{"abstract":"Expectations at older ages are far too small.","category":"Actuarial life tables","checks":8,"contract":"Input l (survivors by age, last entry is the open interval) and m_open (per mille central rate of the open interval, <=0 -> 'invalid open rate'). L_x = l_{x+1} + d_x/2, L_open = l_open/m, T_x = sum of L from x, e_x = T_x/l_x rounded to 4 places (None where l_x=0).","contract_signature":"x","evaluation_group":"w2-actuarial_life_tables-lifetable-columns","failed_approach":"Dividing by mid-year survivors mixes a central quantity into an initial ratio.","family":"w2-actuarial_life_tables-lifetable-columns-expectation-divisor","id":"FA-63381","implementations":{"attempt":{"sha256":"30734a729b7ea497b321737a3998b95de95b72d348bf90d1d1f510e1772f62e0","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(x):\n    l=x['l']; m=Fraction(x['m_open'],1000)\n    if m<=0: return 'invalid open rate'\n    L=[]\n    for i in range(len(l)-1):\n        d=l[i]-l[i+1]\n        L.append(l[i+1]+Fraction(d,2))\n    L.append(l[-1]/m)\n    T=[]; acc=Fraction(0)\n    for v in reversed(L):\n        acc+=v; T.append(acc)\n    T.reverse()\n    return [round(float(T[i]/(l[i]-Fraction(l[i]-l[i+1] if i+1<len(l) else 0,2))),4) if l[i] else None for i in range(len(l))]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['table 0', {'l': [100000, 99736, 99400, 99024, 98587, 98055, 97450, 96745], 'm_open': 800}, [8.1156, 7.1357, 6.1581, 5.1796, 4.2004, 3.2205, 2.2373, 1.25]], ['table 1', {'l': [100000, 99688, 99329, 98881, 98385, 97779, 97092], 'm_open': 250}, [9.8098, 8.8389, 7.869, 6.9024, 5.9347, 4.9684, 4.0]], ['table 2', {'l': [100000, 99380, 98687, 97892, 96992, 95970, 94815, 93535], 'm_open': 400}, [9.1434, 8.1973, 7.2514, 6.3062, 5.3601, 4.4118, 3.4595, 2.5]], ['table 3', {'l': [100000, 99494, 98897, 98225, 97474, 96626], 'm_open': 250}, [8.7891, 7.8312, 6.8755, 5.9191, 4.9609, 4.0]], ['table 4', {'l': [100000, 99458, 98844, 98161, 97382, 96516], 'm_open': 800}, [6.1275, 5.1581, 4.1871, 3.2127, 2.2344, 1.25]], ['extinct before open interval', {'l': [1000, 601, 200, 0], 'm_open': 500}, [1.301, 0.8328, 0.5, None]], ['two-age table', {'l': [5000, 1001], 'm_open': 1000}, [0.8003, 1.0]], ['zero open rate rejected', {'l': [100, 50], 'm_open': 0}, 'invalid open rate']], [['table 0', {'l': [100000, 99580, 99059, 98462, 97802], 'm_open': 500}, [5.9161, 4.9389, 3.9622, 2.9832, 2.0]], ['table 1', {'l': [100000, 99560, 99034, 98428, 97736], 'm_open': 400}, [6.4023, 5.4284, 4.4546, 3.4789, 2.5]], ['table 2', {'l': [100000, 99658, 99276, 98811, 98264, 97604], 'm_open': 800}, [6.1682, 5.1876, 4.2056, 3.2231, 2.2382, 1.25]], ['table 3', {'l': [100000, 99474, 98827, 98088], 'm_open': 250}, [6.897, 5.9308, 4.9664, 4.0]], ['table 4', {'l': [100000, 99385, 98714, 97935, 97044], 'm_open': 400}, [6.3717, 5.408, 4.4414, 3.4727, 2.5]], ['extinct