FA-68221 / Traffic signal timing plans / Open access

Transit signal priority decision: early green always uses the maximum advance · case 01

Transit signal priority decision returns a wrong result when early green always uses the maximum advance.

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

ROOT CAUSE

Early green is not limited by max_early, truncating conflicting phases arbitrarily.

VERIFIED REPAIR

Restore the early green amount rule so that the step reads `min(x['max_early'], wait)`.

Unsuccessful approach: Always taking the maximum advance can start green before the bus even needs it.

Case contract

Input {cycle, green_start, green_end (exclusive), max_ext, max_early, arrival (seconds, reduced modulo cycle), last_granted (cycle index or null), cycle_index, lockout}. A request within lockout cycles of the last grant (difference <= lockout) returns ['locked', 0]. Arrival in green needs nothing. If the arrival is less than max_ext seconds after green end (cyclically) green is extended through the arrival second: ['extend', d+1]. Otherwise green starts early by min(max_early, seconds until next green start).

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

N = 1
observations = []
def solve(x):
    C = x['cycle']
    a = x['arrival'] % C
    last = x['last_granted']
    if last is not None and x['cycle_index'] - last <= x['lockout']:
        return ['locked', 0]
    gs, ge = x['green_start'], x['green_end']
    if gs <= a < ge:
        return ['none', 0]
    d = (a - ge) % C
    if d < x['max_ext']:
        return ['extend', d + 1]
    wait = (gs - a) % C
    return ['early', wait]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[({'cycle': 100, 'green_start': 30, 'green_end': 45, 'max_ext': 20, 'max_early': 10, 'arrival': 28, 'last_granted': 1, 'cycle_index': 6, 'lockout': 2}, ['early', 2]), ({'cycle': 80, 'green_start': 28, 'green_end': 61, 'max_ext': 15, 'max_early': 12, 'arrival': 236, 'last_granted': 0, 'cycle_index': 17, 'lockout': 3}, ['early', 12]), ({'cycle': 140, 'green_start': 18, 'green_end': 72, 'max_ext': 19, 'max_early': 15, 'arrival': 359, 'last_granted': 1, 'cycle_index': 10, 'lockout': 2}, ['extend', 8]), ({'cycle': 100, 'green_start': 40, 'green_end': 85, 'max_ext': 20, 'max_early': 14, 'arrival': 228, 'last_granted': 0, 'cycle_index': 12, 'lockout': 1}, ['early', 12]), ({'cycle': 110, 'green_start': 52, 'green_end': 85, 'max_ext': 13, 'max_early': 14, 'arrival': 329, 'last_granted': None, 'cycle_index': 10, 'lockout': 2}, ['early', 14]), ({'cycle': 100, 'green_start': 10, 'green_end': 50, 'max_ext': 10, 'max_early': 10, 'arrival': 250, 'last_granted': 3, 'cycle_index': 5, 'lockout': 2}, ['locked', 0]), ({'cycle': 90, 'green_start': 0, 'green_end': 40, 'max_ext': 12, 'max_early': 8, 'arrival': 40, 'last_granted': None, 'cycle_index': 0, 'lockout': 1}, ['extend', 1]), ({'cycle': 110, 'green_start': 40, 'green_end': 91, 'max_ext': 19, 'max_early': 8, 'arrival': 226, 