{"abstract":"The monthly escrow deposit is a cent short for many tax bills.","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":"Always rounding up over-collects for remainders under half.","family":"w2-loan-amortization-schedules-escrow-analysis-monthly-base-rounding","id":"FA-58691","implementations":{"attempt":{"sha256":"6f82471a503c5e4c6edcc5c86eb2b5c6001ed3d4bb123c3a281af786e910da03","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 = (total + 11) // 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: monthly base rounding', {'disbursements': [99999, 250000], 'low_point': 80000, 'cushion_months': 1, 'refund_threshold': 0}, {'base': 29167, 'cushion': 29167, 'shortage': 0, 'refund': 50833, 'monthly': 29167}], ['regression: monthly base rounding, partial-repair probe', {'disbursements': [120000, 36000, 99999], 'low_point': -5000, 'cushion_months': 2, 'refund_threshold': 20000}, {'base': 21333, 'cushion': 42667, 'shortage': 47667, 'refund': 0, 'monthly': 25306}], ['control 1', {'disbursements': [120000], 'low_point': 0, 'cushion_months': 1, 'refund_threshold': 20000}, {'base': 10000, 'cushion': 10000, 'shortage': 10000, 'refund': 0, 'monthly': 10834}], ['control 2', {'disbursements': [99999, 250000, 7], 'low_point': -5000, 'cushion_months': 1, 'refund_threshold': 20000}, {'base': 29167, 'cushion': 29167, 'shortage': 34167, 'refund': 0, 'monthly': 32015}], ['control 3', {'disbursements': [36000, 36000, 120000], 'low_point': 150000, 'cushion_months': 2, 'refund_threshold': 5000}, {'base': 16000, 'cushion': 32000, 'shortage': 0, 'refund': 118000, 'monthly': 16000}], ['control 4', {'disbursements': [99999], 'low_point': 10000, 'cushion_months': 2, 'refund_threshold': 5000}, {'base': 8333, 'cushion': 16667, 'shortage': 6667, 'refund': 0, 'monthly': 8889}], ['control 5', {'disbursements': [36000, 36000, 99999], 'low_point': -5000, 'cushion_months': 0, 'refund_threshold': 20000}, {'base': 14333, 'cushion': 0, 'shortage': 5000, 'refund': 0, 'monthly': 14750}]], [['regression: monthly base rounding', {'disbursements': [7, 36000], 'low_point': 0, 'cushion_months': 0, 'refund_threshold': 0}, {'base': 3001, 'cushion': 0, 'shortage': 0, 'refund': 0, 'monthly': 3001}], ['regression: monthly base rounding, partial-repair probe', {'disbursements': [250000, 7, 99999], 'low_point': 0, 'cushion_months': 1, 'refund_threshold': 20000}, {'base': 29167, 'cushion': 29167, 'shortage': 29167, 'refund': 0, 'monthly': 31598}], ['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': [36000], 'low_point': 10000, 'cushion_months': 2, 'refund_threshold': 5000}, {'base': 3000, 'cushion': 6000, 'shortage': 0, 'refund': 0, 'monthly': 2667}], ['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': [120000], 'low_point': 150000, 'cushion_months': 1, 'refund_threshold': 5000}, {'base': 10000, 'cushion': 10000, 'shortage': 0, 'refund': 140000, 'monthly': 10000}], ['control 5', {'disbursements': [250000], 'low_point': 0, 'cushion_months': 0, 'refund_threshold': 20000}, {'base': 20833, 'cushion': 0, 'shortage': 0, 'refund': 0, 'monthly': 20833}]], [['regression: monthly base rounding', {'disbursements': [7, 250000], 'low_point': 80000, 'cushion_months': 0, 'refund_threshold': 5000}, {'base': 20834, 'cushion': 0, 'shortage': 0, 'refund': 80000, 'monthly': 20834}], ['regression: monthly base rounding, partial-repair probe', {'disbursements': [250000, 120000], 'low_point': 80000, 'cushion_months': 1, 'refund_threshold': 20000}, {'base': 30833, 'cushion': 30833, 'shortage': 0, 'refund': 49167, 'monthly': 30833}], ['control 1', {'disbursements': [36000], 'low_point': 0, 'cushion_months': 5, 'refund_threshold': 5000}, {'base': 3000, 'cushion': 15000, 'shortage': 15000, 'refund': 0, 'monthly': 4250}], ['control 