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FA-67986 / Traffic signal timing plans / Open access

Actuated phase gap-out and max-out: the passage timer is started only after min green · case 01

Actuated phase gap-out and max-out returns a wrong result when the passage timer is started only after min green.

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

ROOT CAUSE

Counting the actuation second as part of the gap expires every extension one second early.

VERIFIED REPAIR

Restore the passage expiry instant rule so that the step reads `exp = max(exp, a + p)`.

Unsuccessful approach: Delaying the passage timer until the end of min green extends phases for actuations the contract counts from their own time.

Case contract

Input {min_green, gap, max_green, actuations: integer seconds since green start (any order), conflict_call: seconds or null}. Each actuation at a keeps the phase eligible until a+gap; an actuation exactly at expiry extends; actuations during min green always extend. Gap-out time = max(min_green, final expiry). With no conflicting call return ['rest', gap time]. The max timer starts at the call (a call before green start counts as 0); max-out at call+max_green. If gap time <= max-out the phase ends by 'gap-out' at max(gap time, call), else by 'max-out'.

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):
    m, p, M = x['min_green'], x['gap'], x['max_green']
    exp = 0
    for a in sorted(x['actuations']):
        if a > exp and a > m:
            break
        exp = max(exp, a + p - 1)
    gap_end = max(m, exp)
    tc = x['conflict_call']
    if tc is None:
        return ['rest', gap_end]
    tc = max(tc, 0)
    max_end = tc + M
    if gap_end <= max_end:
        return ['gap-out', max(gap_end, tc)]
    return ['max-out', max_end]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[({'min_green': 6, 'gap': 2, 'max_green': 15, 'actuations': [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38], 'conflict_call': -3}, ['max-out', 15]), ({'min_green': 8, 'gap': 3, 'max_green': 30, 'actuations': [2, 6], 'conflict_call': 20}, ['gap-out', 20]), ({'min_green': 9, 'gap': 2, 'max_green': 27, 'actuations': [2, 4, 6, 12, 13, 19, 22, 25, 39, 42], 'conflict_call': 8}, ['gap-out', 9]), ({'min_green': 9, 'gap': 2, 'max_green': 28, 'actuations': [1, 6, 8, 12, 14, 16, 18, 19, 21, 22, 24, 33, 34, 37, 40, 47, 50, 52, 58], 'conflict_call': 21}, ['gap-out', 21]), ({'min_green': 5, 'gap': 3, 'max_green': 20, 'actuations': [1, 4, 7, 10, 13], 'conflict_call': 2}, ['gap-out', 16]), ({'min_green': 8, 'gap': 3, 'max_green': 34, 'actuations': [25, 15, 18, 8, 49, 45, 14, 40, 51, 13, 33, 42, 36, 11, 58, 16, 10, 55, 3], 'conflict_call': -1}, ['gap-out', 21]), ({'min_green': 4, 'gap': 3, 'max_green': 27, 'actuations': [0, 10, 18, 