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FA-68021 / Traffic signal timing plans / Open access

Volume-density added initial and gap reduction: the minimum gap is reached after time_to_reduce alone · case 01

Volume-density added initial and gap reduction returns a wrong result when the minimum gap is reached after time_to_reduce alone.

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ROOT CAUSE

The end of reduction ignores the time-before-reduction offset, so the gap snaps to the minimum early.

THE FAILURE

The end of reduction ignores the time-before-reduction offset, so the gap snaps to the minimum early.

Unsuccessful approach: Taking the larger of the two periods still does not add them.

Case contract

Input {min_green, added_per_act_tenths, max_initial, red_actuations, initial_gap_tenths, min_gap_tenths, time_before_reduction, time_to_reduce, call, t}. Variable initial = min(max_initial, max(min_green, ceil(actuations*added/10))) seconds. Gap reduction is timed from the conflicting call (a call before green start counts from 0): until time_before_reduction elapses the allowed gap is the initial gap; during time_to_reduce it falls linearly with the reduction amount truncated to whole tenths; afterwards it is the minimum gap. Return {initial, gap_tenths}.

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 = x['min_green']
    initial = min(x['max_initial'], max(m, -(-x['red_actuations'] * x['added_per_act_tenths'] // 10)))
    g0, gm = x['initial_gap_tenths'], x['min_gap_tenths']
    el = x['t'] - max(x['call'], 0)
    if el <= x['time_before_reduction']:
        gap = g0
    elif el >= x['time_to_reduce']:
        gap = gm
    else:
        done = el - x['time_before_reduction']
        gap = g0 - (g0 - gm) * done // x['time_to_reduce']
    return {'initial': initial, 'gap_tenths': gap}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[({'min_green': 10, 'added_per_act_tenths': 25, 'max_initial': 14, 'red_actuations': 20, 'initial_gap_tenths': 35, 'min_gap_tenths': 10, 'time_before_reduction': 3, 'time_to_reduce': 6, 'call': 3, 't': 27}, {'initial': 14, 'gap_tenths': 10}), ({'min_green': 6, 'added_per_act_tenths': 10, 'max_initial': 12, 'red_actuations': 1, 'initial_gap_tenths': 50, 'min_gap_tenths': 10, 'time_before_reduction': 8, 'time_to_reduce': 19, 'call': 4, 't': 2}, {'initial': 6, 'gap_tenths': 50}), ({'min_green': 9, 'added_per_act_tenths': 25, 'max_initial': 17, 'red_actuations': 9, 'initial_gap_tenths': 50, 'min_gap_tenths': 20, 'time_before_reduction': 7, 'time_to_reduce': 23, 'call': -4, 't': 60}, {'initial': 17, 'gap_tenths': 20}), ({'min_green': 10, 'added_per_act_tenths': 10, 'max_initial': 16, 'red_actuations': 20, 'initial_gap_tenths': 30, 'min_gap_tenths': 20, 'time_before_reduction': 9, 'time_to_reduce': 15, 'call': 14, 't': 29}, {'initial': 16, 'gap_tenths': 26}), ({'min_green': 6, 'added_per_act_tenths': 25, 'max_initial': 25, 'red_actuations': 3, 'initial_gap_tenths': 50, 'min_gap_tenths': 20, 'time_before_reduction': 8, 'time_to_reduce': 12, 'call': 0, 't': 40}, {'initial': 