FA-67071 / Railway interlocking logic / Open access
ATP braking curve supervision: permitted speed rounding · case 01
The permitted speed is one km/h above the braking curve.
ROOT CAUSE
The curve speed is rounded to nearest, which can round up.
VERIFIED REPAIR
Truncate the curve speed so the permitted speed never exceeds the curve.
Unsuccessful approach: Ceiling always rounds fractional curve speeds up.
Case contract
Permitted speed at the train is sqrt(vt^2 + 2*a*d) with vt the target speed in m/s, a = decel_cms2/100 m/s^2 and d = max(distance - safety margin, 0); convert back to km/h, truncate to an integer (never round up) and cap at line speed. Action is brake if speed > permitted + brake margin, else warning if speed > permitted + warn margin, else none.
Why this case matters
Interlocking logic decides whether trains may be given authority; a wrong decision at this point either grants unsafe movements or strands traffic.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
vt = x['target_kmh'] / 3.6
d = max(x['distance_m'] - x['safety_margin_m'], 0)
a = x['decel_cms2'] / 100
vp = math.sqrt(vt * vt + 2 * a * d) * 3.6
permitted = min(round(vp), x['line_kmh'])
v = x['speed_kmh']
if v > permitted + x['brake_margin_kmh']:
action = 'brake'
elif v > permitted + x['warn_margin_kmh']:
action = 'warning'
else:
action = 'none'
return {'permitted': permitted, 'action': action}
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: curve below line speed', {'target_kmh': 0, 'distance_m': 600, 'safety_margin_m': 50, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 100, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 99, 'action': 'none'}), ('sampled regression 10', {'target_kmh': 20, 'distance_m': 40, 'safety_margin_m': 20, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 33, 'warn_margin_kmh': 5, 'brake_margin_kmh': 15}, {'permitted': 27, 'action': 'warning'}), ('boundary: fractional permitted speed', {'target_kmh': 20, 'distance_m': 100, 'safety_margin_m': 0, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 60, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 47, 'action': 'brake'}), ('boundary: stop target inside the margin', {'target_kmh': 0, 'distance_m': 40, 'safety_margin_m': 50, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 10, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 0, 'action': 'warning'}), ('boundary: target speed release', {'target_kmh': 40, 'distance_m': 0, 'safety_margin_m': 50, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 44, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 40, 'action': 'none'}), ('control 1', {'target_kmh': 0, 'distance_m': 0, 'safety_margin_m': 0, 'decel_cms2': 100, 'line_kmh': 160, 'speed_kmh': 139, 'warn_margin_kmh': 5, 'brake_margin_kmh': 15}, {'permitted': 0, 'action': 'brake'}), ('sampled regression 4', {'target_kmh': 0, 'distance_m': 100, 'safety_margin_m': 20, 'decel_cms2': 100, 'line_kmh': 80, 'speed_kmh': 136, 'warn_margin_kmh': 5, 'brake_margin_kmh': 15}, {'permitted': 45, 'action': 'brake'}), ('control 7', {'target_kmh': 40, 'distance_m': 2500, 'safety_margin_m': 20, 'decel_cms2': 50, 'line_kmh': 160, 'speed_kmh': 59, 'warn_margin_kmh': 3, 'brake_margin_kmh': 10}, {'permitted': 160, 'action': 'none'})], [('regression: curve below line speed', {'target_kmh': 0, 'distance_m': 600, 'safety_margin_m': 50, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 100, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 99, 'action': 'none'}), ('boundary: fractional permitted speed', {'target_kmh': 20, 'distance_m': 100, 'safety_margin_m': 0, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 60, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 47, 'action': 'brake'}), ('sampled regression 43', {'target_kmh': 40, 'distance_m': 250, 'safety_margin_m': 20, 'decel_cms2': 100, 'line_kmh': 160, 'speed_kmh': 33, 'warn_margin_kmh': 5, 'brake_margin_kmh': 15}, {'permitted': 86, 'action': 'none'}), ('control 11', {'target_kmh': 0, 'distance_m': 250, 'safety_margin_m': 20, 'decel_cms2': 100, 'line_kmh': 120, 'speed_kmh': 158, 'warn_margin_kmh': 5, 'brake_margin_kmh': 