20, 23, 25, 36, 39, 40, 50, 54, 58], 'conflict_call': None}, ['rest', 4]), ({'min_green': 4, 'gap': 5, 'max_green': 24, 'actuations': [4, 18, 35, 45, 48, 49], 'conflict_call': 31}, ['gap-out', 31])], [({'min_green': 6, 'gap': 5, 'max_green': 32, 'actuations': [2, 5, 6, 7, 8, 11, 12, 15, 16, 17, 19, 21, 23, 26, 27, 28, 29, 32, 35, 37, 42, 44, 45, 47, 49, 50, 52, 56, 57, 59], 'conflict_call': 25}, ['max-out', 57]), ({'min_green': 5, 'gap': 4, 'max_green': 23, 'actuations': [0, 2, 4, 16, 19, 21, 22, 24, 28, 40, 44, 45, 46, 54, 55, 57, 58], 'conflict_call': None}, ['rest', 8]), ({'min_green': 5, 'gap': 3, 'max_green': 10, 'actuations': [0, 3, 6, 9, 12], 'conflict_call': 5}, ['gap-out', 15]), ({'min_green': 7, 'gap': 4, 'max_green': 21, 'actuations': [3, 6, 8, 9, 11, 12, 15, 17, 19, 21, 23, 25, 28, 33, 34, 35, 39, 47, 52, 54, 56, 58, 59], 'conflict_call': 7}, ['max-out', 28]), ({'min_green': 6, 'gap': 2, 'max_green': 12, 'actuations': [1, 3, 5, 7, 9, 11, 13], 'conflict_call': 3}, ['gap-out', 15]), ({'min_green': 4, 'gap': 4, 'max_green': 15, 'actuations': [1, 2, 4, 6, 11, 13, 15, 19, 20, 22, 23, 26, 27, 37, 41, 44, 47, 48, 50, 52, 53, 54, 56, 58, 59], 'conflict_call': 26}, ['gap-out', 26]), ({'min_green': 12, 'gap': 3, 'max_green': 5, 'actuations': [1], 'conflict_call': 2}, ['max-out', 7]), ({'min_green': 8, 'gap': 5, 'max_green': 16, 'actuations': [2, 17, 23, 41, 50, 54, 57, 59], 'conflict_call': -2}, ['gap-out', 8])], [({'min_green': 5, 'gap': 3, 'max_green': 20, 'actuations': [1, 4, 7, 10, 13], 'conflict_call': 2}, ['gap-out', 16]), ({'min_green': 6, 'gap': 2, 'max_green': 29, 'actuations': [0, 1, 2, 3, 7, 8, 9, 10, 11, 12, 16, 17, 19, 24, 27, 29, 32, 34, 36, 40, 41, 42, 43, 45, 46, 47, 48, 49, 50, 53, 56, 58, 59], 'conflict_call': -3}, ['gap-out', 6]), ({'min_green': 4, 'gap': 5, 'max_green': 22, 'actuations': [1, 2, 8, 11, 18, 20, 24, 26, 35, 37, 39, 45, 47, 50, 51, 54, 55, 56, 57, 59], 'conflict_call': 31}, ['gap-out', 31]), ({'min_green': 7, 'gap': 5, 'max_green': 42, 'actuations': [1, 3, 5, 8, 10, 29, 33, 38, 42, 44, 50, 53, 55], 'conflict_call': -5}, ['gap-out', 15]), ({'min_green': 6, 'gap': 2, 'max_green': 12, 'actuations': [1, 3, 5, 7, 9, 11, 13], 'conflict_call': 3}, ['gap-out', 15]), ({'min_green': 7, 'gap': 4, 'max_green': 34, 'actuations': [49, 44, 18, 9, 59, 20, 16, 5, 26, 24, 37, 54, 32, 3, 27, 6, 15, 53, 28, 57, 52, 47, 46, 19, 38, 51, 58, 23, 40, 30], 'conflict_call': 24}, ['gap-out', 24]), ({'min_green': 5, 'gap': 5, 'max_green': 30, 'actuations': [3, 12, 14, 28, 29, 34, 37, 42, 44, 45, 48, 52, 54, 56, 59], 'conflict_call': None}, ['rest', 8]), ({'min_green': 12, 'gap': 3, 'max_green': 5, 'actuations': [1], 'conflict_call': 2}, ['max-out', 7])], [({'min_green': 10, 'gap': 2, 'max_green': 15, 'actuations': [2, 5, 6, 8, 9, 14, 15, 