2', {'disbursements': [120000, 36000], 'low_point': 0, 'cushion_months': 1, 'refund_threshold': 0}, {'base': 13000, 'cushion': 13000, 'shortage': 13000, 'refund': 0, 'monthly': 14084}], ['control 3', {'disbursements': [120000], 'low_point': 40000, 'cushion_months': 2, 'refund_threshold': 5000}, {'base': 10000, 'cushion': 20000, 'shortage': 0, 'refund': 20000, 'monthly': 10000}], ['control 4', {'disbursements': [7, 36000, 7], 'low_point': 80000, 'cushion_months': 1, 'refund_threshold': 20000}, {'base': 3001, 'cushion': 3001, 'shortage': 0, 'refund': 76999, 'monthly': 3001}], ['control 5', {'disbursements': [36000], 'low_point': 80000, 'cushion_months': 2, 'refund_threshold': 0}, {'base': 3000, 'cushion': 6000, 'shortage': 0, 'refund': 74000, 'monthly': 3000}]], [['regression: monthly base rounding', {'disbursements': [36000, 7], 'low_point': 150000, 'cushion_months': 5, 'refund_threshold': 0}, {'base': 3001, 'cushion': 15003, 'shortage': 0, 'refund': 134997, 'monthly': 3001}], ['regression: monthly base rounding, partial-repair probe', {'disbursements': [99999, 36000], 'low_point': 150000, 'cushion_months': 1, 'refund_threshold': 20000}, {'base': 11333, 'cushion': 11333, 'shortage': 0, 'refund': 138667, 'monthly': 11333}], ['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': [36000], 'low_point': 10000, 'cushion_months': 2, 'refund_threshold': 0}, {'base': 3000, 'cushion': 6000, 'shortage': 0, 'refund': 4000, 'monthly': 3000}], ['control 3', {'disbursements': [36000], 'low_point': 0, 'cushion_months': 2, 'refund_threshold': 0}, {'base': 3000, 'cushion': 6000, 'shortage': 6000, 'refund': 0, 'monthly': 3500}], ['control 4', {'disbursements': [99999], 'low_point': 150000, 'cushion_months': 1, 'refund_threshold': 5000}, {'base': 8333, 'cushion': 8333, 'shortage': 0, 'refund': 141667, 'monthly': 8333}], ['control 5', {'disbursements': [36000, 99999], 'low_point': 150000, 'cushion_months': 5, 'refund_threshold': 0}, {'base': 11333, 'cushion': 56666, 'shortage': 0, 'refund': 93334, 'monthly': 11333}]], [['regression: monthly base rounding', {'disbursements': [7], 'low_point': 80000, 'cushion_months': 5, 'refund_threshold': 20000}, {'base': 1, 'cushion': 3, 'shortage': 0, 'refund': 79997, 'monthly': 1}], ['regression: monthly base rounding, partial-repair probe', {'disbursements': [99999], 'low_point': -5000, 'cushion_months': 0, 'refund_threshold': 20000}, {'base': 8333, 'cushion': 0, 'shortage': 5000, 'refund': 0, 'monthly': 8750}], ['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': [120000], 'low_point': 80000, 'cushion_months': 5, 'refund_threshold': 20000}, {'base': 10000, 'cushion': 50000, 'shortage': 0, 'refund': 30000, 'monthly': 10000}], ['control 3', {'disbursements': [120000, 36000, 99999], 'low_point': 40000, 'cushion_months': 0, 'refund_threshold': 5000}, {'base': 21333, 'cushion': 0, 'shortage': 0, 'refund': 40000, 'monthly': 21333}], ['control 4', {'disbursements': [36000, 99999], 'low_point': 40000, 'cushion_months': 1, 'refund_threshold': 20000}, {'base': 11333, 'cushion': 11333, 'shortage': 0, 'refund': 28667, 'monthly': 11333}], ['control 5', {'disbursements': [250000, 36000], 'low_point': 40000, 'cushion_months': 2, 'refund_threshold': 20000}, {'base': 23833, 'cushion': 47667, 'shortage': 7667, 'refund': 0, 'monthly': 24472}]]]\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":"c047b8408030e434113489803bd97fad9081243d35a07d5f55cf5685ca37379b","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 = 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: monthly base rounding', {'disbursements': [99999, 250000], 'low_point': 80000, 'cushion_months': 1, 'refund_threshold': 0}, {'base': 29167, 'cushion': 29167, 'shortage': 0, 'refund': 50833, 'monthly': 29167}], ['regression: monthly base rounding, partial-repair probe', {'disbursements': [120000, 36000, 99999], 'low_point': -5000, 'cushion_months': 2, 'refund_threshold': 20000}, {'base': 21333, 'cushion': 42667, 'shortage': 47667, 'refund': 0, 'monthly': 25306}], ['control 1', {'disbursements': [120000], 'low_point': 0, 'cushion_months': 1, 'refund_threshold': 20000}, {'base': 10000, 'cushion': 10000, 'shortage': 10000, 'refund': 0, 'monthly': 10834}], ['control 2', {'disbursements': [99999, 250000, 7], 'low_point': -5000, 'cushion_months': 1, 'refund_threshold': 20000}, {'base': 29167, 'cushion': 29167, 'shortage': 34167, 'refund': 0, 'monthly': 32015}], ['control 3', {'disbursements': [36000, 36000, 120000], 'low_point': 150000, 'cushion_months': 2, 'refund_threshold': 5000}, {'base': 16000, 'cushion': 32000, 'shortage': 0, 'refund': 118000, 'monthly': 16000}], ['control 4', {'disbursements': [99999], 'low_point': 10000, 'cushion_months': 2, 'refund_threshold': 5000}, {'base': 8333, 'cushion': 16667, 'shortage': 6667, 'refund': 0, 'monthly': 8889}], ['control 5', {'disbursements': [36000, 36000, 99999], 'low_point': -5000, 'cushion_months': 0, 'refund_threshold': 20000}, {'base': 14333, 'cushion': 0, 'shortage': 5000, 'refund': 0, 'monthly': 14750}]], [['regression: monthly base rounding', {'disbursements': [7, 36000], 'low_point': 0, 'cushion_months': 0, 'refund_threshold': 0}, {'base': 3001, 'cushion': 0, 'shortage': 0, 'refund': 0, 'monthly': 3001}], ['regression: monthly base rounding, partial-repair probe', {'disbursements': [250000, 7, 99999], 'low_point': 0, 'cushion_months': 1, 'refund_threshold': 20000}, {'base': 29167, 'cushion': 29167, 'shortage': 29167, 'refund': 0, 'monthly': 31598}], ['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': [36000], 'low_point': 10000, 'cushion_months': 2, 'refund_threshold': 5000}, {'base': 3000, 'cushion': 6000, 'shortage': 0, 'refund': 0, 'monthly': 2667}], ['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': [120000], 'low_point': 150000, 'cushion_months': 1, 'refund_threshold': 5000}, {'base': 10000, 'cushion': 10000, 'shortage': 0, 'refund': 140000, 'monthly': 10000}], ['control 5', {'disbursements': [250000], 'low_point': 0, 'cushion_months': 0, 'refund_threshold': 20000}, {'base': 20833, 'cushion': 0, 'shortage': 0, 'refund': 0, 'monthly': 20833}]], [['regression: monthly base rounding', {'disbursements': [7, 250000], 'low_point': 80000, 'cushion_months': 0, 'refund_threshold': 5000}, {'base': 20834, 'cushion': 0, 'shortage': 0, 'refund': 80000, 'monthly': 20834}], ['regression: monthly base rounding, partial-repair probe', {'disbursements': [250000, 120000], 'low_point': 80000, 'cushion_months': 1, 'refund_threshold': 20000}, {'base': 30833, 'cushion': 30833, 'shortage': 0, 'refund': 49167, 'monthly': 30833}], ['control 1', {'disbursements': [36000], 'low_point': 0, 'cushion_months': 5, 'refund_threshold': 5000}, {'base': 3000, 'cushion': 15000, 'shortage': 15000, 'refund': 0, 'monthly': 4250}], ['control 2', {'disbursements': [120000, 36000], 'low_point': 0, 'cushion_months': 1, 'refund_threshold': 0}, {'base': 13000, 'cushion': 13000, 'shortage': 13000, 'refund': 0, 'monthly': 14084}], ['control 3', {'disbursements': [120000], 'low_point': 40000, 'cushion_months': 2, 'refund_threshold': 5000}, {'base': 10000, 'cushion': 20000, 'shortage': 0, 'refund': 20000, 'monthly': 10000}], ['control 4', {'disbursements': [7, 36000, 7], 'low_point': 80000, 'cushion_months': 1, 'refund_threshold': 20000}, {'base': 3001, 'cushion': 3001, 'shortage': 0, 'refund': 76999, 'monthly': 3001}], ['control 5', {'disbursements': [36000], 'low_point': 80000, 'cushion_months': 2, 'refund_threshold': 0}, {'base': 3000, 'cushion': 6000, 'shortage': 0, 'refund': 