15}, {'permitted': 77, 'action': 'brake'}), ('boundary: curve above line speed', {'target_kmh': 0, 'distance_m': 2500, 'safety_margin_m': 50, 'decel_cms2': 70, 'line_kmh': 120, 'speed_kmh': 150, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 120, 'action': 'brake'}), ('sampled regression 12', {'target_kmh': 40, 'distance_m': 600, 'safety_margin_m': 20, 'decel_cms2': 100, 'line_kmh': 160, 'speed_kmh': 133, 'warn_margin_kmh': 3, 'brake_margin_kmh': 15}, {'permitted': 128, 'action': 'warning'}), ('sampled regression 15', {'target_kmh': 0, 'distance_m': 600, 'safety_margin_m': 20, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 43, 'warn_margin_kmh': 3, 'brake_margin_kmh': 10}, {'permitted': 102, 'action': 'none'}), ('control 18', {'target_kmh': 60, 'distance_m': 1200, 'safety_margin_m': 20, 'decel_cms2': 70, 'line_kmh': 120, 'speed_kmh': 6, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 120, 'action': 'none'})], [('regression: curve below line speed', {'target_kmh': 0, 'distance_m': 600, 'safety_margin_m': 50, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 100, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 99, 'action': 'none'}), ('sampled regression 61', {'target_kmh': 0, 'distance_m': 250, 'safety_margin_m': 20, 'decel_cms2': 50, 'line_kmh': 120, 'speed_kmh': 75, 'warn_margin_kmh': 5, 'brake_margin_kmh': 15}, {'permitted': 54, 'action': 'brake'}), ('control 22', {'target_kmh': 0, 'distance_m': 250, 'safety_margin_m': 0, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 57, 'warn_margin_kmh': 3, 'brake_margin_kmh': 8}, {'permitted': 67, 'action': 'none'}), ('boundary: warning boundary', {'target_kmh': 40, 'distance_m': 0, 'safety_margin_m': 50, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 45, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 40, 'action': 'none'}), ('boundary: brake boundary', {'target_kmh': 40, 'distance_m': 0, 'safety_margin_m': 50, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 50, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 40, 'action': 'warning'}), ('control 23', {'target_kmh': 60, 'distance_m': 100, 'safety_margin_m': 50, 'decel_cms2': 70, 'line_kmh': 80, 'speed_kmh': 13, 'warn_margin_kmh': 5, 'brake_margin_kmh': 8}, {'permitted': 67, 'action': 'none'}), ('control 26', {'target_kmh': 60, 'distance_m': 2500, 'safety_margin_m': 50, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 86, 'warn_margin_kmh': 3, 'brake_margin_kmh': 10}, {'permitted': 160, 'action': 'none'}), ('control 29', {'target_kmh': 0, 'distance_m': 250, 'safety_margin_m': 0, 'decel_cms2': 70, 'line_kmh': 120, 'speed_kmh': 4, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 67, 'action': 'none'})], [('regression: curve below line speed', {'target_kmh': 0, 'distance_m': 600, 'safety_margin_m': 50, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 100, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 99, 'action': 'none'}), ('boundary: fractional permitted speed', {'target_kmh': 20, 'distance_m': 100, 'safety_margin_m': 0, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 60, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 47, 'action': 'brake'}), ('sampled regression 4', {'target_kmh': 0, 'distance_m': 100, 'safety_margin_m': 20, 'decel_cms2': 100, 'line_kmh': 80, 'speed_kmh': 136, 'warn_margin_kmh': 5, 'brake_margin_kmh': 15}, {'permitted': 45, 'action': 'brake'}), ('control 30', {'target_kmh': 0, 'distance_m': 100, 'safety_margin_m': 50, 'decel_cms2': 50, 'line_kmh': 160, 'speed_kmh': 155, 'warn_margin_kmh': 3, 'brake_margin_kmh': 10}, {'permitted': 25, 'action': 'brake'}), ('boundary: between warning and brake', {'target_kmh': 40, 'distance_m': 0, 'safety_margin_m': 50, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 48, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 40, 'action': 'warning'}), ('control 34', {'target_kmh': 0, 'distance_m': 0, 'safety_margin_m': 0, 'decel_cms2': 70, 'line_kmh': 120, 'speed_kmh': 96, 'warn_margin_kmh': 5, 'brake_margin_kmh': 15}, {'permitted': 0, 'action': 'brake'}), ('control 37', {'target_kmh': 20, 'distance_m': 2500, 