'last_granted': 8, 'cycle_index': 16, 'lockout': 1}, ['early', 8])], [({'cycle': 120, 'green_start': 37, 'green_end': 94, 'max_ext': 13, 'max_early': 20, 'arrival': 14, 'last_granted': None, 'cycle_index': 2, 'lockout': 2}, ['early', 20]), ({'cycle': 100, 'green_start': 10, 'green_end': 50, 'max_ext': 10, 'max_early': 10, 'arrival': 250, 'last_granted': 3, 'cycle_index': 5, 'lockout': 2}, ['locked', 0]), ({'cycle': 90, 'green_start': 0, 'green_end': 40, 'max_ext': 12, 'max_early': 8, 'arrival': 40, 'last_granted': None, 'cycle_index': 0, 'lockout': 1}, ['extend', 1]), ({'cycle': 120, 'green_start': 21, 'green_end': 39, 'max_ext': 5, 'max_early': 15, 'arrival': 133, 'last_granted': 14, 'cycle_index': 21, 'lockout': 2}, ['early', 8]), ({'cycle': 130, 'green_start': 37, 'green_end': 74, 'max_ext': 16, 'max_early': 18, 'arrival': 6, 'last_granted': 9, 'cycle_index': 14, 'lockout': 1}, ['early', 18]), ({'cycle': 90, 'green_start': 27, 'green_end': 67, 'max_ext': 11, 'max_early': 10, 'arrival': 89, 'last_granted': 11, 'cycle_index': 6, 'lockout': 1}, ['locked', 0]), ({'cycle': 100, 'green_start': 30, 'green_end': 45, 'max_ext': 20, 'max_early': 10, 'arrival': 28, 'last_granted': 1, 'cycle_index': 6, 'lockout': 2}, ['early', 2]), ({'cycle': 100, 'green_start': 45, 'green_end': 87, 'max_ext': 6, 'max_early': 20, 'arrival': 121, 'last_granted': None, 'cycle_index': 7, 'lockout': 3}, ['early', 20])], [({'cycle': 80, 'green_start': 33, 'green_end': 69, 'max_ext': 9, 'max_early': 10, 'arrival': 169, 'last_granted': None, 'cycle_index': 21, 'lockout': 1}, ['early', 10]), ({'cycle': 140, 'green_start': 27, 'green_end': 68, 'max_ext': 6, 'max_early': 9, 'arrival': 217, 'last_granted': None, 'cycle_index': 21, 'lockout': 2}, ['early', 9]), ({'cycle': 90, 'green_start': 2, 'green_end': 25, 'max_ext': 16, 'max_early': 17, 'arrival': 132, 'last_granted': None, 'cycle_index': 18, 'lockout': 1}, ['early', 17]), ({'cycle': 100, 'green_start': 10, 'green_end': 45, 'max_ext': 10, 'max_early': 10, 'arrival': 110, 'last_granted': None, 'cycle_index': 4, 'lockout': 1}, ['none', 0]), ({'cycle': 110, 'green_start': 26, 'green_end': 51, 'max_ext': 5, 'max_early': 15, 'arrival': 129, 'last_granted': 8, 'cycle_index': 17, 'lockout': 3}, ['early', 7]), ({'cycle': 100, 'green_start': 10, 'green_end': 50, 'max_ext': 10, 'max_early': 10, 'arrival': 250, 'last_granted': 3, 'cycle_index': 5, 'lockout': 2}, ['locked', 0]), ({'cycle': 140, 'green_start': 52, 'green_end': 106, 'max_ext': 6, 'max_early': 8, 'arrival': 98, 'last_granted': None, 'cycle_index': 1, 'lockout': 1}, ['none', 0]), ({'cycle': 100, 'green_start': 30, 'green_end': 45, 'max_ext': 20, 'max_early': 10, 'arrival': 28, 'last_granted': 1, 'cycle_index': 6, 'lockout': 2}, ['early', 2])], [({'cycle': 100, 'green_start': 9, 'green_end': 55, 'max_ext': 8, 'max_early': 6, 'arrival': 190, 'last_granted': 9, 'cycle_index': 20, 'lockout': 3}, ['early', 6]), ({'cycle': 80, 'green_start': 