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FA-68121 / Traffic signal timing plans / Open access

Dual-ring barrier sequencing: lead-lag is keyed on the second phase of the pair · case 01

Dual-ring barrier sequencing returns a wrong result when lead-lag is keyed on the second phase of the pair.

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

ROOT CAUSE

The lag test inspects the second phase, so configured lagging phases keep their default order.

THE FAILURE

The lag test inspects the second phase, so configured lagging phases keep their default order.

Unsuccessful approach: Checking either phase only on the left side ignores lag settings on the right of the barrier.

Case contract

Input {ring1: [[1,d],[2,d],[3,d],[4,d]], ring2: [[5,d],[6,d],[7,d],[8,d]] with durations including clearance, calls, lag}. Phases 1-2/5-6 are left of the barrier and 3-4/7-8 right of it. On each side both rings start together at the barrier; if the first phase of a ring's pair is in lag the pair is swapped. Phases without calls are skipped and take no time. Both rings cross a barrier together when the slower ring finishes. Return {starts: sorted [phase, start], cycle}.

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):
    calls = set(x['calls'])
    lag = set(x['lag'])
    t0 = 0
    starts = []
    for side in (0, 1):
        ends = []
        for ring in (x['ring1'], x['ring2']):
            pair = ring[2 * side:2 * side + 2]
            if pair[1][0] in lag:
                pair = [pair[1], pair[0]]
            t = t0
            for ph, dur in pair:
                if ph in calls:
                    starts.append([ph, t])
                    t += dur
            ends.append(t)
        t0 = max(ends)
    return {'starts': sorted(starts), 'cycle': t0}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[({'ring1': [[1, 29], [2, 20], [3, 11], [4, 24]], 'ring2': [[5, 27], [6, 10], [7, 13], [8, 10]], 'calls': [1, 2, 3, 4, 6, 7], 'lag': [5]}, {'starts': [[1, 0], [2, 29], [3, 49], [4, 60], [6, 0], [7, 49]], 'cycle': 84}), ({'ring1': [[1, 34], [2, 24], [3, 27], [4, 40]], 'ring2': [[5, 32], [6, 23], [7, 20], [8, 25]], 'calls': [2, 4, 5, 6, 8], 'lag': [1, 6, 7]}, {'starts': [[2, 0], [4, 55], [5, 0], [6, 32], [8, 55]], 'cycle': 95}), ({'ring1': [[1, 12], [2, 30], [3, 10], [4, 25]], 'ring2': [[5, 15], [6, 20], [7, 12], [8, 30]], 'calls': [1, 2, 3, 4, 5, 6, 7, 8], 'lag': [1]}, {'starts': [[1, 30], [2, 0], [3, 42], [4, 52], [5, 0], [6, 15], [7, 42], [8, 54]], 'cycle': 84}), ({'ring1': [[1, 12], [2, 30], [3, 10], [4, 25]], 'ring2': [[5, 15], [6, 20], [7, 12], [8, 30]], 'calls': [2, 4, 6, 7, 8], 'lag': []}, {'starts': [[2, 0], [4, 30], [6, 0], [7, 30], [8, 42]], 'cycle': 72}), ({'ring1': [[1, 14], [2, 11], [3, 27], [4, 39]], 'ring2': [[5, 34], [6, 26], [7, 10], [8, 39]], 'calls': [1, 2, 4, 5, 6, 7, 8], 'lag': [3, 7, 8]}, {'starts': [[1, 0], [2, 14], [4, 60], [5, 0], [6, 34], [7, 99], [8, 60]], 'cycle': 109}), ({'ring1': [[1, 31], [2, 8], [3, 38], [4, 22]], 'ring2': [[5, 32], [6, 9], [7, 