 0, 'refund': 5000, 'monthly': 10000}], ['regression: refund threshold test', {'disbursements': [99999, 99999, 250000], 'low_point': 80000, 'cushion_months': 2, 'refund_threshold': 5000}, {'base': 37500, 'cushion': 75000, 'shortage': 0, 'refund': 5000, 'monthly': 37500}], ['regression: refund threshold test, partial-repair probe', {'disbursements': [120000, 36000], 'low_point': 80000, 'cushion_months': 5, 'refund_threshold': 20000}, {'base': 13000, 'cushion': 65000, 'shortage': 0, 'refund': 0, 'monthly': 11750}], ['control 1', {'disbursements': [250000, 120000], 'low_point': 80000, 'cushion_months': 1, 'refund_threshold': 20000}, {'base': 30833, 'cushion': 30833, 'shortage': 0, 'refund': 49167, 'monthly': 30833}], ['control 2', {'disbursements': [36000], 'low_point': 0, 'cushion_months': 5, 'refund_threshold': 5000}, {'base': 3000, 'cushion': 15000, 'shortage': 15000, 'refund': 0, 'monthly': 4250}], ['control 3', {'disbursements': [7, 250000], 'low_point': 80000, 'cushion_months': 0, 'refund_threshold': 5000}, {'base': 20834, 'cushion': 0, 'shortage': 0, 'refund': 80000, 'monthly': 20834}], ['control 4', {'disbursements': [7, 36000], 'low_point': 80000, 'cushion_months': 1, 'refund_threshold': 0}, {'base': 3001, 'cushion': 3001, 'shortage': 0, 'refund': 76999, 'monthly': 3001}]], [['regression: surplus exactly at threshold', {'disbursements': [120000], 'low_point': 25000, 'cushion_months': 2, 'refund_threshold': 5000}, {'base': 10000, 'cushion': 20000, 'shortage': 0, 'refund': 5000, 'monthly': 10000}], ['regression: refund threshold test, partial-repair probe', {'disbursements': [99999, 250000], 'low_point': 150000, 'cushion_months': 5, 'refund_threshold': 5000}, {'base': 29167, 'cushion': 145833, 'shortage': 0, 'refund': 0, 'monthly': 28820}], ['control 1', {'disbursements': [36000], 'low_point': -5000, 'cushion_months': 0, 'refund_threshold': 0}, {'base': 3000, 'cushion': 0, 'shortage': 5000, 'refund': 0, 'monthly': 3417}], ['control 2', {'disbursements': [99999, 36000], 'low_point': 150000, 'cushion_months': 1, 'refund_threshold': 20000}, {'base': 11333, 'cushion': 11333, 'shortage': 0, 'refund': 138667, 'monthly': 11333}], ['control 3', {'disbursements': [36000, 7], 'low_point': 150000, 'cushion_months': 5, 'refund_threshold': 0}, {'base': 3001, 'cushion': 15003, 'shortage': 0, 'refund': 134997, 'monthly': 3001}], ['control 4', {'disbursements': [120000, 250000, 99999], 'low_point': 80000, 'cushion_months': 1, 'refund_threshold': 20000}, {'base': 39167, 'cushion': 39167, 'shortage': 0, 'refund': 40833, 'monthly': 39167}], ['control 5', {'disbursements': [36000, 7, 250000], 'low_point': 150000, 'cushion_months': 2, 'refund_threshold': 20000}, {'base': 23834, 'cushion': 47668, 'shortage': 0, 'refund': 102332, 'monthly': 23834}]], [['regression: surplus exactly at threshold', {'disbursements': [120000], 'low_point': 25000, 'cushion_months': 2, 'refund_threshold': 5000}, {'base': 10000, 'cushion': 20000, 'shortage': 0, 'refund': 5000, 'monthly': 10000}], ['regression: refund threshold test', {'disbursements': [120000], 'low_point': 40000, 'cushion_months': 2, 'refund_threshold': 20000}, {'base': 10000, 'cushion': 20000, 'shortage': 0, 'refund': 20000, 'monthly': 10000}], ['regression: refund threshold test, partial-repair probe', {'disbursements': [99999, 99999, 250000], 'low_point': 80000, 'cushion_months': 2, 'refund_threshold': 20000}, {'base': 37500, 'cushion': 75000, 'shortage': 0, 'refund': 0, 'monthly': 37084}], ['control 1', {'disbursements': [120000], 'low_point': 150000, 'cushion_months': 5, 'refund_threshold': 20000}, {'base': 10000, 'cushion': 50000, 'shortage': 0, 'refund': 100000, 'monthly': 10000}], ['control 2', {'disbursements': [7], 'low_point': 80000, 'cushion_months': 5, 'refund_threshold': 20000}, {'base': 1, 'cushion': 3, 'shortage': 0, 'refund': 79997, 'monthly': 1}], ['control 3', {'disbursements': [99999], 'low_point': -5000, 'cushion_months': 0, 'refund_threshold': 20000}, {'base': 8333, 'cushion': 0, 'shortage': 5000, 'refund': 0, 'monthly': 8750}], ['control 4', {'disbursements': [120000, 7], 'low_point': 0, 'cushion_months': 2, 'refund_threshold': 20000}, {'base': 10001, 'cushion': 20001, 'shortage': 20001, 'refund': 0, 'monthly': 11668}]]]\nfor label, args, expected in fixtures[N-1]:\n    try:\n        actual = solve(args)\n    except Exception as exc:\n        actual = 'raised ' + type(exc).