8, 'gap_tenths': 20}), ({'min_green': 5, 'added_per_act_tenths': 15, 'max_initial': 20, 'red_actuations': 7, 'initial_gap_tenths': 40, 'min_gap_tenths': 20, 'time_before_reduction': 10, 'time_to_reduce': 15, 'call': 3, 't': 20}, {'initial': 11, 'gap_tenths': 31}), ({'min_green': 5, 'added_per_act_tenths': 20, 'max_initial': 27, 'red_actuations': 18, 'initial_gap_tenths': 50, 'min_gap_tenths': 20, 'time_before_reduction': 13, 'time_to_reduce': 24, 'call': 7, 't': 33}, {'initial': 27, 'gap_tenths': 34}), ({'min_green': 8, 'added_per_act_tenths': 20, 'max_initial': 12, 'red_actuations': 9, 'initial_gap_tenths': 35, 'min_gap_tenths': 15, 'time_before_reduction': 5, 'time_to_reduce': 20, 'call': -4, 't': 12}, {'initial': 12, 'gap_tenths': 28})], [({'min_green': 5, 'added_per_act_tenths': 15, 'max_initial': 20, 'red_actuations': 7, 'initial_gap_tenths': 40, 'min_gap_tenths': 20, 'time_before_reduction': 10, 'time_to_reduce': 15, 'call': 3, 't': 20}, {'initial': 11, 'gap_tenths': 31}), ({'min_green': 8, 'added_per_act_tenths': 15, 'max_initial': 20, 'red_actuations': 4, 'initial_gap_tenths': 30, 'min_gap_tenths': 15, 'time_before_reduction': 7, 'time_to_reduce': 17, 'call': 0, 't': 20}, {'initial': 8, 'gap_tenths': 19}), ({'min_green': 8, 'added_per_act_tenths': 10, 'max_initial': 29, 'red_actuations': 6, 'initial_gap_tenths': 50, 'min_gap_tenths': 20, 'time_before_reduction': 12, 'time_to_reduce': 15, 'call': 5, 't': 24}, {'initial': 8, 'gap_tenths': 36}), ({'min_green': 6, 'added_per_act_tenths': 25, 'max_initial': 25, 'red_actuations': 3, 'initial_gap_tenths': 50, 'min_gap_tenths': 20, 'time_before_reduction': 8, 'time_to_reduce': 12, 'call': 0, 't': 40}, {'initial': 8, 'gap_tenths': 20}), ({'min_green': 8, 'added_per_act_tenths': 20, 'max_initial': 12, 'red_actuations': 9, 'initial_gap_tenths': 35, 'min_gap_tenths': 15, 'time_before_reduction': 5, 'time_to_reduce': 20, 'call': -4, 't': 12}, {'initial': 12, 'gap_tenths': 28}), ({'min_green': 5, 'added_per_act_tenths': 20, 'max_initial': 14, 'red_actuations': 3, 'initial_gap_tenths': 40, 'min_gap_tenths': 10, 'time_before_reduction': 15, 'time_to_reduce': 10, 'call': 14, 't': 39}, {'initial': 6, 'gap_tenths': 10}), ({'min_green': 8, 'added_per_act_tenths': 10, 'max_initial': 12, 'red_actuations': 14, 'initial_gap_tenths': 40, 'min_gap_tenths': 15, 'time_before_reduction': 5, 'time_to_reduce': 11, 'call': 7, 't': 49}, {'initial': 12, 'gap_tenths': 15}), ({'min_green': 5, 'added_per_act_tenths': 15, 'max_initial': 16, 'red_actuations': 9, 'initial_gap_tenths': 35, 'min_gap_tenths': 20, 'time_before_reduction': 3, 'time_to_reduce': 25, 'call': 1, 't': 20}, {'initial': 14, 'gap_tenths': 26})], [({'min_green': 6, 'added_per_act_tenths': 25, 'max_initial': 25, 'red_actuations': 3, 'initial_gap_tenths': 50, 'min_gap_tenths': 20, 'time_before_reduction': 8, 'time_to_reduce': 12, 'call': 0, 't': 40}, {'initial': 8, 'gap_tenths': 20}), ({'min_green': 5, 'added_per_act_tenths': 15, 'max_initial': 20, 'red_actuations': 7, 'initial_gap_tenths': 40, 'min_gap_tenths': 20, 