12], [8, 36]], 'calls': [1, 2, 3, 4, 5, 6, 7, 8], 'lag': [1, 4]}, {'starts': [[1, 8], [2, 0], [3, 41], [4, 79], [5, 0], [6, 32], [7, 41], [8, 53]], 'cycle': 101}), ({'ring1': [[1, 30], [2, 18], [3, 13], [4, 16]], 'ring2': [[5, 8], [6, 17], [7, 18], [8, 12]], 'calls': [3, 4, 6, 7, 8], 'lag': [1, 6]}, {'starts': [[3, 17], [4, 30], [6, 0], [7, 17], [8, 35]], 'cycle': 47}), ({'ring1': [[1, 13], [2, 29], [3, 19], [4, 40]], 'ring2': [[5, 20], [6, 14], [7, 40], [8, 21]], 'calls': [1, 2, 3, 4, 6, 7, 8], 'lag': [1, 5, 6]}, {'starts': [[1, 29], [2, 0], [3, 42], [4, 61], [6, 0], [7, 42], [8, 82]], 'cycle': 103})], [({'ring1': [[1, 40], [2, 36], [3, 35], [4, 14]], 'ring2': [[5, 13], [6, 30], [7, 27], [8, 28]], 'calls': [1, 2, 3, 4, 5, 6, 7, 8], 'lag': [1, 2, 4, 5]}, {'starts': [[1, 36], [2, 0], [3, 76], [4, 111], [5, 30], [6, 0], [7, 76], [8, 103]], 'cycle': 131}), ({'ring1': [[1, 19], [2, 30], [3, 26], [4, 8]], 'ring2': [[5, 32], [6, 24], [7, 25], [8, 14]], 'calls': [1, 2, 3, 6, 7], 'lag': [3]}, {'starts': [[1, 0], [2, 19], [3, 49], [6, 0], [7, 49]], 'cycle': 75}), ({'ring1': [[1, 12], [2, 30], [3, 10], [4, 25]], 'ring2': [[5, 15], [6, 20], [7, 12], [8, 30]], 'calls': [2, 4, 6, 7, 8], 'lag': []}, {'starts': [[2, 0], [4, 30], [6, 0], [7, 30], [8, 42]], 'cycle': 72}), ({'ring1': [[1, 12], [2, 30], [3, 10], [4, 25]], 'ring2': [[5, 15], [6, 20], [7, 12], [8, 30]], 'calls': [1, 2, 3, 4, 5, 6, 7, 8], 'lag': [1]}, {'starts': [[1, 30], [2, 0], [3, 42], [4, 52], [5, 0], [6, 15], [7, 42], [8, 54]], 'cycle': 84}), ({'ring1': [[1, 35], [2, 14], [3, 39], [4, 40]], 'ring2': [[5, 26], [6, 37], [7, 22], [8, 14]], 'calls': [1, 2, 3, 4, 5, 8], 'lag': [7]}, {'starts': [[1, 0], [2, 35], [3, 49], [4, 88], [5, 0], [8, 49]], 'cycle': 128}), ({'ring1': [[1, 15], [2, 10], [3, 17], [4, 24]], 'ring2': [[5, 20], [6, 38], [7, 19], [8, 34]], 'calls': [2, 5, 6, 7, 8], 'lag': [2, 4, 5, 7, 8]}, {'starts': [[2, 0], [5, 38], [6, 0], [7, 92], [8, 58]], 'cycle': 111}), ({'ring1': [[1, 28], [2, 40], [3, 10], [4, 17]], 'ring2': [[5, 35], [6, 17], [7, 26], [8, 38]], 'calls': [1, 3, 5, 7, 8], 'lag': [1]}, {'starts': [[1, 0], [3, 35], [5, 0], [7, 35], [8, 61]], 'cycle': 99}), ({'ring1': [[1, 21], [2, 21], [3, 33], [4, 12]], 'ring2': [[5, 40], [6, 10], [7, 11], [8, 26]], 'calls': [1, 3, 4, 5, 6, 7, 8], 'lag': [3, 5]}, {'starts': [[1, 0], [3, 62], [4, 50], [5, 10], [6, 0], [7, 50], [8, 61]], 'cycle': 95})], [({'ring1': [[1, 21], [2, 14], [3, 14], [4, 24]], 'ring2': [[5, 15], [6, 12], [7, 13], [8, 16]], 'calls': [1, 2, 3, 5, 6, 7, 8], 'lag': [3, 6]}, {'starts': [[1, 0], [2, 21], [3, 35], [5, 0], [6, 15], [7, 35], [8, 48]], 'cycle': 64}), ({'ring1': [[1, 32], [2, 32], [3, 26], [4, 19]], 'ring2': [[5, 31], [6, 11], [7, 36], [8, 12]], 'calls': [1, 2, 3, 4, 5, 8], 'lag': [1, 7]}, {'starts': [[1, 32], [2, 0], [3, 64], [4, 90], [5, 0], [8, 64]], 'cycle': 109}), ({'ring1': [[1, 18], [2, 16], [3, 17], [4, 37]], 'ring2': [[5, 27], [6, 13], [7, 20], [8, 14]], 'calls': [1, 3, 5, 8], 'lag': [1, 2, 3, 5]}, {'starts': [[1, 0], [3, 27], [5, 0], [8, 27]], 