17, 18, 22, 25, 26, 30, 31, 33, 36, 40, 42, 50], 'conflict_call': 6}, ['gap-out', 11]), ({'min_green': 12, 'gap': 3, 'max_green': 5, 'actuations': [1], 'conflict_call': 2}, ['max-out', 7]), ({'min_green': 4, 'gap': 5, 'max_green': 25, 'actuations': [1, 9, 10, 12, 13, 14, 15, 16, 17, 21, 24, 26, 27, 29, 30, 36, 37, 38, 41, 42, 43, 46, 47, 48, 49, 51, 53, 55, 58], 'conflict_call': 10}, ['gap-out', 10]), ({'min_green': 7, 'gap': 3, 'max_green': 15, 'actuations': [54, 34, 26, 11, 41, 56, 5], 'conflict_call': 10}, ['gap-out', 10]), ({'min_green': 5, 'gap': 3, 'max_green': 20, 'actuations': [1, 4, 7, 10, 13], 'conflict_call': 2}, ['gap-out', 16]), ({'min_green': 6, 'gap': 2, 'max_green': 12, 'actuations': [1, 3, 5, 7, 9, 11, 13], 'conflict_call': 3}, ['gap-out', 15]), ({'min_green': 4, 'gap': 3, 'max_green': 19, 'actuations': [0, 4, 7, 8, 13, 15, 17, 18, 21, 22, 23, 26, 28, 29, 30, 33, 35, 37, 41, 43, 45, 46, 47, 49, 50, 53, 56, 57], 'conflict_call': 30}, ['gap-out', 30]), ({'min_green': 4, 'gap': 3, 'max_green': 45, 'actuations': [0, 4, 5, 6, 8, 16, 17, 22, 23, 27, 31, 39, 40, 42, 45, 47, 48, 52, 54, 58], 'conflict_call': 27}, ['gap-out', 27])], [({'min_green': 4, 'gap': 2, 'max_green': 32, 'actuations': [10, 16, 21, 24, 25, 27, 30, 34, 39, 42, 49, 50, 52, 53, 56], 'conflict_call': 9}, ['gap-out', 9]), ({'min_green': 4, 'gap': 3, 'max_green': 31, 'actuations': [14, 21, 44, 47], 'conflict_call': 0}, ['gap-out', 4]), ({'min_green': 12, 'gap': 3, 'max_green': 5, 'actuations': [1], 'conflict_call': 2}, ['max-out', 7]), ({'min_green': 6, 'gap': 2, 'max_green': 15, 'actuations': [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38], 'conflict_call': -3}, ['max-out', 15]), ({'min_green': 10, 'gap': 3, 'max_green': 39, 'actuations': [1, 2, 3, 4, 5, 8, 9, 11, 13, 15, 16, 17, 20, 21, 23, 29, 31, 32, 35, 36, 37, 42, 44, 45, 47, 48, 52, 55, 56, 59], 'conflict_call': 12}, ['gap-out', 26]), ({'min_green': 9, 'gap': 4, 'max_green': 29, 'actuations': [2, 4, 7, 17, 23, 25, 27, 36, 37, 45, 50], 'conflict_call': None}, ['rest', 11]), ({'min_green': 5, 'gap': 3, 'max_green': 20, 'actuations': [1, 4, 7, 10, 13], 'conflict_call': 2}, ['gap-out', 16]), ({'min_green': 8, 'gap': 2, 'max_green': 31, 'actuations': [2, 11, 12, 14, 15, 27, 37, 41, 46, 49], 'conflict_call': None}, ['rest', 8])]]
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 fixtureActualExpectedOutcome
timing oracle 0['gap-out', 7]['max-out', 15]Failed
timing oracle 1['gap-out', 20]['gap-out', 20]Passed
timing oracle 2['gap-out', 9]['gap-out', 9]Passed
timing oracle 3['gap-out', 21]['gap-out', 21]Passed
timing oracle 4['gap-out', 6]['gap-out', 16]Failed
timing oracle 5['gap-out', 20]['gap-out', 21]Failed
timing oracle 6['rest', 4]['rest', 4]Passed
timing oracle 7['gap-out', 31]['gap-out', 31]Passed