before open interval', {'l': [1000, 602, 200, 0], 'm_open': 500}, [1.302, 0.8322, 0.5, None]], ['two-age table', {'l': [5000, 1002], 'm_open': 1000}, [0.8006, 1.0]], ['zero open rate rejected', {'l': [100, 50], 'm_open': 0}, 'invalid open rate']], [['table 0', {'l': [100000, 99748, 99427, 99064, 98638], 'm_open': 800}, [5.2086, 4.2205, 3.2325, 2.2425, 1.25]], ['table 1', {'l': [100000, 99540, 98977, 98365, 97658], 'm_open': 500}, [5.9103, 4.9353, 3.9605, 2.982, 2.0]], ['table 2', {'l': [100000, 99695, 99290, 98834, 98304], 'm_open': 500}, [5.9358, 4.9524, 3.9706, 2.9866, 2.0]], ['table 3', {'l': [100000, 99416, 98740, 97979, 97117, 96159], 'm_open': 250}, [8.7597, 7.8082, 6.8582, 5.9076, 4.9556, 4.0]], ['table 4', {'l': [100000, 99727, 99393, 98994, 98502, 97935, 97305], 'm_open': 800}, [7.1483, 6.1665, 5.1856, 4.2045, 3.223, 2.2387, 1.25]], ['extinct before open interval', {'l': [1000, 603, 200, 0], 'm_open': 500}, [1.303, 0.8317, 0.5, None]], ['two-age table', {'l': [5000, 1003], 'm_open': 1000}, [0.8009, 1.0]], ['zero open rate rejected', {'l': [100, 50], 'm_open': 0}, 'invalid open rate']], [['table 0', {'l': [100000, 99373, 98660, 97828, 96893], 'm_open': 400}, [6.3654, 5.4024, 4.4378, 3.4713, 2.5]], ['table 1', {'l': [100000, 99504, 98936, 98264], 'm_open': 500}, [4.941, 3.9631, 2.983, 2.0]], ['table 2', {'l': [100000, 99438, 98785, 98036, 97220, 96288, 95262, 94105], 'm_open': 500}, [8.7029, 7.7493, 6.7972, 5.8453, 4.8902, 3.9327, 2.9696, 2.0]], ['table 3', {'l': [100000, 99509, 98902, 98199, 97416, 96521, 95521], 'm_open': 250}, [9.7039, 8.7493, 7.8, 6.8522, 5.9033, 4.9534, 4.0]], ['table 4', {'l': [100000, 99565, 99005, 98381, 97680], 'm_open': 250}, [7.8651, 6.8973, 5.9335, 4.9679, 4.0]], ['extinct before open interval', {'l': [1000, 604, 200, 0], 'm_open': 500}, [1.304, 0.8311, 0.5, None]], ['two-age table', {'l': [5000, 1004], 'm_open': 1000}, [0.8012, 1.0]], ['zero open rate rejected', {'l': [100, 50], 'm_open': 0}, 'invalid open rate']], [['table 0', {'l': [100000, 99457, 98786, 98018, 97163, 96196, 95080, 93823], 'm_open': 250}, [10.569, 9.624, 8.686, 7.7501, 6.8139, 5.8774, 4.9405, 4.0]], ['table 1', {'l': [100000, 99396, 98710, 97875, 96955], 'm_open': 250}, [7.8228, 6.8673, 5.9115, 4.9577, 4.0]], ['table 2', {'l': [100000, 99541, 99001, 98405], 'm_open': 500}, [4.9455, 3.966, 2.9849, 2.0]], ['table 3', {'l': [100000, 99775, 99473, 99125, 98710, 98213, 97648], 'm_open': 250}, [9.8471, 8.8682, 7.8936, 6.9196, 5.9466, 4.9741, 4.0]], ['table 4', {'l': [100000, 99459, 98858, 98167, 97346, 96409], 'm_open': 800}, [6.1255, 5.1561, 4.1844, 3.2103, 2.2332, 1.25]], ['extinct before open interval', {'l': [1000, 605, 200, 0], 'm_open': 500}, [1.305, 0.8306, 0.5, None]], ['two-age table', {'l': [5000, 1005], 'm_open': 1000}, [0.8015, 1.0]], ['zero open rate rejected', {'l': [100, 50], 'm_open': 0}, 'invalid