'cycle': 44}), ({'ring1': [[1, 17], [2, 35], [3, 31], [4, 27]], 'ring2': [[5, 38], [6, 35], [7, 13], [8, 38]], 'calls': [2, 3, 4, 6, 7], 'lag': [7]}, {'starts': [[2, 0], [3, 35], [4, 66], [6, 0], [7, 35]], 'cycle': 93}), ({'ring1': [[1, 9], [2, 27], [3, 15], [4, 27]], 'ring2': [[5, 32], [6, 8], [7, 8], [8, 38]], 'calls': [2, 3, 4, 6, 7, 8], 'lag': [2]}, {'starts': [[2, 0], [3, 27], [4, 42], [6, 0], [7, 27], [8, 35]], 'cycle': 73}), ({'ring1': [[1, 21], [2, 12], [3, 28], [4, 27]], 'ring2': [[5, 20], [6, 25], [7, 40], [8, 40]], 'calls': [2, 3, 5, 6, 7, 8], 'lag': [4, 6, 7]}, {'starts': [[2, 0], [3, 45], [5, 0], [6, 20], [7, 85], [8, 45]], 'cycle': 125}), ({'ring1': [[1, 12], [2, 30], [3, 10], [4, 25]], 'ring2': [[5, 15], [6, 20], [7, 12], [8, 30]], 'calls': [2, 4, 6, 7, 8], 'lag': []}, {'starts': [[2, 0], [4, 30], [6, 0], [7, 30], [8, 42]], 'cycle': 72}), ({'ring1': [[1, 12], [2, 30], [3, 10], [4, 25]], 'ring2': [[5, 15], [6, 20], [7, 12], [8, 30]], 'calls': [1, 2, 3, 4, 5, 6, 7, 8], 'lag': [1]}, {'starts': [[1, 30], [2, 0], [3, 42], [4, 52], [5, 0], [6, 15], [7, 42], [8, 54]], 'cycle': 84})], [({'ring1': [[1, 40], [2, 32], [3, 40], [4, 35]], 'ring2': [[5, 28], [6, 35], [7, 36], [8, 38]], 'calls': [2, 3, 4, 8], 'lag': [1, 4]}, {'starts': [[2, 0], [3, 32], [4, 72], [8, 32]], 'cycle': 107}), ({'ring1': [[1, 12], [2, 30], [3, 10], [4, 25]], 'ring2': [[5, 15], [6, 20], [7, 12], [8, 30]], 'calls': [2, 4, 6, 7, 8], 'lag': []}, {'starts': [[2, 0], [4, 30], [6, 0], [7, 30], [8, 42]], 'cycle': 72}), ({'ring1': [[1, 13], [2, 29], [3, 36], [4, 38]], 'ring2': [[5, 27], [6, 17], [7, 40], [8, 37]], 'calls': [2, 3, 4, 5, 6, 7, 8], 'lag': [1, 2, 5, 8]}, {'starts': [[2, 0], [3, 44], [4, 80], [5, 17], [6, 0], [7, 44], [8, 84]], 'cycle': 121}), ({'ring1': [[1, 32], [2, 27], [3, 14], [4, 40]], 'ring2': [[5, 23], [6, 10], [7, 15], [8, 25]], 'calls': [2, 5, 6, 7, 8], 'lag': [2, 3, 5, 6, 7]}, {'starts': [[2, 0], [5, 10], [6, 0], [7, 58], [8, 33]], 'cycle': 73}), ({'ring1': [[1, 12], [2, 30], [3, 10], [4, 25]], 'ring2': [[5, 15], [6, 20], [7, 12], [8, 30]], 'calls': [1, 2, 3, 4, 5, 6, 7, 8], 'lag': [1]}, {'starts': [[1, 30], [2, 0], [3, 42], [4, 52], [5, 0], [6, 15], [7, 42], [8, 54]], 'cycle': 84}), ({'ring1': [[1, 12], [2, 15], [3, 22], [4, 16]], 'ring2': [[5, 22], [6, 13], [7, 27], [8, 13]], 'calls': [1, 5, 6, 8], 'lag': []}, {'starts': [[1, 0], [5, 0], [6, 22], [8, 35]], 'cycle': 48}), ({'ring1': [[1, 25], [2, 35], [3, 33], [4, 17]], 'ring2': [[5, 26], [6, 22], [7, 37], [8, 17]], 'calls': [2, 3, 4, 7], 'lag': [3, 4, 7]}, {'starts': [[2, 0], [3, 52], [4, 35], [7, 35]], 'cycle': 85}), ({'ring1': [[1, 38], [2, 29], [3, 12], [4, 27]], 'ring2': [[5, 10], [6, 27], [7, 27], [8, 30]], 'calls': [2, 3, 4, 5, 7], 'lag': []}, {'starts': [[2, 0], [3, 29], [4, 41], [5, 0], [7, 29]], 'cycle': 68})], [({'ring1': [[1, 12], [2, 35], [3, 13], [4, 35]], 'ring2': [[5, 24], [6, 14], [7, 30], [8, 13]], 'calls': [1, 2, 3, 4, 6, 7, 8], 'lag': [1, 2, 3, 5, 8]}, {'starts': [[1, 35], [2, 0], [3, 82], [4, 47], [6, 0], [7, 47], [8, 