SHA-256 / 6dd39b93f2413ed483221d4fc1d1061344194ef1f7506e0e77f646e210c38c1e

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(x):
    m, p, M = x['min_green'], x['gap'], x['max_green']
    exp = 0
    for a in sorted(x['actuations']):
        if a > exp and a > m:
            break
        exp = max(exp, max(a, m) + p)
    gap_end = max(m, exp)
    tc = x['conflict_call']
    if tc is None:
        return ['rest', gap_end]
    tc = max(tc, 0)
    max_end = tc + M
    if gap_end <= max_end:
        return ['gap-out', max(gap_end, tc)]
    return ['max-out', max_end]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[({'min_green': 6, 'gap': 2, 'max_green': 15, 'actuations': [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38], 'conflict_call': -3}, ['max-out', 15]), ({'min_green': 8, 'gap': 3, 'max_green': 30, 'actuations': [2, 6], 'conflict_call': 20}, ['gap-out', 20]), ({'min_green': 9, 'gap': 2, 'max_green': 27, 'actuations': [2, 4, 6, 12, 13, 19, 22, 25, 39, 42], 'conflict_call': 8}, ['gap-out', 9]), ({'min_green': 9, 'gap': 2, 'max_green': 28, 'actuations': [1, 6, 8, 12, 14, 16, 18, 19, 21, 22, 24, 33, 34, 37, 40, 47, 50, 52, 58], 'conflict_call': 21}, ['gap-out', 21]), ({'min_green': 5, 'gap': 3, 'max_green': 20, 'actuations': [1, 4, 7, 10, 13], 'conflict_call': 2}, ['gap-out', 16]), ({'min_green': 8, 'gap': 3, 'max_green': 34, 'actuations': [25, 15, 18, 8, 49, 45, 14, 40, 51, 13, 33, 42, 36, 11, 58, 16, 10, 55, 3], 'conflict_call': -1}, ['gap-out', 21]), ({'min_green': 4, 'gap': 3, 'max_green': 27, 'actuations': [0, 10, 18, 20, 23, 25, 36, 39, 40, 50, 54, 58], 'conflict_call': None}, ['rest', 4]), ({'min_green': 4, 'gap': 5, 'max_green': 24, 'actuations': [4, 18, 35, 45, 48, 49], 'conflict_call': 31}, ['gap-out', 31])], [({'min_green': 6, 'gap': 5, 'max_green': 32, 'actuations': [2, 5, 6, 7, 8, 11, 12, 15, 16, 17, 19, 21, 23, 26, 27, 28, 29, 32, 35, 37, 42, 44, 45, 47, 49, 50, 52, 56, 57, 59], 'conflict_call': 25}, ['max-out', 57]), ({'min_green': 5, 'gap': 4, 'max_green': 23, 'actuations': [0, 2, 4, 16, 19, 21, 22, 24, 28, 40, 44, 45, 46, 54, 55, 57, 58], 'conflict_call': None}, ['rest', 8]), ({'min_green': 5, 'gap': 3, 'max_green': 10, 'actuations': [0, 3, 6, 9, 12], 'conflict_call': 5}, ['gap-out', 15]), ({'min_green': 7, 'gap': 4, 'max_green': 21, 'actuations': [3, 6, 8, 9, 11, 12, 15, 17, 19, 21, 23, 25, 28, 33, 34, 35, 39, 47, 52, 54, 56, 58, 59], 'conflict_call': 7}, ['max-out', 28]), ({'min_green': 6, 'gap': 2, 'max_green': 12, 'actuations': [1, 3, 5, 7, 9, 11, 13], 'conflict_call': 3}, ['gap-out', 15]), ({'min_green': 4, 'gap': 4, 'max_green': 15, 'actuations': [1, 2, 4, 6, 11, 13, 15, 19, 20, 22, 23, 26, 27, 37, 41, 44, 47, 48, 50, 52, 53, 54, 56, 58, 59], 'conflict_call': 26}, ['gap-out', 26]), ({'min_green': 12, 'gap': 3, 'max_green': 5, 'actuations': [1], 'conflict_call': 2}, ['max-out', 7]), ({'min_green': 8, 'gap': 5, 'max_green': 16, 'actuations': [2, 17, 23, 41, 50, 54, 57, 59], 'conflict_call': -2}, ['gap-out', 8])], [({'min_green': 5, 'gap': 3, 'max_green': 20, 'actuations': [1, 4, 7, 10, 13], 'conflict_call': 2}, ['gap-out', 16]), ({'min_green': 6, 'gap': 2, 'max_green': 29, 'actuations': [0, 1, 2, 3, 7, 8, 9, 10, 11, 12, 16, 17, 19, 24, 27, 29, 32, 34, 36, 40, 41, 42, 43, 45, 46, 47, 48, 49, 50, 53, 56, 58, 59], 'conflict_call': -3}, ['gap-out', 6]), ({'min_green': 4, 'gap': 5, 'max_green': 22, 'actuations': [1, 2, 8, 11, 18, 20, 24, 26, 35, 37, 39, 45, 47, 50, 51, 54, 55, 56, 57, 59], 'conflict_call': 31}, ['gap-out', 31]), ({'min_green': 7, 'gap': 5, 'max_green': 42, 