__name__\n    check(label, actual, 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":"da69ad383f97ba0fc0d9fd062119e9cb5a3729a1a0084e8194f02fadb7f16506","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(x):\n    def rnd(n, d):\n        q, r = divmod(n, d)\n        return q + (1 if 2 * r >= d else 0)\n    total = sum(x['disbursements'])\n    base = rnd(total, 12)\n    cushion = rnd(total * x['cushion_months'], 12)\n    diff = x['low_point'] - cushion\n    shortage = max(0, -diff)\n    surplus = max(0, diff)\n    refund = surplus if surplus > x['refund_threshold'] else 0\n    monthly = base + (shortage + 11) // 12 - (0 if refund else surplus // 12)\n    return {'base': base, 'cushion': cushion, 'shortage': shortage, 'refund': refund, 'monthly': monthly}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['regression: surplus exactly at threshold', {'disbursements': [120000], 'low_point': 25000, 'cushion_months': 2, 'refund_threshold': 5000}, {'base': 10000, 'cushion': 20000, 'shortage': 0, 'refund': 5000, 'monthly': 10000}], ['regression: refund threshold test, partial-repair probe', {'disbursements': [7, 120000, 7], 'low_point': 40000, 'cushion_months': 2, 'refund_threshold': 20000}, {'base': 10001, 'cushion': 20002, 'shortage': 0, 'refund': 0, 'monthly': 8335}], ['control 1', {'disbursements': [120000, 36000, 99999], 'low_point': -5000, 'cushion_months': 2, 'refund_threshold': 20000}, {'base': 21333, 'cushion': 42667, 'shortage': 47667, 'refund': 0, 'monthly': 25306}], ['control 2', {'disbursements': [99999, 250000], 'low_point': 80000, 'cushion_months': 1, 'refund_threshold': 0}, {'base': 29167, 'cushion': 29167, 'shortage': 0, 'refund': 50833, 'monthly': 29167}], ['control 3', {'disbursements': [120000], 'low_point': 0, 'cushion_months': 1, 'refund_threshold': 20000}, {'base': 10000, 'cushion': 10000, 'shortage': 10000, 'refund': 0, 'monthly': 10834}], ['control 4', {'disbursements': [36000, 120000, 7], 'low_point': -5000, 'cushion_months': 2, 'refund_threshold': 20000}, {'base': 13001, 'cushion': 26001, 'shortage': 31001, 'refund': 0, 'monthly': 15585}], ['control 5', {'disbursements': [99999, 250000, 7], 'low_point': -5000, 'cushion_months': 1, 'refund_threshold': 20000}, {'base': 29167, 'cushion': 29167, 'shortage': 34167, 'refund': 0, 'monthly': 32015}]], [['regression: surplus exactly at threshold', {'disbursements': [120000], 'low_point': 25000, 'cushion_months': 2, 'refund_threshold': 5000}, {'base': 10000, 'cushion': 20000, 'shortage': 0, 'refund': 5000, 'monthly': 10000}], ['regression: refund threshold test', {'disbursements': [120000], 'low_point': 40000, 'cushion_months': 2, 'refund_threshold': 20000}, {'base': 10000, 'cushion': 20000, 'shortage': 0, 'refund': 20000, 'monthly': 10000}], ['regression: refund threshold test, partial-repair probe', {'disbursements': [36000], 'low_point': 10000, 'cushion_months': 2, 'refund_threshold': 5000}, {'base': 3000, 'cushion': 6000, 'shortage': 0, 'refund': 0, 'monthly': 2667}], ['control 1', {'disbursements': [120000, 36000], 'low_point': 80000, 'cushion_months': 1, 'refund_threshold': 0}, {'base': 13000, 'cushion': 13000, 'shortage': 0, 'refund': 67000, 'monthly': 13000}], ['control 2', {'disbursements': [7, 36000], 'low_point': 0, 'cushion_months': 0, 'refund_threshold': 0}, {'base': 3001, 'cushion': 0, 'shortage': 0, 'refund': 0, 'monthly': 3001}], ['control 3', {'disbursements': [120000, 120000], 'low_point': 40000, 'cushion_months': 2, 'refund_threshold': 5000}, {'base': 20000, 'cushion': 40000, 'shortage': 0, 'refund': 0, 'monthly': 20000}], ['control 4', {'disbursements': [250000, 99999, 120000], 'low_point': 150000, 'cushion_months': 5, 'refund_threshold': 20000}, {'base': 39167, 'cushion': 195833, 'shortage': 45833, 