{"abstract":"Income above the second base amount includes less benefit than stipulated.","category":"Tax bracket computation","checks":8,"contract":"solve(agi, exempt_interest, benefits, status): stipulated benefit inclusion. Provisional income PI = agi + exempt_interest + benefits/2. Base amounts (b1, b2): single (25000, 34000), mfj (32000, 44000), mfs (0, 0). If PI <= b1 nothing is included; if PI <= b2, include min(benefits/2, (PI - b1)/2); otherwise include min(0.85*benefits, 0.85*(PI - b2) + min(benefits/2, (b2 - b1)/2)). Return the included amount rounded down to whole dollars.","evaluation_group":"w2-tax_bracket_computation-benefit-inclusion-tiers","failed_approach":"Adding the full half-gap without comparing to half the benefits over-includes small benefits.","family":"w2-tax_bracket_computation-benefit-inclusion-tiers-second-tier-carry","id":"FA-62751","implementations":{"attempt":{"sha256":"eb589ba816cdb8422e8e563aaf46977a32b31ee53cae1422c4c938aa33e7864d","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(agi, exempt_interest, benefits, status):\n    b1, b2 = {'single': (25000, 34000), 'mfj': (32000, 44000), 'mfs': (0, 0)}[status]\n    B = Fraction(benefits)\n    pi = agi + exempt_interest + B / 2\n    if pi <= b1: t = Fraction(0)\n    elif pi <= b2: t = min(B / 2, (pi - b1) / 2)\n    else: t = min(B * 85 / 100, (pi - b2) * 85 / 100 + Fraction(b2 - b1, 2))\n    return int(t)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[('regression second-tier-carry 1', (40000, 0, 20000, 'single'), 17000),\n  ('regression second-tier-carry 2', (35000, 0, 4000, 'single'), 3400),\n  ('partial repair guard 1', (30000, 1000, 8000, 'single'), 4850),\n  ('partial repair guard 2', (30775, 1000, 8000, 'single'), 5508),\n  ('control: first tier', (20000, 0, 12000, 'single'), 500), ('control: below base', (10000, 0, 10000, 'single'), 0),\n  ('control: joint with exempt interest', (30000, 1000, 20000, 'mfj'), 4500),\n  ('control: separate filer', (5000, 0, 8000, 'mfs'), 6800)],\n [('regression second-tier-carry 1', (45000, 0, 30934, 'mfj'), 19996),\n  ('regression second-tier-carry 2', (30000, 1000, 8000, 'single'), 4850),\n  ('partial repair guard 2', (30775, 1000, 8000, 'single'), 5508),\n  ('control: joint with exempt interest', (30000, 1000, 20000, 'mfj'), 4500),\n  ('control: separate filer', (5000, 0, 8000, 'mfs'), 6800),\n  ('control: small benefit first tier', (28000, 0, 2000, 'single'), 1000),\n  ('control: large income', (150000, 5000, 40000, 'mfj'), 34000)],\n [('regression second-tier-carry 1', (20000, 1000, 45562, 'single'), 12813),\n  ('regression second-tier-carry 2', (30000, 1000, 42192, 'mfj'), 12881),\n  ('partial repair guard 1', (30000, 1000, 8000, 'single'), 4850),\n  ('partial repair guard 2', (30775, 1000, 8000, 'single'), 5508),\n  ('control: large income', (150000, 5000, 40000, 'mfj'), 34000),\n  ('control: first tier', (20000, 0, 12000, 'single'), 500),\n  ('control: second tier', (40000, 0, 20000, 'single'), 17000),\n  ('control: below base', (10000, 0, 10000, 'single'), 0)],\n [('regression second-tier-carry 1', (30000, 0, 20000, 'single'), 9600),\n  ('regression second-tier-carry 2', (45000, 1000, 40000, 'single'), 31700),\n  ('partial repair guard 1', (30000, 1000, 8000, 'single'), 4850),\n  ('partial repair guard 2', (30775, 1000, 8000, 'single'), 5508),\n  ('control: below base', (10000, 0, 10000, 'single'), 0),\n  ('control: joint with exempt interest', (30000, 1000, 20000, 'mfj'), 4500),\n  ('control: separate filer', (5000, 0, 8000, 'mfs'), 6800),\n  ('control: small benefit first tier', (28000, 0, 2000, 'single'), 1000)],\n [('regression second-tier-carry 1', (45000, 0, 41916, 'single'), 31664),\n  ('regression second-tier-carry 2', (30000, 0, 40000, 'mfj'), 11100),\n  ('partial repair guard 1', (30000, 1000, 8000, 'single'), 4850),\n  ('partial repair guard 2', (30775, 1000, 8000, 'single'), 5508),\n  ('control: small benefit first tier', (28000, 0, 2000, 'single'), 1000),\n  ('control: large income', (150000, 5000, 40000, 'mfj'), 34000),\n  ('control: first tier', (20000, 0, 12000, 'single'), 500),\n  ('control: second tier', (40000, 0, 20000, 'single'), 17000)]]\nfor label, args, expected in cases[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":"44c799e254f55aaa0b8f91cef988150fdf767e8dc25a9ed305f11b5fe8d1e43a","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(agi, exempt_interest, benefits, status):\n    b1, b2 = {'single': (25000, 34000), 'mfj': (32000, 44000), 'mfs': (0, 0)}[status]\n    B = Fraction(benefits)\n    pi = agi + exempt_interest + B / 2\n    if pi <= b1: t = Fraction(0)\n    elif pi <= b2: t = min(B / 2, (pi - b1) / 2)\n    else: t = min(B * 85 / 100, (pi - b2) * 85 / 100)\n    return int(t)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[('regression second-tier-carry 1', (40000, 0, 20000, 'single'), 17000),\n  ('regression second-tier-carry 2', (35000, 0, 4000, 'single'), 3400),\n  ('partial repair guard 1', (30000, 1000, 8000, 'single'), 4850),\n  ('partial repair guard 2', (30775, 1000, 8000, 'single'), 5508),\n  ('control: first tier', (20000, 0, 12000, 'single'), 500), ('control: below base', (10000, 0, 10000, 'single'), 0),\n  ('control: joint with exempt interest', (30000, 1000, 20000, 'mfj'), 4500),\n  ('control: separate filer', (5000, 0, 8000, 'mfs'), 6800)],\n [('regression second-tier-carry 1', (45000, 0, 30934, 'mfj'), 19996),\n  ('regression second-tier-carry 2', (30000, 1000, 8000, 'single'), 4850),\n  ('partial repair guard 2', (30775, 1000, 8000, 'single'), 5508),\n  ('control: joint with exempt interest', (30000, 1000, 20000, 'mfj'), 4500),\n  ('control: separate filer', (5000, 0, 8000, 'mfs'), 6800),\n  ('control: small benefit first tier', (28000, 0, 2000, 'single'), 1000),\n  ('control: large income', (150000, 5000, 40000, 'mfj'), 34000)],\n [('regression second-tier-carry 1', (20000, 1000, 45562, 'single'), 12813),\n  ('regression second-tier-carry 2', (30000, 1000, 42192, 'mfj'), 12881),\n  ('partial repair guard 1', (30000, 1000, 8000, 'single'), 4850),\n  ('partial repair guard 2', (30775, 1000, 8000, 'single'), 5508),\n  ('control: large income', (150000, 5000, 40000, 'mfj'), 34000),\n  ('control: first tier', (20000, 0, 12000, 'single'), 500),\n  ('control: second tier', (40000, 0, 20000, 'single'), 17000),\n  ('control: below base', (10000, 0, 10000, 'single'), 0)],\n [('regression second-tier-carry 1', (30000, 0, 20000, 'single'), 9600),\n  ('regression second-tier-carry 2', (45000, 1000, 40000, 'single'), 31700),\n  ('partial repair guard 1', (30000, 1000, 8000, 'single'), 4850),\n  ('partial repair guard 2', (30775, 1000, 8000, 'single'), 5508),\n  ('control: below base', (10000, 0, 10000, 'single'), 0),\n  ('control: joint with exempt interest', (30000, 1000, 20000, 'mfj'), 4500),\n  ('control: separate filer', (5000, 0, 8000, 'mfs'), 6800),\n  ('control: small benefit first tier', (28000, 0, 2000, 'single'), 1000)],\n [('regression second-tier-carry 1', (45000, 0, 41916, 'single'), 31664),\n  ('regression second-tier-carry 2', (30000, 0, 40000, 'mfj'), 11100),\n  ('partial repair guard 1', (30000, 1000, 8000, 'single'), 4850),\n  ('partial repair guard 2', (30775, 1000, 8000, 'single'), 5508),\n  ('control: small benefit first tier', (28000, 0, 2000, 'single'), 1000),\n  ('control: large income', (150000, 5000, 40000, 'mfj'), 34000),\n  ('control: first tier', (20000, 0, 12000, 'single'), 500),\n  ('control: second tier', (40000, 0, 20000, 'single'), 17000)]]\nfor label, args, expected in cases[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"},"fixed":{"sha256":"f2a84698f6929c211f98c21b7aebc225a579d758aee74b6a85da73a3bbbbb2b2","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(agi, exempt_interest, benefits, status):\n    b1, b2 = {'single': (25000, 34000), 'mfj': (32000, 44000), 'mfs': (0, 0)}[status]\n    B = Fraction(benefits)\n    pi = agi + exempt_interest + B / 2\n    if pi <= b1: t = Fraction(0)\n    elif pi <= b2: t = min(B / 2, (pi - b1) / 2)\n    else: t = min(B * 85 / 100, (pi - b2) * 85 / 100 + min(B / 2, Fraction(b2 - b1, 2)))\n    return int(t)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[('regression second-tier-carry 1', (40000, 