'actuations': [1, 3, 5, 8, 10, 29, 33, 38, 42, 44, 50, 53, 55], 'conflict_call': -5}, ['gap-out', 15]), ({'min_green': 6, 'gap': 2, 'max_green': 12, 'actuations': [1, 3, 5, 7, 9, 11, 13], 'conflict_call': 3}, ['gap-out', 15]), ({'min_green': 7, 'gap': 4, 'max_green': 34, 'actuations': [49, 44, 18, 9, 59, 20, 16, 5, 26, 24, 37, 54, 32, 3, 27, 6, 15, 53, 28, 57, 52, 47, 46, 19, 38, 51, 58, 23, 40, 30], 'conflict_call': 24}, ['gap-out', 24]), ({'min_green': 5, 'gap': 5, 'max_green': 30, 'actuations': [3, 12, 14, 28, 29, 34, 37, 42, 44, 45, 48, 52, 54, 56, 59], 'conflict_call': None}, ['rest', 8]), ({'min_green': 12, 'gap': 3, 'max_green': 5, 'actuations': [1], 'conflict_call': 2}, ['max-out', 7])], [({'min_green': 10, 'gap': 2, 'max_green': 15, 'actuations': [2, 5, 6, 8, 9, 14, 15, 17, 18, 22, 25, 26, 30, 31, 33, 36, 40, 42, 50], 'conflict_call': 6}, ['gap-out', 11]), ({'min_green': 12, 'gap': 3, 'max_green': 5, 'actuations': [1], 'conflict_call': 2}, ['max-out', 7]), ({'min_green': 4, 'gap': 5, 'max_green': 25, 'actuations': [1, 9, 10, 12, 13, 14, 15, 16, 17, 21, 24, 26, 27, 29, 30, 36, 37, 38, 41, 42, 43, 46, 47, 48, 49, 51, 53, 55, 58], 'conflict_call': 10}, ['gap-out', 10]), ({'min_green': 7, 'gap': 3, 'max_green': 15, 'actuations': [54, 34, 26, 11, 41, 56, 5], 'conflict_call': 10}, ['gap-out', 10]), ({'min_green': 5, 'gap': 3, 'max_green': 20, 'actuations': [1, 4, 7, 10, 13], 'conflict_call': 2}, ['gap-out', 16]), ({'min_green': 6, 'gap': 2, 'max_green': 12, 'actuations': [1, 3, 5, 7, 9, 11, 13], 'conflict_call': 3}, ['gap-out', 15]), ({'min_green': 4, 'gap': 3, 'max_green': 19, 'actuations': [0, 4, 7, 8, 13, 15, 17, 18, 21, 22, 23, 26, 28, 29, 30, 33, 35, 37, 41, 43, 45, 46, 47, 49, 50, 53, 56, 57], 'conflict_call': 30}, ['gap-out', 30]), ({'min_green': 4, 'gap': 3, 'max_green': 45, 'actuations': [0, 4, 5, 6, 8, 16, 17, 22, 23, 27, 31, 39, 40, 42, 45, 47, 48, 52, 54, 58], 'conflict_call': 27}, ['gap-out', 27])], [({'min_green': 4, 'gap': 2, 'max_green': 32, 'actuations': [10, 16, 21, 24, 25, 27, 30, 34, 39, 42, 49, 50, 52, 53, 56], 'conflict_call': 9}, ['gap-out', 9]), ({'min_green': 4, 'gap': 3, 'max_green': 31, 'actuations': [14, 21, 44, 47], 'conflict_call': 0}, ['gap-out', 4]), ({'min_green': 12, 'gap': 3, 'max_green': 5, 'actuations': [1], 'conflict_call': 2}, ['max-out', 7]), ({'min_green': 6, 'gap': 2, 'max_green': 15, 'actuations': [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38], 'conflict_call': -3}, ['max-out', 15]), ({'min_green': 10, 'gap': 3, 'max_green': 39, 'actuations': [1, 2, 3, 4, 5, 8, 9, 11, 13, 15, 16, 17, 20, 21, 23, 29, 31, 32, 35, 36, 37, 42, 44, 45, 47, 48, 52, 55, 56, 59], 'conflict_call': 12}, ['gap-out', 26]), ({'min_green': 9, 'gap': 4, 'max_green': 29, 'actuations': [2, 4, 7, 17, 23, 25, 27, 36, 37, 45, 50], 'conflict_call': None}, ['rest', 11]), ({'min_green': 5, 'gap': 3, 'max_green': 20, 'actuations': [1, 4, 7, 10, 13], 'conflict_call': 2}, ['gap-out', 16]), ({'min_green': 8, 'gap': 2, 'max_green': 31, 'actuations': [2, 11, 12, 14, 15, 27, 37, 41, 46, 49], 'conflict_call': None}, ['rest', 8])]]
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 fixtureActualExpectedOutcome
timing oracle 0['max-out', 15]['max-out', 15]Passed
timing oracle 1['gap-out', 20]['gap-out', 20]Passed
timing oracle 2['gap-out', 11]['gap-out', 9]Failed
timing oracle 3['gap-out', 21]['gap-out', 21]Passed
timing oracle 4['gap-out', 16]['gap-out', 16]Passed
timing oracle 5['gap-out', 21]['gap-out', 21]Passed
timing oracle 6['rest', 7]['rest', 4]Failed
timing oracle 7['gap-out', 31]['gap-out', 31]Passed

