FA-65921 / Aviation weight and balance / Open access

Loaded item weights left out of the conversion weight · case 01

%MAC drifts further from the chart the heavier the payload, while the index itself is correct.

Verified by executionVariant 1 · 9 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The loop adds item indices but never adds item weights, so the index is converted back to an arm with the dry operating weight only.

VERIFIED REPAIR

Add every item weight to the total weight used for the index-to-arm conversion.

Unsuccessful approach: Adding only items aft of the reference still omits forward-loaded weight from the divisor.

Case contract

Input {'dow','doi','ref','c','k','lemac','mac','items':[[kg,arm m]]}. Item index = kg*(arm-ref)/c; the dry operating index already contains K. Total index = doi + item indices; CG arm = ref + (index-K)*c/total weight; %MAC = (CG-LEMAC)/MAC*100. Return [index r2, %MAC r1].

Why this case matters

Airline loadsheets carry balance as a dimensionless index offset by K; converting back to %MAC requires removing K and scaling by C over total weight.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(x):
    ref, c, k = x['ref'], x['c'], x['k']
    w = x['dow']
    ti = x['doi']
    for iw, arm in x['items']:
        ti += iw * (arm - ref) / c
    cg = ref + (ti - k) * c / w
    pmac = (cg - x['lemac']) / x['mac'] * 100
    return [round(ti, 2), round(pmac, 1)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['typical cabin and hold', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3100.0, 14.0], [5000.0, 19.5], [1200.0, 24.0]]}, [50.3, 37.6]], ['empty operating aircraft', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': []}, [48.0, 36.3]], ['aft hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[4000.0, 26.1]]}, [80.4, 54.0]], ['forward hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3500.0, 9.2]]}, [17.2, 19.5]], ['item at reference arm', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[2500.0, 18.0]]}, [48.0, 36.4]], ['different constants', {'dow': 36050.0, 'doi': 40.0, 'ref': 20.0, 'c': 500.0, 'k': 45.0, 'lemac': 18.0, 'mac': 3.2, 'items': [[1800.0, 22.0], [2200.0, 17.0]]}, [34.0, 58.2]], ['sampled case 1', {'dow': 33485.0, 'doi': 37.0, 'ref': 20.4, 'c': 500.0, 'k': 44.4, 'lemac': 18.68, 'mac': 3.58, 'items': [[4603.0, 5.73], [2919.0, 25.41], [5509.0, 29.73], [5663.0, 28.02]]}, [120.3, 68.4]], ['sampled case 2', {'dow': 45884.0, 'doi': 51.2, 'ref': 20.0, 'c': 200.0, 'k': 57.4, 'lemac': 14.39, 'mac': 4.79, 'items': [[4694.0, 15.31], [4327.0, 9.7], [185.0, 15.41], [4752.0, 22.51], [992.0, 14.27]]}, [-254.74, 95.7]], ['sampled case 3', {'dow': 36007.0, 'doi': 45.2, 'ref': 20.5, 'c': 2000.0, 'k': 46.9, 'lemac': 17.4, 'mac': 3.61, 'items': []}, [45.2, 83.3]]], [['typical