'time_before_reduction': 10, 'time_to_reduce': 15, 'call': 3, 't': 20}, {'initial': 11, 'gap_tenths': 31}), ({'min_green': 8, 'added_per_act_tenths': 20, 'max_initial': 12, 'red_actuations': 9, 'initial_gap_tenths': 35, 'min_gap_tenths': 15, 'time_before_reduction': 5, 'time_to_reduce': 20, 'call': -4, 't': 12}, {'initial': 12, 'gap_tenths': 28}), ({'min_green': 4, 'added_per_act_tenths': 20, 'max_initial': 10, 'red_actuations': 13, 'initial_gap_tenths': 40, 'min_gap_tenths': 20, 'time_before_reduction': 10, 'time_to_reduce': 21, 'call': 5, 't': 13}, {'initial': 10, 'gap_tenths': 40}), ({'min_green': 10, 'added_per_act_tenths': 25, 'max_initial': 28, 'red_actuations': 18, 'initial_gap_tenths': 30, 'min_gap_tenths': 10, 'time_before_reduction': 3, 'time_to_reduce': 30, 'call': 14, 't': 33}, {'initial': 28, 'gap_tenths': 20}), ({'min_green': 9, 'added_per_act_tenths': 10, 'max_initial': 19, 'red_actuations': 0, 'initial_gap_tenths': 30, 'min_gap_tenths': 10, 'time_before_reduction': 7, 'time_to_reduce': 20, 'call': 2, 't': 38}, {'initial': 9, 'gap_tenths': 10}), ({'min_green': 7, 'added_per_act_tenths': 15, 'max_initial': 19, 'red_actuations': 9, 'initial_gap_tenths': 50, 'min_gap_tenths': 10, 'time_before_reduction': 5, 'time_to_reduce': 15, 'call': 9, 't': 26}, {'initial': 14, 'gap_tenths': 18}), ({'min_green': 5, 'added_per_act_tenths': 20, 'max_initial': 10, 'red_actuations': 7, 'initial_gap_tenths': 40, 'min_gap_tenths': 10, 'time_before_reduction': 12, 'time_to_reduce': 9, 'call': 12, 't': 31}, {'initial': 10, 'gap_tenths': 17})], [({'min_green': 8, 'added_per_act_tenths': 20, 'max_initial': 12, 'red_actuations': 9, 'initial_gap_tenths': 35, 'min_gap_tenths': 15, 'time_before_reduction': 5, 'time_to_reduce': 20, 'call': -4, 't': 12}, {'initial': 12, 'gap_tenths': 28}), ({'min_green': 6, 'added_per_act_tenths': 20, 'max_initial': 26, 'red_actuations': 2, 'initial_gap_tenths': 35, 'min_gap_tenths': 20, 'time_before_reduction': 3, 'time_to_reduce': 14, 'call': 12, 't': 28}, {'initial': 6, 'gap_tenths': 22}), ({'min_green': 8, 'added_per_act_tenths': 25, 'max_initial': 24, 'red_actuations': 0, 'initial_gap_tenths': 30, 'min_gap_tenths': 15, 'time_before_reduction': 14, 'time_to_reduce': 27, 'call': 1, 't': 34}, {'initial': 8, 'gap_tenths': 20}), ({'min_green': 6, 'added_per_act_tenths': 25, 'max_initial': 25, 'red_actuations': 3, 'initial_gap_tenths': 50, 'min_gap_tenths': 20, 'time_before_reduction': 8, 'time_to_reduce': 12, 'call': 0, 't': 40}, {'initial': 8, 'gap_tenths': 20}), ({'min_green': 7, 'added_per_act_tenths': 10, 'max_initial': 29, 'red_actuations': 1, 'initial_gap_tenths': 35, 'min_gap_tenths': 10, 'time_before_reduction': 1, 'time_to_reduce': 21, 'call': 14, 't': 30}, {'initial': 7, 'gap_tenths': 18}), ({'min_green': 8, 'added_per_act_tenths': 25, 'max_initial': 28, 'red_actuations': 14, 'initial_gap_tenths': 40, 'min_gap_tenths': 10, 'time_before_reduction': 15, 'time_to_reduce': 30, 'call': 10, 't': 56}, {'initial': 28, 'gap_tenths': 10}), ({'min_green': 8, 'added_per_act_tenths': 20, 'max_initial': 30, 'red_actuations': 