77]], 'cycle': 95}), ({'ring1': [[1, 8], [2, 22], [3, 23], [4, 38]], 'ring2': [[5, 16], [6, 33], [7, 19], [8, 20]], 'calls': [1, 2, 3, 5, 6], 'lag': [1]}, {'starts': [[1, 22], [2, 0], [3, 49], [5, 0], [6, 16]], 'cycle': 72}), ({'ring1': [[1, 37], [2, 39], [3, 21], [4, 29]], 'ring2': [[5, 19], [6, 18], [7, 40], [8, 26]], 'calls': [1, 2, 5, 6, 7, 8], 'lag': [3]}, {'starts': [[1, 0], [2, 37], [5, 0], [6, 19], [7, 76], [8, 116]], 'cycle': 142}), ({'ring1': [[1, 12], [2, 30], [3, 10], [4, 25]], 'ring2': [[5, 15], [6, 20], [7, 12], [8, 30]], 'calls': [1, 2, 3, 4, 5, 6, 7, 8], 'lag': [1]}, {'starts': [[1, 30], [2, 0], [3, 42], [4, 52], [5, 0], [6, 15], [7, 42], [8, 54]], 'cycle': 84}), ({'ring1': [[1, 18], [2, 17], [3, 14], [4, 27]], 'ring2': [[5, 19], [6, 11], [7, 39], [8, 22]], 'calls': [1, 2, 3, 6, 8], 'lag': [3, 7]}, {'starts': [[1, 0], [2, 18], [3, 35], [6, 0], [8, 35]], 'cycle': 57}), ({'ring1': [[1, 12], [2, 30], [3, 10], [4, 25]], 'ring2': [[5, 15], [6, 20], [7, 12], [8, 30]], 'calls': [2, 4, 6, 7, 8], 'lag': []}, {'starts': [[2, 0], [4, 30], [6, 0], [7, 30], [8, 42]], 'cycle': 72}), ({'ring1': [[1, 26], [2, 20], [3, 13], [4, 19]], 'ring2': [[5, 14], [6, 19], [7, 22], [8, 13]], 'calls': [3, 4, 5, 7], 'lag': [1, 4, 5]}, {'starts': [[3, 14], [4, 27], [5, 0], [7, 14]], 'cycle': 46}), ({'ring1': [[1, 8], [2, 18], [3, 20], [4, 27]], 'ring2': [[5, 16], [6, 16], [7, 28], [8, 16]], 'calls': [1, 2, 3, 4, 5, 6, 7], 'lag': [2]}, {'starts': [[1, 0], [2, 8], [3, 32], [4, 52], [5, 0], [6, 16], [7, 32]], 'cycle': 79})]]
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{'cycle': 84, 'starts': [[1, 0], [2, 29], [3, 49], [4, 60], [6, 0], [7, 49]]}{'cycle': 84, 'starts': [[1, 0], [2, 29], [3, 49], [4, 60], [6, 0], [7, 49]]}Passed
timing oracle 1{'cycle': 95, 'starts': [[2, 0], [4, 55], [5, 23], [6, 0], [8, 55]]}{'cycle': 95, 'starts': [[2, 0], [4, 55], [5, 0], [6, 32], [8, 55]]}Failed
timing oracle 2{'cycle': 84, 'starts': [[1, 0], [2, 12], [3, 42], [4, 52], [5, 0], [6, 15], [7, 42], [8, 54]]}{'cycle': 84, 'starts': [[1, 30], [2, 0], [3, 42], [4, 52], [5, 0], [6, 15], [7, 42], [8, 54]]}Failed
timing oracle 3{'cycle': 72, 'starts': [[2, 0], [4, 30], [6, 0], [7, 30], [8, 42]]}{'cycle': 72, 'starts': [[2, 0], [4, 30], [6, 0], [7, 30], [8, 42]]}Passed
timing oracle 4{'cycle': 109, 'starts': [[1, 0], [2, 14], [4, 60], [5, 0], [6, 34], [7, 99], [8, 60]]}{'cycle': 109, 'starts': [[1, 0], [2, 14], [4, 60], [5, 0], [6, 34], [7, 99], [8, 60]]}Passed
timing oracle 5{'cycle': 101, 'starts': [[1, 0], [2, 31], [3, 63], [4, 41], [5, 0], [6, 32], [7, 41], [8, 53]]}{'cycle': 101, 'starts': [[1, 8], [2, 0], [3, 41], [4, 79], [5, 0], [6, 32], [7, 41], [8, 53]]}Failed
timing oracle 6{'cycle': 47, 'starts': [[3, 17], [4, 30], [6, 0], [7, 17], [8, 35]]}{'cycle': 47, 'starts': [[3, 17], [4, 30], [6, 0], [7, 17], [8, 35]]}Passed
timing oracle 7{'cycle': 103, 'starts': [[1, 0], [2, 13], [3, 42], [4, 61], [6, 0], [7, 42], [8, 82]]}{'cycle': 103, 'starts': [[1, 29], [2, 0], [3, 42], [4, 61], [6, 0], [7, 42], [8, 82]]}Failed

