FA-67911 / Traffic signal timing plans / Open access

Yellow and all-red intervals: the grade term omits the factor of two · case 01

Yellow and all-red intervals returns a wrong result when the grade term omits the factor of two.

Verified by executionVariant 1 · 8 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The denominator uses gG instead of 2g*G, halving the effect of grade relative to deceleration.

VERIFIED REPAIR

Restore the grade term coefficient rule so that the step reads `2 * Fraction(322, 10) *`.

Unsuccessful approach: Using 9.8 m/s^2 inside a feet-based formula keeps the factor two but the wrong unit system.

Case contract

Input {speed_mph, grade_pct (uphill positive), reaction_tenths, decel ft/s^2, width_ft, veh_len_ft, crosswalk_ft, ped}. v = 1.467*speed ft/s; yellow = t + v/(2a + 2*32.2*grade/100), rounded UP to 0.1 s and clamped to [3.0, 6.0]; a non-positive denominator returns 'invalid'. All-red = (W + vehicle length)/v where W includes the far crosswalk when ped is true, rounded UP to 0.1 s and clamped to [1.0, 6.0]. Return tenths.

Why this case matters

Signal timing arithmetic is exact and integer or rational; a wrong rule silently produces unsafe or inefficient timing plans.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
import math
N = 1
observations = []
def solve(x):
    v = Fraction(x['speed_mph']) * Fraction(1467, 1000)
    t = Fraction(x['reaction_tenths'], 10)
    den = 2 * x['decel'] + Fraction(322, 10) * Fraction(x['grade_pct'], 100)
    if den <= 0:
        return 'invalid'
    yl = max(30, min(60, math.ceil((t + v / den) * 10)))
    w = x['width_ft'] + (x['crosswalk_ft'] if x['ped'] else 0)
    rd = max(10, min(60, math.ceil((w + x['veh_len_ft']) / v * 10)))
    return {'yellow_tenths': yl, 'red_tenths': rd}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[({'speed_mph': 45, 'grade_pct': -4, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 80, 'veh_len_ft': 20, 'crosswalk_ft': 10, 'ped': True}, {'yellow_tenths': 48, 'red_tenths': 17}), ({'speed_mph': 65, 'grade_pct': -7, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 120, 'veh_len_ft': 20, 'crosswalk_ft': 10, 'ped': True}, {'yellow_tenths': 60, 'red_tenths': 16}), ({'speed_mph': 30, 'grade_pct': 1, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 130, 'veh_len_ft': 40, 'crosswalk_ft': 10, 'ped': True}, {'yellow_tenths': 32, 'red_tenths': 41}), ({'speed_mph': 50, 'grade_pct': 1, 'reaction_tenths': 8, 'decel': 11, 'width_ft': 71, 'veh_len_ft': 20, 'crosswalk_ft': 8, 'ped': False}, {'yellow_tenths': 41, 'red_tenths': 13}), ({'speed_mph': 20, 'grade_pct': 4, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 70, 'veh_len_ft': 20, 'crosswalk_ft': 8, 'ped': False}, {'yellow_tenths': 30, 'red_tenths': 31}), ({'speed_mph': 30, 'grade_pct': 0, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 60, 'veh_len_ft': 20, 'crosswalk_ft': 12, 'ped': False}, {'yellow_tenths': 33, 'red_tenths': 19}), ({'speed_mph': 50, 'grade_pct': 5, 'reaction_tenths': 12, 'decel': 10, 'width_ft': 70, 'veh_len_ft': 16, 'crosswalk_ft': 12, 'ped': True}, {'yellow_tenths': 44, 'red_tenths': 14}), ({'speed_mph': 45, 'grade_pct': -2, 'reaction_tenths': 10, 'decel': 12, 'width_ft': 61, 'veh_len_ft': 16, 'crosswalk_ft': 12, 'ped': False}, {'yellow_tenths': 40, 'red_tenths': 12})], [({'speed_mph': 65, 'grade_pct': -7, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 120, 