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FA-68051 / Traffic signal timing plans / Open access

Coordinated local cycle timer: split start accumulates green only · case 01

Coordinated local cycle timer returns a wrong result when split start accumulates green only.

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

ROOT CAUSE

Resetting the start to the previous split length places the third and later phases at the wrong local time.

VERIFIED REPAIR

Restore the split start accumulation rule so that the step reads `start += s`.

Unsuccessful approach: Accumulating only green time drops the clearance intervals from every later split start.

Case contract

Input {cycle, offset, master, splits: [[phase, split s]] in sequence starting with the coordinated phase, yellow, red, ref}. Splits must sum to the cycle, else 'bad-splits'. Local time = (master - offset) mod cycle, where the offset marks the start of coordinated green (ref 'begin') or the end of coordinated green (ref 'end'). Each split is green then yellow then all-red. Return [phase, interval, seconds remaining].

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']
    sp = x['splits']
    y, r = x['yellow'], x['red']
    if sum(s for _, s in sp) != C:
        return 'bad-splits'
    lc = (x['master'] - x['offset']) % C
    if x['ref'] == 'end':
        lc = (lc + sp[0][1] - y - r) % C
    start = 0
    for ph, s in sp:
        ge = start + s - y - r
        if lc < ge:
            return [ph, 'green', ge - lc]
        if lc < ge + y:
            return [ph, 'yellow', ge + y - lc]
        if lc < start + s:
            return [ph, 'red', start + s - lc]
        start = s
    return ['free', 'dark', 0]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[({'cycle': 80, 'offset': 70, 'master': 10, 'splits': [[2, 50], [4, 30]], 'yellow': 3, 'red': 2, 'ref': 'begin'}, [2, 'green', 25]), ({'cycle': 75, 'offset': 33, 'master': 335, 'splits': [[2, 35], [4, 40]], 'yellow': 4, 'red': 2, 'ref': 'begin'}, [2, 'green', 27]), ({'cycle': 58, 'offset': 7, 'master': 869, 'splits': [[2, 13], [4, 31], [6, 14]], 'yellow': 4, 'red': 2, 'ref': 'end'}, [6, 'red', 1]), ({'cycle': 90, 'offset': 30, 'master': 45, 'splits': [[2, 40], [4, 25], [6, 25]], 'yellow': 4, 'red': 1, 'ref': 'end'}, [4, 'green', 10]), ({'cycle': 100, 'offset': 5, 'master': 3, 'splits': [[2, 50], [4, 30], [8, 25]], 'yellow': 4, 'red': 2, 'ref': 'begin'}, 'bad-splits'), ({'cycle': 97, 'offset': 19, 'master': 312, 'splits': [[2, 36], [4, 31], [6, 35]], 'yellow': 4, 'red': 2, 'ref': 'begin'}, 'bad-splits'), ({'cycle': 104, 'offset': 12, 'master': 419, 