'safety_margin_m': 20, 'decel_cms2': 70, 'line_kmh': 80, 'speed_kmh': 168, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 80, 'action': 'brake'}), ('control 40', {'target_kmh': 0, 'distance_m': 600, 'safety_margin_m': 50, 'decel_cms2': 50, 'line_kmh': 160, 'speed_kmh': 70, 'warn_margin_kmh': 5, 'brake_margin_kmh': 15}, {'permitted': 84, 'action': 'none'})], [('regression: curve below line speed', {'target_kmh': 0, 'distance_m': 600, 'safety_margin_m': 50, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 100, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 99, 'action': 'none'}), ('sampled regression 36', {'target_kmh': 40, 'distance_m': 600, 'safety_margin_m': 0, 'decel_cms2': 100, 'line_kmh': 160, 'speed_kmh': 124, 'warn_margin_kmh': 3, 'brake_margin_kmh': 15}, {'permitted': 130, 'action': 'none'}), ('control 42', {'target_kmh': 40, 'distance_m': 40, 'safety_margin_m': 20, 'decel_cms2': 50, 'line_kmh': 160, 'speed_kmh': 115, 'warn_margin_kmh': 5, 'brake_margin_kmh': 8}, {'permitted': 43, 'action': 'brake'}), ('boundary: stop target inside the margin', {'target_kmh': 0, 'distance_m': 40, 'safety_margin_m': 50, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 10, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 0, 'action': 'warning'}), ('boundary: target speed release', {'target_kmh': 40, 'distance_m': 0, 'safety_margin_m': 50, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 44, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 40, 'action': 'none'}), ('control 45', {'target_kmh': 20, 'distance_m': 40, 'safety_margin_m': 50, 'decel_cms2': 70, 'line_kmh': 80, 'speed_kmh': 133, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 20, 'action': 'brake'}), ('sampled regression 48', {'target_kmh': 40, 'distance_m': 100, 'safety_margin_m': 20, 'decel_cms2': 100, 'line_kmh': 160, 'speed_kmh': 75, 'warn_margin_kmh': 3, 'brake_margin_kmh': 15}, {'permitted': 60, 'action': 'warning'}), ('sampled regression 51', {'target_kmh': 60, 'distance_m': 600, 'safety_margin_m': 0, 'decel_cms2': 50, 'line_kmh': 160, 'speed_kmh': 8, 'warn_margin_kmh': 5, 'brake_margin_kmh': 8}, {'permitted': 106, 'action': 'none'})]]
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 |
|---|---|---|---|
| regression: curve below line speed | {'action': 'none', 'permitted': 100} | {'action': 'none', 'permitted': 99} | Failed |
| sampled regression 10 | {'action': 'none', 'permitted': 28} | {'action': 'warning', 'permitted': 27} | Failed |
| boundary: fractional permitted speed | {'action': 'brake', 'permitted': 47} | {'action': 'brake', 'permitted': 47} | Passed |
| boundary: stop target inside the margin | {'action': 'warning', 'permitted': 0} | {'action': 'warning', 'permitted': 0} | Passed |
| boundary: target speed release | {'action': 'none', 'permitted': 40} | {'action': 'none', 'permitted': 40} | Passed |
| control 1 | {'action': 'brake', 'permitted': 0} | {'action': 'brake', 'permitted': 0} | Passed |
| sampled regression 4 | {'action': 'brake', 'permitted': 46} | {'action': 'brake', 'permitted': 45} | Failed |
| control 7 | {'action': 'none', 'permitted': 160} | {'action': 'none', 'permitted': 160} | Passed |
SHA-256 / 0c84a6a769479ccf67547df1eb1d3b7742843a35a2a67b564390e4c99c3afc15
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
vt = x['target_kmh'] / 3.6
d = max(x['distance_m'] - x['safety_margin_m'], 0)
a = x['decel_cms2'] / 100
vp = math.sqrt(vt * vt + 2 * a * d) * 3.6
permitted = min(math.ceil(vp), x['line_kmh'])
v = x['speed_kmh']
if v > permitted + x['brake_margin_kmh']:
action = 'brake'
elif v > permitted + x['warn_margin_kmh']:
action = 'warning'
else:
action = 'none'
return {'permitted': permitted, 'action': action}