'veh_len_ft': 20, 'crosswalk_ft': 10, 'ped': True}, {'yellow_tenths': 60, 'red_tenths': 16}), ({'speed_mph': 65, 'grade_pct': 1, 'reaction_tenths': 15, 'decel': 10, 'width_ft': 47, 'veh_len_ft': 25, 'crosswalk_ft': 12, 'ped': True}, {'yellow_tenths': 60, 'red_tenths': 10}), ({'speed_mph': 35, 'grade_pct': 7, 'reaction_tenths': 8, 'decel': 10, 'width_ft': 133, 'veh_len_ft': 16, 'crosswalk_ft': 10, 'ped': False}, {'yellow_tenths': 30, 'red_tenths': 30}), ({'speed_mph': 45, 'grade_pct': -4, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 80, 'veh_len_ft': 20, 'crosswalk_ft': 10, 'ped': True}, {'yellow_tenths': 48, 'red_tenths': 17}), ({'speed_mph': 20, 'grade_pct': 3, 'reaction_tenths': 10, 'decel': 11, 'width_ft': 91, 'veh_len_ft': 16, 'crosswalk_ft': 15, 'ped': True}, {'yellow_tenths': 30, 'red_tenths': 42}), ({'speed_mph': 35, 'grade_pct': -5, 'reaction_tenths': 15, 'decel': 12, 'width_ft': 129, 'veh_len_ft': 40, 'crosswalk_ft': 12, 'ped': True}, {'yellow_tenths': 40, 'red_tenths': 36}), ({'speed_mph': 60, 'grade_pct': -8, 'reaction_tenths': 12, 'decel': 8, 'width_ft': 53, 'veh_len_ft': 20, 'crosswalk_ft': 8, 'ped': True}, {'yellow_tenths': 60, 'red_tenths': 10}), ({'speed_mph': 30, 'grade_pct': 0, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 60, 'veh_len_ft': 20, 'crosswalk_ft': 12, 'ped': False}, {'yellow_tenths': 33, 'red_tenths': 19})], [({'speed_mph': 40, 'grade_pct': 5, 'reaction_tenths': 12, 'decel': 12, 'width_ft': 98, 'veh_len_ft': 20, 'crosswalk_ft': 10, 'ped': False}, {'yellow_tenths': 34, 'red_tenths': 21}), ({'speed_mph': 45, 'grade_pct': -4, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 80, 'veh_len_ft': 20, 'crosswalk_ft': 10, 'ped': True}, {'yellow_tenths': 48, 'red_tenths': 17}), ({'speed_mph': 70, 'grade_pct': -6, 'reaction_tenths': 12, 'decel': 10, 'width_ft': 101, 'veh_len_ft': 25, 'crosswalk_ft': 15, 'ped': False}, {'yellow_tenths': 60, 'red_tenths': 13}), ({'speed_mph': 65, 'grade_pct': -7, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 120, 'veh_len_ft': 20, 'crosswalk_ft': 10, 'ped': True}, {'yellow_tenths': 60, 'red_tenths': 16}), ({'speed_mph': 70, 'grade_pct': -8, 'reaction_tenths': 12, 'decel': 10, 'width_ft': 119, 'veh_len_ft': 25, 'crosswalk_ft': 8, 'ped': False}, {'yellow_tenths': 60, 'red_tenths': 15}), ({'speed_mph': 30, 'grade_pct': 0, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 60, 'veh_len_ft': 20, 'crosswalk_ft': 12, 'ped': False}, {'yellow_tenths': 33, 'red_tenths': 19}), ({'speed_mph': 70, 'grade_pct': -6, 'reaction_tenths': 12, 'decel': 12, 'width_ft': 116, 'veh_len_ft': 25, 'crosswalk_ft': 8, 'ped': True}, {'yellow_tenths': 60, 'red_tenths': 15}), ({'speed_mph': 70, 'grade_pct': -3, 'reaction_tenths': 8, 'decel': 12, 'width_ft': 53, 'veh_len_ft': 20, 'crosswalk_ft': 12, 'ped': True}, {'yellow_tenths': 55, 'red_tenths': 10})], [({'speed_mph': 45, 'grade_pct': -4, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 80, 'veh_len_ft': 20, 'crosswalk_ft': 10, 'ped': True}, {'yellow_tenths': 48, 'red_tenths': 17}), ({'speed_mph': 45, 'grade_pct': 6, 'reaction_tenths': 10, 'decel': 12, 'width_ft': 131, 'veh_len_ft': 25, 'crosswalk_ft': 8, 'ped': True}, {'yellow_tenths': 34, 'red_tenths': 25}), ({'speed_mph': 20, 'grade_pct': -5, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 83, 'veh_len_ft': 16, 'crosswalk_ft': 10, 'ped': True}, {'yellow_tenths': 30, 'red_tenths': 38}), ({'speed_mph': 