12, 'initial_gap_tenths': 40, 'min_gap_tenths': 20, 'time_before_reduction': 11, 'time_to_reduce': 25, 'call': -2, 't': 12}, {'initial': 24, 'gap_tenths': 40}), ({'min_green': 5, 'added_per_act_tenths': 15, 'max_initial': 20, 'red_actuations': 7, 'initial_gap_tenths': 40, 'min_gap_tenths': 20, 'time_before_reduction': 10, 'time_to_reduce': 15, 'call': 3, 't': 20}, {'initial': 11, 'gap_tenths': 31})], [({'min_green': 4, 'added_per_act_tenths': 25, 'max_initial': 20, 'red_actuations': 9, 'initial_gap_tenths': 40, 'min_gap_tenths': 20, 'time_before_reduction': 6, 'time_to_reduce': 23, 'call': 2, 't': 17}, {'initial': 20, 'gap_tenths': 33}), ({'min_green': 5, 'added_per_act_tenths': 25, 'max_initial': 13, 'red_actuations': 11, 'initial_gap_tenths': 50, 'min_gap_tenths': 20, 'time_before_reduction': 8, 'time_to_reduce': 16, 'call': 6, 't': 27}, {'initial': 13, 'gap_tenths': 26}), ({'min_green': 4, 'added_per_act_tenths': 15, 'max_initial': 17, 'red_actuations': 7, 'initial_gap_tenths': 40, 'min_gap_tenths': 20, 'time_before_reduction': 14, 'time_to_reduce': 8, 'call': 3, 't': 50}, {'initial': 11, 'gap_tenths': 20}), ({'min_green': 5, 'added_per_act_tenths': 15, 'max_initial': 20, 'red_actuations': 7, 'initial_gap_tenths': 40, 'min_gap_tenths': 20, 'time_before_reduction': 10, 'time_to_reduce': 15, 'call': 3, 't': 20}, {'initial': 11, 'gap_tenths': 31}), ({'min_green': 6, 'added_per_act_tenths': 25, 'max_initial': 25, 'red_actuations': 3, 'initial_gap_tenths': 50, 'min_gap_tenths': 20, 'time_before_reduction': 8, 'time_to_reduce': 12, 'call': 0, 't': 40}, {'initial': 8, 'gap_tenths': 20}), ({'min_green': 8, 'added_per_act_tenths': 20, 'max_initial': 12, 'red_actuations': 9, 'initial_gap_tenths': 35, 'min_gap_tenths': 15, 'time_before_reduction': 5, 'time_to_reduce': 20, 'call': -4, 't': 12}, {'initial': 12, 'gap_tenths': 28}), ({'min_green': 6, 'added_per_act_tenths': 25, 'max_initial': 16, 'red_actuations': 4, 'initial_gap_tenths': 50, 'min_gap_tenths': 15, 'time_before_reduction': 10, 'time_to_reduce': 22, 'call': 5, 't': 28}, {'initial': 10, 'gap_tenths': 30}), ({'min_green': 8, 'added_per_act_tenths': 25, 'max_initial': 23, 'red_actuations': 3, 'initial_gap_tenths': 50, 'min_gap_tenths': 10, 'time_before_reduction': 3, 'time_to_reduce': 30, 'call': 3, 't': 53}, {'initial': 8, 'gap_tenths': 10})]]
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_tenths': 10, 'initial': 14}{'gap_tenths': 10, 'initial': 14}Passed
timing oracle 1{'gap_tenths': 50, 'initial': 6}{'gap_tenths': 50, 'initial': 6}Passed
timing oracle 2{'gap_tenths': 20, 'initial': 17}{'gap_tenths': 20, 'initial': 17}Passed
timing oracle 3{'gap_tenths': 20, 'initial': 16}{'gap_tenths': 26, 'initial': 16}Failed
timing oracle 4{'gap_tenths': 20, 'initial': 8}{'gap_tenths': 20, 'initial': 8}Passed
timing oracle 5{'gap_tenths': 20, 'initial': 11}{'gap_tenths': 31, 'initial': 11}Failed
timing oracle 6{'gap_tenths': 20, 'initial': 27}{'gap_tenths': 34, 'initial': 27}Failed
timing oracle 7{'gap_tenths': 28, 'initial': 12}{'gap_tenths': 28, 'initial': 12}Passed

