FA-65966 / Aviation weight and balance / Open access

Impossible shift direction answered with a positive weight · case 01

Moving cargo forward is recommended to move the CG aft.

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

ROOT CAUSE

Absolute values hide the sign mismatch between the requested CG change and the station move.

VERIFIED REPAIR

Reject requests where the CG change and the arm change have opposite signs.

Unsuccessful approach: Checking only the aft-CG case still accepts forward CG targets with an aft station move.

Case contract

Input [total lb, current CG, target CG, from-station arm, to-station arm]. Weight to move = W*dCG/dArm, rounded UP to a whole pound after clearing float noise at 6 decimals. Same station -> 'ERR_SAME_STATION'; zero dCG -> 0; a move that shifts CG the wrong way -> 'ERR_DIRECTION'.

Why this case matters

The weight-shift formula moves existing load between stations without changing total weight; the answer must be conservative (rounded up).

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    W, cg0, cg1, a_from, a_to = x
    if a_from == a_to: return 'ERR_SAME_STATION'
    dcg = cg1 - cg0
    darm = a_to - a_from
    if dcg == 0: return 0
    moved = W * abs(dcg) / abs(darm)
    return math.ceil(round(moved, 6))
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['baggage moved aft', [2400, 40.0, 41.1, 70.0, 120.0], 53], ['exact whole-pound shift', [3000, 42.0, 42.3, 50.0, 140.0], 10], ['shift forward', [2610, 46.5, 45.0, 140.0, 60.0], 49], ['wrong direction request', [2500, 40.0, 41.0, 120.0, 69.0], 'ERR_DIRECTION'], ['already at target', [2300, 43.2, 43.2, 70.0, 120.0], 0], ['same station', [2300, 43.2, 44.0, 95.0, 95.0], 'ERR_SAME_STATION'], ['sampled case 1', [3980, 45.3, 44.23, 41.8, 92.7], 'ERR_DIRECTION'], ['sampled case 2', [2707, 38.32, 40.1, 125.8, 85.0], 'ERR_DIRECTION'], ['sampled case 3', [3239, 40.39, 40.5, 103.2, 113.0], 37]], [['baggage moved aft', [2400, 40.0, 41.2, 70.0, 120.0], 58], ['exact whole-pound shift', [3000, 42.0, 42.3, 50.0, 140.0], 10], ['shift forward', [2620, 46.5, 45.0, 140.0, 60.0], 50], ['wrong direction request', [2500, 40.0, 41.0, 120.0, 68.0], 'ERR_DIRECTION'], ['already at target', [2300, 43.2, 43.2, 70.0, 120.0], 0], ['same station', [2300, 43.2, 44.0, 95.0, 95.0], 'ERR_SAME_STATION'], ['sampled case 1', [2415, 40.34, 38.4, 91.5, 122.3], 'ERR_DIRECTION'], ['sampled case 2', [3730, 