25, 'grade_pct': -5, 'reaction_tenths': 15, 'decel': 11, 'width_ft': 121, 'veh_len_ft': 20, 'crosswalk_ft': 8, 'ped': True}, {'yellow_tenths': 35, 'red_tenths': 41}), ({'speed_mph': 20, 'grade_pct': 1, 'reaction_tenths': 12, 'decel': 10, 'width_ft': 133, 'veh_len_ft': 16, 'crosswalk_ft': 15, 'ped': False}, {'yellow_tenths': 30, 'red_tenths': 51}), ({'speed_mph': 65, 'grade_pct': 8, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 133, 'veh_len_ft': 20, 'crosswalk_ft': 15, 'ped': True}, {'yellow_tenths': 48, 'red_tenths': 18}), ({'speed_mph': 65, 'grade_pct': -7, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 120, 'veh_len_ft': 20, 'crosswalk_ft': 10, 'ped': True}, {'yellow_tenths': 60, 'red_tenths': 16}), ({'speed_mph': 30, 'grade_pct': 0, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 60, 'veh_len_ft': 20, 'crosswalk_ft': 12, 'ped': False}, {'yellow_tenths': 33, 'red_tenths': 19})], [({'speed_mph': 25, 'grade_pct': 4, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 48, 'veh_len_ft': 16, 'crosswalk_ft': 12, 'ped': False}, {'yellow_tenths': 30, 'red_tenths': 18}), ({'speed_mph': 45, 'grade_pct': -4, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 80, 'veh_len_ft': 20, 'crosswalk_ft': 10, 'ped': True}, {'yellow_tenths': 48, 'red_tenths': 17}), ({'speed_mph': 30, 'grade_pct': 1, 'reaction_tenths': 15, 'decel': 10, 'width_ft': 71, 'veh_len_ft': 20, 'crosswalk_ft': 15, 'ped': True}, {'yellow_tenths': 37, 'red_tenths': 25}), ({'speed_mph': 70, 'grade_pct': 3, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 104, 'veh_len_ft': 20, 'crosswalk_ft': 15, 'ped': True}, {'yellow_tenths': 57, 'red_tenths': 14}), ({'speed_mph': 25, 'grade_pct': -5, 'reaction_tenths': 10, 'decel': 8, 'width_ft': 59, 'veh_len_ft': 25, 'crosswalk_ft': 12, 'ped': False}, {'yellow_tenths': 39, 'red_tenths': 23}), ({'speed_mph': 30, 'grade_pct': 0, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 60, 'veh_len_ft': 20, 'crosswalk_ft': 12, 'ped': False}, {'yellow_tenths': 33, 'red_tenths': 19}), ({'speed_mph': 40, 'grade_pct': 1, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 126, 'veh_len_ft': 20, 'crosswalk_ft': 12, 'ped': False}, {'yellow_tenths': 39, 'red_tenths': 25}), ({'speed_mph': 65, 'grade_pct': -7, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 120, 'veh_len_ft': 20, 'crosswalk_ft': 10, 'ped': True}, {'yellow_tenths': 60, 'red_tenths': 16})]]
for i, (args, expected) in enumerate(fixtures[N-1]):
    check('timing oracle' + ' %d' % i, 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
timing oracle 0	`{'red_tenths': 17, 'yellow_tenths': 46}`	`{'red_tenths': 17, 'yellow_tenths': 48}`	Failed
timing oracle 1	`{'red_tenths': 16, 'yellow_tenths': 60}`	`{'red_tenths': 16, 'yellow_tenths': 60}`	Passed
timing oracle 2	`{'red_tenths': 41, 'yellow_tenths': 32}`	`{'red_tenths': 41, 'yellow_tenths': 32}`	Passed
timing oracle 3	`{'red_tenths': 13, 'yellow_tenths': 41}`	`{'red_tenths': 13, 'yellow_tenths': 41}`	Passed
timing oracle 4	`{'red_tenths': 31, 'yellow_tenths': 30}`	`{'red_tenths': 31, 'yellow_tenths': 30}`	Passed
timing oracle 5	`{'red_tenths': 19, 'yellow_tenths': 33}`	`{'red_tenths': 19, 'yellow_tenths': 33}`	Passed
timing oracle 6	`{'red_tenths': 14, 'yellow_tenths': 46}`	`{'red_tenths': 14, 'yellow_tenths': 44}`	Failed
timing oracle 7	`{'red_tenths': 12, 'yellow_tenths': 39}`	`{'red_tenths': 12, 'yellow_tenths': 40}`	Failed