SHA-256 / 8cd1f4a389542c7b8b66cba24cc3ffc0ca356e259482fb18cd7bcc0c2680dbec

3 / The verified repair

Exit 0
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(x):
    m, p, M = x['min_green'], x['gap'], x['max_green']
    exp = 0
    for a in sorted(x['actuations']):
        if a > exp and a > m:
            break
        exp = max(exp, a + p)
    gap_end = max(m, exp)
    tc = x['conflict_call']
    if tc is None:
        return ['rest', gap_end]
    tc = max(tc, 0)
    max_end = tc + M
    if gap_end <= max_end:
        return ['gap-out', max(gap_end, tc)]
    return ['max-out', max_end]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[({'min_green': 6, 'gap': 2, 'max_green': 15, 'actuations': [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38], 'conflict_call': -3}, ['max-out', 15]), ({'min_green': 8, 'gap': 3, 'max_green': 30, 'actuations': [2, 6], 'conflict_call': 20}, ['gap-out', 20]), ({'min_green': 9, 'gap': 2, 'max_green': 27, 'actuations': [2, 4, 6, 12, 13, 19, 22, 25, 39, 42], 'conflict_call': 8}, ['gap-out', 9]), ({'min_green': 9, 'gap': 2, 'max_green': 28, 'actuations': [1, 6, 8, 12, 14, 16, 18, 19, 21, 22, 24, 33, 34, 37, 40, 47, 50, 52, 58], 'conflict_call': 21}, ['gap-out', 21]), ({'min_green': 5, 'gap': 3, 'max_green': 20, 'actuations': [1, 4, 7, 10, 13], 'conflict_call': 2}, ['gap-out', 16]), ({'min_green': 8, 'gap': 3, 'max_green': 34, 'actuations': [25, 15, 18, 8, 49, 45, 14, 40, 51, 13, 33, 42, 36, 11, 58, 16, 10, 55, 3], 'conflict_call': -1}, ['gap-out', 21]), ({'min_green': 4, 'gap': 3, 'max_green': 27, 'actuations': [0, 10, 18, 20, 23, 25, 36, 39, 40, 50, 54, 58], 'conflict_call': None}, ['rest', 4]), ({'min_green': 4, 'gap': 5, 'max_green': 24, 'actuations': [4, 18, 35, 45, 48, 49], 'conflict_call': 31}, ['gap-out', 31])], [({'min_green': 6, 'gap': 5, 'max_green': 32, 'actuations': [2, 5, 6, 7, 8, 11, 12, 15, 16, 17, 19, 21, 23, 26, 27, 28, 29, 32, 35, 37, 42, 44, 45, 47, 49, 50, 52, 56, 57, 59], 'conflict_call': 25}, ['max-out', 57]), ({'min_green': 5, 'gap': 4, 'max_green': 23, 'actuations': [0, 2, 4, 16, 19, 21, 22, 24, 28, 40, 44, 45, 46, 54, 55, 57, 58], 'conflict_call': None}, ['rest', 8]), ({'min_green': 5, 'gap': 3, 'max_green': 10, 'actuations': [0, 3, 6, 9, 12], 'conflict_call': 5}, ['gap-out', 15]), ({'min_green': 7, 'gap': 4, 'max_green': 21, 'actuations': [3, 6, 8, 9, 11, 12, 15, 17, 19, 21, 23, 25, 28, 33, 34, 35, 39, 47, 52, 54, 56, 58, 59], 'conflict_call': 7}, ['max-out', 