SHA-256 / da007bae0b1da42bb77132e542367a1b691b95388f70cf56bece2c5b8e55777f

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(x):
    calls = set(x['calls'])
    lag = set(x['lag'])
    t0 = 0
    starts = []
    for side in (0, 1):
        ends = []
        for ring in (x['ring1'], x['ring2']):
            pair = ring[2 * side:2 * side + 2]
            if any(p in lag for p, _ in pair) and side == 0:
                pair = [pair[1], pair[0]]
            t = t0
            for ph, dur in pair:
                if ph in calls:
                    starts.append([ph, t])
                    t += dur
            ends.append(t)
        t0 = max(ends)
    return {'starts': sorted(starts), 'cycle': t0}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[({'ring1': [[1, 29], [2, 20], [3, 11], [4, 24]], 'ring2': [[5, 27], [6, 10], [7, 13], [8, 10]], 'calls': [1, 2, 3, 4, 6, 7], 'lag': [5]}, {'starts': [[1, 0], [2, 29], [3, 49], [4, 60], [6, 0], [7, 49]], 'cycle': 84}), ({'ring1': [[1, 34], [2, 24], [3, 27], [4, 40]], 'ring2': [[5, 32], [6, 23], [7, 20], [8, 25]], 'calls': [2, 4, 5, 6, 8], 'lag': [1, 6, 7]}, {'starts': [[2, 0], [4, 55], [5, 0], [6, 32], [8, 55]], 'cycle': 95}), ({'ring1': [[1, 12], [2, 30], [3, 10], [4, 25]], 'ring2': [[5, 15], [6, 20], [7, 12], [8, 30]], 'calls': [1, 2, 3, 4, 5, 6, 7, 8], 'lag': [1]}, {'starts': [[1, 30], [2, 0], [3, 42], [4, 52], [5, 0], [6, 15], [7, 42], [8, 54]], 'cycle': 84}), ({'ring1': [[1, 12], [2, 30], [3, 10], [4, 25]], 'ring2': [[5, 15], [6, 20], [7, 12], [8, 30]], 'calls': [2, 4, 6, 7, 8], 'lag': []}, {'starts': [[2, 0], [4, 30], [6, 0], [7, 30], [8, 42]], 'cycle': 72}), ({'ring1': [[1, 14], [2, 11], [3, 27], [4, 39]], 'ring2': [[5, 34], [6, 26], [7, 10], [8, 39]], 'calls': [1, 2, 4, 5, 6, 7, 8], 'lag': [3, 7, 8]}, {'starts': [[1, 0], [2, 14], [4, 60], [5, 0], [6, 34], [7, 99], [8, 60]], 'cycle': 109}), ({'ring1': [[1, 31], [2, 8], [3, 38], [4, 22]], 'ring2': [[5, 32], [6, 9], [7, 12], [8, 36]], 'calls': [1, 2, 3, 4, 5, 6, 7, 8], 'lag': [1, 4]}, {'starts': [[1, 8], [2, 0], [3, 41], [4, 79], [5, 0], [6, 32], [7, 41], [8, 53]], 'cycle': 101}), ({'ring1': [[1, 30], [2, 18], [3, 13], [4, 16]], 'ring2': [[5, 8], [6, 17], [7, 18], [8, 12]], 'calls': [3, 4, 6, 7, 8], 'lag': [1, 6]}, {'starts': [[3, 17], [4, 30], [6, 0], [7, 17], [8, 35]], 'cycle': 47}), ({'ring1': [[1, 13], [2, 29], [3, 19], [4, 40]], 'ring2': [[5, 20], [6, 14], [7, 40], [8, 21]], 'calls': [1, 2, 3, 4, 6, 7, 8], 'lag': [1, 5, 6]}, {'starts': [[1, 29], [2, 0], [3, 42], [4, 61], [6, 0], [7, 42], [8, 82]], 'cycle': 103})], [({'ring1': [[1, 40], [2, 36], [3, 35], [4, 14]], 'ring2': [[5, 13], [6, 30], [7, 27], [8, 28]], 'calls': [1, 2, 3, 4, 5, 6, 7, 8], 'lag': [1, 2, 4, 5]}, {'starts': [[1, 36], [2, 0], [3, 76], [4, 111], [5, 30], [6, 0], [7, 76], [8, 103]], 'cycle': 131}), ({'ring1': [[1, 19], [2, 30], [3, 26], [4, 8]], 'ring2': [[5, 32], [6, 