42.18, 40.8, 132.4, 79.3], 97], ['sampled case 3', [2931, 40.9, 40.9, 127.0, 108.6], 0]], [['baggage moved aft', [2400, 40.0, 41.3, 70.0, 120.0], 63], ['exact whole-pound shift', [3000, 42.0, 42.3, 50.0, 140.0], 10], ['shift forward', [2630, 46.5, 45.0, 140.0, 60.0], 50], ['wrong direction request', [2500, 40.0, 41.0, 120.0, 67.0], 'ERR_DIRECTION'], ['already at target', [2300, 43.2, 43.2, 70.0, 120.0], 0], ['same station', [2300, 43.2, 44.0, 95.0, 95.0], 'ERR_SAME_STATION'], ['sampled case 1', [3390, 43.8, 43.8, 81.2, 142.7], 0], ['sampled case 2', [2280, 42.43, 43.6, 91.3, 32.9], 'ERR_DIRECTION'], ['sampled case 3', [3550, 38.5, 38.5, 60.9, 57.1], 0], ['regression: shift direction validation', [3244, 38.84, 38.2, 97.2, 145.9], 'ERR_DIRECTION']], [['baggage moved aft', [2400, 40.0, 41.4, 70.0, 120.0], 68], ['exact whole-pound shift', [3000, 42.0, 42.3, 50.0, 140.0], 10], ['shift forward', [2640, 46.5, 45.0, 140.0, 60.0], 50], ['wrong direction request', [2500, 40.0, 41.0, 120.0, 66.0], 'ERR_DIRECTION'], ['already at target', [2300, 43.2, 43.2, 70.0, 120.0], 0], ['same station', [2300, 43.2, 44.0, 95.0, 95.0], 'ERR_SAME_STATION'], ['sampled case 1', [2103, 45.94, 44.79, 82.0, 59.6], 108], ['sampled case 2', [1930, 43.1, 41.2, 104.4, 84.0], 180], ['sampled case 3', [2160, 40.97, 40.7, 113.1, 93.1], 30], ['regression: shift direction validation', [2518, 38.76, 37.61, 80.6, 84.3], 'ERR_DIRECTION']], [['baggage moved aft', [2400, 40.0, 41.5, 70.0, 120.0], 72], ['exact whole-pound shift', [3000, 42.0, 42.3, 50.0, 140.0], 10], ['shift forward', [2650, 46.5, 45.0, 140.0, 60.0], 50], ['wrong direction request', [2500, 40.0, 41.0, 120.0, 65.0], 'ERR_DIRECTION'], ['already at target', [2300, 43.2, 43.2, 70.0, 120.0], 0], ['same station', [2300, 43.2, 44.0, 95.0, 95.0], 'ERR_SAME_STATION'], ['sampled case 1', [2243, 42.7, 42.6, 141.2, 133.0], 28], ['sampled case 2', [3954, 45.3, 43.62, 97.4, 126.8], 'ERR_DIRECTION'], ['sampled case 3', [3960, 41.6, 42.67, 35.8, 103.5], 63]]]
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
baggage moved aft	`53`	`53`	Passed
exact whole-pound shift	`10`	`10`	Passed
shift forward	`49`	`49`	Passed
wrong direction request	`50`	`ERR_DIRECTION`	Failed
already at target	`0`	`0`	Passed
same station	`ERR_SAME_STATION`	`ERR_SAME_STATION`	Passed
sampled case 1	`84`	`ERR_DIRECTION`	Failed
sampled case 2	`119`	`ERR_DIRECTION`	Failed
sampled case 3	`37`	`37`	Passed