28]), ({'min_green': 6, 'gap': 2, 'max_green': 12, 'actuations': [1, 3, 5, 7, 9, 11, 13], 'conflict_call': 3}, ['gap-out', 15]), ({'min_green': 4, 'gap': 4, 'max_green': 15, 'actuations': [1, 2, 4, 6, 11, 13, 15, 19, 20, 22, 23, 26, 27, 37, 41, 44, 47, 48, 50, 52, 53, 54, 56, 58, 59], 'conflict_call': 26}, ['gap-out', 26]), ({'min_green': 12, 'gap': 3, 'max_green': 5, 'actuations': [1], 'conflict_call': 2}, ['max-out', 7]), ({'min_green': 8, 'gap': 5, 'max_green': 16, 'actuations': [2, 17, 23, 41, 50, 54, 57, 59], 'conflict_call': -2}, ['gap-out', 8])], [({'min_green': 5, 'gap': 3, 'max_green': 20, 'actuations': [1, 4, 7, 10, 13], 'conflict_call': 2}, ['gap-out', 16]), ({'min_green': 6, 'gap': 2, 'max_green': 29, 'actuations': [0, 1, 2, 3, 7, 8, 9, 10, 11, 12, 16, 17, 19, 24, 27, 29, 32, 34, 36, 40, 41, 42, 43, 45, 46, 47, 48, 49, 50, 53, 56, 58, 59], 'conflict_call': -3}, ['gap-out', 6]), ({'min_green': 4, 'gap': 5, 'max_green': 22, 'actuations': [1, 2, 8, 11, 18, 20, 24, 26, 35, 37, 39, 45, 47, 50, 51, 54, 55, 56, 57, 59], 'conflict_call': 31}, ['gap-out', 31]), ({'min_green': 7, 'gap': 5, 'max_green': 42, 'actuations': [1, 3, 5, 8, 10, 29, 33, 38, 42, 44, 50, 53, 55], 'conflict_call': -5}, ['gap-out', 15]), ({'min_green': 6, 'gap': 2, 'max_green': 12, 'actuations': [1, 3, 5, 7, 9, 11, 13], 'conflict_call': 3}, ['gap-out', 15]), ({'min_green': 7, 'gap': 4, 'max_green': 34, 'actuations': [49, 44, 18, 9, 59, 20, 16, 5, 26, 24, 37, 54, 32, 3, 27, 6, 15, 53, 28, 57, 52, 47, 46, 19, 38, 51, 58, 23, 40, 30], 'conflict_call': 24}, ['gap-out', 24]), ({'min_green': 5, 'gap': 5, 'max_green': 30, 'actuations': [3, 12, 14, 28, 29, 34, 37, 42, 44, 45, 48, 52, 54, 56, 59], 'conflict_call': None}, ['rest', 8]), ({'min_green': 12, 'gap': 3, 'max_green': 5, 'actuations': [1], 'conflict_call': 2}, ['max-out', 7])], [({'min_green': 10, 'gap': 2, 'max_green': 15, 'actuations': [2, 5, 6, 8, 9, 14, 15, 17, 18, 22, 25, 26, 30, 31, 33, 36, 40, 42, 50], 'conflict_call': 6}, ['gap-out', 11]), ({'min_green': 12, 'gap': 3, 'max_green': 5, 'actuations': [1], 'conflict_call': 2}, ['max-out', 7]), ({'min_green': 4, 'gap': 5, 'max_green': 25, 'actuations': [1, 9, 10, 12, 13, 14, 15, 16, 17, 21, 24, 26, 27, 29, 30, 36, 37, 38, 41, 42, 43, 46, 47, 48, 49, 51, 53, 55, 58], 'conflict_call': 10}, ['gap-out', 10]), ({'min_green': 7, 'gap': 3, 'max_green': 15, 'actuations': [54, 34, 26, 11, 41, 56, 5], 'conflict_call': 10}, ['gap-out', 10]), ({'min_green': 5, 'gap': 3, 