74000, 'monthly': 3000}]], [['regression: monthly base rounding', {'disbursements': [36000, 7], 'low_point': 150000, 'cushion_months': 5, 'refund_threshold': 0}, {'base': 3001, 'cushion': 15003, 'shortage': 0, 'refund': 134997, 'monthly': 3001}], ['regression: monthly base rounding, partial-repair probe', {'disbursements': [99999, 36000], 'low_point': 150000, 'cushion_months': 1, 'refund_threshold': 20000}, {'base': 11333, 'cushion': 11333, 'shortage': 0, 'refund': 138667, 'monthly': 11333}], ['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': [36000], 'low_point': 10000, 'cushion_months': 2, 'refund_threshold': 0}, {'base': 3000, 'cushion': 6000, 'shortage': 0, 'refund': 4000, 'monthly': 3000}], ['control 3', {'disbursements': [36000], 'low_point': 0, 'cushion_months': 2, 'refund_threshold': 0}, {'base': 3000, 'cushion': 6000, 'shortage': 6000, 'refund': 0, 'monthly': 3500}], ['control 4', {'disbursements': [99999], 'low_point': 150000, 'cushion_months': 1, 'refund_threshold': 5000}, {'base': 8333, 'cushion': 8333, 'shortage': 0, 'refund': 141667, 'monthly': 8333}], ['control 5', {'disbursements': [36000, 99999], 'low_point': 150000, 'cushion_months': 5, 'refund_threshold': 0}, {'base': 11333, 'cushion': 56666, 'shortage': 0, 'refund': 93334, 'monthly': 11333}]], [['regression: monthly base rounding', {'disbursements': [7], 'low_point': 80000, 'cushion_months': 5, 'refund_threshold': 20000}, {'base': 1, 'cushion': 3, 'shortage': 0, 'refund': 79997, 'monthly': 1}], ['regression: monthly base rounding, partial-repair probe', {'disbursements': [99999], 'low_point': -5000, 'cushion_months': 0, 'refund_threshold': 20000}, {'base': 8333, 'cushion': 0, 'shortage': 5000, 'refund': 0, 'monthly': 8750}], ['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': [120000], 'low_point': 80000, 'cushion_months': 5, 'refund_threshold': 20000}, {'base': 10000, 'cushion': 50000, 'shortage': 0, 'refund': 30000, 'monthly': 10000}], ['control 3', {'disbursements': [120000, 36000, 99999], 'low_point': 40000, 'cushion_months': 0, 'refund_threshold': 5000}, {'base': 21333, 'cushion': 0, 'shortage': 0, 'refund': 40000, 'monthly': 21333}], ['control 4', {'disbursements': [36000, 99999], 'low_point': 40000, 'cushion_months': 1, 'refund_threshold': 20000}, {'base': 11333, 'cushion': 11333, 'shortage': 0, 'refund': 28667, 'monthly': 11333}], ['control 5', {'disbursements': [250000, 36000], 'low_point': 40000, 'cushion_months': 2, 'refund_threshold': 20000}, {'base': 23833, 'cushion': 47667, 'shortage': 7667, 'refund': 0, 'monthly': 24472}]]]\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":"fc78e88f0848ac05059126da59cc0258b2aa738af6a7e2b829130d710a189929","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: monthly base rounding', {'disbursements': [99999, 250000], 'low_point': 80000, 'cushion_months': 1, 'refund_threshold': 0}, {'base': 29167, 'cushion': 29167, 'shortage': 0, 'refund': 50833, 'monthly': 29167}], ['regression: monthly base rounding, partial-repair probe', {'disbursements': [120000, 36000, 99999], 'low_point': -5000, 'cushion_months': 2, 'refund_threshold': 20000}, {'base': 21333, 'cushion': 42667, 'shortage': 47667, 'refund': 0, 'monthly': 25306}], ['control 1', {'disbursements': [120000], 'low_point': 0, 'cushion_months': 1, 'refund_threshold': 20000}, {'base': 10000, 'cushion': 10000, 'shortage': 10000, 'refund': 0, 'monthly': 10834}], ['control 2', {'disbursements': [99999, 250000, 7], 'low_point': -5000, 'cushion_months': 1, 'refund_threshold': 20000}, {'base': 29167, 'cushion': 29167, 'shortage': 34167, 'refund': 0, 'monthly': 32015}], ['control 3', {'disbursements': [36000, 36000, 120000], 'low_point': 150000, 'cushion_months': 2, 'refund_threshold': 5000}, {'base': 16000, 