SHA-256 / aa91e1f50535f10bdb03f1349473231aaef58487b530125b07c20c1c357262a3

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
import math
N = 1
observations = []
def solve(x):
    v = Fraction(x['speed_mph']) * Fraction(1467, 1000)
    t = Fraction(x['reaction_tenths'], 10)
    den = 2 * x['decel'] + 2 * Fraction(98, 10) * Fraction(x['grade_pct'], 100)
    if den <= 0:
        return 'invalid'
    yl = max(30, min(60, math.ceil((t + v / den) * 10)))
    w = x['width_ft'] + (x['crosswalk_ft'] if x['ped'] else 0)
    rd = max(10, min(60, math.ceil((w + x['veh_len_ft']) / v * 10)))
    return {'yellow_tenths': yl, 'red_tenths': rd}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[({'speed_mph': 45, 'grade_pct': -4, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 80, 'veh_len_ft': 20, 'crosswalk_ft': 10, 'ped': True}, {'yellow_tenths': 48, 'red_tenths': 17}), ({'speed_mph': 65, 'grade_pct': -7, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 120, 'veh_len_ft': 20, 'crosswalk_ft': 10, 'ped': True}, {'yellow_tenths': 60, 'red_tenths': 16}), ({'speed_mph': 30, 'grade_pct': 1, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 130, 'veh_len_ft': 40, 'crosswalk_ft': 10, 'ped': True}, {'yellow_tenths': 32, 'red_tenths': 41}), ({'speed_mph': 50, 'grade_pct': 1, 'reaction_tenths': 8, 'decel': 11, 'width_ft': 71, 'veh_len_ft': 20, 'crosswalk_ft': 8, 'ped': False}, {'yellow_tenths': 41, 'red_tenths': 13}), ({'speed_mph': 20, 'grade_pct': 4, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 70, 'veh_len_ft': 20, 'crosswalk_ft': 8, 'ped': False}, {'yellow_tenths': 30, 'red_tenths': 31}), ({'speed_mph': 30, 'grade_pct': 0, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 60, 'veh_len_ft': 20, 'crosswalk_ft': 12, 'ped': False}, {'yellow_tenths': 33, 'red_tenths': 19}), ({'speed_mph': 50, 'grade_pct': 5, 'reaction_tenths': 12, 'decel': 10, 'width_ft': 70, 'veh_len_ft': 16, 'crosswalk_ft': 12, 'ped': True}, {'yellow_tenths': 44, 'red_tenths': 14}), ({'speed_mph': 45, 'grade_pct': -2, 'reaction_tenths': 10, 'decel': 12, 'width_ft': 61, 'veh_len_ft': 16, 'crosswalk_ft': 12, 'ped': False}, {'yellow_tenths': 40, 'red_tenths': 12})], [({'speed_mph': 65, 'grade_pct': -7, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 120, 'veh_len_ft': 20, 'crosswalk_ft': 10, 'ped': True}, {'yellow_tenths': 60, 'red_tenths': 16}), ({'speed_mph': 65, 'grade_pct': 1, 'reaction_tenths': 15, 'decel': 10, 'width_ft': 47, 'veh_len_ft': 25, 'crosswalk_ft': 12, 'ped': True}, {'yellow_tenths': 60, 'red_tenths': 10}), ({'speed_mph': 35, 'grade_pct': 7, 'reaction_tenths': 8, 'decel': 10, 'width_ft': 133, 'veh_len_ft': 16, 'crosswalk_ft': 10, 'ped': False}, {'yellow_tenths': 30, 'red_tenths': 30}), ({'speed_mph': 45, 'grade_pct': -4, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 80, 'veh_len_ft': 20, 'crosswalk_ft': 10, 'ped': True}, {'yellow_tenths': 48, 'red_tenths': 17}), ({'speed_mph': 20, 'grade_pct': 3, 'reaction_tenths': 10, 'decel': 11, 'width_ft': 91, 'veh_len_ft': 16, 'crosswalk_ft': 15, 'ped': True}, {'yellow_tenths': 30, 'red_tenths': 42}), ({'speed_mph': 35, 'grade_pct': -5, 'reaction_tenths': 15, 'decel': 12, 'width_ft': 129, 'veh_len_ft': 40, 'crosswalk_ft': 12, 'ped': True}, {'yellow_tenths': 40, 'red_tenths': 36}), ({'speed_mph': 60, 'grade_pct': -8, 'reaction_tenths': 12, 'decel': 8, 'width_ft': 53, 'veh_len_ft': 20, 'crosswalk_ft': 8, 'ped': True}, {'yellow_tenths': 60, 'red_tenths': 10}), ({'speed_mph': 30, 'grade_pct': 0, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 60, 'veh_len_ft': 20, 'crosswalk_ft': 12, 'ped': False}, {'yellow_tenths': 33, 'red_tenths': 19})], [({'speed_mph': 40, 'grade_pct': 5, 'reaction_tenths': 12, 'decel': 12, 'width_ft': 98, 'veh_len_ft': 20, 'crosswalk_ft': 10, 'ped': False}, {'yellow_tenths': 34, 'red_tenths': 21}), ({'speed_mph': 45, 'grade_pct': -4, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 80, 'veh_len_ft': 20, 'crosswalk_ft': 10, 'ped': True}, {'yellow_tenths': 48, 'red_tenths': 17}), ({'speed_mph': 70, 'grade_pct': -6, 'reaction_tenths': 12, 'decel': 10, 'width_ft': 101, 'veh_len_ft': 25, 'crosswalk_ft': 15, 'ped': False}, {'yellow_tenths': 60, 'red_tenths': 13}), ({'speed_mph': 65, 'grade_pct': -7, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 120, 'veh_len_ft': 20, 'crosswalk_ft': 10, 'ped': True}, {'yellow_tenths': 60, 'red_tenths': 16}), ({'speed_mph': 70, 'grade_pct': -8, 'reaction_tenths': 12, 'decel': 10, 'width_ft': 119, 'veh_len_ft': 25, 'crosswalk_ft': 8, 'ped': False}, {'yellow_tenths': 60, 