'refund': 0, 'monthly': 42987}]], [['regression: surplus exactly at threshold', {'disbursements': [120000], 'low_point': 25000, 'cushion_months': 2, 'refund_threshold': 5000}, {'base': 10000, 'cushion': 20000, 'shortage': 0, 'refund': 5000, 'monthly': 10000}], ['regression: refund threshold test', {'disbursements': [99999, 99999, 250000], 'low_point': 80000, 'cushion_months': 2, 'refund_threshold': 5000}, {'base': 37500, 'cushion': 75000, 'shortage': 0, 'refund': 5000, 'monthly': 37500}], ['regression: refund threshold test, partial-repair probe', {'disbursements': [120000, 36000], 'low_point': 80000, 'cushion_months': 5, 'refund_threshold': 20000}, {'base': 13000, 'cushion': 65000, 'shortage': 0, 'refund': 0, 'monthly': 11750}], ['control 1', {'disbursements': [250000, 120000], 'low_point': 80000, 'cushion_months': 1, 'refund_threshold': 20000}, {'base': 30833, 'cushion': 30833, 'shortage': 0, 'refund': 49167, 'monthly': 30833}], ['control 2', {'disbursements': [36000], 'low_point': 0, 'cushion_months': 5, 'refund_threshold': 5000}, {'base': 3000, 'cushion': 15000, 'shortage': 15000, 'refund': 0, 'monthly': 4250}], ['control 3', {'disbursements': [7, 250000], 'low_point': 80000, 'cushion_months': 0, 'refund_threshold': 5000}, {'base': 20834, 'cushion': 0, 'shortage': 0, 'refund': 80000, 'monthly': 20834}], ['control 4', {'disbursements': [7, 36000], 'low_point': 80000, 'cushion_months': 1, 'refund_threshold': 0}, {'base': 3001, 'cushion': 3001, 'shortage': 0, 'refund': 76999, 'monthly': 3001}]], [['regression: surplus exactly at threshold', {'disbursements': [120000], 'low_point': 25000, 'cushion_months': 2, 'refund_threshold': 5000}, {'base': 10000, 'cushion': 20000, 'shortage': 0, 'refund': 5000, 'monthly': 10000}], ['regression: refund threshold test, partial-repair probe', {'disbursements': [99999, 250000], 'low_point': 150000, 'cushion_months': 5, 'refund_threshold': 5000}, {'base': 29167, 'cushion': 145833, 'shortage': 0, 'refund': 0, 'monthly': 28820}], ['control 1', {'disbursements': [36000], 'low_point': -5000, 'cushion_months': 0, 'refund_threshold': 0}, {'base': 3000, 'cushion': 0, 'shortage': 5000, 'refund': 0, 'monthly': 3417}], ['control 2', {'disbursements': [99999, 36000], 'low_point': 150000, 'cushion_months': 1, 'refund_threshold': 20000}, {'base': 11333, 'cushion': 11333, 'shortage': 0, 'refund': 138667, 'monthly': 11333}], ['control 3', {'disbursements': [36000, 7], 'low_point': 150000, 'cushion_months': 5, 'refund_threshold': 0}, {'base': 3001, 'cushion': 15003, 'shortage': 0, 'refund': 134997, 'monthly': 3001}], ['control 4', {'disbursements': [120000, 250000, 99999], 'low_point': 80000, 'cushion_months': 1, 'refund_threshold': 20000}, {'base': 39167, 'cushion': 39167, 'shortage': 0, 'refund': 40833, 'monthly': 39167}], ['control 5', {'disbursements': [36000, 7, 250000], 'low_point': 150000, 'cushion_months': 2, 'refund_threshold': 20000}, {'base': 23834, 'cushion': 47668, 'shortage': 0, 'refund': 102332, 'monthly': 23834}]], [['regression: surplus exactly at threshold', {'disbursements': [120000], 'low_point': 25000, 'cushion_months': 2, 'refund_threshold': 5000}, {'base': 10000, 'cushion': 20000, 'shortage': 0, 'refund': 5000, 'monthly': 10000}], ['regression: refund threshold test', {'disbursements': [120000], 'low_point': 40000, 'cushion_months': 2, 'refund_threshold': 20000}, {'base': 10000, 'cushion': 20000, 'shortage': 0, 'refund': 20000, 'monthly': 10000}], ['regression: refund threshold test, partial-repair probe', {'disbursements': [99999, 99999, 250000], 'low_point': 80000, 'cushion_months': 2, 'refund_threshold': 20000}, {'base': 37500, 'cushion': 75000, 'shortage': 0, 'refund': 0, 'monthly': 37084}], ['control 1', {'disbursements': [120000], 'low_point': 150000, 'cushion_months': 5, 'refund_threshold': 20000}, {'base': 10000, 'cushion': 50000, 'shortage': 0, 'refund': 100000, 'monthly': 10000}], ['control 2', {'disbursements': [7], 'low_point': 80000, 'cushion_months': 5, 'refund_threshold': 20000}, {'base': 1, 'cushion': 3, 'shortage': 0, 'refund': 79997, 'monthly': 1}], ['control 3', {'disbursements': [99999], 'low_point': -5000, 'cushion_months': 0, 'refund_threshold': 20000}, {'base': 8333, 'cushion': 0, 'shortage': 5000, 'refund': 0, 'monthly': 8750}], ['control 4', {'disbursements': [120000, 7], 'low_point': 0, 'cushion_months': 2, 'refund_threshold': 20000}, {'base': 10001, 'cushion': 20001, 'shortage': 20001, 'refund': 0, 'monthly': 11668}]]]\nfor label, args, expected in fixtures[N-1]:\n    try:\n        actual = solve(args)\n    except Exception as exc:\n        actual = 'raised ' + type(exc).