'cushion': 32000, 'shortage': 0, 'refund': 118000, 'monthly': 16000}], ['control 4', {'disbursements': [99999], 'low_point': 10000, 'cushion_months': 2, 'refund_threshold': 5000}, {'base': 8333, 'cushion': 16667, 'shortage': 6667, 'refund': 0, 'monthly': 8889}], ['control 5', {'disbursements': [36000, 36000, 99999], 'low_point': -5000, 'cushion_months': 0, 'refund_threshold': 20000}, {'base': 14333, 'cushion': 0, 'shortage': 5000, 'refund': 0, 'monthly': 14750}]], [['regression: monthly base rounding', {'disbursements': [7, 36000], 'low_point': 0, 'cushion_months': 0, 'refund_threshold': 0}, {'base': 3001, 'cushion': 0, 'shortage': 0, 'refund': 0, 'monthly': 3001}], ['regression: monthly base rounding, partial-repair probe', {'disbursements': [250000, 7, 99999], 'low_point': 0, 'cushion_months': 1, 'refund_threshold': 20000}, {'base': 29167, 'cushion': 29167, 'shortage': 29167, 'refund': 0, 'monthly': 31598}], ['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': [36000], 'low_point': 10000, 'cushion_months': 2, 'refund_threshold': 5000}, {'base': 3000, 'cushion': 6000, 'shortage': 0, 'refund': 0, 'monthly': 2667}], ['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': [120000], 'low_point': 150000, 'cushion_months': 1, 'refund_threshold': 5000}, {'base': 10000, 'cushion': 10000, 'shortage': 0, 'refund': 140000, 'monthly': 10000}], ['control 5', {'disbursements': [250000], 'low_point': 0, 'cushion_months': 0, 'refund_threshold': 20000}, {'base': 20833, 'cushion': 0, 'shortage': 0, 'refund': 0, 'monthly': 20833}]], [['regression: monthly base rounding', {'disbursements': [7, 250000], 'low_point': 80000, 'cushion_months': 0, 'refund_threshold': 5000}, {'base': 20834, 'cushion': 0, 'shortage': 0, 'refund': 80000, 'monthly': 20834}], ['regression: monthly base rounding, partial-repair probe', {'disbursements': [250000, 120000], 'low_point': 80000, 'cushion_months': 1, 'refund_threshold': 20000}, {'base': 30833, 'cushion': 30833, 'shortage': 0, 'refund': 49167, 'monthly': 30833}], ['control 1', {'disbursements': [36000], 'low_point': 0, 'cushion_months': 5, 'refund_threshold': 5000}, {'base': 3000, 'cushion': 15000, 'shortage': 15000, 'refund': 0, 'monthly': 4250}], ['control 2', {'disbursements': [120000, 36000], 'low_point': 0, 'cushion_months': 1, 'refund_threshold': 0}, {'base': 13000, 'cushion': 13000, 'shortage': 13000, 'refund': 0, 'monthly': 14084}], ['control 3', {'disbursements': [120000], 'low_point': 40000, 'cushion_months': 2, 'refund_threshold': 5000}, {'base': 10000, 'cushion': 20000, 'shortage': 0, 'refund': 20000, 'monthly': 10000}], ['control 4', {'disbursements': [7, 36000, 7], 'low_point': 80000, 'cushion_months': 1, 'refund_threshold': 20000}, {'base': 3001, 'cushion': 3001, 'shortage': 0, 'refund': 76999, 'monthly': 3001}], ['control 5', {'disbursements': [36000], 'low_point': 80000, 'cushion_months': 2, 'refund_threshold': 0}, {'base': 3000, 'cushion': 6000, 'shortage': 0, 'refund': 74000, 'monthly': 3000}]], [['regression: monthly base rounding', {'disbursements': [36000, 7], 'low_point': 150000, 'cushion_months': 5, 'refund_threshold': 0}, {'base': 3001, 'cushion': 15003, 'shortage': 0, 'refund': 134997, 'monthly': 3001}], ['regression: monthly base rounding, partial-repair probe', {'disbursements': [99999, 36000], 'low_point': 150000, 'cushion_months': 1, 'refund_threshold': 20000}, {'base': 11333, 'cushion': 11333, 'shortage': 0, 'refund': 138667, 'monthly': 11333}], ['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': [36000], 'low_point': 10000, 'cushion_months': 2, 'refund_threshold': 0}, {'base': 3000, 'cushion': 6000, 'shortage': 0, 'refund': 4000, 'monthly': 3000}], ['control 3', {'disbursements': [36000], 'low_point': 0, 'cushion_months': 2, 