'red_tenths': 15}), ({'speed_mph': 30, 'grade_pct': 0, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 60, 'veh_len_ft': 20, 'crosswalk_ft': 12, 'ped': False}, {'yellow_tenths': 33, 'red_tenths': 19}), ({'speed_mph': 70, 'grade_pct': -6, 'reaction_tenths': 12, 'decel': 12, 'width_ft': 116, 'veh_len_ft': 25, 'crosswalk_ft': 8, 'ped': True}, {'yellow_tenths': 60, 'red_tenths': 15}), ({'speed_mph': 70, 'grade_pct': -3, 'reaction_tenths': 8, 'decel': 12, 'width_ft': 53, 'veh_len_ft': 20, 'crosswalk_ft': 12, 'ped': True}, {'yellow_tenths': 55, 'red_tenths': 10})], [({'speed_mph': 45, 'grade_pct': -4, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 80, 'veh_len_ft': 20, 'crosswalk_ft': 10, 'ped': True}, {'yellow_tenths': 48, 'red_tenths': 17}), ({'speed_mph': 45, 'grade_pct': 6, 'reaction_tenths': 10, 'decel': 12, 'width_ft': 131, 'veh_len_ft': 25, 'crosswalk_ft': 8, 'ped': True}, {'yellow_tenths': 34, 'red_tenths': 25}), ({'speed_mph': 20, 'grade_pct': -5, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 83, 'veh_len_ft': 16, 'crosswalk_ft': 10, 'ped': True}, {'yellow_tenths': 30, 'red_tenths': 38}), ({'speed_mph': 25, 'grade_pct': -5, 'reaction_tenths': 15, 'decel': 11, 'width_ft': 121, 'veh_len_ft': 20, 'crosswalk_ft': 8, 'ped': True}, {'yellow_tenths': 35, 'red_tenths': 41}), ({'speed_mph': 20, 'grade_pct': 1, 'reaction_tenths': 12, 'decel': 10, 'width_ft': 133, 'veh_len_ft': 16, 'crosswalk_ft': 15, 'ped': False}, {'yellow_tenths': 30, 'red_tenths': 51}), ({'speed_mph': 65, 'grade_pct': 8, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 133, 'veh_len_ft': 20, 'crosswalk_ft': 15, 'ped': True}, {'yellow_tenths': 48, 'red_tenths': 18}), ({'speed_mph': 65, 'grade_pct': -7, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 120, 'veh_len_ft': 20, 'crosswalk_ft': 10, 'ped': True}, {'yellow_tenths': 60, 'red_tenths': 16}), ({'speed_mph': 30, 'grade_pct': 0, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 60, 'veh_len_ft': 20, 'crosswalk_ft': 12, 'ped': False}, {'yellow_tenths': 33, 'red_tenths': 19})], [({'speed_mph': 25, 'grade_pct': 4, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 48, 'veh_len_ft': 16, 'crosswalk_ft': 12, 'ped': False}, {'yellow_tenths': 30, 'red_tenths': 18}), ({'speed_mph': 45, 'grade_pct': -4, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 80, 'veh_len_ft': 20, 'crosswalk_ft': 10, 'ped': True}, {'yellow_tenths': 48, 'red_tenths': 17}), ({'speed_mph': 30, 'grade_pct': 1, 'reaction_tenths': 15, 'decel': 10, 'width_ft': 71, 'veh_len_ft': 20, 'crosswalk_ft': 15, 'ped': True}, {'yellow_tenths': 37, 'red_tenths': 25}), ({'speed_mph': 70, 'grade_pct': 3, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 104, 'veh_len_ft': 20, 'crosswalk_ft': 15, 'ped': True}, {'yellow_tenths': 57, 'red_tenths': 14}), ({'speed_mph': 25, 'grade_pct': -5, 'reaction_tenths': 10, 'decel': 8, 'width_ft': 59, 'veh_len_ft': 25, 'crosswalk_ft': 12, 'ped': False}, {'yellow_tenths': 39, 'red_tenths': 23}), ({'speed_mph': 30, 'grade_pct': 0, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 60, 'veh_len_ft': 20, 'crosswalk_ft': 12, 'ped': False}, {'yellow_tenths': 33, 'red_tenths': 19}), ({'speed_mph': 40, 'grade_pct': 1, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 126, 'veh_len_ft': 20, 'crosswalk_ft': 12, 'ped': False}, {'yellow_tenths': 39, 'red_tenths': 25}), ({'speed_mph': 65, 'grade_pct': -7, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 120, 'veh_len_ft': 20, 'crosswalk_ft': 10, 'ped': True}, {'yellow_tenths': 60, 'red_tenths': 16})]]
for i, (args, expected) in enumerate(fixtures[N-1]):
    check('timing oracle' + ' %d' % i, 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
timing oracle 0	`{'red_tenths': 17, 'yellow_tenths': 45}`	`{'red_tenths': 17, 'yellow_tenths': 48}`	Failed
timing oracle 1	`{'red_tenths': 16, 'yellow_tenths': 60}`	`{'red_tenths': 16, 'yellow_tenths': 60}`	Passed
timing oracle 2	`{'red_tenths': 41, 'yellow_tenths': 32}`	`{'red_tenths': 41, 'yellow_tenths': 32}`	Passed
timing oracle 3	`{'red_tenths': 13, 'yellow_tenths': 42}`	`{'red_tenths': 13, 'yellow_tenths': 41}`	Failed
timing oracle 4	`{'red_tenths': 31, 'yellow_tenths': 30}`	`{'red_tenths': 31, 'yellow_tenths': 30}`	Passed
timing oracle 5	`{'red_tenths': 19, 'yellow_tenths': 33}`	`{'red_tenths': 19, 'yellow_tenths': 33}`	Passed
timing oracle 6	`{'red_tenths': 14, 'yellow_tenths': 47}`	`{'red_tenths': 14, 'yellow_tenths': 44}`	Failed
timing oracle 7	`{'red_tenths': 12, 'yellow_tenths': 38}`	`{'red_tenths': 12, 'yellow_tenths': 40}`	Failed