24], [7, 25], [8, 14]], 'calls': [1, 2, 3, 6, 7], 'lag': [3]}, {'starts': [[1, 0], [2, 19], [3, 49], [6, 0], [7, 49]], 'cycle': 75}), ({'ring1': [[1, 12], [2, 30], [3, 10], [4, 25]], 'ring2': [[5, 15], [6, 20], [7, 12], [8, 30]], 'calls': [2, 4, 6, 7, 8], 'lag': []}, {'starts': [[2, 0], [4, 30], [6, 0], [7, 30], [8, 42]], 'cycle': 72}), ({'ring1': [[1, 12], [2, 30], [3, 10], [4, 25]], 'ring2': [[5, 15], [6, 20], [7, 12], [8, 30]], 'calls': [1, 2, 3, 4, 5, 6, 7, 8], 'lag': [1]}, {'starts': [[1, 30], [2, 0], [3, 42], [4, 52], [5, 0], [6, 15], [7, 42], [8, 54]], 'cycle': 84}), ({'ring1': [[1, 35], [2, 14], [3, 39], [4, 40]], 'ring2': [[5, 26], [6, 37], [7, 22], [8, 14]], 'calls': [1, 2, 3, 4, 5, 8], 'lag': [7]}, {'starts': [[1, 0], [2, 35], [3, 49], [4, 88], [5, 0], [8, 49]], 'cycle': 128}), ({'ring1': [[1, 15], [2, 10], [3, 17], [4, 24]], 'ring2': [[5, 20], [6, 38], [7, 19], [8, 34]], 'calls': [2, 5, 6, 7, 8], 'lag': [2, 4, 5, 7, 8]}, {'starts': [[2, 0], [5, 38], [6, 0], [7, 92], [8, 58]], 'cycle': 111}), ({'ring1': [[1, 28], [2, 40], [3, 10], [4, 17]], 'ring2': [[5, 35], [6, 17], [7, 26], [8, 38]], 'calls': [1, 3, 5, 7, 8], 'lag': [1]}, {'starts': [[1, 0], [3, 35], [5, 0], [7, 35], [8, 61]], 'cycle': 99}), ({'ring1': [[1, 21], [2, 21], [3, 33], [4, 12]], 'ring2': [[5, 40], [6, 10], [7, 11], [8, 26]], 'calls': [1, 3, 4, 5, 6, 7, 8], 'lag': [3, 5]}, {'starts': [[1, 0], [3, 62], [4, 50], [5, 10], [6, 0], [7, 50], [8, 61]], 'cycle': 95})], [({'ring1': [[1, 21], [2, 14], [3, 14], [4, 24]], 'ring2': [[5, 15], [6, 12], [7, 13], [8, 16]], 'calls': [1, 2, 3, 5, 6, 7, 8], 'lag': [3, 6]}, {'starts': [[1, 0], [2, 21], [3, 35], [5, 0], [6, 15], [7, 35], [8, 48]], 'cycle': 64}), ({'ring1': [[1, 32], [2, 32], [3, 26], [4, 19]], 'ring2': [[5, 31], [6, 11], [7, 36], [8, 12]], 'calls': [1, 2, 3, 4, 5, 8], 'lag': [1, 7]}, {'starts': [[1, 32], [2, 0], [3, 64], [4, 90], [5, 0], [8, 64]], 'cycle': 109}), ({'ring1': [[1, 18], [2, 16], [3, 17], [4, 37]], 'ring2': [[5, 27], [6, 13], [7, 20], [8, 14]], 'calls': [1, 3, 5, 8], 'lag': [1, 2, 3, 5]}, {'starts': [[1, 0], [3, 27], [5, 0], [8, 27]], 'cycle': 44}), ({'ring1': [[1, 17], [2, 35], [3, 31], [4, 27]], 'ring2': [[5, 38], [6, 35], [7, 13], [8, 38]], 'calls': [2, 3, 4, 6, 7], 'lag': [7]}, {'starts': [[2, 0], [3, 35], [4, 66], [6, 0], [7, 35]], 'cycle': 93}), ({'ring1': [[1, 9], [2, 27], [3, 15], [4, 27]], 'ring2': [[5, 32], [6, 8], [7, 8], [8, 38]], 'calls': [2, 3, 4, 6, 7, 8], 'lag': [2]}, {'starts': [[2, 0], [3, 27], [4, 42], [6, 0], [7, 27], [8, 35]], 'cycle': 73}), ({'ring1': [[1, 21], [2, 12], [3, 28], [4, 27]], 'ring2': [[5, 20], [6, 25], [7, 40], [8, 40]], 'calls': [2, 3, 5, 6, 7, 8], 'lag': [4, 6, 7]}, {'starts': [[2, 0], [3, 45], [5, 0], [6, 20], [7, 85], [8, 45]], 'cycle': 125}), ({'ring1': [[1, 12], [2, 30], [3, 10], [4, 25]], 'ring2': [[5, 15], [6, 20], [7, 12], [8, 30]], 'calls': [2, 4, 6, 7, 8], 