FA-65891 / Aviation weight and balance / Open access

Exactly empty-weight load rejected as below empty · case 01

A ferry configuration at exactly the minimum weight returns ERR_BELOW_EMPTY.

Verified by executionVariant 1 · 12 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The guard treats the 1500 lb minimum as exclusive.

THE FAILURE

The guard treats the 1500 lb minimum as exclusive.

Unsuccessful approach: Making the guard depend on CG lets impossible sub-empty weights through whenever the CG looks normal.

Case contract

Input [weight lb, CG in, 'normal'|'utility']. Below 1500 lb -> 'ERR_BELOW_EMPTY'. Max weight 2550 normal / 2200 utility -> 'OVERWEIGHT' first. Forward limit 35.0 in up to 1950 lb then linear to 41.0 in at 2550 lb; aft limit 47.3 normal / 40.5 utility. Limits inclusive; else 'FWD','AFT','IN'.

Why this case matters

A category-dependent CG envelope with a sloped forward boundary; limit lines are part of the approved envelope.

1 / The failure

Exit 1

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

N = 1
observations = []
def solve(x):
    w, cg, cat = x
    if w <= 1500: return 'ERR_BELOW_EMPTY'
    maxw = 2550 if cat == 'normal' else 2200
    if w > maxw: return 'OVERWEIGHT'
    if w <= 1950:
        fwd = 35.0
    else:
        fwd = 35.0 + (w - 1950) * (41.0 - 35.0) / (2550 - 1950)
    aft = 47.3 if cat == 'normal' else 40.5
    if cg < fwd - 1e-9: return 'FWD'
    if cg > aft + 1e-9: return 'AFT'
    return 'IN'
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['mid-envelope normal', [2110, 42.0, 'normal'], 'IN'], ['on sloped forward line', [2250, 38.0, 'normal'], 'IN'], ['on aft limit utility', [2000, 40.5, 'utility'], 'IN'], ['utility overweight but normal legal', [2301, 42.0, 'utility'], 'OVERWEIGHT'], ['exactly max gross normal', [2550, 41.0, 'normal'], 'IN'], ['forward of sloped line', [2400, 39.1, 'normal'], 'FWD'], ['aft of utility limit', [2100, 41.1, 'utility'], 'AFT'], ['below empty weight', [1499, 40.0, 'normal'], 'ERR_BELOW_EMPTY'], ['exactly empty weight', [1500, 36.0, 'utility'], 'IN'], ['sampled case 1', [2415, 48.96, 'normal'], 'AFT'], ['sampled case 2', [2550, 34.9, 'normal'], 'FWD'], ['sampled case 3', [1950, 42.86, 'utility'], 'AFT']], [['mid-envelope normal', [2120, 42.0, 'normal'], 'IN'], ['on sloped forward line', [2250, 38.0, 'normal'], 'IN'], ['on aft limit utility', [2000, 40.5, 'utility'], 'IN'], ['utility overweight but normal legal', [2302, 42.0, 'utility'], 'OVERWEIGHT'], ['exactly max gross normal', [2550, 41.0, 'normal'], 'IN'], ['forward of sloped line', [2400, 39.2, 'normal'], 'FWD'], ['aft of utility limit', [2100, 41.2, 'utility'], 'AFT'], ['below empty weight', [1498, 40.0, 'normal'], 'ERR_BELOW_EMPTY'], ['exactly empty weight', [1500, 36.0, 'utility'], 'IN'], ['sampled case 1', [1950, 37.89, 