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: curve below line speed', {'target_kmh': 0, 'distance_m': 600, 'safety_margin_m': 50, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 100, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 99, 'action': 'none'}), ('sampled regression 10', {'target_kmh': 20, 'distance_m': 40, 'safety_margin_m': 20, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 33, 'warn_margin_kmh': 5, 'brake_margin_kmh': 15}, {'permitted': 27, 'action': 'warning'}), ('boundary: fractional permitted speed', {'target_kmh': 20, 'distance_m': 100, 'safety_margin_m': 0, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 60, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 47, 'action': 'brake'}), ('boundary: stop target inside the margin', {'target_kmh': 0, 'distance_m': 40, 'safety_margin_m': 50, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 10, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 0, 'action': 'warning'}), ('boundary: target speed release', {'target_kmh': 40, 'distance_m': 0, 'safety_margin_m': 50, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 44, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 40, 'action': 'none'}), ('control 1', {'target_kmh': 0, 'distance_m': 0, 'safety_margin_m': 0, 'decel_cms2': 100, 'line_kmh': 160, 'speed_kmh': 139, 'warn_margin_kmh': 5, 'brake_margin_kmh': 15}, {'permitted': 0, 'action': 'brake'}), ('sampled regression 4', {'target_kmh': 0, 'distance_m': 100, 'safety_margin_m': 20, 'decel_cms2': 100, 'line_kmh': 80, 'speed_kmh': 136, 'warn_margin_kmh': 5, 'brake_margin_kmh': 15}, {'permitted': 45, 'action': 'brake'}), ('control 7', {'target_kmh': 40, 'distance_m': 2500, 'safety_margin_m': 20, 'decel_cms2': 50, 'line_kmh': 160, 'speed_kmh': 59, 'warn_margin_kmh': 3, 'brake_margin_kmh': 10}, {'permitted': 160, 'action': 'none'})], [('regression: curve below line speed', {'target_kmh': 0, 'distance_m': 600, 'safety_margin_m': 50, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 100, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 99, 'action': 'none'}), ('boundary: fractional permitted speed', {'target_kmh': 20, 'distance_m': 100, 'safety_margin_m': 0, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 60, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 47, 'action': 'brake'}), ('sampled regression 43', {'target_kmh': 40, 'distance_m': 250, 'safety_margin_m': 20, 'decel_cms2': 100, 'line_kmh': 160, 'speed_kmh': 33, 'warn_margin_kmh': 5, 'brake_margin_kmh': 15}, {'permitted': 86, 'action': 'none'}), ('control 11', {'target_kmh': 0, 'distance_m': 250, 'safety_margin_m': 20, 'decel_cms2': 100, 'line_kmh': 120, 'speed_kmh': 158, 'warn_margin_kmh': 5, 'brake_margin_kmh': 15}, {'permitted': 77, 'action': 'brake'}), ('boundary: curve above line speed', {'target_kmh': 0, 'distance_m': 2500, 'safety_margin_m': 50, 'decel_cms2': 70, 'line_kmh': 120, 'speed_kmh': 150, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 120, 'action': 'brake'}), ('sampled regression 12', {'target_kmh': 40, 'distance_m': 600, 'safety_margin_m': 20, 'decel_cms2': 100, 'line_kmh': 160, 'speed_kmh': 133, 'warn_margin_kmh': 3, 'brake_margin_kmh': 15}, {'permitted': 128, 'action': 'warning'}), ('sampled regression 15', {'target_kmh': 0, 'distance_m': 600, 'safety_margin_m': 20, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 43, 'warn_margin_kmh': 3, 'brake_margin_kmh': 10}, {'permitted': 102, 'action': 'none'}), ('control 18', {'target_kmh': 60, 'distance_m': 1200, 'safety_margin_m': 20, 'decel_cms2': 70, 'line_kmh': 120, 'speed_kmh': 6, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 120, 'action': 'none'})], [('regression: curve below line speed', {'target_kmh': 0, 'distance_m': 600, 'safety_margin_m': 50, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 100, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 99, 'action': 'none'}), ('sampled regression 61', {'target_kmh': 0, 'distance_m': 250, 'safety_margin_m': 20, 'decel_cms2': 50, 'line_kmh': 120, 'speed_kmh': 75, 'warn_margin_kmh': 5, 'brake_margin_kmh': 15}, {'permitted': 54, 'action': 'brake'}), ('control 22', {'target_kmh': 0, 'distance_m': 250, 'safety_margin_m': 0, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 57, 'warn_margin_kmh': 3, 'brake_margin_kmh': 8}, {'permitted': 67, 'action': 'none'}), ('boundary: warning boundary', {'target_kmh': 40, 'distance_m': 0, 'safety_margin_m': 50, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 45, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 