'splits': [[2, 35], [4, 31], [6, 38]], 'yellow': 3, 'red': 2, 'ref': 'begin'}, [6, 'green', 4]), ({'cycle': 112, 'offset': 58, 'master': 105, 'splits': [[2, 36], [4, 16], [6, 28], [8, 32]], 'yellow': 3, 'red': 2, 'ref': 'end'}, [6, 'red', 2])], [({'cycle': 55, 'offset': 54, 'master': 609, 'splits': [[2, 33], [4, 22]], 'yellow': 4, 'red': 2, 'ref': 'begin'}, [2, 'green', 22]), ({'cycle': 101, 'offset': 40, 'master': 329, 'splits': [[2, 22], [4, 28], [6, 38], [8, 13]], 'yellow': 3, 'red': 2, 'ref': 'begin'}, [6, 'red', 1]), ({'cycle': 125, 'offset': 85, 'master': 573, 'splits': [[2, 29], [4, 23], [6, 40], [8, 33]], 'yellow': 4, 'red': 1, 'ref': 'begin'}, [8, 'green', 7]), ({'cycle': 100, 'offset': 5, 'master': 3, 'splits': [[2, 50], [4, 30], [8, 25]], 'yellow': 4, 'red': 2, 'ref': 'begin'}, 'bad-splits'), ({'cycle': 80, 'offset': 70, 'master': 10, 'splits': [[2, 50], [4, 30]], 'yellow': 3, 'red': 2, 'ref': 'begin'}, [2, 'green', 25]), ({'cycle': 115, 'offset': 109, 'master': 857, 'splits': [[2, 24], [4, 29], [6, 39], [8, 23]], 'yellow': 3, 'red': 1, 'ref': 'end'}, [6, 'green', 10]), ({'cycle': 90, 'offset': 30, 'master': 45, 'splits': [[2, 40], [4, 25], [6, 25]], 'yellow': 4, 'red': 1, 'ref': 'end'}, [4, 'green', 10]), ({'cycle': 78, 'offset': 52, 'master': 624, 'splits': [[2, 18], [4, 32], [6, 28]], 'yellow': 4, 'red': 2, 'ref': 'begin'}, [4, 'green', 18])], [({'cycle': 63, 'offset': 10, 'master': 656, 'splits': [[2, 34], [4, 29]], 'yellow': 4, 'red': 2, 'ref': 'begin'}, [2, 'green', 12]), ({'cycle': 93, 'offset': 24, 'master': 66, 'splits': [[2, 32], [4, 23], [6, 38]], 'yellow': 3, 'red': 1, 'ref': 'end'}, [6, 'green', 19]), ({'cycle': 92, 'offset': 24, 'master': 289, 'splits': [[2, 19], [4, 20], [6, 39], [8, 14]], 'yellow': 3, 'red': 2, 'ref': 'begin'}, [8, 'green', 6]), ({'cycle': 58, 'offset': 12, 'master': 441, 'splits': [[2, 15], [4, 38]], 'yellow': 3, 'red': 1, 'ref': 'begin'}, 'bad-splits'), ({'cycle': 90, 'offset': 30, 'master': 45, 'splits': [[2, 40], [4, 25], [6, 25]], 'yellow': 4, 'red': 1, 'ref': 'end'}, [4, 'green', 10]), ({'cycle': 100, 'offset': 5, 'master': 3, 'splits': [[2, 50], [4, 30], [8, 25]], 'yellow': 4, 'red': 2, 'ref': 'begin'}, 'bad-splits'), ({'cycle': 82, 'offset': 23, 'master': 673, 'splits': [[2, 38], [4, 28], [6, 16]], 'yellow': 4, 'red': 1, 'ref': 'begin'}, [6, 'green', 1]), ({'cycle': 80, 'offset': 70, 'master': 10, 'splits': [[2, 50], [4, 30]], 'yellow': 3, 'red': 2, 'ref': 'begin'}, [2, 'green', 25])], [({'cycle': 96, 'offset': 42, 'master': 942, 'splits': [[2, 39], [4, 25], [6, 22], [8, 15]], 'yellow': 3, 'red': 1, 'ref': 'end'}, 