SHA-256 / 743bdcd34e7671d257b5246c23cca8d24f610f6bb7308bae3b7c5608434a0b0b

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
import math
N = 1
observations = []
def solve(x):
    v = Fraction(x['speed_mph']) * Fraction(1467, 1000)
    t = Fraction(x['reaction_tenths'], 10)
    den = 2 * x['decel'] + 2 * Fraction(322, 10) * Fraction(x['grade_pct'], 100)
    if den <= 0:
        return 'invalid'
    yl = max(30, min(60, math.ceil((t + v / den) * 10)))
    w = x['width_ft'] + (x['crosswalk_ft'] if x['ped'] else 0)
    rd = max(10, min(60, math.ceil((w + x['veh_len_ft']) / v * 10)))
    return {'yellow_tenths': yl, 'red_tenths': rd}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[({'speed_mph': 45, 'grade_pct': -4, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 80, 'veh_len_ft': 20, 'crosswalk_ft': 10, 'ped': True}, {'yellow_tenths': 48, 'red_tenths': 17}), ({'speed_mph': 65, 'grade_pct': -7, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 120, 'veh_len_ft': 20, 'crosswalk_ft': 10, 'ped': True}, {'yellow_tenths': 60, 'red_tenths': 16}), ({'speed_mph': 30, 'grade_pct': 1, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 130, 'veh_len_ft': 40, 'crosswalk_ft': 10, 'ped': True}, {'yellow_tenths': 32, 'red_tenths': 41}), ({'speed_mph': 50, 'grade_pct': 1, 'reaction_tenths': 8, 'decel': 11, 'width_ft': 71, 'veh_len_ft': 20, 'crosswalk_ft': 8, 'ped': False}, {'yellow_tenths': 41, 'red_tenths': 13}), ({'speed_mph': 20, 'grade_pct': 4, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 70, 'veh_len_ft': 20, 'crosswalk_ft': 8, 'ped': False}, {'yellow_tenths': 30, 'red_tenths': 31}), ({'speed_mph': 30, 'grade_pct': 0, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 60, 'veh_len_ft': 20, 'crosswalk_ft': 12, 'ped': False}, {'yellow_tenths': 33, 'red_tenths': 19}), ({'speed_mph': 50, 'grade_pct': 5, 'reaction_tenths': 12, 'decel': 10, 'width_ft': 70, 'veh_len_ft': 16, 'crosswalk_ft': 12, 'ped': True}, {'yellow_tenths': 44, 'red_tenths': 14}), ({'speed_mph': 45, 'grade_pct': -2, 'reaction_tenths': 10, 'decel': 12, 'width_ft': 61, 'veh_len_ft': 16, 'crosswalk_ft': 12, 'ped': False}, {'yellow_tenths': 40, 'red_tenths': 12})], [({'speed_mph': 65, 'grade_pct': -7, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 120, 'veh_len_ft': 20, 'crosswalk_ft': 10, 'ped': True}, {'yellow_tenths': 60, 'red_tenths': 16}), ({'speed_mph': 65, 'grade_pct': 1, 'reaction_tenths': 15, 'decel': 10, 'width_ft': 47, 'veh_len_ft': 25, 'crosswalk_ft': 12, 'ped': True}, {'yellow_tenths': 60, 'red_tenths': 10}), ({'speed_mph': 35, 'grade_pct': 7, 'reaction_tenths': 8, 'decel': 10, 'width_ft': 133, 'veh_len_ft': 16, 'crosswalk_ft': 10, 'ped': False}, {'yellow_tenths': 30, 'red_tenths': 30}), ({'speed_mph': 45, 'grade_pct': -4, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 80, 'veh_len_ft': 20, 'crosswalk_ft': 10, 'ped': True}, {'yellow_tenths': 48, 'red_tenths': 17}), ({'speed_mph': 20, 'grade_pct': 3, 'reaction_tenths': 10, 'decel': 11, 'width_ft': 91, 'veh_len_ft': 16, 'crosswalk_ft': 15, 'ped': True}, {'yellow_tenths': 30, 'red_tenths': 42}), ({'speed_mph': 35, 'grade_pct': -5, 'reaction_tenths': 15, 'decel': 