open rate']]]\nfor label, args, expected in fixtures[N-1]:\n    check(label, solve(args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"broken":{"sha256":"b6316cf657dcc971c5ca1cc3bdc9dbc0453d4724c51d9e4dc713a4864c01d96e","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(x):\n    l=x['l']; m=Fraction(x['m_open'],1000)\n    if m<=0: return 'invalid open rate'\n    L=[]\n    for i in range(len(l)-1):\n        d=l[i]-l[i+1]\n        L.append(l[i+1]+Fraction(d,2))\n    L.append(l[-1]/m)\n    T=[]; acc=Fraction(0)\n    for v in reversed(L):\n        acc+=v; T.append(acc)\n    T.reverse()\n    return [round(float(T[i]/l[0]),4) if l[i] else None for i in range(len(l))]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['table 0', {'l': [100000, 99736, 99400, 99024, 98587, 98055, 97450, 96745], 'm_open': 800}, [8.1156, 7.1357, 6.1581, 5.1796, 4.2004, 3.2205, 2.2373, 1.25]], ['table 1', {'l': [100000, 99688, 99329, 98881, 98385, 97779, 97092], 'm_open': 250}, [9.8098, 8.8389, 7.869, 6.9024, 5.9347, 4.9684, 4.0]], ['table 2', {'l': [100000, 99380, 98687, 97892, 96992, 95970, 94815, 93535], 'm_open': 400}, [9.1434, 8.1973, 7.2514, 6.3062, 5.3601, 4.4118, 3.4595, 2.5]], ['table 3', {'l': [100000, 99494, 98897, 98225, 97474, 96626], 'm_open': 250}, [8.7891, 7.8312, 6.8755, 5.9191, 4.9609, 4.0]], ['table 4', {'l': [100000, 99458, 98844, 98161, 97382, 96516], 'm_open': 800}, [6.1275, 5.1581, 4.1871, 3.2127, 2.2344, 1.25]], ['extinct before open interval', {'l': [1000, 601, 200, 0], 'm_open': 500}, [1.301, 0.8328, 0.5, None]], ['two-age table', {'l': [5000, 1001], 'm_open': 1000}, [0.8003, 1.0]], ['zero open rate rejected', {'l': [100, 50], 'm_open': 0}, 'invalid open rate']], [['table 0', {'l': [100000, 99580, 99059, 98462, 97802], 'm_open': 500}, [5.9161, 4.9389, 3.9622, 2.9832, 2.0]], ['table 1', {'l': [100000, 99560, 99034, 98428, 97736], 'm_open': 400}, [6.4023, 5.4284, 4.4546, 3.4789, 2.5]], ['table 2', {'l': [100000, 99658, 99276, 98811, 98264, 97604], 'm_open': 800}, [6.1682, 5.1876, 4.2056, 3.2231, 2.2382, 1.25]], ['table 3', {'l': [100000, 99474, 98827, 98088], 'm_open': 250}, [6.897, 5.9308, 4.9664, 4.0]], ['table 4', {'l': [100000, 99385, 98714, 97935, 97044], 'm_open': 400}, [6.3717, 5.408, 4.4414, 3.4727, 2.5]], ['extinct before open interval', {'l': [1000, 602, 200, 0], 'm_open': 500}, [1.302, 0.8322, 0.5, None]], ['two-age table', {'l': [5000, 1002], 'm_open': 1000}, [0.8006, 1.0]], ['zero open rate rejected', {'l': [100, 50], 'm_open': 0}, 'invalid open rate']], [['table 0', {'l': [100000, 99748, 99427, 99064, 98638], 'm_open': 800}, [5.2086, 4.2205, 3.2325, 2.2425, 1.25]], ['table 1', {'l': [100000, 99540, 98977, 98365, 97658], 'm_open': 500}, [5.9103, 4.9353, 3.9605, 2.982, 2.0]], ['table 2', {'l': [100000, 99695, 99290, 98834, 98304], 'm_open': 500}, [5.9358, 4.9524, 3.9706, 2.9866, 2.0]], ['table 