40, 'action': 'none'}), ('boundary: brake boundary', {'target_kmh': 40, 'distance_m': 0, 'safety_margin_m': 50, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 50, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 40, 'action': 'warning'}), ('control 23', {'target_kmh': 60, 'distance_m': 100, 'safety_margin_m': 50, 'decel_cms2': 70, 'line_kmh': 80, 'speed_kmh': 13, 'warn_margin_kmh': 5, 'brake_margin_kmh': 8}, {'permitted': 67, 'action': 'none'}), ('control 26', {'target_kmh': 60, 'distance_m': 2500, 'safety_margin_m': 50, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 86, 'warn_margin_kmh': 3, 'brake_margin_kmh': 10}, {'permitted': 160, 'action': 'none'}), ('control 29', {'target_kmh': 0, 'distance_m': 250, 'safety_margin_m': 0, 'decel_cms2': 70, 'line_kmh': 120, 'speed_kmh': 4, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 67, 'action': 'none'})], [('regression: curve below line speed', {'target_kmh': 0, 'distance_m': 600, 'safety_margin_m': 50, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 100, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 99, 'action': 'none'}), ('boundary: fractional permitted speed', {'target_kmh': 20, 'distance_m': 100, 'safety_margin_m': 0, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 60, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 47, 'action': 'brake'}), ('sampled regression 4', {'target_kmh': 0, 'distance_m': 100, 'safety_margin_m': 20, 'decel_cms2': 100, 'line_kmh': 80, 'speed_kmh': 136, 'warn_margin_kmh': 5, 'brake_margin_kmh': 15}, {'permitted': 45, 'action': 'brake'}), ('control 30', {'target_kmh': 0, 'distance_m': 100, 'safety_margin_m': 50, 'decel_cms2': 50, 'line_kmh': 160, 'speed_kmh': 155, 'warn_margin_kmh': 3, 'brake_margin_kmh': 10}, {'permitted': 25, 'action': 'brake'}), ('boundary: between warning and brake', {'target_kmh': 40, 'distance_m': 0, 'safety_margin_m': 50, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 48, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 40, 'action': 'warning'}), ('control 34', {'target_kmh': 0, 'distance_m': 0, 'safety_margin_m': 0, 'decel_cms2': 70, 'line_kmh': 120, 'speed_kmh': 96, 'warn_margin_kmh': 5, 'brake_margin_kmh': 15}, {'permitted': 0, 'action': 'brake'}), ('control 37', {'target_kmh': 20, 'distance_m': 2500, 'safety_margin_m': 20, 'decel_cms2': 70, 'line_kmh': 80, 'speed_kmh': 168, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 80, 'action': 'brake'}), ('control 40', {'target_kmh': 0, 'distance_m': 600, 'safety_margin_m': 50, 'decel_cms2': 50, 'line_kmh': 160, 'speed_kmh': 70, 'warn_margin_kmh': 5, 'brake_margin_kmh': 15}, {'permitted': 84, 'action': 'none'})], [('regression: curve below line speed', {'target_kmh': 0, 'distance_m': 600, 'safety_margin_m': 50, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 100, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 99, 'action': 'none'}), ('sampled regression 36', {'target_kmh': 40, 'distance_m': 600, 'safety_margin_m': 0, 'decel_cms2': 100, 'line_kmh': 160, 'speed_kmh': 124, 'warn_margin_kmh': 3, 'brake_margin_kmh': 15}, {'permitted': 130, 'action': 'none'}), ('control 42', {'target_kmh': 40, 'distance_m': 40, 'safety_margin_m': 20, 'decel_cms2': 50, 'line_kmh': 160, 'speed_kmh': 115, 'warn_margin_kmh': 5, 'brake_margin_kmh': 8}, {'permitted': 43, 'action': 'brake'}), ('boundary: stop target inside the margin', {'target_kmh': 0, 'distance_m': 40, 'safety_margin_m': 50, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 10, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 0, 'action': 'warning'}), ('boundary: target speed release', {'target_kmh': 40, 'distance_m': 0, 'safety_margin_m': 50, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 44, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 40, 'action': 'none'}), ('control 45', {'target_kmh': 20, 'distance_m': 40, 'safety_margin_m': 50, 'decel_cms2': 70, 'line_kmh': 80, 'speed_kmh': 133, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 20, 'action': 'brake'}), ('sampled regression 48', {'target_kmh': 40, 'distance_m': 100, 'safety_margin_m': 20, 'decel_cms2': 100, 'line_kmh': 160, 'speed_kmh': 75, 'warn_margin_kmh': 3, 'brake_margin_kmh': 15}, {'permitted': 60, 'action': 'warning'}), ('sampled regression 51', {'target_kmh': 60, 'distance_m': 600, 'safety_margin_m': 0, 'decel_cms2': 50, 'line_kmh': 160, 'speed_kmh': 8, 'warn_margin_kmh': 5, 'brake_margin_kmh': 8}, {'permitted': 106, 'action': 'none'})]]