'bad-splits'), ({'cycle': 90, 'offset': 30, 'master': 45, 'splits': [[2, 40], [4, 25], [6, 25]], 'yellow': 4, 'red': 1, 'ref': 'end'}, [4, 'green', 10]), ({'cycle': 67, 'offset': 65, 'master': 64, 'splits': [[2, 21], [4, 33], [6, 13]], 'yellow': 4, 'red': 1, 'ref': 'begin'}, [6, 'red', 1]), ({'cycle': 132, 'offset': 4, 'master': 870, 'splits': [[2, 27], [4, 35], [6, 39], [8, 31]], 'yellow': 4, 'red': 1, 'ref': 'begin'}, [6, 'green', 22]), ({'cycle': 64, 'offset': 6, 'master': 411, 'splits': [[2, 22], [4, 16], [6, 13], [8, 13]], 'yellow': 3, 'red': 2, 'ref': 'begin'}, [2, 'red', 1]), ({'cycle': 100, 'offset': 5, 'master': 3, 'splits': [[2, 50], [4, 30], [8, 25]], 'yellow': 4, 'red': 2, 'ref': 'begin'}, 'bad-splits'), ({'cycle': 58, 'offset': 42, 'master': 894, 'splits': [[2, 16], [4, 17], [6, 25]], 'yellow': 4, 'red': 1, 'ref': 'begin'}, [6, 'green', 13]), ({'cycle': 80, 'offset': 70, 'master': 10, 'splits': [[2, 50], [4, 30]], 'yellow': 3, 'red': 2, 'ref': 'begin'}, [2, 'green', 25])], [({'cycle': 99, 'offset': 85, 'master': 843, 'splits': [[2, 25], [4, 40], [6, 34]], 'yellow': 4, 'red': 2, 'ref': 'begin'}, [6, 'green', 28]), ({'cycle': 80, 'offset': 70, 'master': 10, 'splits': [[2, 50], [4, 30]], 'yellow': 3, 'red': 2, 'ref': 'begin'}, [2, 'green', 25]), ({'cycle': 120, 'offset': 49, 'master': 612, 'splits': [[2, 34], [4, 36], [6, 26], [8, 24]], 'yellow': 4, 'red': 2, 'ref': 'begin'}, [6, 'green', 7]), ({'cycle': 100, 'offset': 5, 'master': 3, 'splits': [[2, 50], [4, 30], [8, 25]], 'yellow': 4, 'red': 2, 'ref': 'begin'}, 'bad-splits'), ({'cycle': 40, 'offset': 17, 'master': 388, 'splits': [[2, 24], [4, 16]], 'yellow': 4, 'red': 2, 'ref': 'end'}, [4, 'green', 5]), ({'cycle': 90, 'offset': 30, 'master': 45, 'splits': [[2, 40], [4, 25], [6, 25]], 'yellow': 4, 'red': 1, 'ref': 'end'}, [4, 'green', 10]), ({'cycle': 63, 'offset': 11, 'master': 608, 'splits': [[2, 35], [4, 12], [6, 16]], 'yellow': 3, 'red': 1, 'ref': 'begin'}, [2, 'green', 1]), ({'cycle': 99, 'offset': 65, 'master': 228, 'splits': [[2, 22], [4, 29], [6, 15], [8, 33]], 'yellow': 4, 'red': 1, 'ref': 'begin'}, [6, 'yellow', 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 fixtureActualExpectedOutcome
timing oracle 0[2, 'green', 25][2, 'green', 25]Passed
timing oracle 1[2, 'green', 27][2, 'green', 27]Passed
timing oracle 2['free', 'dark', 0][6, 'red', 1]Failed
timing oracle 3[4, 'green', 10][4, 'green', 10]Passed
timing oracle 4bad-splitsbad-splitsPassed
timing oracle 5bad-splitsbad-splitsPassed
timing oracle 6['free', 'dark', 0][6, 'green', 4]Failed
timing oracle 7['free', 'dark', 0][6, 'red', 2]Failed