12, 'width_ft': 129, 'veh_len_ft': 40, 'crosswalk_ft': 12, 'ped': True}, {'yellow_tenths': 40, 'red_tenths': 36}), ({'speed_mph': 60, 'grade_pct': -8, 'reaction_tenths': 12, 'decel': 8, 'width_ft': 53, 'veh_len_ft': 20, 'crosswalk_ft': 8, 'ped': True}, {'yellow_tenths': 60, 'red_tenths': 10}), ({'speed_mph': 30, 'grade_pct': 0, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 60, 'veh_len_ft': 20, 'crosswalk_ft': 12, 'ped': False}, {'yellow_tenths': 33, 'red_tenths': 19})], [({'speed_mph': 40, 'grade_pct': 5, 'reaction_tenths': 12, 'decel': 12, 'width_ft': 98, 'veh_len_ft': 20, 'crosswalk_ft': 10, 'ped': False}, {'yellow_tenths': 34, 'red_tenths': 21}), ({'speed_mph': 45, 'grade_pct': -4, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 80, 'veh_len_ft': 20, 'crosswalk_ft': 10, 'ped': True}, {'yellow_tenths': 48, 'red_tenths': 17}), ({'speed_mph': 70, 'grade_pct': -6, 'reaction_tenths': 12, 'decel': 10, 'width_ft': 101, 'veh_len_ft': 25, 'crosswalk_ft': 15, 'ped': False}, {'yellow_tenths': 60, 'red_tenths': 13}), ({'speed_mph': 65, 'grade_pct': -7, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 120, 'veh_len_ft': 20, 'crosswalk_ft': 10, 'ped': True}, {'yellow_tenths': 60, 'red_tenths': 16}), ({'speed_mph': 70, 'grade_pct': -8, 'reaction_tenths': 12, 'decel': 10, 'width_ft': 119, 'veh_len_ft': 25, 'crosswalk_ft': 8, 'ped': False}, {'yellow_tenths': 60, 'red_tenths': 15}), ({'speed_mph': 30, 'grade_pct': 0, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 60, 'veh_len_ft': 20, 'crosswalk_ft': 12, 'ped': False}, {'yellow_tenths': 33, 'red_tenths': 19}), ({'speed_mph': 70, 'grade_pct': -6, 'reaction_tenths': 12, 'decel': 12, 'width_ft': 116, 'veh_len_ft': 25, 'crosswalk_ft': 8, 'ped': True}, {'yellow_tenths': 60, 'red_tenths': 15}), ({'speed_mph': 70, 'grade_pct': -3, 'reaction_tenths': 8, 'decel': 12, 'width_ft': 53, 'veh_len_ft': 20, 'crosswalk_ft': 12, 'ped': True}, {'yellow_tenths': 55, 'red_tenths': 10})], [({'speed_mph': 45, 'grade_pct': -4, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 80, 'veh_len_ft': 20, 'crosswalk_ft': 10, 'ped': True}, {'yellow_tenths': 48, 'red_tenths': 17}), ({'speed_mph': 45, 'grade_pct': 6, 'reaction_tenths': 10, 'decel': 12, 'width_ft': 131, 'veh_len_ft': 25, 'crosswalk_ft': 8, 'ped': True}, {'yellow_tenths': 34, 'red_tenths': 25}), ({'speed_mph': 20, 'grade_pct': -5, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 83, 'veh_len_ft': 16, 'crosswalk_ft': 10, 'ped': True}, {'yellow_tenths': 30, 'red_tenths': 38}), ({'speed_mph': 25, 'grade_pct': -5, 'reaction_tenths': 15, 'decel': 11, 'width_ft': 121, 'veh_len_ft': 20, 'crosswalk_ft': 8, 'ped': True}, {'yellow_tenths': 35, 'red_tenths': 41}), ({'speed_mph': 20, 'grade_pct': 1, 'reaction_tenths': 12, 'decel': 10, 'width_ft': 133, 'veh_len_ft': 16, 'crosswalk_ft': 15, 'ped': False}, {'yellow_tenths': 30, 'red_tenths': 51}), ({'speed_mph': 65, 'grade_pct': 8, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 133, 'veh_len_ft': 20, 'crosswalk_ft': 15, 'ped': True}, {'yellow_tenths': 48, 'red_tenths': 18}), ({'speed_mph': 65, 'grade_pct': -7, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 120, 