'refund_threshold': 0}, {'base': 3000, 'cushion': 6000, 'shortage': 6000, 'refund': 0, 'monthly': 3500}], ['control 4', {'disbursements': [99999], 'low_point': 150000, 'cushion_months': 1, 'refund_threshold': 5000}, {'base': 8333, 'cushion': 8333, 'shortage': 0, 'refund': 141667, 'monthly': 8333}], ['control 5', {'disbursements': [36000, 99999], 'low_point': 150000, 'cushion_months': 5, 'refund_threshold': 0}, {'base': 11333, 'cushion': 56666, 'shortage': 0, 'refund': 93334, 'monthly': 11333}]], [['regression: monthly base rounding', {'disbursements': [7], 'low_point': 80000, 'cushion_months': 5, 'refund_threshold': 20000}, {'base': 1, 'cushion': 3, 'shortage': 0, 'refund': 79997, 'monthly': 1}], ['regression: monthly base rounding, partial-repair probe', {'disbursements': [99999], 'low_point': -5000, 'cushion_months': 0, 'refund_threshold': 20000}, {'base': 8333, 'cushion': 0, 'shortage': 5000, 'refund': 0, 'monthly': 8750}], ['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': [120000], 'low_point': 80000, 'cushion_months': 5, 'refund_threshold': 20000}, {'base': 10000, 'cushion': 50000, 'shortage': 0, 'refund': 30000, 'monthly': 10000}], ['control 3', {'disbursements': [120000, 36000, 99999], 'low_point': 40000, 'cushion_months': 0, 'refund_threshold': 5000}, {'base': 21333, 'cushion': 0, 'shortage': 0, 'refund': 40000, 'monthly': 21333}], ['control 4', {'disbursements': [36000, 99999], 'low_point': 40000, 'cushion_months': 1, 'refund_threshold': 20000}, {'base': 11333, 'cushion': 11333, 'shortage': 0, 'refund': 28667, 'monthly': 11333}], ['control 5', {'disbursements': [250000, 36000], 'low_point': 40000, 'cushion_months': 2, 'refund_threshold': 20000}, {'base': 23833, 'cushion': 47667, 'shortage': 7667, 'refund': 0, 'monthly': 24472}]]]\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-monthly-base-rounding","generated_at":"2026-09-29T14:46:29.123190+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":"Round the monthly base half-up.","root_cause":"The monthly base is truncated.","sha256":"c445bbeec65c32341906bb0d87c56f8ccabbc926e09f3b4b5dbfaa94aa761245","title":"Annual escrow analysis: monthly base rounding · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":40.211,"exit_code":1,"observations":[{"actual":{"base":29167,"cushion":29167,"monthly":29167,"refund":50833,"shortage":0},"check":"regression: monthly base rounding","expected":{"base":29167,"cushion":29167,"monthly":29167,"refund":50833,"shortage":0},"passed":true},{"actual":{"base":21334,"cushion":42667,"monthly":25307,"refund":0,"shortage":47667},"check":"regression: monthly base rounding, partial-repair probe","expected":{"base":21333,"cushion":42667,"monthly":25306,"refund":0,"shortage":47667},"passed":false},{"actual":{"base":10000,"cushion":10000,"monthly":10834,"refund":0,"shortage":10000},"check":"control 1","expected":{"base":10000,"cushion":10000,"monthly":10834,"refund":0,"shortage":10000},"passed":true},{"actual":{"base":29168,"cushion":29167,"monthly":32016,"refund":0,"shortage":34167},"check":"control 2","expected":{"base":29167,"cushion":29167,"monthly":32015,"refund":0,"shortage":34167},"passed":false},{"actual":{"base":16000,"cushion":32000,"monthly":16000,"refund":118000,"shortage":0},"check":"control 3","expected":{"base":16000,"cushion":32000,"monthly":16000,"refund":118000,"shortage":0},"passed":true},{"actual":{"base":8334,"cushion":16667,"monthly":8890,"refund":0,"shortage":6667},"check":"control 4","expected":{"base":8333,"cushion":16667,"monthly":8889,"refund":0,"shortage":6667},"passed":false},{"actual":{"base":14334,"cushion":0,"monthly":14751,"refund":0,"shortage":5000},"check":"control 5","expected":{"base":14333,"cushion":0,"monthly":14750,"refund":0,"shortage":5000},"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: monthly base rounding\", \"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\": \"regression: monthly base rounding, partial-repair probe\", \"actual\": {\"base\": 21334, \"cushion\": 42667, \"shortage\": 47667, \"refund\": 0, \"monthly\": 25307}, \"expected\": {\"base\": 21333, \"cushion\": 42667, \"shortage\": 47667, \"refund\": 0, \"monthly\": 25306}, \"passed\": false}, {\"check\": \"control 1\", \"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 2\", \"actual\": {\"base\": 29168, \"cushion\": 29167, \"shortage\": 34167, \"refund\": 0, \"monthly\": 32016}, \"expected\": {\"base\": 29167, \"cushion\": 29167, \"shortage\": 34167, \"refund\": 0, \"monthly\": 32015}, \"passed\": false}, {\"check\": \"control 3\", \"actual\": {\"base\": 16000, \"cushion\": 32000, \"shortage\": 0, \"refund\": 118000, \"monthly\": 16000}, \"expected\": {\"base\": 16000, \"cushion\": 32000, \"shortage\": 0, \"refund\": 118000, \"monthly\": 16000}, \"passed\": true}, {\"check\": \"control 4\", \"actual\": {\"base\": 8334, \"cushion\": 16667, \"shortage\": 6667, \"refund\": 0, \"monthly\": 8890}, \"expected\": {\"base\": 8333, \"cushion\": 16667, \"shortage\": 6667, \"refund\": 0, \"monthly\": 8889}, \"passed\": false}, {\"check\": \"control 5\", \"actual\": {\"base\": 14334, \"cushion\": 0, \"shortage\": 5000, \"refund\": 0, \"monthly\": 14751}, \"expected\": {\"base\": 14333, \"cushion\": 0, \"shortage\": 5000, \"refund\": 0, \"monthly\": 14750}, \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":40.885,"exit_code":1,"observations":[{"actual":{"base":29166,"cushion":29167,"monthly":29166,"refund":50833,"shortage":0},"check":"regression: monthly base rounding","expected":{"base":29167,"cushion":29167,"monthly":29167,"refund":50833,"shortage":0},"passed":false},{"actual":{"base":21333,"cushion":42667,"monthly":25306,"refund":0,"shortage":47667},"check":"regression: monthly base rounding, partial-repair probe","expected":{"base":21333,"cushion":42667,"monthly":25306,"refund":0,"shortage":47667},"passed":true},{"actual":{"base":10000,"cushion":10000,"monthly":10834,"refund":0,"shortage":10000},"check":"control 1","expected":{"base":10000,"cushion":10000,"monthly":10834,"refund":0,"shortage":10000},"passed":true},{"actual":{"base":29167,"cushion":29167,"monthly":32015,"refund":0,"shortage":34167},"check":"control 2","expected":{"base":29167,"cushion":29167,"monthly":32015,"refund":0,"shortage":34167},"passed":true},{"actual":{"base":16000,"cushion":32000,"monthly":16000,"refund":118000,"shortage":0},"check":"control 3","expected":{"base":16000,"cushion":32000,"monthly":16000,"refund":118000,"shortage":0},"passed":true},{"actual":{"base":8333,"cushion":16667,"monthly":8889,"refund":0,"shortage":6667},"check":"control 4","expected":{"base":8333,"cushion":16667,"monthly":8889,"refund":0,"shortage":6667},"passed":true},{"actual":{"base":14333,"cushion":0,"monthly":14750,"refund":0,"shortage":5000},"check":"control 5","expected":{"base":14333,"cushion":0,"monthly":14750,"refund":0,"shortage":5000},"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: monthly base rounding\", \"actual\": {\"base\": 29166, \"cushion\": 29167, \"shortage\": 0, \"refund\": 50833, \"monthly\": 29166}, \"expected\": {\"base\": 29167, \"cushion\": 29167, \"shortage\": 0, \"refund\": 50833, \"monthly\": 29167}, \"passed\": false}, {\"check\": \"regression: monthly base rounding, partial-repair probe\", \"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 1\", \"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 2\", \"actual\": {\"base\": 29167, \"cushion\": 29167, \"shortage\": 34167, \"refund\": 0, \"monthly\": 32015}, \"expected\": {\"base\": 29167, \"cushion\": 29167, \"shortage\": 