SHA-256 / 1b6eaa11d9ff2edd7ee28ff2e6e463ad986440751cedbbc1fc9678c6b86a0bb5

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']
    sp = x['splits']
    y, r = x['yellow'], x['red']
    if sum(s for _, s in sp) != C:
        return 'bad-splits'
    lc = (x['master'] - x['offset']) % C
    if x['ref'] == 'end':
        lc = (lc + sp[0][1] - y - r) % C
    start = 0
    for ph, s in sp:
        ge = start + s - y - r
        if lc < ge:
            return [ph, 'green', ge - lc]
        if lc < ge + y:
            return [ph, 'yellow', ge + y - lc]
        if lc < start + s:
            return [ph, 'red', start + s - lc]
        start += s - y - r
    return ['free', 'dark', 0]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[({'cycle': 80, 'offset': 70, 'master': 10, 'splits': [[2, 50], [4, 30]], 'yellow': 3, 'red': 2, 'ref': 'begin'}, [2, 'green', 25]), ({'cycle': 75, 'offset': 33, 'master': 335, 'splits': [[2, 35], [4, 40]], 'yellow': 4, 'red': 2, 'ref': 'begin'}, [2, 'green', 27]), ({'cycle': 58, 'offset': 7, 'master': 869, 'splits': [[2, 13], [4, 31], [6, 14]], 'yellow': 4, 'red': 2, 'ref': 'end'}, [6, 'red', 1]), ({'cycle': 90, 'offset': 30, 'master': 45, 'splits': [[2, 40], [4, 25], [6, 25]], 'yellow': 4, 'red': 1, 'ref': 'end'}, [4, 'green', 10]), ({'cycle': 100, 'offset': 5, 'master': 3, 'splits': [[2, 50], [4, 30], [8, 25]], 'yellow': 4, 'red': 2, 'ref': 'begin'}, 'bad-splits'), ({'cycle': 97, 'offset': 19, 'master': 312, 'splits': [[2, 36], [4, 31], [6, 35]], 'yellow': 4, 'red': 2, 'ref': 'begin'}, 'bad-splits'), ({'cycle': 104, 'offset': 12, 'master': 419, 'splits': [[2, 35], [4, 31], [6, 38]], 'yellow': 3, 'red': 2, 'ref': 'begin'}, [6, 'green', 4]), ({'cycle': 112, 'offset': 58, 'master': 105, 'splits': [[2, 36], [4, 16], [6, 28], [8, 32]], 'yellow': 3, 'red': 2, 'ref': 'end'}, [6, 'red', 2])], [({'cycle': 55, 'offset': 54, 'master': 609, 'splits': [[2, 33], [4, 22]], 'yellow': 4, 'red': 2, 'ref': 'begin'}, [2, 'green', 22]), ({'cycle': 101, 'offset': 40, 'master': 329, 'splits': [[2, 22], [4, 28], [6, 38], [8, 13]], 'yellow': 3, 'red': 2, 'ref': 'begin'}, [6, 'red', 1]), ({'cycle': 125, 'offset': 85, 'master': 573, 'splits': [[2, 29], [4, 23], [6, 40], [8, 33]], 'yellow': 4, 'red': 1, 'ref': 'begin'}, [8, 'green', 7]), ({'cycle': 100, 'offset': 5, 'master': 3, 'splits': [[2, 50], [4, 30], [8, 25]], 'yellow': 4, 'red': 2, 'ref': 'begin'}, 'bad-splits'), ({'cycle': 80, 'offset': 70, 'master': 10, 'splits': [[2, 50], [4, 30]], 'yellow': 3, 'red': 2, 'ref': 'begin'}, [2, 'green', 25]), ({'cycle': 115, 'offset': 109, 'master': 857, 'splits': [[2, 24], [4, 29], [6, 39], [8, 23]], 'yellow': 3, 'red': 1, 'ref': 'end'}, [6, 'green', 10]), ({'cycle': 90, 'offset': 30, 'master': 45, 'splits': [[2, 40], [4, 25], [6, 25]], 'yellow': 4, 'red': 1, 'ref': 'end'}, [4, 'green', 10]), ({'cycle': 78, 'offset': 52, 'master': 624, 'splits': [[2, 18], [4, 32], [6, 28]], 'yellow': 4, 'red': 2, 'ref': 'begin'}, [4, 'green', 18])], [({'cycle': 63, 'offset': 10, 'master': 656, 'splits': [[2, 34], [4, 29]], 'yellow': 4, 'red': 2, 'ref': 'begin'}, [2, 'green', 12]), ({'cycle': 93, 'offset': 24, 'master': 66, 'splits': [[2, 32], [4, 23], [6, 38]], 'yellow': 3, 'red': 1, 'ref': 'end'}, [6, 'green', 19]), ({'cycle': 92, 'offset': 24, 'master': 289, 'splits': [[2, 19], [4, 20], [6, 39], [8, 14]], 'yellow': 3, 'red': 2, 'ref': 'begin'}, [8, 'green', 6]), ({'cycle': 