3', {'l': [100000, 99416, 98740, 97979, 97117, 96159], 'm_open': 250}, [8.7597, 7.8082, 6.8582, 5.9076, 4.9556, 4.0]], ['table 4', {'l': [100000, 99727, 99393, 98994, 98502, 97935, 97305], 'm_open': 800}, [7.1483, 6.1665, 5.1856, 4.2045, 3.223, 2.2387, 1.25]], ['extinct before open interval', {'l': [1000, 603, 200, 0], 'm_open': 500}, [1.303, 0.8317, 0.5, None]], ['two-age table', {'l': [5000, 1003], 'm_open': 1000}, [0.8009, 1.0]], ['zero open rate rejected', {'l': [100, 50], 'm_open': 0}, 'invalid open rate']], [['table 0', {'l': [100000, 99373, 98660, 97828, 96893], 'm_open': 400}, [6.3654, 5.4024, 4.4378, 3.4713, 2.5]], ['table 1', {'l': [100000, 99504, 98936, 98264], 'm_open': 500}, [4.941, 3.9631, 2.983, 2.0]], ['table 2', {'l': [100000, 99438, 98785, 98036, 97220, 96288, 95262, 94105], 'm_open': 500}, [8.7029, 7.7493, 6.7972, 5.8453, 4.8902, 3.9327, 2.9696, 2.0]], ['table 3', {'l': [100000, 99509, 98902, 98199, 97416, 96521, 95521], 'm_open': 250}, [9.7039, 8.7493, 7.8, 6.8522, 5.9033, 4.9534, 4.0]], ['table 4', {'l': [100000, 99565, 99005, 98381, 97680], 'm_open': 250}, [7.8651, 6.8973, 5.9335, 4.9679, 4.0]], ['extinct before open interval', {'l': [1000, 604, 200, 0], 'm_open': 500}, [1.304, 0.8311, 0.5, None]], ['two-age table', {'l': [5000, 1004], 'm_open': 1000}, [0.8012, 1.0]], ['zero open rate rejected', {'l': [100, 50], 'm_open': 0}, 'invalid open rate']], [['table 0', {'l': [100000, 99457, 98786, 98018, 97163, 96196, 95080, 93823], 'm_open': 250}, [10.569, 9.624, 8.686, 7.7501, 6.8139, 5.8774, 4.9405, 4.0]], ['table 1', {'l': [100000, 99396, 98710, 97875, 96955], 'm_open': 250}, [7.8228, 6.8673, 5.9115, 4.9577, 4.0]], ['table 2', {'l': [100000, 99541, 99001, 98405], 'm_open': 500}, [4.9455, 3.966, 2.9849, 2.0]], ['table 3', {'l': [100000, 99775, 99473, 99125, 98710, 98213, 97648], 'm_open': 250}, [9.8471, 8.8682, 7.8936, 6.9196, 5.9466, 4.9741, 4.0]], ['table 4', {'l': [100000, 99459, 98858, 98167, 97346, 96409], 'm_open': 800}, [6.1255, 5.1561, 4.1844, 3.2103, 2.2332, 1.25]], ['extinct before open interval', {'l': [1000, 605, 200, 0], 'm_open': 500}, [1.305, 0.8306, 0.5, None]], ['two-age table', {'l': [5000, 1005], 'm_open': 1000}, [0.8015, 1.0]], ['zero open rate rejected', {'l': [100, 50], 'm_open': 0}, 'invalid open rate']]]\nfor label, args, expected in fixtures[N-1]:\n    check(label, solve(args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"}},"limitations":"A deterministic bounded teaching model of a stipulated toy actuarial contract. Rates are small synthetic tables, exact rationals are used where practical and floats are rounded at the output; it makes no claim of conformance with any published table, standard of practice or regulation. 