35, 'green_end': 60, 'max_ext': 19, 'max_early': 12, 'arrival': 62, 'last_granted': None, 'cycle_index': 9, 'lockout': 3}, ['extend', 3]), ({'cycle': 120, 'green_start': 17, 'green_end': 67, 'max_ext': 15, 'max_early': 10, 'arrival': 10, 'last_granted': None, 'cycle_index': 5, 'lockout': 2}, ['early', 7]), ({'cycle': 120, 'green_start': 31, 'green_end': 81, 'max_ext': 14, 'max_early': 11, 'arrival': 340, 'last_granted': 0, 'cycle_index': 8, 'lockout': 3}, ['early', 11]), ({'cycle': 100, 'green_start': 30, 'green_end': 45, 'max_ext': 20, 'max_early': 10, 'arrival': 28, 'last_granted': 1, 'cycle_index': 6, 'lockout': 2}, ['early', 2]), ({'cycle': 90, 'green_start': 0, 'green_end': 40, 'max_ext': 12, 'max_early': 8, 'arrival': 40, 'last_granted': None, 'cycle_index': 0, 'lockout': 1}, ['extend', 1]), ({'cycle': 100, 'green_start': 10, 'green_end': 45, 'max_ext': 10, 'max_early': 10, 'arrival': 110, 'last_granted': None, 'cycle_index': 4, 'lockout': 1}, ['none', 0]), ({'cycle': 80, 'green_start': 37, 'green_end': 55, 'max_ext': 5, 'max_early': 9, 'arrival': 11, 'last_granted': 7, 'cycle_index': 11, 'lockout': 2}, ['early', 9])], [({'cycle': 100, 'green_start': 30, 'green_end': 45, 'max_ext': 20, 'max_early': 10, 'arrival': 28, 'last_granted': 1, 'cycle_index': 6, 'lockout': 2}, ['early', 2]), ({'cycle': 110, 'green_start': 19, 'green_end': 57, 'max_ext': 8, 'max_early': 12, 'arrival': 305, 'last_granted': 14, 'cycle_index': 11, 'lockout': 2}, ['locked', 0]), ({'cycle': 80, 'green_start': 3, 'green_end': 37, 'max_ext': 9, 'max_early': 10, 'arrival': 224, 'last_granted': 2, 'cycle_index': 14, 'lockout': 3}, ['early', 10]), ({'cycle': 120, 'green_start': 54, 'green_end': 83, 'max_ext': 7, 'max_early': 15, 'arrival': 7, 'last_granted': None, 'cycle_index': 1, 'lockout': 2}, ['early', 15]), ({'cycle': 140, 'green_start': 2, 'green_end': 49, 'max_ext': 8, 'max_early': 8, 'arrival': 204, 'last_granted': 0, 'cycle_index': 15, 'lockout': 3}, ['early', 8]), ({'cycle': 100, 'green_start': 10, 'green_end': 45, 'max_ext': 10, 'max_early': 10, 'arrival': 110, 'last_granted': None, 'cycle_index': 4, 'lockout': 1}, ['none', 0]), ({'cycle': 130, 'green_start': 18, 'green_end': 47, 'max_ext': 19, 'max_early': 16, 'arrival': 138, 'last_granted': 4, 'cycle_index': 20, 'lockout': 1}, ['early', 10]), ({'cycle': 90, 'green_start': 0, 'green_end': 40, 'max_ext': 12, 'max_early': 8, 'arrival': 40, 'last_granted': None, 'cycle_index': 0, 'lockout': 1}, ['extend', 1])]]
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	`['early', 2]`	`['early', 2]`	Passed
timing oracle 1	`['early', 32]`	`['early', 12]`	Failed
timing oracle 2	`['extend', 8]`	`['extend', 8]`	Passed
timing oracle 3	`['early', 12]`	`['early', 12]`	Passed
timing oracle 4	`['early', 53]`	`['early', 14]`	Failed
timing oracle 5	`['locked', 0]`	`['locked', 0]`	Passed
timing oracle 6	`['extend', 1]`	`['extend', 1]`	Passed
timing oracle 7	`['early', 34]`	`['early', 8]`	Failed