58, 'offset': 12, 'master': 441, 'splits': [[2, 15], [4, 38]], 'yellow': 3, 'red': 1, 'ref': 'begin'}, 'bad-splits'), ({'cycle': 90, 'offset': 30, 'master': 45, 'splits': [[2, 40], [4, 25], [6, 25]], 'yellow': 4, 'red': 1, 'ref': 'end'}, [4, 'green', 10]), ({'cycle': 100, 'offset': 5, 'master': 3, 'splits': [[2, 50], [4, 30], [8, 25]], 'yellow': 4, 'red': 2, 'ref': 'begin'}, 'bad-splits'), ({'cycle': 82, 'offset': 23, 'master': 673, 'splits': [[2, 38], [4, 28], [6, 16]], 'yellow': 4, 'red': 1, 'ref': 'begin'}, [6, 'green', 1]), ({'cycle': 80, 'offset': 70, 'master': 10, 'splits': [[2, 50], [4, 30]], 'yellow': 3, 'red': 2, 'ref': 'begin'}, [2, 'green', 25])], [({'cycle': 96, 'offset': 42, 'master': 942, 'splits': [[2, 39], [4, 25], [6, 22], [8, 15]], 'yellow': 3, 'red': 1, 'ref': 'end'}, 'bad-splits'), ({'cycle': 90, 'offset': 30, 'master': 45, 'splits': [[2, 40], [4, 25], [6, 25]], 'yellow': 4, 'red': 1, 'ref': 'end'}, [4, 'green', 10]), ({'cycle': 67, 'offset': 65, 'master': 64, 'splits': [[2, 21], [4, 33], [6, 13]], 'yellow': 4, 'red': 1, 'ref': 'begin'}, [6, 'red', 1]), ({'cycle': 132, 'offset': 4, 'master': 870, 'splits': [[2, 27], [4, 35], [6, 39], [8, 31]], 'yellow': 4, 'red': 1, 'ref': 'begin'}, [6, 'green', 22]), ({'cycle': 64, 'offset': 6, 'master': 411, 'splits': [[2, 22], [4, 16], [6, 13], [8, 13]], 'yellow': 3, 'red': 2, 'ref': 'begin'}, [2, 'red', 1]), ({'cycle': 100, 'offset': 5, 'master': 3, 'splits': [[2, 50], [4, 30], [8, 25]], 'yellow': 4, 'red': 2, 'ref': 'begin'}, 'bad-splits'), ({'cycle': 58, 'offset': 42, 'master': 894, 'splits': [[2, 16], [4, 17], [6, 25]], 'yellow': 4, 'red': 1, 'ref': 'begin'}, [6, 'green', 13]), ({'cycle': 80, 'offset': 70, 'master': 10, 'splits': [[2, 50], [4, 30]], 'yellow': 3, 'red': 2, 'ref': 'begin'}, [2, 'green', 25])], [({'cycle': 99, 'offset': 85, 'master': 843, 'splits': [[2, 25], [4, 40], [6, 34]], 'yellow': 4, 'red': 2, 'ref': 'begin'}, [6, 'green', 28]), ({'cycle': 80, 'offset': 70, 'master': 10, 'splits': [[2, 50], [4, 30]], 'yellow': 3, 'red': 2, 'ref': 'begin'}, [2, 'green', 25]), ({'cycle': 120, 'offset': 49, 'master': 612, 'splits': [[2, 34], [4, 36], [6, 26], [8, 24]], 'yellow': 4, 'red': 2, 'ref': 'begin'}, [6, 'green', 7]), ({'cycle': 100, 'offset': 5, 'master': 3, 'splits': [[2, 50], [4, 30], [8, 25]], 'yellow': 4, 'red': 2, 'ref': 'begin'}, 'bad-splits'), ({'cycle': 40, 'offset': 17, 'master': 388, 'splits': [[2, 24], [4, 16]], 'yellow': 4, 'red': 2, 'ref': 'end'}, [4, 'green', 5]), ({'cycle': 90, 'offset': 30, 'master': 45, 'splits': [[2, 40], [4, 25], [6, 25]], 'yellow': 4, 'red': 1, 'ref': 'end'}, [4, 'green', 10]), ({'cycle': 63, 'offset': 11, 'master': 608, 'splits': [[2, 35], [4, 12], [6, 16]], 'yellow': 3, 'red': 1, 'ref': 'begin'}, [2, 'green', 1]), ({'cycle': 99, 'offset': 65, 'master': 228, 'splits': [[2, 22], [4, 29], [6, 15], [8, 33]], 'yellow': 4, 'red': 1, 'ref': 'begin'}, [6, 'yellow', 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 fixtureActualExpectedOutcome
timing oracle 0[2, 'green', 25][2, 'green', 25]Passed
timing oracle 1[2, 'green', 27][2, 'green', 27]Passed
timing oracle 2['free', 'dark', 0][6, 'red', 1]Failed
timing oracle 3[4, 'green', 5][4, 'green', 10]Failed
timing oracle 4bad-splitsbad-splitsPassed
timing oracle 5bad-splitsbad-splitsPassed
timing oracle 6['free', 'dark', 0][6, 'green', 4]Failed
timing oracle 7[8, 'green', 14][6, 'red', 2]Failed