cabin and hold', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3200.0, 14.0], [5000.0, 19.5], [1200.0, 24.0]]}, [49.9, 37.5]], ['empty operating aircraft', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': []}, [48.0, 36.3]], ['aft hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[4000.0, 26.2]]}, [80.8, 54.2]], ['forward hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3500.0, 9.4]]}, [17.9, 19.9]], ['item at reference arm', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[5000.0, 18.0]]}, [48.0, 36.4]], ['different constants', {'dow': 36100.0, 'doi': 40.0, 'ref': 20.0, 'c': 500.0, 'k': 45.0, 'lemac': 18.0, 'mac': 3.2, 'items': [[1800.0, 22.0], [2200.0, 17.0]]}, [34.0, 58.2]], ['sampled case 1', {'dow': 41485.0, 'doi': 53.7, 'ref': 17.2, 'c': 500.0, 'k': 53.6, 'lemac': 14.91, 'mac': 4.7, 'items': [[323.0, 8.3], [3020.0, 17.98], [2440.0, 14.22]]}, [38.12, 45.2]], ['sampled case 2', {'dow': 36221.0, 'doi': 55.1, 'ref': 19.8, 'c': 2000.0, 'k': 56.4, 'lemac': 18.06, 'mac': 3.42, 'items': [[1053.0, 22.91]]}, [56.74, 51.4]], ['sampled case 3', {'dow': 36359.0, 'doi': 27.6, 'ref': 16.4, 'c': 200.0, 'k': 30.8, 'lemac': 14.16, 'mac': 3.79, 'items': [[2072.0, 5.02]]}, [-90.3, 42.5]]], [['typical cabin and hold', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3300.0, 14.0], [5000.0, 19.5], [1200.0, 24.0]]}, [49.5, 37.3]], ['empty operating aircraft', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': []}, [48.0, 36.3]], ['aft hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[4000.0, 26.3]]}, [81.2, 54.5]], ['forward hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3500.0, 9.6]]}, [18.6, 20.2]], ['item at reference arm', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[7500.0, 18.0]]}, [48.0, 36.5]], ['different constants', {'dow': 36150.0, 'doi': 40.0, 'ref': 20.0, 'c': 500.0, 'k': 45.0, 'lemac': 18.0, 'mac': 3.2, 'items': [[1800.0, 22.0], [2200.0, 17.0]]}, [34.0, 58.2]], ['sampled case 1', {'dow': 33923.0, 'doi': 39.1, 'ref': 19.3, 'c': 200.0, 'k': 45.3, 'lemac': 16.18, 'mac': 4.5, 'items': [[3739.0, 10.15]]}, [-131.96, 48.4]], ['sampled case 2', {'dow': 40403.0, 'doi': 39.1, 'ref': 21.4, 'c': 1000.0, 'k': 44.8, 'lemac': 14.64, 'mac': 4.94, 'items': [[4674.0, 28.04]]}, [70.14, 148.2]], ['sampled case 3', {'dow': 30111.0, 'doi': 38.1, 'ref': 15.0, 'c': 200.0, 'k': 36.0, 'lemac': 15.26, 'mac': 4.8, 'items': [[5589.0, 17.22]]}, [100.14, 2.1]]], [['typical cabin and hold', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3400.0, 14.0], [5000.0, 19.5], [1200.0, 24.0]]}, [49.1, 37.1]], ['empty operating aircraft', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': []}, [48.0, 36.3]], ['aft hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[4000.0, 26.4]]}, [81.6, 54.7]], ['forward hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3500.0, 9.8]]}, [19.3, 20.6]], ['item at reference arm', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[10000.0, 18.0]]}, [48.0, 36.5]], ['different constants', {'dow': 36200.0, 'doi': 40.0, 'ref': 20.0, 'c': 500.0, 'k': 45.0, 'lemac': 18.0, 'mac': 3.2, 'items': [[1800.0, 22.0], [2200.0, 17.0]]}, [34.0, 58.2]], ['sampled case 1', {'dow': 40381.0, 'doi': 38.2, 'ref': 17.2, 'c': 200.0, 'k': 35.3, 'lemac': 17.91, 'mac': 3.25, 'items': [[1141.0, 14.25], [3763.0, 12.45]]}, [-68.0, -35.9]], ['sampled case 2', {'dow': 40833.0, 'doi': 53.7, 'ref': 21.5, 'c': 2000.0, 'k': 48.5, 'lemac': 17.83, 'mac': 3.22, 'items': [[4174.0, 19.61], [2120.0, 18.46], [4779.0, 27.55], [1973.0, 12.04]]}, [51.66, 117.6]], ['sampled case 3', {'dow': 33856.0, 'doi': 31.0, 'ref': 19.9, 'c': 200.0, 'k': 36.6, 'lemac': 18.08, 'mac': 4.82, 'items': []}, [31.0, 37.1]]], [['typical cabin and hold', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3500.0, 14.0], [5000.0, 19.5], [1200.0, 24.0]]}, [48.7, 36.9]], ['empty operating aircraft', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': []}, [48.0, 36.3]], ['aft hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[4000.0, 26.5]]}, [82.0, 54.9]], ['forward hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3500.0, 10.0]]}, [20.0, 21.0]], ['item at reference arm', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[12500.0, 18.0]]}, [48.0, 36.6]], ['different constants', {'dow': 36250.0, 'doi': 40.0, 'ref': 20.0, 'c': 500.0, 'k': 45.0, 'lemac': 18.0, 'mac': 3.2, 'items': [[1800.0, 22.0], [2200.0, 17.0]]}, [34.0, 58.2]], ['sampled case 1', {'dow': 34075.0, 'doi': 33.7, 'ref': 19.6, 'c': 2000.0, 'k': 36.1, 'lemac': 15.76, 'mac': 3.12, 'items': [[4801.0, 23.6], [3956.0, 16.47], [1810.0, 18.75], [1491.0, 15.01], [3514.0, 6.44]]}, [9.8, 89.1]], ['sampled case 2', {'dow': 33834.0, 'doi': 57.4, 'ref': 20.6, 'c': 500.0, 'k': 55.3, 'lemac': 15.75, 'mac': 3.95, 'items': [[3292.0, 11.8], [4846.0, 14.0], [3222.0, 25.52], [2090.0, 7.1], [168.0, 27.97]]}, [-86.76, 84.9]], ['sampled case 3', {'dow': 46921.0, 'doi': 51.0, 'ref': 17.8, 'c': 500.0, 'k': 52.3, 'lemac': 14.61, 'mac': 3.01, 'items': [[2487.0, 11.85], [4542.0, 19.68]]}, [38.48, 101.7]]]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
typical cabin and hold	`[50.3, 37.7]`	`[50.3, 37.6]`	Failed
empty operating aircraft	`[48.0, 36.3]`	`[48.0, 36.3]`	Passed
aft hold heavy	`[80.4, 55.6]`	`[80.4, 54.0]`	Failed
forward hold heavy	`[17.2, 18.0]`	`[17.2, 19.5]`	Failed
item at reference arm	`[48.0, 36.3]`	`[48.0, 36.4]`	Failed
different constants	`[34.0, 57.7]`	`[34.0, 58.2]`	Failed
sampled case 1	`[120.3, 79.7]`	`[120.3, 68.4]`	Failed
sampled case 2	`[-254.74, 88.7]`	`[-254.74, 95.7]`	Failed
sampled case 3	`[45.2, 83.3]`	`[45.2, 83.3]`	Passed