SHA-256 / 3fb42e9aeb0b68d646023bbd0b2e4594a9af07bfd2de4cfd8be259569956e676

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    W, cg0, cg1, a_from, a_to = x
    if a_from == a_to: return 'ERR_SAME_STATION'
    dcg = cg1 - cg0
    darm = a_to - a_from
    if dcg == 0: return 0
    if dcg > 0 and darm < 0: return 'ERR_DIRECTION'
    moved = W * dcg / darm
    return math.ceil(round(moved, 6))
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['baggage moved aft', [2400, 40.0, 41.1, 70.0, 120.0], 53], ['exact whole-pound shift', [3000, 42.0, 42.3, 50.0, 140.0], 10], ['shift forward', [2610, 46.5, 45.0, 140.0, 60.0], 49], ['wrong direction request', [2500, 40.0, 41.0, 120.0, 69.0], 'ERR_DIRECTION'], ['already at target', [2300, 43.2, 43.2, 70.0, 120.0], 0], ['same station', [2300, 43.2, 44.0, 95.0, 95.0], 'ERR_SAME_STATION'], ['sampled case 1', [3980, 45.3, 44.23, 41.8, 92.7], 'ERR_DIRECTION'], ['sampled case 2', [2707, 38.32, 40.1, 125.8, 85.0], 'ERR_DIRECTION'], ['sampled case 3', [3239, 40.39, 40.5, 103.2, 113.0], 37]], [['baggage moved aft', [2400, 40.0, 41.2, 70.0, 120.0], 58], ['exact whole-pound shift', [3000, 42.0, 42.3, 50.0, 140.0], 10], ['shift forward', [2620, 46.5, 45.0, 140.0, 60.0], 50], ['wrong direction request', [2500, 40.0, 41.0, 120.0, 68.0], 'ERR_DIRECTION'], ['already at target', [2300, 43.2, 43.2, 70.0, 120.0], 0], ['same station', [2300, 43.2, 44.0, 95.0, 95.0], 'ERR_SAME_STATION'], ['sampled case 1', [2415, 40.34, 38.4, 91.5, 122.3], 'ERR_DIRECTION'], ['sampled case 2', [3730, 42.18, 40.8, 132.4, 79.3], 97], ['sampled case 3', [2931, 40.9, 40.9, 127.0, 108.6], 0]], [['baggage moved aft', [2400, 40.0, 41.3, 70.0, 120.0], 63], ['exact whole-pound shift', [3000, 42.0, 42.3, 50.0, 140.0], 10], ['shift forward', [2630, 46.5, 45.0, 140.0, 60.0], 50], ['wrong direction request', [2500, 40.0, 41.0, 120.0, 67.0], 'ERR_DIRECTION'], ['already at target', [2300, 43.2, 43.2, 70.0, 120.0], 0], ['same station', [2300, 43.2, 44.0, 95.0, 95.0], 'ERR_SAME_STATION'], ['sampled case 1', [3390, 43.8, 43.8, 81.2, 142.7], 0], ['sampled case 2', [2280, 42.43, 43.6, 91.3, 32.9], 'ERR_DIRECTION'], ['sampled case 3', [3550, 38.5, 38.5, 60.9, 57.1], 0], ['regression: shift direction validation', [3244, 38.84, 38.2, 97.2, 145.9], 'ERR_DIRECTION']], [['baggage moved aft', [2400, 40.0, 41.4, 70.0, 120.0], 68], ['exact whole-pound shift', [3000, 42.0, 42.3, 50.0, 140.0], 10], ['shift forward', [2640, 46.5, 45.0, 140.0, 60.0], 50], ['wrong direction request', [2500, 40.0, 41.0, 120.0, 66.0], 'ERR_DIRECTION'], ['already at target', [2300, 43.2, 43.2, 70.0, 120.0], 0], ['same station', [2300, 43.2, 44.0, 95.0, 95.0], 'ERR_SAME_STATION'], ['sampled case 1', [2103, 45.94, 44.79, 82.0, 59.6], 108], ['sampled case 2', [1930, 43.1, 41.2, 104.4, 84.0], 180], ['sampled case 3', [2160, 40.97, 40.7, 113.1, 93.1], 30], ['regression: shift direction validation', [2518, 38.76, 37.61, 80.6, 84.3], 'ERR_DIRECTION']], [['baggage moved aft', [2400, 40.0, 41.5, 70.0, 120.0], 72], ['exact whole-pound shift', [3000, 42.0, 42.3, 50.0, 140.0], 10], ['shift forward', [2650, 46.5, 45.0, 140.0, 60.0], 50], ['wrong direction request', [2500, 40.0, 41.0, 120.0, 65.0], 'ERR_DIRECTION'], ['already at target', [2300, 43.2, 43.2, 70.0, 120.0], 0], ['same station', [2300, 43.2, 44.0, 95.0, 95.0], 'ERR_SAME_STATION'], ['sampled case 1', [2243, 42.7, 42.6, 141.2, 133.0], 28], ['sampled case 2', [3954, 45.3, 43.62, 97.4, 126.8], 'ERR_DIRECTION'], ['sampled case 3', [3960, 41.6, 42.67, 35.8, 103.5], 63]]]
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
baggage moved aft	`53`	`53`	Passed
exact whole-pound shift	`10`	`10`	Passed
shift forward	`49`	`49`	Passed
wrong direction request	`ERR_DIRECTION`	`ERR_DIRECTION`	Passed
already at target	`0`	`0`	Passed
same station	`ERR_SAME_STATION`	`ERR_SAME_STATION`	Passed
sampled case 1	`-83`	`ERR_DIRECTION`	Failed
sampled case 2	`ERR_DIRECTION`	`ERR_DIRECTION`	Passed
sampled case 3	`37`	`37`	Passed