SHA-256 / 613bb08ba6295bca337d23581ac9929e98411baf6f2a8c23d96cce787b752125

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']
    sp = x['splits']
    y, r = x['yellow'], x['red']
    if sum(s for _, s in sp) != C:
        return 'bad-splits'
    lc = (x['master'] - x['offset']) % C
    if x['ref'] == 'end':
        lc = (lc + sp[0][1] - y - r) % C
    start = 0
    for ph, s in sp:
        ge = start + s - y - r
        if lc < ge:
            return [ph, 'green', ge - lc]
        if lc < ge + y:
            return [ph, 'yellow', ge + y - lc]
        if lc < start + s:
            return [ph, 'red', start + s - lc]
        start += s
    return ['free', 'dark', 0]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[({'cycle': 80, 'offset': 70, 'master': 10, 'splits': [[2, 50], [4, 30]], 'yellow': 3, 'red': 2, 'ref': 'begin'}, [2, 'green', 25]), ({'cycle': 75, 'offset': 33, 'master': 335, 'splits': [[2, 35], [4, 40]], 'yellow': 4, 'red': 2, 'ref': 'begin'}, [2, 'green', 27]), ({'cycle': 58, 'offset': 7, 'master': 869, 'splits': [[2, 13], [4, 31], [6, 14]], 'yellow': 4, 'red': 2, 'ref': 'end'}, [6, 'red', 1]), ({'cycle': 90, 'offset': 30, 'master': 45, 'splits': [[2, 40], [4, 25], [6, 25]], 'yellow': 4, 'red': 1, 'ref': 'end'}, [4, 'green', 10]), ({'cycle': 100, 'offset': 5, 'master': 3, 'splits': [[2, 50], [4, 30], [8, 25]], 'yellow': 4, 'red': 2, 'ref': 'begin'}, 'bad-splits'), ({'cycle': 97, 'offset': 19, 'master': 312, 'splits': [[2, 36], [4, 31], [6, 35]], 'yellow': 4, 'red': 2, 'ref': 'begin'}, 'bad-splits'), ({'cycle': 104, 'offset': 12, 'master': 419, 'splits': [[2, 35], [4, 31], [6, 38]], 'yellow': 3, 'red': 2, 'ref': 'begin'}, [6, 'green', 4]), ({'cycle': 112, 'offset': 58, 'master': 105, 'splits': [[2, 36], [4, 16], [6, 28], [8, 32]], 'yellow': 3, 'red': 2, 'ref': 'end'}, [6, 'red', 2])], [({'cycle': 55, 'offset': 54, 'master': 609, 'splits': [[2, 33], [4, 22]], 'yellow': 4, 'red': 2, 'ref': 'begin'}, [2, 'green', 22]), ({'cycle': 101, 'offset': 40, 'master': 329, 'splits': [[2, 22], [4, 28], [6, 38], [8, 13]], 'yellow': 3, 'red': 2, 'ref': 'begin'}, [6, 'red', 1]), ({'cycle': 125, 'offset': 85, 'master': 573, 'splits': [[2, 29], [4, 23], [6, 40], [8, 33]], 'yellow': 4, 'red': 1, 'ref': 'begin'}, [8, 'green', 7]), ({'cycle': 100, 'offset': 5, 'master': 3, 'splits': [[2, 50], [4, 30], [8, 