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 |
|---|---|---|---|
| regression: curve below line speed | {'action': 'none', 'permitted': 100} | {'action': 'none', 'permitted': 99} | Failed |
| sampled regression 10 | {'action': 'none', 'permitted': 28} | {'action': 'warning', 'permitted': 27} | Failed |
| boundary: fractional permitted speed | {'action': 'brake', 'permitted': 48} | {'action': 'brake', 'permitted': 47} | Failed |
| boundary: stop target inside the margin | {'action': 'warning', 'permitted': 0} | {'action': 'warning', 'permitted': 0} | Passed |
| boundary: target speed release | {'action': 'none', 'permitted': 40} | {'action': 'none', 'permitted': 40} | Passed |
| control 1 | {'action': 'brake', 'permitted': 0} | {'action': 'brake', 'permitted': 0} | Passed |
| sampled regression 4 | {'action': 'brake', 'permitted': 46} | {'action': 'brake', 'permitted': 45} | Failed |
| control 7 | {'action': 'none', 'permitted': 160} | {'action': 'none', 'permitted': 160} | Passed |
SHA-256 / 782f4ec61f7afa9088c219b5122f32b6daa8946dbf311b1aa562c1b41f054d79
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
vt = x['target_kmh'] / 3.6
d = max(x['distance_m'] - x['safety_margin_m'], 0)
a = x['decel_cms2'] / 100
vp = math.sqrt(vt * vt + 2 * a * d) * 3.6
permitted = min(int(vp), x['line_kmh'])
v = x['speed_kmh']
if v > permitted + x['brake_margin_kmh']:
action = 'brake'
elif v > permitted + x['warn_margin_kmh']:
action = 'warning'
else:
action = 'none'
return {'permitted': permitted, 'action': action}
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: curve below line speed', {'target_kmh': 0, 'distance_m': 600, 'safety_margin_m': 50, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 100, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 99, 'action': 'none'}), ('sampled regression 10', {'target_kmh': 20, 'distance_m': 40, 'safety_margin_m': 20, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 33, 'warn_margin_kmh': 5, 'brake_margin_kmh': 15}, {'permitted': 27, 'action': 'warning'}), ('boundary: fractional permitted speed', {'target_kmh': 20, 'distance_m': 100, 'safety_margin_m': 0, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 60, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 47, 'action': 'brake'}), ('boundary: stop target inside the margin', {'target_kmh': 0, 'distance_m': 40, 'safety_margin_m': 50, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 10, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 0, 'action': 'warning'}), ('boundary: target speed release', {'target_kmh': 40, 'distance_m': 0, 'safety_margin_m': 50, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 44, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 40, 'action': 'none'}), ('control 1', {'target_kmh': 0, 'distance_m': 0, 'safety_margin_m': 0, 'decel_cms2': 100, 'line_kmh': 160, 'speed_kmh': 139, 'warn_margin_kmh': 5, 'brake_margin_kmh': 15}, {'permitted': 0, 'action': 'brake'}), ('sampled regression 4', {'target_kmh': 0, 'distance_m': 100, 'safety_margin_m': 20, 'decel_cms2': 100, 'line_kmh': 80, 'speed_kmh': 136, 'warn_margin_kmh': 5, 'brake_margin_kmh': 15}, {'permitted': 45, 'action': 'brake'}), ('control 7', {'target_kmh': 40, 'distance_m': 2500, 'safety_margin_m': 20, 'decel_cms2': 50, 'line_kmh': 160, 'speed_kmh': 59, 'warn_margin_kmh': 3, 'brake_margin_kmh': 10}, {'permitted': 160, 'action': 'none'})], [('regression: curve below line speed', {'target_kmh': 0, 'distance_m': 600, 'safety_margin_m': 50, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 100, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 99, 'action': 'none'}), ('boundary: fractional permitted speed', {'target_kmh': 20, 'distance_m': 100, 'safety_margin_m': 0, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 60, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 47, 'action': 'brake'}), ('sampled regression 43', {'target_kmh': 40, 'distance_m': 250, 'safety_margin_m': 20, 'decel_cms2': 100, 'line_kmh': 160, 'speed_kmh': 33, 'warn_margin_kmh': 5, 'brake_margin_kmh': 15}, {'permitted': 86, 'action': 'none'}), ('control 11', {'target_kmh': 0, 'distance_m': 250, 'safety_margin_m': 20, 'decel_cms2': 100, 'line_kmh': 120, 'speed_kmh': 158, 'warn_margin_kmh': 5, 'brake_margin_kmh': 15}, {'permitted': 77, 'action': 'brake'}), ('boundary: curve above line speed', {'target_kmh': 0, 'distance_m': 2500, 'safety_margin_m': 50, 'decel_cms2': 70, 'line_kmh': 120, 'speed_kmh': 150, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 120, 'action': 'brake'}), ('sampled regression 12', {'target_kmh': 40, 'distance_m': 600, 'safety_margin_m': 20, 'decel_cms2': 100, 'line_kmh': 160, 'speed_kmh': 133, 'warn_margin_kmh': 3, 'brake_margin_kmh': 15}, {'permitted': 128, 'action': 'warning'}), ('sampled regression 15', {'target_kmh': 0, 'distance_m': 600, 'safety_margin_m': 20, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 43, 'warn_margin_kmh': 3, 'brake_margin_kmh': 10}, {'permitted': 102, 'action': 'none'}), ('control 18', {'target_kmh': 60, 'distance_m': 1200, 'safety_margin_m': 20, 'decel_cms2': 70, 'line_kmh': 120, 'speed_kmh': 6, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 120, 'action': 'none'})], [('regression: curve below line speed', {'target_kmh': 0, 'distance_m': 600, 'safety_margin_m': 50, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 100, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 99, 'action': 'none'}), ('sampled regression 61', {'target_kmh': 0, 'distance_m': 250, 'safety_margin_m': 20, 'decel_cms2': 50, 'line_kmh': 120, 'speed_kmh': 75, 'warn_margin_kmh': 5, 'brake_margin_kmh': 15}, {'permitted': 54, 'action': 'brake'}), ('control 22', {'target_kmh': 0, 'distance_m': 250, 'safety_margin_m': 0, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 57, 'warn_margin_kmh': 3, 'brake_margin_kmh': 8}, {'permitted': 67, 'action': 'none'}), ('boundary: warning boundary', {'target_kmh': 40, 'distance_m': 0, 'safety_margin_m': 50, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 45, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 40, 'action': 'none'}), ('boundary: brake boundary', {'target_kmh': 40, 'distance_m': 0, 'safety_margin_m': 50, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 50, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 40, 'action': 'warning'}), ('control 23', {'target_kmh': 60, 'distance_m': 100, 'safety_margin_m': 50, 'decel_cms2': 70, 'line_kmh': 80, 'speed_kmh': 13, 'warn_margin_kmh': 5, 'brake_margin_kmh': 8}, {'permitted': 67, 'action': 'none'}), ('control 26', {'target_kmh': 60, 'distance_m': 2500, 'safety_margin_m': 50, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 86, 'warn_margin_kmh': 3, 'brake_margin_kmh': 10}, {'permitted': 160, 'action': 'none'}), ('control 29', {'target_kmh': 0, 'distance_m': 250, 'safety_margin_m': 0, 'decel_cms2': 70, 'line_kmh': 120, 'speed_kmh': 4, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 67, 'action': 'none'})], [('regression: curve below line speed', {'target_kmh': 0, 'distance_m': 600, 'safety_margin_m': 50, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 100, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 99, 'action': 'none'}), ('boundary: fractional permitted speed', {'target_kmh': 20, 'distance_m': 100, 'safety_margin_m': 0, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 60, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 47, 'action': 'brake'}), ('sampled regression 4', {'target_kmh': 0, 'distance_m': 100, 'safety_margin_m': 20, 'decel_cms2': 100, 'line_kmh': 80, 'speed_kmh': 136, 'warn_margin_kmh': 5, 'brake_margin_kmh': 15}, {'permitted': 45, 'action': 'brake'}), ('control 30', {'target_kmh': 0, 'distance_m': 100, 'safety_margin_m': 50, 'decel_cms2': 50, 'line_kmh': 160, 'speed_kmh': 155, 'warn_margin_kmh': 3, 'brake_margin_kmh': 10}, {'permitted': 25, 'action': 