'veh_len_ft': 20, 'crosswalk_ft': 10, 'ped': True}, {'yellow_tenths': 60, 'red_tenths': 16}), ({'speed_mph': 30, 'grade_pct': 0, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 60, 'veh_len_ft': 20, 'crosswalk_ft': 12, 'ped': False}, {'yellow_tenths': 33, 'red_tenths': 19})], [({'speed_mph': 25, 'grade_pct': 4, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 48, 'veh_len_ft': 16, 'crosswalk_ft': 12, 'ped': False}, {'yellow_tenths': 30, 'red_tenths': 18}), ({'speed_mph': 45, 'grade_pct': -4, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 80, 'veh_len_ft': 20, 'crosswalk_ft': 10, 'ped': True}, {'yellow_tenths': 48, 'red_tenths': 17}), ({'speed_mph': 30, 'grade_pct': 1, 'reaction_tenths': 15, 'decel': 10, 'width_ft': 71, 'veh_len_ft': 20, 'crosswalk_ft': 15, 'ped': True}, {'yellow_tenths': 37, 'red_tenths': 25}), ({'speed_mph': 70, 'grade_pct': 3, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 104, 'veh_len_ft': 20, 'crosswalk_ft': 15, 'ped': True}, {'yellow_tenths': 57, 'red_tenths': 14}), ({'speed_mph': 25, 'grade_pct': -5, 'reaction_tenths': 10, 'decel': 8, 'width_ft': 59, 'veh_len_ft': 25, 'crosswalk_ft': 12, 'ped': False}, {'yellow_tenths': 39, 'red_tenths': 23}), ({'speed_mph': 30, 'grade_pct': 0, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 60, 'veh_len_ft': 20, 'crosswalk_ft': 12, 'ped': False}, {'yellow_tenths': 33, 'red_tenths': 19}), ({'speed_mph': 40, 'grade_pct': 1, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 126, 'veh_len_ft': 20, 'crosswalk_ft': 12, 'ped': False}, {'yellow_tenths': 39, 'red_tenths': 25}), ({'speed_mph': 65, 'grade_pct': -7, 'reaction_tenths': 10, 'decel': 10, 'width_ft': 120, 'veh_len_ft': 20, 'crosswalk_ft': 10, 'ped': True}, {'yellow_tenths': 60, 'red_tenths': 16})]]
for i, (args, expected) in enumerate(fixtures[N-1]):
    check('timing oracle' + ' %d' % i, 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
timing oracle 0	`{'red_tenths': 17, 'yellow_tenths': 48}`	`{'red_tenths': 17, 'yellow_tenths': 48}`	Passed
timing oracle 1	`{'red_tenths': 16, 'yellow_tenths': 60}`	`{'red_tenths': 16, 'yellow_tenths': 60}`	Passed
timing oracle 2	`{'red_tenths': 41, 'yellow_tenths': 32}`	`{'red_tenths': 41, 'yellow_tenths': 32}`	Passed
timing oracle 3	`{'red_tenths': 13, 'yellow_tenths': 41}`	`{'red_tenths': 13, 'yellow_tenths': 41}`	Passed
timing oracle 4	`{'red_tenths': 31, 'yellow_tenths': 30}`	`{'red_tenths': 31, 'yellow_tenths': 30}`	Passed
timing oracle 5	`{'red_tenths': 19, 'yellow_tenths': 33}`	`{'red_tenths': 19, 'yellow_tenths': 33}`	Passed
timing oracle 6	`{'red_tenths': 14, 'yellow_tenths': 44}`	`{'red_tenths': 14, 'yellow_tenths': 44}`	Passed
timing oracle 7	`{'red_tenths': 12, 'yellow_tenths': 40}`	`{'red_tenths': 12, 'yellow_tenths': 40}`	Passed

SHA-256 / efe07ade11073996ec553052bb5570f42fdd14718b5d6335d5cc3f9798c77ba8

Verification & scope

A deterministic, bounded toy model with a stipulated contract; it makes no claim of conformance to any agency manual or standard. 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 2026-09-29T14:47:57.237988+00:00.

Case digest / ba69c50affbcf80a072814aa280bbb96b2b4315fa9cd7443f8bc761b78745fc2