__name__\n    check(label, actual, 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"},"fixed":{"sha256":"85c1a2cacc3f9a9472beb84bf04a449a0f05613675601fce820d44c37e02da0b","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(x):\n    def rnd(n, d):\n        q, r = divmod(n, d)\n        return q + (1 if 2 * r >= d else 0)\n    total = sum(x['disbursements'])\n    base = rnd(total, 12)\n    cushion = rnd(total * x['cushion_months'], 12)\n    diff = x['low_point'] - cushion\n    shortage = max(0, -diff)\n    surplus = max(0, diff)\n    refund = surplus if surplus >= x['refund_threshold'] else 0\n    monthly = base + (shortage + 11) // 12 - (0 if refund else surplus // 12)\n    return {'base': base, 'cushion': cushion, 'shortage': shortage, 'refund': refund, 'monthly': monthly}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['regression: surplus exactly at threshold', {'disbursements': [120000], 'low_point': 25000, 'cushion_months': 2, 'refund_threshold': 5000}, {'base': 10000, 'cushion': 20000, 'shortage': 0, 'refund': 5000, 'monthly': 10000}], ['regression: refund threshold test, partial-repair probe', {'disbursements': [7, 120000, 7], 'low_point': 40000, 'cushion_months': 2, 'refund_threshold': 20000}, {'base': 10001, 'cushion': 20002, 'shortage': 0, 'refund': 0, 'monthly': 8335}], ['control 1', {'disbursements': [120000, 36000, 99999], 'low_point': -5000, 'cushion_months': 2, 'refund_threshold': 20000}, {'base': 21333, 'cushion': 42667, 'shortage': 47667, 'refund': 0, 'monthly': 25306}], ['control 2', {'disbursements': [99999, 250000], 'low_point': 80000, 'cushion_months': 1, 'refund_threshold': 0}, {'base': 29167, 'cushion': 29167, 'shortage': 0, 'refund': 50833, 'monthly': 29167}], ['control 3', {'disbursements': [120000], 'low_point': 0, 'cushion_months': 1, 'refund_threshold': 20000}, {'base': 10000, 'cushion': 10000, 'shortage': 10000, 'refund': 0, 'monthly': 10834}], ['control 4', {'disbursements': [36000, 120000, 7], 'low_point': -5000, 'cushion_months': 2, 'refund_threshold': 20000}, {'base': 13001, 'cushion': 26001, 'shortage': 31001, 'refund': 0, 'monthly': 15585}], ['control 5', {'disbursements': [99999, 250000, 7], 'low_point': -5000, 'cushion_months': 1, 'refund_threshold': 20000}, {'base': 29167, 'cushion': 29167, 'shortage': 34167, 'refund': 0, 'monthly': 32015}]], [['regression: surplus exactly at threshold', {'disbursements': [120000], 'low_point': 25000, 'cushion_months': 2, 'refund_threshold': 5000}, {'base': 10000, 'cushion': 20000, 'shortage': 0, 'refund': 5000, 'monthly': 10000}], ['regression: refund threshold test', {'disbursements': [120000], 'low_point': 40000, 'cushion_months': 2, 'refund_threshold': 20000}, {'base': 10000, 'cushion': 20000, 'shortage': 0, 'refund': 20000, 'monthly': 10000}], ['regression: refund threshold test, partial-repair probe', {'disbursements': [36000], 'low_point': 10000, 'cushion_months': 2, 'refund_threshold': 5000}, {'base': 3000, 'cushion': 6000, 'shortage': 0, 'refund': 0, 'monthly': 2667}], ['control 1', {'disbursements': [120000, 36000], 'low_point': 80000, 'cushion_months': 1, 'refund_threshold': 0}, {'base': 13000, 'cushion': 13000, 'shortage': 0, 'refund': 67000, 'monthly': 13000}], ['control 2', {'disbursements': [7, 36000], 'low_point': 0, 'cushion_months': 0, 'refund_threshold': 0}, {'base': 3001, 'cushion': 0, 'shortage': 0, 'refund': 0, 'monthly': 3001}], ['control 3', {'disbursements': [120000, 120000], 'low_point': 40000, 'cushion_months': 2, 'refund_threshold': 5000}, {'base': 20000, 'cushion': 