'lag': []}, {'starts': [[2, 0], [4, 30], [6, 0], [7, 30], [8, 42]], 'cycle': 72}), ({'ring1': [[1, 12], [2, 30], [3, 10], [4, 25]], 'ring2': [[5, 15], [6, 20], [7, 12], [8, 30]], 'calls': [1, 2, 3, 4, 5, 6, 7, 8], 'lag': [1]}, {'starts': [[1, 30], [2, 0], [3, 42], [4, 52], [5, 0], [6, 15], [7, 42], [8, 54]], 'cycle': 84})], [({'ring1': [[1, 40], [2, 32], [3, 40], [4, 35]], 'ring2': [[5, 28], [6, 35], [7, 36], [8, 38]], 'calls': [2, 3, 4, 8], 'lag': [1, 4]}, {'starts': [[2, 0], [3, 32], [4, 72], [8, 32]], 'cycle': 107}), ({'ring1': [[1, 12], [2, 30], [3, 10], [4, 25]], 'ring2': [[5, 15], [6, 20], [7, 12], [8, 30]], 'calls': [2, 4, 6, 7, 8], 'lag': []}, {'starts': [[2, 0], [4, 30], [6, 0], [7, 30], [8, 42]], 'cycle': 72}), ({'ring1': [[1, 13], [2, 29], [3, 36], [4, 38]], 'ring2': [[5, 27], [6, 17], [7, 40], [8, 37]], 'calls': [2, 3, 4, 5, 6, 7, 8], 'lag': [1, 2, 5, 8]}, {'starts': [[2, 0], [3, 44], [4, 80], [5, 17], [6, 0], [7, 44], [8, 84]], 'cycle': 121}), ({'ring1': [[1, 32], [2, 27], [3, 14], [4, 40]], 'ring2': [[5, 23], [6, 10], [7, 15], [8, 25]], 'calls': [2, 5, 6, 7, 8], 'lag': [2, 3, 5, 6, 7]}, {'starts': [[2, 0], [5, 10], [6, 0], [7, 58], [8, 33]], 'cycle': 73}), ({'ring1': [[1, 12], [2, 30], [3, 10], [4, 25]], 'ring2': [[5, 15], [6, 20], [7, 12], [8, 30]], 'calls': [1, 2, 3, 4, 5, 6, 7, 8], 'lag': [1]}, {'starts': [[1, 30], [2, 0], [3, 42], [4, 52], [5, 0], [6, 15], [7, 42], [8, 54]], 'cycle': 84}), ({'ring1': [[1, 12], [2, 15], [3, 22], [4, 16]], 'ring2': [[5, 22], [6, 13], [7, 27], [8, 13]], 'calls': [1, 5, 6, 8], 'lag': []}, {'starts': [[1, 0], [5, 0], [6, 22], [8, 35]], 'cycle': 48}), ({'ring1': [[1, 25], [2, 35], [3, 33], [4, 17]], 'ring2': [[5, 26], [6, 22], [7, 37], [8, 17]], 'calls': [2, 3, 4, 7], 'lag': [3, 4, 7]}, {'starts': [[2, 0], [3, 52], [4, 35], [7, 35]], 'cycle': 85}), ({'ring1': [[1, 38], [2, 29], [3, 12], [4, 27]], 'ring2': [[5, 10], [6, 27], [7, 27], [8, 30]], 'calls': [2, 3, 4, 5, 7], 'lag': []}, {'starts': [[2, 0], [3, 29], [4, 41], [5, 0], [7, 29]], 'cycle': 68})], [({'ring1': [[1, 12], [2, 35], [3, 13], [4, 35]], 'ring2': [[5, 24], [6, 14], [7, 30], [8, 13]], 'calls': [1, 2, 3, 4, 6, 7, 8], 'lag': [1, 2, 3, 5, 8]}, {'starts': [[1, 35], [2, 0], [3, 82], [4, 47], [6, 0], [7, 47], [8, 77]], 'cycle': 95}), ({'ring1': [[1, 8], [2, 22], [3, 23], [4, 38]], 'ring2': [[5, 16], [6, 33], [7, 19], [8, 20]], 'calls': [1, 2, 3, 5, 6], 'lag': [1]}, {'starts': [[1, 22], [2, 0], [3, 49], [5, 0], [6, 16]], 'cycle': 72}), ({'ring1': [[1, 37], [2, 39], [3, 21], [4, 29]], 'ring2': [[5, 19], [6, 18], [7, 40], [8, 26]], 'calls': [1, 2, 5, 6, 7, 8], 'lag': [3]}, {'starts': [[1, 0], [2, 37], [5, 0], [6, 19], [7, 76], [8, 116]], 'cycle': 142}), ({'ring1': [[1, 12], [2, 30], [3, 10], [4, 25]], 'ring2': [[5, 15], [6, 20], [7, 12], [8, 30]], 'calls': [1, 2, 3, 4, 5, 6, 7, 8], 'lag': [1]}, {'starts': [[1, 30], [2, 0], [3, 42], [4, 52], [5, 0], [6, 15], [7, 