SHA-256 / 0029dc11d3215b7b4969c91539a41c3e71873231b46cffd1dc5d598788343145

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(x):
    ref, c, k = x['ref'], x['c'], x['k']
    w = x['dow']
    ti = x['doi']
    for iw, arm in x['items']:
        w += iw if arm > ref else 0.0
        ti += iw * (arm - ref) / c
    cg = ref + (ti - k) * c / w
    pmac = (cg - x['lemac']) / x['mac'] * 100
    return [round(ti, 2), round(pmac, 1)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['typical cabin and hold', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3100.0, 14.0], [5000.0, 19.5], [1200.0, 24.0]]}, [50.3, 37.6]], ['empty operating aircraft', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': []}, [48.0, 36.3]], ['aft hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[4000.0, 26.1]]}, [80.4, 54.0]], ['forward hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3500.0, 9.2]]}, [17.2, 19.5]], ['item at reference arm', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[2500.0, 18.0]]}, [48.0, 36.4]], ['different constants', {'dow': 36050.0, 'doi': 40.0, 'ref': 20.0, 'c': 500.0, 'k': 45.0, 'lemac': 18.0, 'mac': 3.2, 'items': [[1800.0, 22.0], [2200.0, 17.0]]}, [34.0, 58.2]], ['sampled case 1', {'dow': 33485.0, 'doi': 37.0, 'ref': 20.4, 'c': 500.0, 'k': 44.4, 'lemac': 18.68, 'mac': 3.58, 'items': [[4603.0, 5.73], [2919.0, 25.41], [5509.0, 29.73], [5663.0, 28.02]]}, [120.3, 68.4]], ['sampled case 2', {'dow': 45884.0, 'doi': 51.2, 'ref': 20.0, 'c': 200.0, 'k': 57.4, 'lemac': 14.39, 'mac': 4.79, 'items': [[4694.0, 15.31], [4327.0, 9.7], [185.0, 15.41], [4752.0, 22.51], [992.0, 14.27]]}, [-254.74, 95.7]], ['sampled case 3', {'dow': 36007.0, 'doi': 45.2, 'ref': 20.5, 'c': 2000.0, 'k': 46.9, 'lemac': 17.4, 'mac': 3.61, 'items': []}, [45.2, 83.3]]], [['typical cabin and hold', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3200.0, 14.0], [5000.0, 19.5], [1200.0, 24.0]]}, [49.9, 37.5]], ['empty operating aircraft', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': []}, [48.0, 36.3]], ['aft hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[4000.0, 26.2]]}, [80.8, 54.2]], ['forward hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3500.0, 9.4]]}, [17.9, 19.9]], ['item at reference arm', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[5000.0, 18.0]]}, [48.0, 36.4]], ['different constants', {'dow': 36100.0, 'doi': 40.0, 'ref': 20.0, 'c': 500.0, 'k': 45.0, 'lemac': 18.0, 'mac': 3.2, 'items': [[1800.0, 22.0], [2200.0, 17.0]]}, [34.0, 58.2]], ['sampled case 1', {'dow': 41485.0, 'doi': 53.7, 'ref': 17.2, 'c': 500.0, 'k': 53.6, 'lemac': 14.91, 'mac': 4.7, 'items': [[323.0, 8.3], [3020.0, 17.98], [2440.0, 14.22]]}, [38.12, 45.2]], ['sampled case 2', {'dow': 36221.0, 'doi': 55.1, 'ref': 19.8, 'c': 2000.0, 'k': 56.4, 'lemac': 18.06, 'mac': 3.42, 'items': [[1053.0, 22.91]]}, [56.74, 51.4]], ['sampled case 3', {'dow': 36359.0, 'doi': 27.6, 'ref': 16.4, 'c': 200.0, 'k': 30.8, 'lemac': 14.16, 'mac': 3.79, 'items': [[2072.0, 5.02]]}, [-90.3, 42.5]]], [['typical cabin and hold', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3300.0, 14.0], [5000.0, 19.5], [1200.0, 24.0]]}, [49.5, 37.3]], ['empty operating aircraft', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': []}, [48.0, 36.3]], ['aft hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[4000.0, 26.3]]}, [81.2, 54.5]], ['forward hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3500.0, 9.6]]}, [18.6, 20.2]], ['item at reference arm', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[7500.0, 18.0]]}, [48.0, 36.5]], ['different constants', {'dow': 36150.0, 'doi': 40.0, 'ref': 20.0, 'c': 500.0, 'k': 45.0, 'lemac': 18.0, 'mac': 3.2, 'items': [[1800.0, 