SHA-256 / c47be2f3e65aa4623ff589e7c612050fc9aaa99ee05394a27b673bf4cca23542

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    W, cg0, cg1, a_from, a_to = x
    if a_from == a_to: return 'ERR_SAME_STATION'
    dcg = cg1 - cg0
    darm = a_to - a_from
    if dcg == 0: return 0
    if (dcg > 0) != (darm > 0): return 'ERR_DIRECTION'
    moved = W * dcg / darm
    return math.ceil(round(moved, 6))
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['baggage moved aft', [2400, 40.0, 41.1, 70.0, 120.0], 53], ['exact whole-pound shift', [3000, 42.0, 42.3, 50.0, 140.0], 10], ['shift forward', [2610, 46.5, 45.0, 140.0, 60.0], 49], ['wrong direction request', [2500, 40.0, 41.0, 120.0, 69.0], 'ERR_DIRECTION'], ['already at target', [2300, 43.2, 43.2, 70.0, 120.0], 0], ['same station', [2300, 43.2, 44.0, 95.0, 95.0], 'ERR_SAME_STATION'], ['sampled case 1', [3980, 45.3, 44.23, 41.8, 92.7], 'ERR_DIRECTION'], ['sampled case 2', [2707, 38.32, 40.1, 125.8, 85.0], 'ERR_DIRECTION'], ['sampled case 3', [3239, 40.39, 40.5, 103.2, 113.0], 37]], [['baggage moved aft', [2400, 40.0, 41.2, 70.0, 120.0], 58], ['exact whole-pound shift', [3000, 42.0, 42.3, 50.0, 140.0], 10], ['shift forward', [2620, 46.5, 45.0, 140.0, 60.0], 50], ['wrong direction request', [2500, 40.0, 41.0, 120.0, 68.0], 'ERR_DIRECTION'], ['already at target', [2300, 43.2, 43.2, 70.0, 120.0], 0], ['same station', [2300, 43.2, 44.0, 95.0, 95.0], 'ERR_SAME_STATION'], ['sampled case 1', [2415, 40.34, 38.4, 91.5, 122.3], 'ERR_DIRECTION'], ['sampled case 2', [3730, 42.18, 40.8, 132.4, 79.3], 97], ['sampled case 3', [2931, 40.9, 40.9, 127.0, 108.6], 0]], [['baggage moved aft', [2400, 40.0, 41.3, 70.0, 120.0], 63], ['exact whole-pound shift', [3000, 42.0, 42.3, 50.0, 140.0], 10], ['shift forward', [2630, 46.5, 45.0, 140.0, 60.0], 50], ['wrong direction request', [2500, 40.0, 41.0, 120.0, 67.0], 'ERR_DIRECTION'], ['already at target', [2300, 43.2, 43.2, 70.0, 120.0], 0], ['same station', [2300, 43.2, 44.0, 95.0, 95.0], 'ERR_SAME_STATION'], ['sampled case 1', [3390, 43.8, 43.8, 81.2, 142.7], 0], ['sampled case 2', [2280, 42.43, 43.6, 91.3, 32.9], 'ERR_DIRECTION'], ['sampled case 3', [3550, 38.5, 38.5, 60.9, 57.1], 0], ['regression: shift direction validation', [3244, 38.84, 38.2, 97.2, 145.9], 'ERR_DIRECTION']], [['baggage moved aft', [2400, 40.0, 41.4, 70.0, 120.0], 68], ['exact whole-pound shift', [3000, 42.0, 42.3, 50.0, 140.0], 10], ['shift forward', [2640, 46.5, 45.0, 140.0, 60.0], 50], ['wrong direction request', [2500, 40.0, 41.0, 120.0, 66.0], 'ERR_DIRECTION'], ['already at target', [2300, 43.2, 43.2, 70.0, 120.0], 0], ['same station', [2300, 43.2, 44.0, 95.0, 95.0], 'ERR_SAME_STATION'], ['sampled case 1', [2103, 45.94, 44.79, 82.0, 59.6], 108], ['sampled case 2', [1930, 43.1, 41.2, 104.4, 84.0], 180], ['sampled case 3', [2160, 40.97, 40.7, 113.1, 93.1], 30], ['regression: shift direction validation', [2518, 38.76, 37.61, 80.6, 84.3], 'ERR_DIRECTION']], [['baggage moved aft', [2400, 40.0, 41.5, 70.0, 120.0], 72], ['exact whole-pound shift', [3000, 42.0, 42.3, 50.0, 140.0], 10], ['shift forward', [2650, 46.5, 45.0, 140.0, 60.0], 50], ['wrong direction request', [2500, 40.0, 41.0, 120.0, 65.0], 'ERR_DIRECTION'], ['already at target', [2300, 43.2, 43.2, 70.0, 120.0], 0], ['same station', [2300, 43.2, 44.0, 95.0, 95.0], 'ERR_SAME_STATION'], ['sampled case 1', [2243, 42.7, 42.6, 141.2, 133.0], 28], ['sampled case 2', [3954, 45.3, 43.62, 97.4, 126.8], 'ERR_DIRECTION'], ['sampled case 3', [3960, 41.6, 42.67, 35.8, 103.5], 63]]]
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
baggage moved aft	`53`	`53`	Passed
exact whole-pound shift	`10`	`10`	Passed
shift forward	`49`	`49`	Passed
wrong direction request	`ERR_DIRECTION`	`ERR_DIRECTION`	Passed
already at target	`0`	`0`	Passed
same station	`ERR_SAME_STATION`	`ERR_SAME_STATION`	Passed
sampled case 1	`ERR_DIRECTION`	`ERR_DIRECTION`	Passed
sampled case 2	`ERR_DIRECTION`	`ERR_DIRECTION`	Passed
sampled case 3	`37`	`37`	Passed

SHA-256 / 44163697516c7ad3b09638e6c0522ac4266b4cb5147a6941bfbf29f676231752

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 2026-09-29T14:47:38.903094+00:00.

Case digest / 89a257b058b1c81c72fae584e02ab6a0a6dfcb03129e7964d9fc8107478b34f9