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-actuarial_life_tables-lifetable-columns-expectation-divisor","generated_at":"2026-09-29T14:47:13.783106+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Life-table arithmetic compounds across ages, so one misplaced index or assumption shifts every downstream value.","root_cause":"T_x is divided by l_0 instead of l_x.","sha256":"20aab757084c4ab5f80c8727b429f0762e3ae06da0af1cb3e22383dd5d5f62c9","title":"Life table person-years and expectation: Expectation divides by the radix · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verified":true,"visibility":"public","verification":{"attempt":{"elapsed_ms":43.757,"exit_code":1,"observations":[{"actual":[8.1263,7.1478,6.1698,5.1911,4.2117,3.2304,2.2455,1.25],"check":"table 0","expected":[8.1156,7.1357,6.1581,5.1796,4.2004,3.2205,2.2373,1.25],"passed":false},{"actual":[9.8251,8.8548,7.8868,6.9198,5.953,4.9859,4.0],"check":"table 1","expected":[9.8098,8.8389,7.869,6.9024,5.9347,4.9684,4.0],"passed":false},{"actual":[9.1718,8.226,7.2807,6.3353,5.3885,4.4386,3.483,2.5],"check":"table 2","expected":[9.1434,8.1973,7.2514,6.3062,5.3601,4.4118,3.4595,2.5],"passed":false},{"actual":[8.8114,7.8548,6.8989,5.9418,4.9825,4.0],"check":"table 3","expected":[8.7891,7.8312,6.8755,5.9191,4.9609,4.0],"passed":false},{"actual":[6.1441,5.1741,4.2016,3.2255,2.2444,1.25],"check":"table 4","expected":[6.1275,5.1581,4.1871,3.2127,2.2344,1.25],"passed":false},{"actual":[1.6252,1.2497,1.0,null],"check":"extinct before open interval","expected":[1.301,0.8328,0.5,null],"passed":false},{"actual":[1.3336,1.0],"check":"two-age table","expected":[0.8003,1.0],"passed":false},{"actual":"invalid open rate","check":"zero open rate rejected","expected":"invalid open rate","passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"table 0\", \"actual\": [8.1263, 7.1478, 6.1698, 5.1911, 4.2117, 3.2304, 2.2455, 1.25], \"expected\": [8.1156, 7.1357, 6.1581, 5.1796, 4.2004, 3.2205, 2.2373, 1.25], \"passed\": false}, {\"check\": \"table 1\", \"actual\": [9.8251, 8.8548, 7.8868, 6.9198, 5.953, 4.9859, 4.0], \"expected\": [9.8098, 8.8389, 7.869, 6.9024, 5.9347, 4.9684, 4.0], \"passed\": false}, {\"check\": \"table 2\", \"actual\": [9.1718, 8.226, 7.2807, 6.3353, 5.3885, 4.4386, 3.483, 2.5], \"expected\": [9.1434, 8.1973, 7.2514, 6.3062, 5.3601, 4.4118, 3.4595, 2.5], \"passed\": false}, {\"check\": \"table 3\", \"actual\": [8.8114, 7.8548, 6.8989, 5.9418, 4.9825, 4.0], \"expected\": [8.7891, 7.8312, 6.8755, 5.9191, 4.9609, 4.0], \"passed\": false}, {\"check\": \"table 4\", \"actual\": [6.1441, 5.1741, 4.2016, 3.2255, 2.2444, 1.25], \"expected\": [6.1275, 5.1581, 4.1871, 3.2127, 2.2344, 1.25], \"passed\": false}, {\"check\": \"extinct before open interval\", \"actual\": [1.6252, 1.2497, 1.0, null], \"expected\": [1.301, 0.8328, 0.5, null], \"passed\": false}, {\"check\": \"two-age table\", \"actual\": [1.3336, 1.0], \"expected\": [0.8003, 1.0], \"passed\": false}, {\"check\": \"zero open rate