34167, \"refund\": 0, \"monthly\": 32015}, \"passed\": true}, {\"check\": \"control 3\", \"actual\": {\"base\": 16000, \"cushion\": 32000, \"shortage\": 0, \"refund\": 118000, \"monthly\": 16000}, \"expected\": {\"base\": 16000, \"cushion\": 32000, \"shortage\": 0, \"refund\": 118000, \"monthly\": 16000}, \"passed\": true}, {\"check\": \"control 4\", \"actual\": {\"base\": 8333, \"cushion\": 16667, \"shortage\": 6667, \"refund\": 0, \"monthly\": 8889}, \"expected\": {\"base\": 8333, \"cushion\": 16667, \"shortage\": 6667, \"refund\": 0, \"monthly\": 8889}, \"passed\": true}, {\"check\": \"control 5\", \"actual\": {\"base\": 14333, \"cushion\": 0, \"shortage\": 5000, \"refund\": 0, \"monthly\": 14750}, \"expected\": {\"base\": 14333, \"cushion\": 0, \"shortage\": 5000, \"refund\": 0, \"monthly\": 14750}, \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":38.859,"exit_code":0,"observations":[{"actual":{"base":29167,"cushion":29167,"monthly":29167,"refund":50833,"shortage":0},"check":"regression: monthly base rounding","expected":{"base":29167,"cushion":29167,"monthly":29167,"refund":50833,"shortage":0},"passed":true},{"actual":{"base":21333,"cushion":42667,"monthly":25306,"refund":0,"shortage":47667},"check":"regression: monthly base rounding, partial-repair probe","expected":{"base":21333,"cushion":42667,"monthly":25306,"refund":0,"shortage":47667},"passed":true},{"actual":{"base":10000,"cushion":10000,"monthly":10834,"refund":0,"shortage":10000},"check":"control 1","expected":{"base":10000,"cushion":10000,"monthly":10834,"refund":0,"shortage":10000},"passed":true},{"actual":{"base":29167,"cushion":29167,"monthly":32015,"refund":0,"shortage":34167},"check":"control 2","expected":{"base":29167,"cushion":29167,"monthly":32015,"refund":0,"shortage":34167},"passed":true},{"actual":{"base":16000,"cushion":32000,"monthly":16000,"refund":118000,"shortage":0},"check":"control 3","expected":{"base":16000,"cushion":32000,"monthly":16000,"refund":118000,"shortage":0},"passed":true},{"actual":{"base":8333,"cushion":16667,"monthly":8889,"refund":0,"shortage":6667},"check":"control 4","expected":{"base":8333,"cushion":16667,"monthly":8889,"refund":0,"shortage":6667},"passed":true},{"actual":{"base":14333,"cushion":0,"monthly":14750,"refund":0,"shortage":5000},"check":"control 5","expected":{"base":14333,"cushion":0,"monthly":14750,"refund":0,"shortage":5000},"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: monthly base rounding\", \"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\": \"regression: monthly base rounding, partial-repair probe\", \"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 1\", \"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 2\", \"actual\": {\"base\": 29167, \"cushion\": 29167, \"shortage\": 34167, \"refund\": 0, \"monthly\": 32015}, \"expected\": {\"base\": 29167, \"cushion\": 29167, \"shortage\": 34167, \"refund\": 0, \"monthly\": 32015}, \"passed\": true}, {\"check\": \"control 3\", \"actual\": {\"base\": 16000, \"cushion\": 32000, \"shortage\": 0, \"refund\": 118000, \"monthly\": 16000}, \"expected\": {\"base\": 16000, \"cushion\": 32000, \"shortage\": 0, \"refund\": 118000, \"monthly\": 16000}, \"passed\": true}, {\"check\": \"control 4\", \"actual\": {\"base\": 8333, \"cushion\": 16667, \"shortage\": 6667, \"refund\": 0, \"monthly\": 8889}, \"expected\": {\"base\": 8333, \"cushion\": 16667, \"shortage\": 6667, \"refund\": 0, \"monthly\": 8889}, \"passed\": true}, {\"check\": \"control 5\", \"actual\": {\"base\": 14333, \"cushion\": 0, \"shortage\": 5000, \"refund\": 0, \"monthly\": 14750}, \"expected\": {\"base\": 14333, \"cushion\": 0, \"shortage\": 5000, \"refund\": 0, \"monthly\": 14750}, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}