40000, 'shortage': 0, 'refund': 0, 'monthly': 20000}], ['control 4', {'disbursements': [250000, 99999, 120000], 'low_point': 150000, 'cushion_months': 5, 'refund_threshold': 20000}, {'base': 39167, 'cushion': 195833, 'shortage': 45833, 'refund': 0, 'monthly': 42987}]], [['regression: surplus exactly at threshold', {'disbursements': [120000], 'low_point': 25000, 'cushion_months': 2, 'refund_threshold': 5000}, {'base': 10000, 'cushion': 20000, 'shortage': 0, 'refund': 5000, 'monthly': 10000}], ['regression: refund threshold test', {'disbursements': [99999, 99999, 250000], 'low_point': 80000, 'cushion_months': 2, 'refund_threshold': 5000}, {'base': 37500, 'cushion': 75000, 'shortage': 0, 'refund': 5000, 'monthly': 37500}], ['regression: refund threshold test, partial-repair probe', {'disbursements': [120000, 36000], 'low_point': 80000, 'cushion_months': 5, 'refund_threshold': 20000}, {'base': 13000, 'cushion': 65000, 'shortage': 0, 'refund': 0, 'monthly': 11750}], ['control 1', {'disbursements': [250000, 120000], 'low_point': 80000, 'cushion_months': 1, 'refund_threshold': 20000}, {'base': 30833, 'cushion': 30833, 'shortage': 0, 'refund': 49167, 'monthly': 30833}], ['control 2', {'disbursements': [36000], 'low_point': 0, 'cushion_months': 5, 'refund_threshold': 5000}, {'base': 3000, 'cushion': 15000, 'shortage': 15000, 'refund': 0, 'monthly': 4250}], ['control 3', {'disbursements': [7, 250000], 'low_point': 80000, 'cushion_months': 0, 'refund_threshold': 5000}, {'base': 20834, 'cushion': 0, 'shortage': 0, 'refund': 80000, 'monthly': 20834}], ['control 4', {'disbursements': [7, 36000], 'low_point': 80000, 'cushion_months': 1, 'refund_threshold': 0}, {'base': 3001, 'cushion': 3001, 'shortage': 0, 'refund': 76999, 'monthly': 3001}]], [['regression: surplus exactly at threshold', {'disbursements': [120000], 'low_point': 25000, 'cushion_months': 2, 'refund_threshold': 5000}, {'base': 10000, 'cushion': 20000, 'shortage': 0, 'refund': 5000, 'monthly': 10000}], ['regression: refund threshold test, partial-repair probe', {'disbursements': [99999, 250000], 'low_point': 150000, 'cushion_months': 5, 'refund_threshold': 5000}, {'base': 29167, 'cushion': 145833, 'shortage': 0, 'refund': 0, 'monthly': 28820}], ['control 1', {'disbursements': [36000], 'low_point': -5000, 'cushion_months': 0, 'refund_threshold': 0}, {'base': 3000, 'cushion': 0, 'shortage': 5000, 'refund': 0, 'monthly': 3417}], ['control 2', {'disbursements': [99999, 36000], 'low_point': 150000, 'cushion_months': 1, 'refund_threshold': 20000}, {'base': 11333, 'cushion': 11333, 'shortage': 0, 'refund': 138667, 'monthly': 11333}], ['control 3', {'disbursements': [36000, 7], 'low_point': 150000, 'cushion_months': 5, 'refund_threshold': 0}, {'base': 3001, 'cushion': 15003, 'shortage': 0, 'refund': 134997, 'monthly': 3001}], ['control 4', {'disbursements': [120000, 250000, 99999], 'low_point': 80000, 'cushion_months': 1, 'refund_threshold': 20000}, {'base': 39167, 'cushion': 39167, 'shortage': 0, 'refund': 40833, 'monthly': 39167}], ['control 5', {'disbursements': [36000, 7, 250000], 'low_point': 150000, 'cushion_months': 2, 'refund_threshold': 20000}, {'base': 23834, 'cushion': 47668, 'shortage': 0, 'refund': 102332, 'monthly': 23834}]], [['regression: surplus exactly at threshold', {'disbursements': [120000], 'low_point': 25000, 'cushion_months': 2, 'refund_threshold': 5000}, {'base': 10000, 'cushion': 20000, 'shortage': 0, 'refund': 5000, 'monthly': 10000}], ['regression: refund threshold test', {'disbursements': [120000], 'low_point': 40000, 'cushion_months': 2, 'refund_threshold': 20000}, {'base': 10000, 'cushion': 20000, 'shortage': 0, 'refund': 20000, 'monthly': 10000}], ['regression: refund threshold test, partial-repair probe', {'disbursements': [99999, 99999, 250000], 'low_point': 80000, 'cushion_months': 2, 'refund_threshold': 20000}, {'base': 37500, 'cushion': 75000, 'shortage': 0, 'refund': 0, 'monthly': 37084}], ['control 1', {'disbursements': [120000], 'low_point': 150000, 'cushion_months': 5, 'refund_threshold': 20000}, {'base': 10000, 'cushion': 