SHA-256 / 1f0e367ed4fce97b9f3e6c87b72ab5f8ca11e0a14551d0075c7820c57fea2ac1

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(x):
    C = x['cycle']
    a = x['arrival'] % C
    last = x['last_granted']
    if last is not None and x['cycle_index'] - last <= x['lockout']:
        return ['locked', 0]
    gs, ge = x['green_start'], x['green_end']
    if gs <= a < ge:
        return ['none', 0]
    d = (a - ge) % C
    if d < x['max_ext']:
        return ['extend', d + 1]
    wait = (gs - a) % C
    return ['early', x['max_early']]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[({'cycle': 100, 'green_start': 30, 'green_end': 45, 'max_ext': 20, 'max_early': 10, 'arrival': 28, 'last_granted': 1, 'cycle_index': 6, 'lockout': 2}, ['early', 2]), ({'cycle': 80, 'green_start': 28, 'green_end': 61, 'max_ext': 15, 'max_early': 12, 'arrival': 236, 'last_granted': 0, 'cycle_index': 17, 'lockout': 3}, ['early', 12]), ({'cycle': 140, 'green_start': 18, 'green_end': 72, 'max_ext': 19, 'max_early': 15, 'arrival': 359, 'last_granted': 1, 'cycle_index': 10, 'lockout': 2}, ['extend', 8]), ({'cycle': 100, 'green_start': 40, 'green_end': 85, 'max_ext': 20, 'max_early': 14, 'arrival': 228, 'last_granted': 0, 'cycle_index': 12, 'lockout': 1}, ['early', 12]), ({'cycle': 110, 'green_start': 52, 'green_end': 85, 'max_ext': 13, 'max_early': 14, 'arrival': 329, 'last_granted': None, 'cycle_index': 10, 'lockout': 2}, ['early', 14]), ({'cycle': 100, 'green_start': 10, 'green_end': 50, 'max_ext': 10, 'max_early': 10, 'arrival': 250, 'last_granted': 3, 'cycle_index': 5, 'lockout': 2}, ['locked', 0]), ({'cycle': 90, 'green_start': 0, 'green_end': 40, 'max_ext': 12, 'max_early': 8, 'arrival': 40, 'last_granted': None, 'cycle_index': 0, 'lockout': 1}, ['extend', 1]), ({'cycle': 110, 'green_start': 40, 'green_end': 91, 'max_ext': 19, 'max_early': 8, 'arrival': 226, 'last_granted': 8, 'cycle_index': 16, 'lockout': 1}, ['early', 8])], [({'cycle': 120, 'green_start': 37, 'green_end': 94, 'max_ext': 13, 'max_early': 20, 'arrival': 14, 'last_granted': None, 'cycle_index': 2, 'lockout': 2}, ['early', 20]), ({'cycle': 100, 'green_start': 10, 'green_end': 50, 'max_ext': 10, 'max_early': 10, 'arrival': 250, 'last_granted': 3, 'cycle_index': 5, 'lockout': 2}, ['locked', 0]), ({'cycle': 90, 'green_start': 0, 'green_end': 40, 'max_ext': 12, 'max_early': 8, 'arrival': 40, 'last_granted': None, 'cycle_index': 0, 'lockout': 1}, ['extend', 1]), ({'cycle': 120, 'green_start': 21, 'green_end': 39, 'max_ext': 5, 'max_early': 15, 'arrival': 133, 'last_granted': 14, 'cycle_index': 21, 'lockout': 2}, ['early', 8]), ({'cycle': 130, 'green_start': 37, 'green_end': 74, 'max_ext': 16, 'max_early': 18, 'arrival': 6, 'last_granted': 9, 'cycle_index': 14, 'lockout': 1}, ['early', 18]), ({'cycle': 90, 'green_start': 27, 'green_end': 67, 'max_ext': 11, 'max_early': 10, 'arrival': 89, 'last_granted': 11, 'cycle_index': 6, 'lockout': 1}, ['locked', 0]), ({'cycle': 100, 'green_start': 30, 'green_end': 45, 'max_ext': 20, 'max_early': 10, 'arrival': 28, 'last_granted': 1, 'cycle_index': 6, 'lockout': 2}, ['early', 2]), ({'cycle': 100, 'green_start': 45, 'green_end': 87, 'max_ext': 6, 'max_early': 20, 'arrival': 121, 'last_granted': None, 'cycle_index': 7, 'lockout': 3}, ['early', 20])], [({'cycle': 80, 'green_start': 33, 'green_end': 69, 'max_ext': 9, 'max_early': 10, 'arrival': 169, 'last_granted': None, 'cycle_index': 21, 'lockout': 1}, ['early', 10]), ({'cycle': 140, 'green_start': 27, 'green_end': 68, 'max_ext': 6, 'max_early': 9, 'arrival': 217, 'last_granted': None, 'cycle_index': 21, 'lockout': 2}, ['early', 9]), ({'cycle': 90, 'green_start': 2, 'green_end': 25, 'max_ext': 16, 'max_early': 17, 'arrival': 132, 'last_granted': None, 'cycle_index': 18, 'lockout': 1}, ['early', 17]), ({'cycle': 100, 'green_start': 10, 'green_end': 45, 'max_ext': 10, 'max_early': 10, 'arrival': 110, 