25]], 'yellow': 4, 'red': 2, 'ref': 'begin'}, 'bad-splits'), ({'cycle': 80, 'offset': 70, 'master': 10, 'splits': [[2, 50], [4, 30]], 'yellow': 3, 'red': 2, 'ref': 'begin'}, [2, 'green', 25]), ({'cycle': 115, 'offset': 109, 'master': 857, 'splits': [[2, 24], [4, 29], [6, 39], [8, 23]], 'yellow': 3, 'red': 1, 'ref': 'end'}, [6, 'green', 10]), ({'cycle': 90, 'offset': 30, 'master': 45, 'splits': [[2, 40], [4, 25], [6, 25]], 'yellow': 4, 'red': 1, 'ref': 'end'}, [4, 'green', 10]), ({'cycle': 78, 'offset': 52, 'master': 624, 'splits': [[2, 18], [4, 32], [6, 28]], 'yellow': 4, 'red': 2, 'ref': 'begin'}, [4, 'green', 18])], [({'cycle': 63, 'offset': 10, 'master': 656, 'splits': [[2, 34], [4, 29]], 'yellow': 4, 'red': 2, 'ref': 'begin'}, [2, 'green', 12]), ({'cycle': 93, 'offset': 24, 'master': 66, 'splits': [[2, 32], [4, 23], [6, 38]], 'yellow': 3, 'red': 1, 'ref': 'end'}, [6, 'green', 19]), ({'cycle': 92, 'offset': 24, 'master': 289, 'splits': [[2, 19], [4, 20], [6, 39], [8, 14]], 'yellow': 3, 'red': 2, 'ref': 'begin'}, [8, 'green', 6]), ({'cycle': 58, 'offset': 12, 'master': 441, 'splits': [[2, 15], [4, 38]], 'yellow': 3, 'red': 1, 'ref': 'begin'}, 'bad-splits'), ({'cycle': 90, 'offset': 30, 'master': 45, 'splits': [[2, 40], [4, 25], [6, 25]], 'yellow': 4, 'red': 1, 'ref': 'end'}, [4, 'green', 10]), ({'cycle': 100, 'offset': 5, 'master': 3, 'splits': [[2, 50], [4, 30], [8, 25]], 'yellow': 4, 'red': 2, 'ref': 'begin'}, 'bad-splits'), ({'cycle': 82, 'offset': 23, 'master': 673, 'splits': [[2, 38], [4, 28], [6, 16]], 'yellow': 4, 'red': 1, 'ref': 'begin'}, [6, 'green', 1]), ({'cycle': 80, 'offset': 70, 'master': 10, 'splits': [[2, 50], [4, 30]], 'yellow': 3, 'red': 2, 'ref': 'begin'}, [2, 'green', 25])], [({'cycle': 96, 'offset': 42, 'master': 942, 'splits': [[2, 39], [4, 25], [6, 22], [8, 15]], 'yellow': 3, 'red': 1, 'ref': 'end'}, 'bad-splits'), ({'cycle': 90, 'offset': 30, 'master': 45, 'splits': [[2, 40], [4, 25], [6, 25]], 'yellow': 4, 'red': 1, 'ref': 'end'}, [4, 'green', 10]), ({'cycle': 67, 'offset': 65, 'master': 64, 'splits': [[2, 21], [4, 33], [6, 13]], 'yellow': 4, 'red': 1, 'ref': 'begin'}, [6, 'red', 1]), ({'cycle': 132, 'offset': 4, 'master': 870, 'splits': [[2, 27], [4, 35], [6, 39], [8, 31]], 'yellow': 4, 'red': 1, 'ref': 'begin'}, [6, 'green', 22]), ({'cycle': 64, 'offset': 6, 'master': 411, 