'max_green': 20, 'actuations': [1, 4, 7, 10, 13], 'conflict_call': 2}, ['gap-out', 16]), ({'min_green': 6, 'gap': 2, 'max_green': 12, 'actuations': [1, 3, 5, 7, 9, 11, 13], 'conflict_call': 3}, ['gap-out', 15]), ({'min_green': 4, 'gap': 3, 'max_green': 19, 'actuations': [0, 4, 7, 8, 13, 15, 17, 18, 21, 22, 23, 26, 28, 29, 30, 33, 35, 37, 41, 43, 45, 46, 47, 49, 50, 53, 56, 57], 'conflict_call': 30}, ['gap-out', 30]), ({'min_green': 4, 'gap': 3, 'max_green': 45, 'actuations': [0, 4, 5, 6, 8, 16, 17, 22, 23, 27, 31, 39, 40, 42, 45, 47, 48, 52, 54, 58], 'conflict_call': 27}, ['gap-out', 27])], [({'min_green': 4, 'gap': 2, 'max_green': 32, 'actuations': [10, 16, 21, 24, 25, 27, 30, 34, 39, 42, 49, 50, 52, 53, 56], 'conflict_call': 9}, ['gap-out', 9]), ({'min_green': 4, 'gap': 3, 'max_green': 31, 'actuations': [14, 21, 44, 47], 'conflict_call': 0}, ['gap-out', 4]), ({'min_green': 12, 'gap': 3, 'max_green': 5, 'actuations': [1], 'conflict_call': 2}, ['max-out', 7]), ({'min_green': 6, 'gap': 2, 'max_green': 15, 'actuations': [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38], 'conflict_call': -3}, ['max-out', 15]), ({'min_green': 10, 'gap': 3, 'max_green': 39, 'actuations': [1, 2, 3, 4, 5, 8, 9, 11, 13, 15, 16, 17, 20, 21, 23, 29, 31, 32, 35, 36, 37, 42, 44, 45, 47, 48, 52, 55, 56, 59], 'conflict_call': 12}, ['gap-out', 26]), ({'min_green': 9, 'gap': 4, 'max_green': 29, 'actuations': [2, 4, 7, 17, 23, 25, 27, 36, 37, 45, 50], 'conflict_call': None}, ['rest', 11]), ({'min_green': 5, 'gap': 3, 'max_green': 20, 'actuations': [1, 4, 7, 10, 13], 'conflict_call': 2}, ['gap-out', 16]), ({'min_green': 8, 'gap': 2, 'max_green': 31, 'actuations': [2, 11, 12, 14, 15, 27, 37, 41, 46, 49], 'conflict_call': None}, ['rest', 8])]]
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 fixtureActualExpectedOutcome
timing oracle 0['max-out', 15]['max-out', 15]Passed
timing oracle 1['gap-out', 20]['gap-out', 20]Passed
timing oracle 2['gap-out', 9]['gap-out', 9]Passed
timing oracle 3['gap-out', 21]['gap-out', 21]Passed
timing oracle 4['gap-out', 16]['gap-out', 16]Passed
timing oracle 5['gap-out', 21]['gap-out', 21]Passed
timing oracle 6['rest', 4]['rest', 4]Passed
timing oracle 7['gap-out', 31]['gap-out', 31]Passed

SHA-256 / ad9f72e29064931bcb1159575abefe659ae3736a0793c6ecf7b48bf6a7a9a03e

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 2026-09-29T14:47:57.898214+00:00.

Case digest / b76c9b1e047ca2f09773bdd56cdd2c34cc8cb14ff7ed279a717a62e9f3c62561