'last_granted': None, 'cycle_index': 4, 'lockout': 1}, ['none', 0]), ({'cycle': 110, 'green_start': 26, 'green_end': 51, 'max_ext': 5, 'max_early': 15, 'arrival': 129, 'last_granted': 8, 'cycle_index': 17, 'lockout': 3}, ['early', 7]), ({'cycle': 100, 'green_start': 10, 'green_end': 50, 'max_ext': 10, 'max_early': 10, 'arrival': 250, 'last_granted': 3, 'cycle_index': 5, 'lockout': 2}, ['locked', 0]), ({'cycle': 140, 'green_start': 52, 'green_end': 106, 'max_ext': 6, 'max_early': 8, 'arrival': 98, 'last_granted': None, 'cycle_index': 1, 'lockout': 1}, ['none', 0]), ({'cycle': 100, 'green_start': 30, 'green_end': 45, 'max_ext': 20, 'max_early': 10, 'arrival': 28, 'last_granted': 1, 'cycle_index': 6, 'lockout': 2}, ['early', 2])], [({'cycle': 100, 'green_start': 9, 'green_end': 55, 'max_ext': 8, 'max_early': 6, 'arrival': 190, 'last_granted': 9, 'cycle_index': 20, 'lockout': 3}, ['early', 6]), ({'cycle': 80, 'green_start': 35, 'green_end': 60, 'max_ext': 19, 'max_early': 12, 'arrival': 62, 'last_granted': None, 'cycle_index': 9, 'lockout': 3}, ['extend', 3]), ({'cycle': 120, 'green_start': 17, 'green_end': 67, 'max_ext': 15, 'max_early': 10, 'arrival': 10, 'last_granted': None, 'cycle_index': 5, 'lockout': 2}, ['early', 7]), ({'cycle': 120, 'green_start': 31, 'green_end': 81, 'max_ext': 14, 'max_early': 11, 'arrival': 340, 'last_granted': 0, 'cycle_index': 8, 'lockout': 3}, ['early', 11]), ({'cycle': 100, 'green_start': 30, 'green_end': 45, 'max_ext': 20, 'max_early': 10, 'arrival': 28, 'last_granted': 1, 'cycle_index': 6, 'lockout': 2}, ['early', 2]), ({'cycle': 90, 'green_start': 0, 'green_end': 40, 'max_ext': 12, 'max_early': 8, 'arrival': 40, 'last_granted': None, 'cycle_index': 0, 'lockout': 1}, ['extend', 1]), ({'cycle': 100, 'green_start': 10, 'green_end': 45, 'max_ext': 10, 'max_early': 10, 'arrival': 110, 'last_granted': None, 'cycle_index': 4, 'lockout': 1}, ['none', 0]), ({'cycle': 80, 'green_start': 37, 'green_end': 55, 'max_ext': 5, 'max_early': 9, 'arrival': 11, 'last_granted': 7, 'cycle_index': 11, 'lockout': 2}, ['early', 9])], [({'cycle': 100, 'green_start': 30, 'green_end': 45, 'max_ext': 20, 'max_early': 10, 'arrival': 28, 'last_granted': 1, 'cycle_index': 6, 'lockout': 2}, ['early', 2]), ({'cycle': 110, 'green_start': 19, 'green_end': 57, 'max_ext': 8, 'max_early': 12, 'arrival': 305, 'last_granted': 14, 'cycle_index': 11, 'lockout': 2}, ['locked', 0]), ({'cycle': 80, 'green_start': 3, 'green_end': 37, 'max_ext': 9, 'max_early': 10, 'arrival': 224, 'last_granted': 2, 'cycle_index': 14, 'lockout': 3}, ['early', 10]), ({'cycle': 120, 'green_start': 54, 'green_end': 83, 'max_ext': 7, 'max_early': 15, 'arrival': 7, 'last_granted': None, 'cycle_index': 1, 'lockout': 2}, ['early', 15]), ({'cycle': 140, 'green_start': 2, 'green_end': 49, 'max_ext': 8, 'max_early': 8, 'arrival': 204, 'last_granted': 0, 'cycle_index': 15, 'lockout': 3}, ['early', 8]), ({'cycle': 100, 'green_start': 10, 'green_end': 45, 'max_ext': 10, 'max_early': 10, 'arrival': 110, 'last_granted': None, 'cycle_index': 4, 'lockout': 1}, ['none', 0]), ({'cycle': 130, 'green_start': 18, 'green_end': 47, 'max_ext': 19, 'max_early': 16, 'arrival': 138, 'last_granted': 4, 'cycle_index': 20, 'lockout': 1}, ['early', 10]), ({'cycle': 90, 'green_start': 0, 'green_end': 40, 'max_ext': 12, 'max_early': 8, 'arrival': 40, 'last_granted': None, 'cycle_index': 0, 'lockout': 1}, ['extend', 1])]]
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	`['early', 10]`	`['early', 2]`	Failed
timing oracle 1	`['early', 12]`	`['early', 12]`	Passed
timing oracle 2	`['extend', 8]`	`['extend', 8]`	Passed
timing oracle 3	`['early', 14]`	`['early', 12]`	Failed
timing oracle 4	`['early', 14]`	`['early', 14]`	Passed
timing oracle 5	`['locked', 0]`	`['locked', 0]`	Passed
timing oracle 6	`['extend', 1]`	`['extend', 1]`	Passed
timing oracle 7	`['early', 8]`	`['early', 8]`	Passed