'splits': [[2, 22], [4, 16], [6, 13], [8, 13]], 'yellow': 3, 'red': 2, 'ref': 'begin'}, [2, 'red', 1]), ({'cycle': 100, 'offset': 5, 'master': 3, 'splits': [[2, 50], [4, 30], [8, 25]], 'yellow': 4, 'red': 2, 'ref': 'begin'}, 'bad-splits'), ({'cycle': 58, 'offset': 42, 'master': 894, 'splits': [[2, 16], [4, 17], [6, 25]], 'yellow': 4, 'red': 1, 'ref': 'begin'}, [6, 'green', 13]), ({'cycle': 80, 'offset': 70, 'master': 10, 'splits': [[2, 50], [4, 30]], 'yellow': 3, 'red': 2, 'ref': 'begin'}, [2, 'green', 25])], [({'cycle': 99, 'offset': 85, 'master': 843, 'splits': [[2, 25], [4, 40], [6, 34]], 'yellow': 4, 'red': 2, 'ref': 'begin'}, [6, 'green', 28]), ({'cycle': 80, 'offset': 70, 'master': 10, 'splits': [[2, 50], [4, 30]], 'yellow': 3, 'red': 2, 'ref': 'begin'}, [2, 'green', 25]), ({'cycle': 120, 'offset': 49, 'master': 612, 'splits': [[2, 34], [4, 36], [6, 26], [8, 24]], 'yellow': 4, 'red': 2, 'ref': 'begin'}, [6, 'green', 7]), ({'cycle': 100, 'offset': 5, 'master': 3, 'splits': [[2, 50], [4, 30], [8, 25]], 'yellow': 4, 'red': 2, 'ref': 'begin'}, 'bad-splits'), ({'cycle': 40, 'offset': 17, 'master': 388, 'splits': [[2, 24], [4, 16]], 'yellow': 4, 'red': 2, 'ref': 'end'}, [4, 'green', 5]), ({'cycle': 90, 'offset': 30, 'master': 45, 'splits': [[2, 40], [4, 25], [6, 25]], 'yellow': 4, 'red': 1, 'ref': 'end'}, [4, 'green', 10]), ({'cycle': 63, 'offset': 11, 'master': 608, 'splits': [[2, 35], [4, 12], [6, 16]], 'yellow': 3, 'red': 1, 'ref': 'begin'}, [2, 'green', 1]), ({'cycle': 99, 'offset': 65, 'master': 228, 'splits': [[2, 22], [4, 29], [6, 15], [8, 33]], 'yellow': 4, 'red': 1, 'ref': 'begin'}, [6, 'yellow', 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 fixtureActualExpectedOutcome
timing oracle 0[2, 'green', 25][2, 'green', 25]Passed
timing oracle 1[2, 'green', 27][2, 'green', 27]Passed
timing oracle 2[6, 'red', 1][6, 'red', 1]Passed
timing oracle 3[4, 'green', 10][4, 'green', 10]Passed
timing oracle 4bad-splitsbad-splitsPassed
timing oracle 5bad-splitsbad-splitsPassed
timing oracle 6[6, 'green', 4][6, 'green', 4]Passed
timing oracle 7[6, 'red', 2][6, 'red', 2]Passed

SHA-256 / b3cc1223060a6a20fc661a5435cf13dc5f477e4890e953a372786caabf4adfb0

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 2026-09-29T14:47:58.544828+00:00.

Case digest / 8e3bf1e308cca408d09731afa2a563afcbe198c02bbf59b8ba5db5c379b7f1cb