22.0], [2200.0, 17.0]]}, [34.0, 58.2]], ['sampled case 1', {'dow': 33923.0, 'doi': 39.1, 'ref': 19.3, 'c': 200.0, 'k': 45.3, 'lemac': 16.18, 'mac': 4.5, 'items': [[3739.0, 10.15]]}, [-131.96, 48.4]], ['sampled case 2', {'dow': 40403.0, 'doi': 39.1, 'ref': 21.4, 'c': 1000.0, 'k': 44.8, 'lemac': 14.64, 'mac': 4.94, 'items': [[4674.0, 28.04]]}, [70.14, 148.2]], ['sampled case 3', {'dow': 30111.0, 'doi': 38.1, 'ref': 15.0, 'c': 200.0, 'k': 36.0, 'lemac': 15.26, 'mac': 4.8, 'items': [[5589.0, 17.22]]}, [100.14, 2.1]]], [['typical cabin and hold', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3400.0, 14.0], [5000.0, 19.5], [1200.0, 24.0]]}, [49.1, 37.1]], ['empty operating aircraft', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': []}, [48.0, 36.3]], ['aft hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[4000.0, 26.4]]}, [81.6, 54.7]], ['forward hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3500.0, 9.8]]}, [19.3, 20.6]], ['item at reference arm', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[10000.0, 18.0]]}, [48.0, 36.5]], ['different constants', {'dow': 36200.0, 'doi': 40.0, 'ref': 20.0, 'c': 500.0, 'k': 45.0, 'lemac': 18.0, 'mac': 3.2, 'items': [[1800.0, 22.0], [2200.0, 17.0]]}, [34.0, 58.2]], ['sampled case 1', {'dow': 40381.0, 'doi': 38.2, 'ref': 17.2, 'c': 200.0, 'k': 35.3, 'lemac': 17.91, 'mac': 3.25, 'items': [[1141.0, 14.25], [3763.0, 12.45]]}, [-68.0, -35.9]], ['sampled case 2', {'dow': 40833.0, 'doi': 53.7, 'ref': 21.5, 'c': 2000.0, 'k': 48.5, 'lemac': 17.83, 'mac': 3.22, 'items': [[4174.0, 19.61], [2120.0, 18.46], [4779.0, 27.55], [1973.0, 12.04]]}, [51.66, 117.6]], ['sampled case 3', {'dow': 33856.0, 'doi': 31.0, 'ref': 19.9, 'c': 200.0, 'k': 36.6, 'lemac': 18.08, 'mac': 4.82, 'items': []}, [31.0, 37.1]]], [['typical cabin and hold', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3500.0, 14.0], [5000.0, 19.5], [1200.0, 24.0]]}, [48.7, 36.9]], ['empty operating aircraft', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': []}, [48.0, 36.3]], ['aft hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[4000.0, 26.5]]}, [82.0, 54.9]], ['forward hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3500.0, 10.0]]}, [20.0, 21.0]], ['item at reference arm', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[12500.0, 18.0]]}, [48.0, 36.6]], ['different constants', {'dow': 36250.0, 'doi': 40.0, 'ref': 20.0, 'c': 500.0, 'k': 45.0, 'lemac': 18.0, 'mac': 3.2, 'items': [[1800.0, 22.0], [2200.0, 17.0]]}, [34.0, 58.2]], ['sampled case 1', {'dow': 34075.0, 'doi': 33.7, 'ref': 19.6, 'c': 2000.0, 'k': 36.1, 'lemac': 15.76, 'mac': 3.12, 'items': [[4801.0, 23.6], [3956.0, 16.47], [1810.0, 18.75], [1491.0, 15.01], [3514.0, 6.44]]}, [9.8, 89.1]], ['sampled case 2', {'dow': 33834.0, 'doi': 57.4, 'ref': 20.6, 'c': 500.0, 'k': 55.3, 'lemac': 15.75, 'mac': 3.95, 'items': [[3292.0, 11.8], [4846.0, 14.0], [3222.0, 25.52], [2090.0, 7.1], [168.0, 27.97]]}, [-86.76, 84.9]], ['sampled case 3', {'dow': 46921.0, 'doi': 51.0, 'ref': 17.8, 'c': 500.0, 'k': 52.3, 'lemac': 14.61, 'mac': 3.01, 'items': [[2487.0, 11.85], [4542.0, 19.68]]}, [38.48, 101.7]]]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
typical cabin and hold	`[50.3, 37.7]`	`[50.3, 37.6]`	Failed
empty operating aircraft	`[48.0, 36.3]`	`[48.0, 36.3]`	Passed
aft hold heavy	`[80.4, 54.0]`	`[80.4, 54.0]`	Passed
forward hold heavy	`[17.2, 18.0]`	`[17.2, 19.5]`	Failed
item at reference arm	`[48.0, 36.3]`	`[48.0, 36.4]`	Failed
different constants	`[34.0, 58.0]`	`[34.0, 58.2]`	Failed
sampled case 1	`[120.3, 70.3]`	`[120.3, 68.4]`	Failed
sampled case 2	`[-254.74, 91.4]`	`[-254.74, 95.7]`	Failed
sampled case 3	`[45.2, 83.3]`	`[45.2, 83.3]`	Passed