SHA-256 / 806ceb3afe5e6ae32df2f8cb57ef45bf3fc4d33fd71232b7fea65b55c71f7bf3

3 / The verified repair

Exit 0

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

N = 1
observations = []
def solve(x):
    C = x['cycle']
    a = x['arrival'] % C
    last = x['last_granted']
    if last is not None and x['cycle_index'] - last <= x['lockout']:
        return ['locked', 0]
    gs, ge = x['green_start'], x['green_end']
    if gs <= a < ge:
        return ['none', 0]
    d = (a - ge) % C
    if d < x['max_ext']:
        return ['extend', d + 1]
    wait = (gs - a) % C
    return ['early', min(x['max_early'], wait)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[({'cycle': 100, 'green_start': 30, 'green_end': 45, 'max_ext': 20, 'max_early': 10, 'arrival': 28, 'last_granted': 1, 'cycle_index': 6, 'lockout': 2}, ['early', 2]), ({'cycle': 80, 'green_start': 28, 'green_end': 61, 'max_ext': 15, 'max_early': 12, 'arrival': 236, 'last_granted': 0, 'cycle_index': 17, 'lockout': 3}, ['early', 12]), ({'cycle': 140, 'green_start': 18, 'green_end': 72, 'max_ext': 19, 'max_early': 15, 'arrival': 359, 'last_granted': 1, 'cycle_index': 10, 'lockout': 2}, ['extend', 8]), ({'cycle': 100, 'green_start': 40, 'green_end': 85, 'max_ext': 20, 'max_early': 14, 'arrival': 228, 'last_granted': 0, 'cycle_index': 12, 'lockout': 1}, ['early', 12]), ({'cycle': 110, 'green_start': 52, 'green_end': 85, 'max_ext': 13, 'max_early': 14, 'arrival': 329, 'last_granted': None, 'cycle_index': 10, 'lockout': 2}, ['early', 14]), ({'cycle': 100, 'green_start': 10, 'green_end': 50, 'max_ext': 10, 'max_early': 10, 'arrival': 250, 'last_granted': 3, 'cycle_index': 5, 'lockout': 2}, ['locked', 0]), ({'cycle': 90, 'green_start': 0, 'green_end': 40, 'max_ext': 12, 'max_early': 8, 'arrival': 40, 'last_granted': None, 'cycle_index': 0, 'lockout': 1}, ['extend', 1]), ({'cycle': 110, 'green_start': 40, 'green_end': 91, 'max_ext': 19, 'max_early': 8, 'arrival': 226, 'last_granted': 8, 'cycle_index': 16, 'lockout': 1}, ['early', 8])], [({'cycle': 120, 'green_start': 37, 'green_end': 94, 'max_ext': 13, 'max_early': 20, 'arrival': 14, 'last_granted': None, 'cycle_index': 2, 'lockout': 2}, ['early', 20]), ({'cycle': 100, 'green_start': 10, 'green_end': 50, 'max_ext': 10, 'max_early': 10, 'arrival': 250, 'last_granted': 3, 'cycle_index': 5, 'lockout': 2}, ['locked', 0]), ({'cycle': 90, 'green_start': 0, 'green_end': 40, 'max_ext': 12, 'max_early': 8, 'arrival': 40, 'last_granted': None, 'cycle_index': 0, 'lockout': 1}, ['extend', 1]), ({'cycle': 120, 'green_start': 21, 'green_end': 39, 'max_ext': 5, 'max_early': 15, 'arrival': 133, 'last_granted': 14, 'cycle_index': 21, 'lockout': 2}, ['early', 8]), ({'cycle': 