rejected\", \"actual\": \"invalid open rate\", \"expected\": \"invalid open rate\", \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":42.707,"exit_code":1,"observations":[{"actual":[8.1156,7.1169,6.1212,5.1291,4.141,3.1578,2.1803,1.2093],"check":"table 0","expected":[8.1156,7.1357,6.1581,5.1796,4.2004,3.2205,2.2373,1.25],"passed":false},{"actual":[9.8098,8.8113,7.8162,6.8252,5.8389,4.858,3.8837],"check":"table 1","expected":[9.8098,8.8389,7.869,6.9024,5.9347,4.9684,4.0],"passed":false},{"actual":[9.1434,8.1465,7.1562,6.1733,5.1989,4.234,3.2801,2.3384],"check":"table 2","expected":[9.1434,8.1973,7.2514,6.3062,5.3601,4.4118,3.4595,2.5],"passed":false},{"actual":[8.7891,7.7916,6.7996,5.814,4.8355,3.865],"check":"table 3","expected":[8.7891,7.8312,6.8755,5.9191,4.9609,4.0],"passed":false},{"actual":[6.1275,5.1302,4.1387,3.1537,2.1759,1.2065],"check":"table 4","expected":[6.1275,5.1581,4.1871,3.2127,2.2344,1.25],"passed":false},{"actual":[1.301,0.5005,0.1,null],"check":"extinct before open interval","expected":[1.301,0.8328,0.5,null],"passed":false},{"actual":[0.8003,0.2002],"check":"two-age table","expected":[0.8003,1.0],"passed":false},{"actual":"invalid open rate","check":"zero open rate rejected","expected":"invalid open rate","passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"table 0\", \"actual\": [8.1156, 7.1169, 6.1212, 5.1291, 4.141, 3.1578, 2.1803, 1.2093], \"expected\": [8.1156, 7.1357, 6.1581, 5.1796, 4.2004, 3.2205, 2.2373, 1.25], \"passed\": false}, {\"check\": \"table 1\", \"actual\": [9.8098, 8.8113, 7.8162, 6.8252, 5.8389, 4.858, 3.8837], \"expected\": [9.8098, 8.8389, 7.869, 6.9024, 5.9347, 4.9684, 4.0], \"passed\": false}, {\"check\": \"table 2\", \"actual\": [9.1434, 8.1465, 7.1562, 6.1733, 5.1989, 4.234, 3.2801, 2.3384], \"expected\": [9.1434, 8.1973, 7.2514, 6.3062, 5.3601, 4.4118, 3.4595, 2.5], \"passed\": false}, {\"check\": \"table 3\", \"actual\": [8.7891, 7.7916, 6.7996, 5.814, 4.8355, 3.865], \"expected\": [8.7891, 7.8312, 6.8755, 5.9191, 4.9609, 4.0], \"passed\": false}, {\"check\": \"table 4\", \"actual\": [6.1275, 5.1302, 4.1387, 3.1537, 2.1759, 1.2065], \"expected\": [6.1275, 5.1581, 4.1871, 3.2127, 2.2344, 1.25], \"passed\": false}, {\"check\": \"extinct before open interval\", \"actual\": [1.301, 0.5005, 0.1, null], \"expected\": [1.301, 0.8328, 0.5, null], \"passed\": false}, {\"check\": \"two-age table\", \"actual\": [0.8003, 0.2002], \"expected\": [0.8003, 1.0], \"passed\": false}, {\"check\": \"zero open rate rejected\", \"actual\": \"invalid open rate\", \"expected\": \"invalid open rate\", \"passed\": true}], \"passed\": false}\n"}},"member_only":{"stages":["fixed"],"fields":["implementations.fixed","verification.fixed","harness","repair"],"note":"The verified repair, its recorded checks, the repair description, and the scoring harness are available to members."}}