SHA-256 / c7af8bbe2448ca2e9b13613b13cb82ca9d98d1ade06d88a7dad1b396078627d9

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(x):
    ref, c, k = x['ref'], x['c'], x['k']
    w = x['dow']
    ti = x['doi']
    for iw, arm in x['items']:
        w += iw
        ti += iw * (arm - ref) / c
    cg = ref + (ti - k) * c / w
    pmac = (cg - x['lemac']) / x['mac'] * 100
    return [round(ti, 2), round(pmac, 1)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['typical cabin and hold', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3100.0, 14.0], [5000.0, 19.5], [1200.0, 24.0]]}, [50.3, 37.6]], ['empty operating aircraft', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': []}, [48.0, 36.3]], ['aft hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[4000.0, 26.1]]}, [80.4, 54.0]], ['forward hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3500.0, 9.2]]}, [17.2, 19.5]], ['item at reference arm', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[2500.0, 18.0]]}, [48.0, 36.4]], ['different constants', {'dow': 36050.0, 'doi': 40.0, 'ref': 20.0, 'c': 500.0, 'k': 45.0, 'lemac': 18.0, 'mac': 3.2, 'items': [[1800.0, 22.0], [2200.0, 17.0]]}, [34.0, 58.2]], ['sampled case 1', {'dow': 33485.0, 'doi': 37.0, 'ref': 20.4, 'c': 500.0, 'k': 44.4, 'lemac': 18.68, 'mac': 3.58, 'items': [[4603.0, 5.73], [2919.0, 25.41], [5509.0, 29.73], [5663.0, 28.02]]}, [120.3, 68.4]], ['sampled case 2', {'dow': 45884.0, 'doi': 51.2, 'ref': 20.0, 'c': 200.0, 'k': 57.4, 'lemac': 14.39, 'mac': 4.79, 'items': [[4694.0, 15.31], [4327.0, 9.7], [185.0, 15.41], [4752.0, 22.51], [992.0, 14.27]]}, [-254.74, 95.7]], ['sampled case 3', {'dow': 36007.0, 'doi': 45.2, 'ref': 20.5, 'c': 2000.0, 'k': 46.9, 'lemac': 17.4, 'mac': 3.61, 'items': []}, [45.2, 83.3]]], [['typical cabin and hold', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3200.0, 14.0], [5000.0, 19.5], [1200.0, 24.0]]}, [49.9, 37.5]], ['empty operating aircraft', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': []}, [48.0, 36.3]], ['aft hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[4000.0, 26.2]]}, [80.8, 54.2]], ['forward hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3500.0, 9.4]]}, [17.9, 19.9]], ['item at reference arm', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[5000.0, 18.0]]}, [48.0, 36.4]], ['different constants', {'dow': 36100.0, 'doi': 40.0, 'ref': 20.0, 'c': 500.0, 'k': 45.0, 'lemac': 18.0, 'mac': 3.2, 'items': [[1800.0, 22.0], [2200.0, 17.0]]}, [34.0, 58.2]], ['sampled case 1', {'dow': 41485.0, 'doi': 53.7, 'ref': 17.2, 'c': 500.0, 'k': 53.6, 'lemac': 14.91, 'mac': 4.7, 'items': [[323.0, 8.3], [3020.0, 17.98], [2440.0, 14.22]]}, [38.12, 45.2]], ['sampled case 2', {'dow': 36221.0, 'doi': 55.1, 'ref': 19.8, 'c': 2000.0, 'k': 56.4, 'lemac': 18.06, 'mac': 3.42, 'items': [[1053.0, 22.91]]}, [56.74, 51.4]], ['sampled case 3', {'dow': 36359.0, 'doi': 27.6, 'ref': 16.4, 'c': 200.0, 'k': 30.8, 'lemac': 14.16, 'mac': 3.79, 'items': [[2072.0, 5.02]]}, [-90.3, 42.5]]], [['typical cabin and hold', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3300.0, 14.0], [5000.0, 19.5], [1200.0, 24.0]]}, [49.5, 37.3]], ['empty operating aircraft', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': []}, [48.0, 36.3]], ['aft hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[4000.0, 26.3]]}, [81.2, 54.5]], ['forward hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3500.0, 9.6]]}, [18.6, 20.2]], ['item at reference arm', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[7500.0, 18.0]]}, [48.0, 36.5]], ['different constants', {'dow': 36150.0, 'doi': 40.0, 'ref': 20.0, 'c': 500.0, 'k': 45.0, 'lemac': 18.0, 'mac': 3.2, 'items': [[1800.0, 22.0], [2200.0, 17.0]]}, [34.0, 58.2]], ['sampled case 1', {'dow': 33923.0, 'doi': 39.1, 'ref': 19.3, 'c': 200.0, 'k': 45.3, 'lemac': 16.18, 'mac': 4.5, 'items': [[3739.0, 10.15]]}, [-131.96, 48.4]], ['sampled case 2', {'dow': 40403.0, 'doi': 