42], [8, 54]], 'cycle': 84}), ({'ring1': [[1, 18], [2, 17], [3, 14], [4, 27]], 'ring2': [[5, 19], [6, 11], [7, 39], [8, 22]], 'calls': [1, 2, 3, 6, 8], 'lag': [3, 7]}, {'starts': [[1, 0], [2, 18], [3, 35], [6, 0], [8, 35]], 'cycle': 57}), ({'ring1': [[1, 12], [2, 30], [3, 10], [4, 25]], 'ring2': [[5, 15], [6, 20], [7, 12], [8, 30]], 'calls': [2, 4, 6, 7, 8], 'lag': []}, {'starts': [[2, 0], [4, 30], [6, 0], [7, 30], [8, 42]], 'cycle': 72}), ({'ring1': [[1, 26], [2, 20], [3, 13], [4, 19]], 'ring2': [[5, 14], [6, 19], [7, 22], [8, 13]], 'calls': [3, 4, 5, 7], 'lag': [1, 4, 5]}, {'starts': [[3, 14], [4, 27], [5, 0], [7, 14]], 'cycle': 46}), ({'ring1': [[1, 8], [2, 18], [3, 20], [4, 27]], 'ring2': [[5, 16], [6, 16], [7, 28], [8, 16]], 'calls': [1, 2, 3, 4, 5, 6, 7], 'lag': [2]}, {'starts': [[1, 0], [2, 8], [3, 32], [4, 52], [5, 0], [6, 16], [7, 32]], 'cycle': 79})]]
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{'cycle': 84, 'starts': [[1, 0], [2, 29], [3, 49], [4, 60], [6, 0], [7, 49]]}{'cycle': 84, 'starts': [[1, 0], [2, 29], [3, 49], [4, 60], [6, 0], [7, 49]]}Passed
timing oracle 1{'cycle': 95, 'starts': [[2, 0], [4, 55], [5, 23], [6, 0], [8, 55]]}{'cycle': 95, 'starts': [[2, 0], [4, 55], [5, 0], [6, 32], [8, 55]]}Failed
timing oracle 2{'cycle': 84, 'starts': [[1, 30], [2, 0], [3, 42], [4, 52], [5, 0], [6, 15], [7, 42], [8, 54]]}{'cycle': 84, 'starts': [[1, 30], [2, 0], [3, 42], [4, 52], [5, 0], [6, 15], [7, 42], [8, 54]]}Passed
timing oracle 3{'cycle': 72, 'starts': [[2, 0], [4, 30], [6, 0], [7, 30], [8, 42]]}{'cycle': 72, 'starts': [[2, 0], [4, 30], [6, 0], [7, 30], [8, 42]]}Passed
timing oracle 4{'cycle': 109, 'starts': [[1, 0], [2, 14], [4, 60], [5, 0], [6, 34], [7, 60], [8, 70]]}{'cycle': 109, 'starts': [[1, 0], [2, 14], [4, 60], [5, 0], [6, 34], [7, 99], [8, 60]]}Failed
timing oracle 5{'cycle': 101, 'starts': [[1, 8], [2, 0], [3, 41], [4, 79], [5, 0], [6, 32], [7, 41], [8, 53]]}{'cycle': 101, 'starts': [[1, 8], [2, 0], [3, 41], [4, 79], [5, 0], [6, 32], [7, 41], [8, 53]]}Passed
timing oracle 6{'cycle': 47, 'starts': [[3, 17], [4, 30], [6, 0], [7, 17], [8, 35]]}{'cycle': 47, 'starts': [[3, 17], [4, 30], [6, 0], [7, 17], [8, 35]]}Passed
timing oracle 7{'cycle': 103, 'starts': [[1, 29], [2, 0], [3, 42], [4, 61], [6, 0], [7, 42], [8, 82]]}{'cycle': 103, 'starts': [[1, 29], [2, 0], [3, 42], [4, 61], [6, 0], [7, 42], [8, 82]]}Passed

SHA-256 / e491b37705ca3fcbb3098c12cadd67bc1ae09985041137d7b3732c673c3b7e19

HELD IN THE MEMBER ARCHIVE

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

This mechanism has 8 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

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

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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 2026-09-29T14:47:59.187857+00:00.

Case digest / 597bf2c5345b8ffa1b4660abe95cf12b7b176a5da6502d1830ccf1846293138b