50000, 'shortage': 0, 'refund': 100000, 'monthly': 10000}], ['control 2', {'disbursements': [7], 'low_point': 80000, 'cushion_months': 5, 'refund_threshold': 20000}, {'base': 1, 'cushion': 3, 'shortage': 0, 'refund': 79997, 'monthly': 1}], ['control 3', {'disbursements': [99999], 'low_point': -5000, 'cushion_months': 0, 'refund_threshold': 20000}, {'base': 8333, 'cushion': 0, 'shortage': 5000, 'refund': 0, 'monthly': 8750}], ['control 4', {'disbursements': [120000, 7], 'low_point': 0, 'cushion_months': 2, 'refund_threshold': 20000}, {'base': 10001, 'cushion': 20001, 'shortage': 20001, 'refund': 0, 'monthly': 11668}]]]\nfor label, args, expected in fixtures[N-1]:\n    try:\n        actual = solve(args)\n    except Exception as exc:\n        actual = 'raised ' + type(exc).__name__\n    check(label, actual, 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 with stipulated toy lending rules stated in the contract; money is integer cents and rates are basis points; it makes no claim of conformance to any regulation, servicing standard or product. 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-loan-amortization-schedules-escrow-analysis-refund-threshold-test","generated_at":"2026-09-29T14:46:28.963228+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Amortization engines drive borrower statements, payoff quotes and investor remittances; a misplaced rounding step, boundary or ordering rule compounds across hundreds of periods.","repair":"Refund surpluses at or above the threshold.","root_cause":"The refund comparison is strict.","sha256":"ff5d9713a15afcabdcb9d0ae51b15637aae057f1d35105711541db61e50f33df","title":"Annual escrow analysis: refund threshold test · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":43.539,"exit_code":1,"observations":[{"actual":{"base":10000,"cushion":20000,"monthly":10000,"refund":5000,"shortage":0},"check":"regression: surplus exactly at threshold","expected":{"base":10000,"cushion":20000,"monthly":10000,"refund":5000,"shortage":0},"passed":true},{"actual":{"base":10001,"cushion":20002,"monthly":10001,"refund":19998,"shortage":0},"check":"regression: refund threshold test, partial-repair probe","expected":{"base":10001,"cushion":20002,"monthly":8335,"refund":0,"shortage":0},"passed":false},{"actual":{"base":21333,"cushion":42667,"monthly":25306,"refund":0,"shortage":47667},"check":"control 1","expected":{"base":21333,"cushion":42667,"monthly":25306,"refund":0,"shortage":47667},"passed":true},{"actual":{"base":29167,"cushion":29167,"monthly":29167,"refund":50833,"shortage":0},"check":"control 2","expected":{"base":29167,"cushion":29167,"monthly":29167,"refund":50833,"shortage":0},"passed":true},{"actual":{"base":10000,"cushion":10000,"monthly":10834,"refund":0,"shortage":10000},"check":"control 3","expected":{"base":10000,"cushion":10000,"monthly":10834,"refund":0,"shortage":10000},"passed":true},{"actual":{"base":13001,"cushion":26001,"monthly":15585,"refund":0,"shortage":31001},"check":"control 4","expected":{"base":13001,"cushion":26001,"monthly":15585,"refund":0,"shortage":31001},"passed":true},{"actual":{"base":29167,"cushion":29167,"monthly":32015,"refund":0,"shortage":34167},"check":"control 5","expected":{"base":29167,"cushion":29167,"monthly":32015,"refund":0,"shortage":34167},"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: surplus exactly at threshold\", \"actual\": {\"base\": 10000, \"cushion\": 20000, \"shortage\": 0, \"refund\": 5000, \"monthly\": 10000}, \"expected\": {\"base\": 10000, \"cushion\": 20000, \"shortage\": 0, \"refund\": 5000, \"monthly\": 10000}, \"passed\": true}, {\"check\": \"regression: refund threshold test, partial-repair probe\", \"actual\": {\"base\": 10001, \"cushion\": 20002, \"shortage\": 0, \"refund\": 19998, \"monthly\": 10001}, \"expected\": {\"base\": 10001, \"cushion\": 20002, \"shortage\": 0, \"refund\": 0, \"monthly\": 8335}, \"passed\": false}, {\"check\": \"control 1\", \"actual\": {\"base\": 21333, \"cushion\": 42667, \"shortage\": 47667, \"refund\": 0, \"monthly\": 25306}, \"expected\": {\"base\": 