0, 20000, 'single'), 17000),\n  ('regression second-tier-carry 2', (35000, 0, 4000, 'single'), 3400),\n  ('partial repair guard 1', (30000, 1000, 8000, 'single'), 4850),\n  ('partial repair guard 2', (30775, 1000, 8000, 'single'), 5508),\n  ('control: first tier', (20000, 0, 12000, 'single'), 500), ('control: below base', (10000, 0, 10000, 'single'), 0),\n  ('control: joint with exempt interest', (30000, 1000, 20000, 'mfj'), 4500),\n  ('control: separate filer', (5000, 0, 8000, 'mfs'), 6800)],\n [('regression second-tier-carry 1', (45000, 0, 30934, 'mfj'), 19996),\n  ('regression second-tier-carry 2', (30000, 1000, 8000, 'single'), 4850),\n  ('partial repair guard 2', (30775, 1000, 8000, 'single'), 5508),\n  ('control: joint with exempt interest', (30000, 1000, 20000, 'mfj'), 4500),\n  ('control: separate filer', (5000, 0, 8000, 'mfs'), 6800),\n  ('control: small benefit first tier', (28000, 0, 2000, 'single'), 1000),\n  ('control: large income', (150000, 5000, 40000, 'mfj'), 34000)],\n [('regression second-tier-carry 1', (20000, 1000, 45562, 'single'), 12813),\n  ('regression second-tier-carry 2', (30000, 1000, 42192, 'mfj'), 12881),\n  ('partial repair guard 1', (30000, 1000, 8000, 'single'), 4850),\n  ('partial repair guard 2', (30775, 1000, 8000, 'single'), 5508),\n  ('control: large income', (150000, 5000, 40000, 'mfj'), 34000),\n  ('control: first tier', (20000, 0, 12000, 'single'), 500),\n  ('control: second tier', (40000, 0, 20000, 'single'), 17000),\n  ('control: below base', (10000, 0, 10000, 'single'), 0)],\n [('regression second-tier-carry 1', (30000, 0, 20000, 'single'), 9600),\n  ('regression second-tier-carry 2', (45000, 1000, 40000, 'single'), 31700),\n  ('partial repair guard 1', (30000, 1000, 8000, 'single'), 4850),\n  ('partial repair guard 2', (30775, 1000, 8000, 'single'), 5508),\n  ('control: below base', (10000, 0, 10000, 'single'), 0),\n  ('control: joint with exempt interest', (30000, 1000, 20000, 'mfj'), 4500),\n  ('control: separate filer', (5000, 0, 8000, 'mfs'), 6800),\n  ('control: small benefit first tier', (28000, 0, 2000, 'single'), 1000)],\n [('regression second-tier-carry 1', (45000, 0, 41916, 'single'), 31664),\n  ('regression second-tier-carry 2', (30000, 0, 40000, 'mfj'), 11100),\n  ('partial repair guard 1', (30000, 1000, 8000, 'single'), 4850),\n  ('partial repair guard 2', (30775, 1000, 8000, 'single'), 5508),\n  ('control: small benefit first tier', (28000, 0, 2000, 'single'), 1000),\n  ('control: large income', (150000, 5000, 40000, 'mfj'), 34000),\n  ('control: first tier', (20000, 0, 12000, 'single'), 500),\n  ('control: second tier', (40000, 0, 20000, 'single'), 17000)]]\nfor label, args, expected in cases[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 with a stipulated toy contract; it makes no claim of conformance to any real regulation, standard, or institution's rules. 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-tax_bracket_computation-benefit-inclusion-tiers-second-tier-carry","generated_at":"2026-09-29T14:47:07.588056+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Tax computations hinge on which slice, threshold, ordering and rounding rule applies at each step; a misplaced boundary silently misstates liabilities.","repair":"Add the lesser of half the benefits and half the gap between base amounts.","root_cause":"The upper-tier formula lacks the + min(benefits/2, (b2 - b1)/2) term.","sha256":"2fd5712a02636d2d227de26c23826cbb84a0b66a973f1283155217ab9f7cf2d4","title":"The second-tier formula omits the amount included in the first tier · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":45.003,"exit_code":1,"observations":[{"actual":17000,"check":"regression second-tier-carry 1","expected":17000,"passed":true},{"actual":3400,"check":"regression second-tier-carry 2","expected":3400,"passed":true},{"actual":5350,"check":"partial repair guard 1","expected":4850,"passed":false},{"actual":6008,"check":"partial repair guard 2","expected":5508,"passed":false},{"actual":500,"check":"control: first tier","expected":500,"passed":true},{"actual":0,"check":"control: below base","expected":0,"passed":true},{"actual":4500,"check":"control: joint with exempt interest","expected":4500,"passed":true},{"actual":6800,"check":"control: separate filer","expected":6800,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression second-tier-carry 1\", \"actual\": 17000, \"expected\": 17000, \"passed\": true}, {\"check\": \"regression second-tier-carry 2\", \"actual\": 3400, \"expected\": 3400, \"passed\": true}, {\"check\": \"partial repair guard 1\", \"actual\": 5350, \"expected\": 4850, \"passed\": false}, {\"check\": \"partial repair guard 2\", \"actual\": 6008, \"expected\": 5508, \"passed\": false}, {\"check\": \"control: first tier\", \"actual\": 500, \"expected\": 500, \"passed\": true}, {\"check\": \"control: below base\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"control: joint with exempt interest\", \"actual\": 4500, \"expected\": 4500, \"passed\": true}, {\"check\": \"control: separate filer\", \"actual\": 6800, \"expected\": 6800, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":44.31,"exit_code":1,"observations":[{"actual":13600,"check":"regression second-tier-carry 1","expected":17000,"passed":false},{"actual":2550,"check":"regression second-tier-carry 2","expected":3400,"passed":false},{"actual":850,"check":"partial repair guard 1","expected":4850,"passed":false},{"actual":1508,"check":"partial repair guard 2","expected":5508,"passed":false},{"actual":500,"check":"control: first tier","expected":500,"passed":true},{"actual":0,"check":"control: below base","expected":0,"passed":true},{"actual":4500,"check":"control: joint with exempt interest","expected":4500,"passed":true},{"actual":6800,"check":"control: separate filer","expected":6800,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression second-tier-carry 1\", \"actual\": 13600, \"expected\": 17000, \"passed\": false}, {\"check\": \"regression second-tier-carry 2\", \"actual\": 2550, \"expected\": 3400, \"passed\": false}, {\"check\": \"partial repair guard 1\", \"actual\": 850, \"expected\": 4850, \"passed\": false}, {\"check\": \"partial repair guard 2\", \"actual\": 1508, \"expected\": 5508, \"passed\": false}, {\"check\": \"control: first tier\", \"actual\": 500, \"expected\": 500, \"passed\": true}, {\"check\": \"control: below base\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"control: joint with exempt interest\", \"actual\": 4500, \"expected\": 4500, \"passed\": true}, {\"check\": \"control: separate filer\", \"actual\": 6800, \"expected\": 6800, \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":42.915,"exit_code":0,"observations":[{"actual":17000,"check":"regression second-tier-carry 1","expected":17000,"passed":true},{"actual":3400,"check":"regression second-tier-carry 2","expected":3400,"passed":true},{"actual":4850,"check":"partial repair guard 1","expected":4850,"passed":true},{"actual":5508,"check":"partial repair guard 2","expected":5508,"passed":true},{"actual":500,"check":"control: first tier","expected":500,"passed":true},{"actual":0,"check":"control: below base","expected":0,"passed":true},{"actual":4500,"check":"control: joint with exempt interest","expected":4500,"passed":true},{"actual":6800,"check":"control: separate filer","expected":6800,"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression second-tier-carry 1\", \"actual\": 17000, \"expected\": 17000, \"passed\": true}, {\"check\": \"regression second-tier-carry 2\", \"actual\": 3400, \"expected\": 3400, \"passed\": true}, {\"check\": \"partial repair guard 1\", \"actual\": 4850, \"expected\": 4850, \"passed\": true}, {\"check\": \"partial repair guard 2\", \"actual\": 5508, \"expected\": 5508, \"passed\": true}, {\"check\": \"control: first tier\", \"actual\": 500, \"expected\": 500, \"passed\": true}, {\"check\": \"control: below base\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"control: joint with exempt interest\", \"actual\": 4500, \"expected\": 4500, \"passed\": true}, {\"check\": \"control: separate filer\", \"actual\": 6800, \"expected\": 6800, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}