'utility'], 'IN'], ['sampled case 2', [2561, 48.01, 'normal'], 'OVERWEIGHT'], ['sampled case 3', [2550, 45.7, 'normal'], 'IN']], [['mid-envelope normal', [2130, 42.0, 'normal'], 'IN'], ['on sloped forward line', [2250, 38.0, 'normal'], 'IN'], ['on aft limit utility', [2000, 40.5, 'utility'], 'IN'], ['utility overweight but normal legal', [2303, 42.0, 'utility'], 'OVERWEIGHT'], ['exactly max gross normal', [2550, 41.0, 'normal'], 'IN'], ['forward of sloped line', [2400, 39.3, 'normal'], 'FWD'], ['aft of utility limit', [2100, 41.3, 'utility'], 'AFT'], ['below empty weight', [1497, 40.0, 'normal'], 'ERR_BELOW_EMPTY'], ['exactly empty weight', [1500, 36.0, 'utility'], 'IN'], ['sampled case 1', [1950, 34.67, 'utility'], 'FWD'], ['sampled case 2', [1500, 42.58, 'utility'], 'AFT'], ['sampled case 3', [2200, 48.0, 'utility'], 'AFT']], [['mid-envelope normal', [2140, 42.0, 'normal'], 'IN'], ['on sloped forward line', [2250, 38.0, 'normal'], 'IN'], ['on aft limit utility', [2000, 40.5, 'utility'], 'IN'], ['utility overweight but normal legal', [2304, 42.0, 'utility'], 'OVERWEIGHT'], ['exactly max gross normal', [2550, 41.0, 'normal'], 'IN'], ['forward of sloped line', [2400, 39.4, 'normal'], 'FWD'], ['aft of utility limit', [2100, 41.4, 'utility'], 'AFT'], ['below empty weight', [1496, 40.0, 'normal'], 'ERR_BELOW_EMPTY'], ['exactly empty weight', [1500, 36.0, 'utility'], 'IN'], ['sampled case 1', [2200, 42.7, 'normal'], 'IN'], ['sampled case 2', [1969, 47.53, 'normal'], 'AFT'], ['sampled case 3', [1500, 48.2, 'normal'], 'AFT']], [['mid-envelope normal', [2150, 42.0, 'normal'], 'IN'], ['on sloped forward line', [2250, 38.0, 'normal'], 'IN'], ['on aft limit utility', [2000, 40.5, 'utility'], 'IN'], ['utility overweight but normal legal', [2305, 42.0, 'utility'], 'OVERWEIGHT'], ['exactly max gross normal', [2550, 41.0, 'normal'], 'IN'], ['forward of sloped line', [2400, 39.5, 'normal'], 'IN'], ['aft of utility limit', [2100, 41.5, 'utility'], 'AFT'], ['below empty weight', [1495, 40.0, 'normal'], 'ERR_BELOW_EMPTY'], ['exactly empty weight', [1500, 36.0, 'utility'], 'IN'], ['sampled case 1', [1950, 45.06, 'normal'], 'IN'], ['sampled case 2', [2200, 43.63, 'utility'], 'AFT'], ['sampled case 3', [2200, 41.43, 'normal'], 'IN']]]
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
mid-envelope normal	`IN`	`IN`	Passed
on sloped forward line	`IN`	`IN`	Passed
on aft limit utility	`IN`	`IN`	Passed
utility overweight but normal legal	`OVERWEIGHT`	`OVERWEIGHT`	Passed
exactly max gross normal	`IN`	`IN`	Passed
forward of sloped line	`FWD`	`FWD`	Passed
aft of utility limit	`AFT`	`AFT`	Passed
below empty weight	`ERR_BELOW_EMPTY`	`ERR_BELOW_EMPTY`	Passed
exactly empty weight	`ERR_BELOW_EMPTY`	`IN`	Failed
sampled case 1	`AFT`	`AFT`	Passed
sampled case 2	`FWD`	`FWD`	Passed
sampled case 3	`AFT`	`AFT`	Passed