21333, \"cushion\": 42667, \"shortage\": 47667, \"refund\": 0, \"monthly\": 25306}, \"passed\": true}, {\"check\": \"control 2\", \"actual\": {\"base\": 29167, \"cushion\": 29167, \"shortage\": 0, \"refund\": 50833, \"monthly\": 29167}, \"expected\": {\"base\": 29167, \"cushion\": 29167, \"shortage\": 0, \"refund\": 50833, \"monthly\": 29167}, \"passed\": true}, {\"check\": \"control 3\", \"actual\": {\"base\": 10000, \"cushion\": 10000, \"shortage\": 10000, \"refund\": 0, \"monthly\": 10834}, \"expected\": {\"base\": 10000, \"cushion\": 10000, \"shortage\": 10000, \"refund\": 0, \"monthly\": 10834}, \"passed\": true}, {\"check\": \"control 4\", \"actual\": {\"base\": 13001, \"cushion\": 26001, \"shortage\": 31001, \"refund\": 0, \"monthly\": 15585}, \"expected\": {\"base\": 13001, \"cushion\": 26001, \"shortage\": 31001, \"refund\": 0, \"monthly\": 15585}, \"passed\": true}, {\"check\": \"control 5\", \"actual\": {\"base\": 29167, \"cushion\": 29167, \"shortage\": 34167, \"refund\": 0, \"monthly\": 32015}, \"expected\": {\"base\": 29167, \"cushion\": 29167, \"shortage\": 34167, \"refund\": 0, \"monthly\": 32015}, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":42.52,"exit_code":1,"observations":[{"actual":{"base":10000,"cushion":20000,"monthly":9584,"refund":0,"shortage":0},"check":"regression: surplus exactly at threshold","expected":{"base":10000,"cushion":20000,"monthly":10000,"refund":5000,"shortage":0},"passed":false},{"actual":{"base":10001,"cushion":20002,"monthly":8335,"refund":0,"shortage":0},"check":"regression: refund threshold test, partial-repair probe","expected":{"base":10001,"cushion":20002,"monthly":8335,"refund":0,"shortage":0},"passed":true},{"actual":{"base":21333,"cushion":42667,"monthly":25306,"refund":0,"shortage":47667},"check":"control 1","expected":{"base":21333,"cushion":42667,"monthly":25306,"refund":0,"shortage":47667},"passed":true},{"actual":{"base":29167,"cushion":29167,"monthly":29167,"refund":50833,"shortage":0},"check":"control 2","expected":{"base":29167,"cushion":29167,"monthly":29167,"refund":50833,"shortage":0},"passed":true},{"actual":{"base":10000,"cushion":10000,"monthly":10834,"refund":0,"shortage":10000},"check":"control 3","expected":{"base":10000,"cushion":10000,"monthly":10834,"refund":0,"shortage":10000},"passed":true},{"actual":{"base":13001,"cushion":26001,"monthly":15585,"refund":0,"shortage":31001},"check":"control 4","expected":{"base":13001,"cushion":26001,"monthly":15585,"refund":0,"shortage":31001},"passed":true},{"actual":{"base":29167,"cushion":29167,"monthly":32015,"refund":0,"shortage":34167},"check":"control 5","expected":{"base":29167,"cushion":29167,"monthly":32015,"refund":0,"shortage":34167},"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: surplus exactly at threshold\", \"actual\": {\"base\": 10000, \"cushion\": 20000, \"shortage\": 0, \"refund\": 0, \"monthly\": 9584}, \"expected\": {\"base\": 10000, \"cushion\": 20000, \"shortage\": 0, \"refund\": 5000, \"monthly\": 10000}, \"passed\": false}, {\"check\": \"regression: refund threshold test, partial-repair probe\", \"actual\": {\"base\": 10001, \"cushion\": 20002, \"shortage\": 0, \"refund\": 0, \"monthly\": 8335}, \"expected\": {\"base\": 10001, \"cushion\": 20002, \"shortage\": 0, \"refund\": 0, \"monthly\": 8335}, \"passed\": true}, {\"check\": \"control 1\", \"actual\": {\"base\": 21333, \"cushion\": 42667, \"shortage\": 47667, \"refund\": 0, \"monthly\": 25306}, \"expected\": {\"base\": 21333, \"cushion\": 42667, \"shortage\": 47667, \"refund\": 0, \"monthly\": 25306}, \"passed\": true}, {\"check\": \"control 2\", \"actual\": {\"base\": 29167, \"cushion\": 29167, \"shortage\": 0, \"refund\": 50833, \"monthly\": 29167}, \"expected\": {\"base\": 29167, \"cushion\": 29167, \"shortage\": 0, \"refund\": 50833, \"monthly\": 29167}, \"passed\": true}, {\"check\": \"control 3\", \"actual\": {\"base\": 10000, \"cushion\": 10000, \"shortage\": 10000, \"refund\": 0, \"monthly\": 10834}, \"expected\": {\"base\": 10000, \"cushion\": 10000, \"shortage\": 10000, \"refund\": 0, \"monthly\": 