130, 'green_start': 37, 'green_end': 74, 'max_ext': 16, 'max_early': 18, 'arrival': 6, 'last_granted': 9, 'cycle_index': 14, 'lockout': 1}, ['early', 18]), ({'cycle': 90, 'green_start': 27, 'green_end': 67, 'max_ext': 11, 'max_early': 10, 'arrival': 89, 'last_granted': 11, 'cycle_index': 6, 'lockout': 1}, ['locked', 0]), ({'cycle': 100, 'green_start': 30, 'green_end': 45, 'max_ext': 20, 'max_early': 10, 'arrival': 28, 'last_granted': 1, 'cycle_index': 6, 'lockout': 2}, ['early', 2]), ({'cycle': 100, 'green_start': 45, 'green_end': 87, 'max_ext': 6, 'max_early': 20, 'arrival': 121, 'last_granted': None, 'cycle_index': 7, 'lockout': 3}, ['early', 20])], [({'cycle': 80, 'green_start': 33, 'green_end': 69, 'max_ext': 9, 'max_early': 10, 'arrival': 169, 'last_granted': None, 'cycle_index': 21, 'lockout': 1}, ['early', 10]), ({'cycle': 140, 'green_start': 27, 'green_end': 68, 'max_ext': 6, 'max_early': 9, 'arrival': 217, 'last_granted': None, 'cycle_index': 21, 'lockout': 2}, ['early', 9]), ({'cycle': 90, 'green_start': 2, 'green_end': 25, 'max_ext': 16, 'max_early': 17, 'arrival': 132, 'last_granted': None, 'cycle_index': 18, 'lockout': 1}, ['early', 17]), ({'cycle': 100, 'green_start': 10, 'green_end': 45, 'max_ext': 10, 'max_early': 10, 'arrival': 110, 'last_granted': None, 'cycle_index': 4, 'lockout': 1}, ['none', 0]), ({'cycle': 110, 'green_start': 26, 'green_end': 51, 'max_ext': 5, 'max_early': 15, 'arrival': 129, 'last_granted': 8, 'cycle_index': 17, 'lockout': 3}, ['early', 7]), ({'cycle': 100, 'green_start': 10, 'green_end': 50, 'max_ext': 10, 'max_early': 10, 'arrival': 250, 'last_granted': 3, 'cycle_index': 5, 'lockout': 2}, ['locked', 0]), ({'cycle': 140, 'green_start': 52, 'green_end': 106, 'max_ext': 6, 'max_early': 8, 'arrival': 98, 'last_granted': None, 'cycle_index': 1, 'lockout': 1}, ['none', 0]), ({'cycle': 100, 'green_start': 30, 'green_end': 45, 'max_ext': 20, 'max_early': 10, 'arrival': 28, 'last_granted': 1, 'cycle_index': 6, 'lockout': 2}, ['early', 2])], [({'cycle': 100, 'green_start': 9, 'green_end': 55, 'max_ext': 8, 'max_early': 6, 'arrival': 190, 'last_granted': 9, 'cycle_index': 20, 'lockout': 3}, ['early', 6]), ({'cycle': 80, 'green_start': 35, 'green_end': 60, 'max_ext': 19, 'max_early': 12, 'arrival': 62, 'last_granted': None, 'cycle_index': 9, 'lockout': 3}, ['extend', 3]), ({'cycle': 120, 'green_start': 17, 'green_end': 67, 'max_ext': 15, 'max_early': 10, 'arrival': 10, 'last_granted': None, 'cycle_index': 5, 'lockout': 2}, ['early', 7]), ({'cycle': 120, 'green_start': 31, 'green_end': 81, 'max_ext': 14, 'max_early': 11, 'arrival': 340, 'last_granted': 0, 'cycle_index': 8, 'lockout': 3}, ['early', 11]), ({'cycle': 100, 