SHA-256 / accec34a65be31f27819f6ab4c10c867ccacda38fdf9ef56949f5caeeacd8231

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(x):
    w, cg, cat = x
    if w < 1500 and cg < 35.0: return 'ERR_BELOW_EMPTY'
    maxw = 2550 if cat == 'normal' else 2200
    if w > maxw: return 'OVERWEIGHT'
    if w <= 1950:
        fwd = 35.0
    else:
        fwd = 35.0 + (w - 1950) * (41.0 - 35.0) / (2550 - 1950)
    aft = 47.3 if cat == 'normal' else 40.5
    if cg < fwd - 1e-9: return 'FWD'
    if cg > aft + 1e-9: return 'AFT'
    return 'IN'
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['mid-envelope normal', [2110, 42.0, 'normal'], 'IN'], ['on sloped forward line', [2250, 38.0, 'normal'], 'IN'], ['on aft limit utility', [2000, 40.5, 'utility'], 'IN'], ['utility overweight but normal legal', [2301, 42.0, 'utility'], 'OVERWEIGHT'], ['exactly max gross normal', [2550, 41.0, 'normal'], 'IN'], ['forward of sloped line', [2400, 39.1, 'normal'], 'FWD'], ['aft of utility limit', [2100, 41.1, 'utility'], 'AFT'], ['below empty weight', [1499, 40.0, 'normal'], 'ERR_BELOW_EMPTY'], ['exactly empty weight', [1500, 36.0, 'utility'], 'IN'], ['sampled case 1', [2415, 48.96, 'normal'], 'AFT'], ['sampled case 2', [2550, 34.9, 'normal'], 'FWD'], ['sampled case 3', [1950, 42.86, 'utility'], 'AFT']], [['mid-envelope normal', [2120, 42.0, 'normal'], 'IN'], ['on sloped forward line', [2250, 38.0, 'normal'], 'IN'], ['on aft limit utility', [2000, 40.5, 'utility'], 'IN'], ['utility overweight but normal legal', [2302, 42.0, 'utility'], 'OVERWEIGHT'], ['exactly max gross normal', [2550, 41.0, 'normal'], 'IN'], ['forward of sloped line', [2400, 39.2, 'normal'], 'FWD'], ['aft of utility limit', [2100, 41.2, 'utility'], 'AFT'], ['below empty weight', [1498, 40.0, 'normal'], 'ERR_BELOW_EMPTY'], ['exactly empty weight', [1500, 36.0, 'utility'], 'IN'], ['sampled case 1', [1950, 37.89, 'utility'], 'IN'], ['sampled case 2', [2561, 48.01, 'normal'], 'OVERWEIGHT'], ['sampled case 3', [2550, 45.7, 'normal'], 'IN']], [['mid-envelope normal', [2130, 42.0, 'normal'], 'IN'], ['on sloped forward line', [2250, 38.0, 'normal'], 'IN'], ['on aft limit utility', [2000, 40.5, 'utility'], 'IN'], ['utility overweight but normal legal', [2303, 42.0, 'utility'], 'OVERWEIGHT'], ['exactly max gross normal', [2550, 41.0, 'normal'], 'IN'], ['forward of sloped line', [2400, 39.3, 'normal'], 'FWD'], ['aft of utility limit', [2100, 41.3, 'utility'], 'AFT'], ['below empty weight', [1497, 40.0, 'normal'], 'ERR_BELOW_EMPTY'], ['exactly empty weight', [1500, 36.0, 'utility'], 'IN'], ['sampled case 1', [1950, 34.67, 'utility'], 'FWD'], ['sampled case 2', [1500, 42.58, 'utility'], 'AFT'], ['sampled case 3', [2200, 48.0, 'utility'], 'AFT']], [['mid-envelope normal', [2140, 42.0, 'normal'], 'IN'], ['on sloped forward line', [2250, 38.0, 'normal'], 'IN'], ['on aft limit utility', [2000, 40.5, 'utility'], 'IN'], ['utility overweight but normal legal', [2304, 42.0, 'utility'], 'OVERWEIGHT'], ['exactly max gross normal', [2550, 41.0, 'normal'], 'IN'], ['forward of sloped line', [2400, 39.4, 'normal'], 'FWD'], ['aft of utility limit', [2100, 41.4, 'utility'], 'AFT'], ['below empty weight', [1496, 40.0, 'normal'], 'ERR_BELOW_EMPTY'], ['exactly empty weight', [1500, 36.0, 'utility'], 'IN'], ['sampled case 1', [2200, 42.7, 'normal'], 'IN'], ['sampled case 2', [1969, 47.53, 'normal'], 'AFT'], ['sampled case 3', [1500, 48.2, 'normal'], 'AFT']], [['mid-envelope normal', [2150, 42.0, 'normal'], 'IN'], ['on sloped forward line', [2250, 38.0, 'normal'], 'IN'], ['on aft limit utility', [2000, 40.5, 'utility'], 'IN'], ['utility overweight but normal legal', [2305, 42.0, 'utility'], 'OVERWEIGHT'], ['exactly max gross normal', [2550, 41.0, 'normal'], 'IN'], ['forward of sloped line', [2400, 39.5, 'normal'], 'IN'], ['aft of utility limit', [2100, 41.5, 'utility'], 'AFT'], ['below empty weight', [1495, 40.0, 'normal'], 'ERR_BELOW_EMPTY'], ['exactly empty weight', [1500, 36.0, 'utility'], 'IN'], ['sampled case 1', [1950, 45.06, 'normal'], 'IN'], ['sampled case 2', [2200, 43.63, 'utility'], 'AFT'], ['sampled case 3', [2200, 41.43, 'normal'], 'IN']]]
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
mid-envelope normal	`IN`	`IN`	Passed
on sloped forward line	`IN`	`IN`	Passed
on aft limit utility	`IN`	`IN`	Passed
utility overweight but normal legal	`OVERWEIGHT`	`OVERWEIGHT`	Passed
exactly max gross normal	`IN`	`IN`	Passed
forward of sloped line	`FWD`	`FWD`	Passed
aft of utility limit	`AFT`	`AFT`	Passed
below empty weight	`IN`	`ERR_BELOW_EMPTY`	Failed
exactly empty weight	`IN`	`IN`	Passed
sampled case 1	`AFT`	`AFT`	Passed
sampled case 2	`FWD`	`FWD`	Passed
sampled case 3	`AFT`	`AFT`	Passed

SHA-256 / 24692b25ceb7ac423335b858afb0c466245523099c535e1b9d3650a923ecb9fa

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 12 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

Member access is invitation-based. Sign in with your invited account to inspect the repair.

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 2026-09-29T14:47:38.033906+00:00.

Case digest / 8d34702c0fd8954966f7c6b97b370525faaeb9e0c34cff8efd943e35e353c33e