10834}, \"passed\": true}, {\"check\": \"control 4\", \"actual\": {\"base\": 13001, \"cushion\": 26001, \"shortage\": 31001, \"refund\": 0, \"monthly\": 15585}, \"expected\": {\"base\": 13001, \"cushion\": 26001, \"shortage\": 31001, \"refund\": 0, \"monthly\": 15585}, \"passed\": true}, {\"check\": \"control 5\", \"actual\": {\"base\": 29167, \"cushion\": 29167, \"shortage\": 34167, \"refund\": 0, \"monthly\": 32015}, \"expected\": {\"base\": 29167, \"cushion\": 29167, \"shortage\": 34167, \"refund\": 0, \"monthly\": 32015}, \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":38.711,"exit_code":0,"observations":[{"actual":{"base":10000,"cushion":20000,"monthly":10000,"refund":5000,"shortage":0},"check":"regression: surplus exactly at threshold","expected":{"base":10000,"cushion":20000,"monthly":10000,"refund":5000,"shortage":0},"passed":true},{"actual":{"base":10001,"cushion":20002,"monthly":8335,"refund":0,"shortage":0},"check":"regression: refund threshold test, partial-repair probe","expected":{"base":10001,"cushion":20002,"monthly":8335,"refund":0,"shortage":0},"passed":true},{"actual":{"base":21333,"cushion":42667,"monthly":25306,"refund":0,"shortage":47667},"check":"control 1","expected":{"base":21333,"cushion":42667,"monthly":25306,"refund":0,"shortage":47667},"passed":true},{"actual":{"base":29167,"cushion":29167,"monthly":29167,"refund":50833,"shortage":0},"check":"control 2","expected":{"base":29167,"cushion":29167,"monthly":29167,"refund":50833,"shortage":0},"passed":true},{"actual":{"base":10000,"cushion":10000,"monthly":10834,"refund":0,"shortage":10000},"check":"control 3","expected":{"base":10000,"cushion":10000,"monthly":10834,"refund":0,"shortage":10000},"passed":true},{"actual":{"base":13001,"cushion":26001,"monthly":15585,"refund":0,"shortage":31001},"check":"control 4","expected":{"base":13001,"cushion":26001,"monthly":15585,"refund":0,"shortage":31001},"passed":true},{"actual":{"base":29167,"cushion":29167,"monthly":32015,"refund":0,"shortage":34167},"check":"control 5","expected":{"base":29167,"cushion":29167,"monthly":32015,"refund":0,"shortage":34167},"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: surplus exactly at threshold\", \"actual\": {\"base\": 10000, \"cushion\": 20000, \"shortage\": 0, \"refund\": 5000, \"monthly\": 10000}, \"expected\": {\"base\": 10000, \"cushion\": 20000, \"shortage\": 0, \"refund\": 5000, \"monthly\": 10000}, \"passed\": true}, {\"check\": \"regression: refund threshold test, partial-repair probe\", \"actual\": {\"base\": 10001, \"cushion\": 20002, \"shortage\": 0, \"refund\": 0, \"monthly\": 8335}, \"expected\": {\"base\": 10001, \"cushion\": 20002, \"shortage\": 0, \"refund\": 0, \"monthly\": 8335}, \"passed\": true}, {\"check\": \"control 1\", \"actual\": {\"base\": 21333, \"cushion\": 42667, \"shortage\": 47667, \"refund\": 0, \"monthly\": 25306}, \"expected\": {\"base\": 21333, \"cushion\": 42667, \"shortage\": 47667, \"refund\": 0, \"monthly\": 25306}, \"passed\": true}, {\"check\": \"control 2\", \"actual\": {\"base\": 29167, \"cushion\": 29167, \"shortage\": 0, \"refund\": 50833, \"monthly\": 29167}, \"expected\": {\"base\": 29167, \"cushion\": 29167, \"shortage\": 0, \"refund\": 50833, \"monthly\": 29167}, \"passed\": true}, {\"check\": \"control 3\", \"actual\": {\"base\": 10000, \"cushion\": 10000, \"shortage\": 10000, \"refund\": 0, \"monthly\": 10834}, \"expected\": {\"base\": 10000, \"cushion\": 10000, \"shortage\": 10000, \"refund\": 0, \"monthly\": 10834}, \"passed\": true}, {\"check\": \"control 4\", \"actual\": {\"base\": 13001, \"cushion\": 26001, \"shortage\": 31001, \"refund\": 0, \"monthly\": 15585}, \"expected\": {\"base\": 13001, \"cushion\": 26001, \"shortage\": 31001, \"refund\": 0, \"monthly\": 15585}, \"passed\": true}, {\"check\": \"control 5\", \"actual\": {\"base\": 29167, \"cushion\": 29167, \"shortage\": 34167, \"refund\": 0, \"monthly\": 32015}, \"expected\": {\"base\": 29167, \"cushion\": 29167, \"shortage\": 34167, \"refund\": 0, \"monthly\": 32015}, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}