'brake'}), ('boundary: between warning and brake', {'target_kmh': 40, 'distance_m': 0, 'safety_margin_m': 50, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 48, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 40, 'action': 'warning'}), ('control 34', {'target_kmh': 0, 'distance_m': 0, 'safety_margin_m': 0, 'decel_cms2': 70, 'line_kmh': 120, 'speed_kmh': 96, 'warn_margin_kmh': 5, 'brake_margin_kmh': 15}, {'permitted': 0, 'action': 'brake'}), ('control 37', {'target_kmh': 20, 'distance_m': 2500, 'safety_margin_m': 20, 'decel_cms2': 70, 'line_kmh': 80, 'speed_kmh': 168, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 80, 'action': 'brake'}), ('control 40', {'target_kmh': 0, 'distance_m': 600, 'safety_margin_m': 50, 'decel_cms2': 50, 'line_kmh': 160, 'speed_kmh': 70, 'warn_margin_kmh': 5, 'brake_margin_kmh': 15}, {'permitted': 84, 'action': 'none'})], [('regression: curve below line speed', {'target_kmh': 0, 'distance_m': 600, 'safety_margin_m': 50, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 100, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 99, 'action': 'none'}), ('sampled regression 36', {'target_kmh': 40, 'distance_m': 600, 'safety_margin_m': 0, 'decel_cms2': 100, 'line_kmh': 160, 'speed_kmh': 124, 'warn_margin_kmh': 3, 'brake_margin_kmh': 15}, {'permitted': 130, 'action': 'none'}), ('control 42', {'target_kmh': 40, 'distance_m': 40, 'safety_margin_m': 20, 'decel_cms2': 50, 'line_kmh': 160, 'speed_kmh': 115, 'warn_margin_kmh': 5, 'brake_margin_kmh': 8}, {'permitted': 43, 'action': 'brake'}), ('boundary: stop target inside the margin', {'target_kmh': 0, 'distance_m': 40, 'safety_margin_m': 50, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 10, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 0, 'action': 'warning'}), ('boundary: target speed release', {'target_kmh': 40, 'distance_m': 0, 'safety_margin_m': 50, 'decel_cms2': 70, 'line_kmh': 160, 'speed_kmh': 44, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 40, 'action': 'none'}), ('control 45', {'target_kmh': 20, 'distance_m': 40, 'safety_margin_m': 50, 'decel_cms2': 70, 'line_kmh': 80, 'speed_kmh': 133, 'warn_margin_kmh': 5, 'brake_margin_kmh': 10}, {'permitted': 20, 'action': 'brake'}), ('sampled regression 48', {'target_kmh': 40, 'distance_m': 100, 'safety_margin_m': 20, 'decel_cms2': 100, 'line_kmh': 160, 'speed_kmh': 75, 'warn_margin_kmh': 3, 'brake_margin_kmh': 15}, {'permitted': 60, 'action': 'warning'}), ('sampled regression 51', {'target_kmh': 60, 'distance_m': 600, 'safety_margin_m': 0, 'decel_cms2': 50, 'line_kmh': 160, 'speed_kmh': 8, 'warn_margin_kmh': 5, 'brake_margin_kmh': 8}, {'permitted': 106, 'action': 'none'})]]
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 |
|---|---|---|---|
| regression: curve below line speed | {'action': 'none', 'permitted': 99} | {'action': 'none', 'permitted': 99} | Passed |
| sampled regression 10 | {'action': 'warning', 'permitted': 27} | {'action': 'warning', 'permitted': 27} | Passed |
| boundary: fractional permitted speed | {'action': 'brake', 'permitted': 47} | {'action': 'brake', 'permitted': 47} | Passed |
| boundary: stop target inside the margin | {'action': 'warning', 'permitted': 0} | {'action': 'warning', 'permitted': 0} | Passed |
| boundary: target speed release | {'action': 'none', 'permitted': 40} | {'action': 'none', 'permitted': 40} | Passed |
| control 1 | {'action': 'brake', 'permitted': 0} | {'action': 'brake', 'permitted': 0} | Passed |
| sampled regression 4 | {'action': 'brake', 'permitted': 45} | {'action': 'brake', 'permitted': 45} | Passed |
| control 7 | {'action': 'none', 'permitted': 160} | {'action': 'none', 'permitted': 160} | Passed |
SHA-256 / 4d0387bb90bdbddd71184ae78bf7f3bf01778b1d0165b37fceebd7e5a86a2c37
Verification & scope
Stipulated toy interlocking contract for a bounded teaching model; it makes no claim of conformance to any railway signalling standard and omits real safety cases. 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 2026-09-29T14:47:49.439551+00:00.
Case digest / f9080c7f7e35d80340e8200a5204250c46d04096199df1acecb94042f0033c61