'green_start': 30, 'green_end': 45, 'max_ext': 20, 'max_early': 10, 'arrival': 28, 'last_granted': 1, 'cycle_index': 6, 'lockout': 2}, ['early', 2]), ({'cycle': 90, 'green_start': 0, 'green_end': 40, 'max_ext': 12, 'max_early': 8, 'arrival': 40, 'last_granted': None, 'cycle_index': 0, 'lockout': 1}, ['extend', 1]), ({'cycle': 100, 'green_start': 10, 'green_end': 45, 'max_ext': 10, 'max_early': 10, 'arrival': 110, 'last_granted': None, 'cycle_index': 4, 'lockout': 1}, ['none', 0]), ({'cycle': 80, 'green_start': 37, 'green_end': 55, 'max_ext': 5, 'max_early': 9, 'arrival': 11, 'last_granted': 7, 'cycle_index': 11, 'lockout': 2}, ['early', 9])], [({'cycle': 100, 'green_start': 30, 'green_end': 45, 'max_ext': 20, 'max_early': 10, 'arrival': 28, 'last_granted': 1, 'cycle_index': 6, 'lockout': 2}, ['early', 2]), ({'cycle': 110, 'green_start': 19, 'green_end': 57, 'max_ext': 8, 'max_early': 12, 'arrival': 305, 'last_granted': 14, 'cycle_index': 11, 'lockout': 2}, ['locked', 0]), ({'cycle': 80, 'green_start': 3, 'green_end': 37, 'max_ext': 9, 'max_early': 10, 'arrival': 224, 'last_granted': 2, 'cycle_index': 14, 'lockout': 3}, ['early', 10]), ({'cycle': 120, 'green_start': 54, 'green_end': 83, 'max_ext': 7, 'max_early': 15, 'arrival': 7, 'last_granted': None, 'cycle_index': 1, 'lockout': 2}, ['early', 15]), ({'cycle': 140, 'green_start': 2, 'green_end': 49, 'max_ext': 8, 'max_early': 8, 'arrival': 204, 'last_granted': 0, 'cycle_index': 15, 'lockout': 3}, ['early', 8]), ({'cycle': 100, 'green_start': 10, 'green_end': 45, 'max_ext': 10, 'max_early': 10, 'arrival': 110, 'last_granted': None, 'cycle_index': 4, 'lockout': 1}, ['none', 0]), ({'cycle': 130, 'green_start': 18, 'green_end': 47, 'max_ext': 19, 'max_early': 16, 'arrival': 138, 'last_granted': 4, 'cycle_index': 20, 'lockout': 1}, ['early', 10]), ({'cycle': 90, 'green_start': 0, 'green_end': 40, 'max_ext': 12, 'max_early': 8, 'arrival': 40, 'last_granted': None, 'cycle_index': 0, 'lockout': 1}, ['extend', 1])]]
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	`['early', 2]`	`['early', 2]`	Passed
timing oracle 1	`['early', 12]`	`['early', 12]`	Passed
timing oracle 2	`['extend', 8]`	`['extend', 8]`	Passed
timing oracle 3	`['early', 12]`	`['early', 12]`	Passed
timing oracle 4	`['early', 14]`	`['early', 14]`	Passed
timing oracle 5	`['locked', 0]`	`['locked', 0]`	Passed
timing oracle 6	`['extend', 1]`	`['extend', 1]`	Passed
timing oracle 7	`['early', 8]`	`['early', 8]`	Passed

SHA-256 / 9820bd7ff4862345a1f9bafe3bf229120a48f7b81448cf657660d71a86670152

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 2026-09-29T14:48:00.247176+00:00.

Case digest / a528106a85502edc4e81633199c5573ad32f7801156b317b7d0ef396700dd6e0