39.1, 'ref': 21.4, 'c': 1000.0, 'k': 44.8, 'lemac': 14.64, 'mac': 4.94, 'items': [[4674.0, 28.04]]}, [70.14, 148.2]], ['sampled case 3', {'dow': 30111.0, 'doi': 38.1, 'ref': 15.0, 'c': 200.0, 'k': 36.0, 'lemac': 15.26, 'mac': 4.8, 'items': [[5589.0, 17.22]]}, [100.14, 2.1]]], [['typical cabin and hold', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3400.0, 14.0], [5000.0, 19.5], [1200.0, 24.0]]}, [49.1, 37.1]], ['empty operating aircraft', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': []}, [48.0, 36.3]], ['aft hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[4000.0, 26.4]]}, [81.6, 54.7]], ['forward hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3500.0, 9.8]]}, [19.3, 20.6]], ['item at reference arm', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[10000.0, 18.0]]}, [48.0, 36.5]], ['different constants', {'dow': 36200.0, 'doi': 40.0, 'ref': 20.0, 'c': 500.0, 'k': 45.0, 'lemac': 18.0, 'mac': 3.2, 'items': [[1800.0, 22.0], [2200.0, 17.0]]}, [34.0, 58.2]], ['sampled case 1', {'dow': 40381.0, 'doi': 38.2, 'ref': 17.2, 'c': 200.0, 'k': 35.3, 'lemac': 17.91, 'mac': 3.25, 'items': [[1141.0, 14.25], [3763.0, 12.45]]}, [-68.0, -35.9]], ['sampled case 2', {'dow': 40833.0, 'doi': 53.7, 'ref': 21.5, 'c': 2000.0, 'k': 48.5, 'lemac': 17.83, 'mac': 3.22, 'items': [[4174.0, 19.61], [2120.0, 18.46], [4779.0, 27.55], [1973.0, 12.04]]}, [51.66, 117.6]], ['sampled case 3', {'dow': 33856.0, 'doi': 31.0, 'ref': 19.9, 'c': 200.0, 'k': 36.6, 'lemac': 18.08, 'mac': 4.82, 'items': []}, [31.0, 37.1]]], [['typical cabin and hold', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3500.0, 14.0], [5000.0, 19.5], [1200.0, 24.0]]}, [48.7, 36.9]], ['empty operating aircraft', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': []}, [48.0, 36.3]], ['aft hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[4000.0, 26.5]]}, [82.0, 54.9]], ['forward hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3500.0, 10.0]]}, [20.0, 21.0]], ['item at reference arm', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[12500.0, 18.0]]}, [48.0, 36.6]], ['different constants', {'dow': 36250.0, 'doi': 40.0, 'ref': 20.0, 'c': 500.0, 'k': 45.0, 'lemac': 18.0, 'mac': 3.2, 'items': [[1800.0, 22.0], [2200.0, 17.0]]}, [34.0, 58.2]], ['sampled case 1', {'dow': 34075.0, 'doi': 33.7, 'ref': 19.6, 'c': 2000.0, 'k': 36.1, 'lemac': 15.76, 'mac': 3.12, 'items': [[4801.0, 23.6], [3956.0, 16.47], [1810.0, 18.75], [1491.0, 15.01], [3514.0, 6.44]]}, [9.8, 89.1]], ['sampled case 2', {'dow': 33834.0, 'doi': 57.4, 'ref': 20.6, 'c': 500.0, 'k': 55.3, 'lemac': 15.75, 'mac': 3.95, 'items': [[3292.0, 11.8], [4846.0, 14.0], [3222.0, 25.52], [2090.0, 7.1], [168.0, 27.97]]}, [-86.76, 84.9]], ['sampled case 3', {'dow': 46921.0, 'doi': 51.0, 'ref': 17.8, 'c': 500.0, 'k': 52.3, 'lemac': 14.61, 'mac': 3.01, 'items': [[2487.0, 11.85], [4542.0, 19.68]]}, [38.48, 101.7]]]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
typical cabin and hold	`[50.3, 37.6]`	`[50.3, 37.6]`	Passed
empty operating aircraft	`[48.0, 36.3]`	`[48.0, 36.3]`	Passed
aft hold heavy	`[80.4, 54.0]`	`[80.4, 54.0]`	Passed
forward hold heavy	`[17.2, 19.5]`	`[17.2, 19.5]`	Passed
item at reference arm	`[48.0, 36.4]`	`[48.0, 36.4]`	Passed
different constants	`[34.0, 58.2]`	`[34.0, 58.2]`	Passed
sampled case 1	`[120.3, 68.4]`	`[120.3, 68.4]`	Passed
sampled case 2	`[-254.74, 95.7]`	`[-254.74, 95.7]`	Passed
sampled case 3	`[45.2, 83.3]`	`[45.2, 83.3]`	Passed

SHA-256 / 29e9cc4a8fe4ede3b8326c94a7b85ee7eaa307ffd8a5b9bb462fd3ae70532e71

Verification & scope

A deterministic toy loading model with stipulated constants; it is not an approved aircraft flight manual procedure and makes no claim of regulatory conformance. 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.

Observations recorded using Python 3.12.14 at 2026-09-29T14:47:38.506259+00:00.

Case digest / c3acf08ab24e272cbbc5c3a358d8aafec80fd43a7dc7f0124679e0014fd4cffc