SHA-256 / 299ed89a6d9b13c4b7233ef686581380f4aba4da5b11c11715da63becc847aaa

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(x):
    m = x['min_green']
    initial = min(x['max_initial'], max(m, -(-x['red_actuations'] * x['added_per_act_tenths'] // 10)))
    g0, gm = x['initial_gap_tenths'], x['min_gap_tenths']
    el = x['t'] - max(x['call'], 0)
    if el <= x['time_before_reduction']:
        gap = g0
    elif el >= max(x['time_before_reduction'], x['time_to_reduce']):
        gap = gm
    else:
        done = el - x['time_before_reduction']
        gap = g0 - (g0 - gm) * done // x['time_to_reduce']
    return {'initial': initial, 'gap_tenths': gap}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[({'min_green': 10, 'added_per_act_tenths': 25, 'max_initial': 14, 'red_actuations': 20, 'initial_gap_tenths': 35, 'min_gap_tenths': 10, 'time_before_reduction': 3, 'time_to_reduce': 6, 'call': 3, 't': 27}, {'initial': 14, 'gap_tenths': 10}), ({'min_green': 6, 'added_per_act_tenths': 10, 'max_initial': 12, 'red_actuations': 1, 'initial_gap_tenths': 50, 'min_gap_tenths': 10, 'time_before_reduction': 8, 'time_to_reduce': 19, 'call': 4, 't': 2}, {'initial': 6, 'gap_tenths': 50}), ({'min_green': 9, 'added_per_act_tenths': 25, 'max_initial': 17, 'red_actuations': 9, 'initial_gap_tenths': 50, 'min_gap_tenths': 20, 'time_before_reduction': 7, 'time_to_reduce': 23, 'call': -4, 't': 60}, {'initial': 17, 'gap_tenths': 20}), ({'min_green': 10, 'added_per_act_tenths': 10, 'max_initial': 16, 'red_actuations': 20, 'initial_gap_tenths': 30, 'min_gap_tenths': 20, 'time_before_reduction': 9, 'time_to_reduce': 15, 'call': 14, 't': 29}, {'initial': 16, 'gap_tenths': 26}), ({'min_green': 6, 'added_per_act_tenths': 25, 'max_initial': 25, 'red_actuations': 3, 'initial_gap_tenths': 50, 'min_gap_tenths': 20, 'time_before_reduction': 8, 'time_to_reduce': 12, 'call': 0, 't': 40}, {'initial': 8, 'gap_tenths': 20}), ({'min_green': 5, 'added_per_act_tenths': 15, 'max_initial': 20, 'red_actuations': 7, 'initial_gap_tenths': 40, 'min_gap_tenths': 20, 'time_before_reduction': 10, 'time_to_reduce': 15, 'call': 3, 't': 20}, {'initial': 11, 'gap_tenths': 31}), ({'min_green': 5, 'added_per_act_tenths': 20, 'max_initial': 27, 'red_actuations': 18, 'initial_gap_tenths': 50, 'min_gap_tenths': 20, 'time_before_reduction': 13, 'time_to_reduce': 24, 'call': 7, 't': 33}, {'initial': 27, 'gap_tenths': 34}), ({'min_green': 8, 'added_per_act_tenths': 20, 'max_initial': 12, 'red_actuations': 9, 'initial_gap_tenths': 35, 'min_gap_tenths': 15, 'time_before_reduction': 5, 'time_to_reduce': 20, 'call': -4, 't': 12}, {'initial': 12, 'gap_tenths': 28})], [({'min_green': 5, 'added_per_act_tenths': 15, 'max_initial': 20, 'red_actuations': 7, 'initial_gap_tenths': 40, 'min_gap_tenths': 20, 'time_before_reduction': 10, 'time_to_reduce': 15, 'call': 3, 't': 20}, {'initial': 11, 'gap_tenths': 31}), ({'min_green': 8, 'added_per_act_tenths': 15, 'max_initial': 20, 'red_actuations': 4, 'initial_gap_tenths': 30, 'min_gap_tenths': 15, 'time_before_reduction': 7, 'time_to_reduce': 17, 'call': 0, 't': 20}, {'initial': 8, 'gap_tenths': 19}), ({'min_green': 8, 'added_per_act_tenths': 10, 'max_initial': 29, 'red_actuations': 6, 'initial_gap_tenths': 50, 'min_gap_tenths': 20, 'time_before_reduction': 12, 'time_to_reduce': 15, 'call': 5, 't': 24}, {'initial': 8, 'gap_tenths': 36}), ({'min_green': 6, 'added_per_act_tenths': 25, 'max_initial': 25, 'red_actuations': 3, 'initial_gap_tenths': 50, 'min_gap_tenths': 20, 'time_before_reduction': 8, 'time_to_reduce': 12, 'call': 0, 't': 40}, {'initial': 8, 'gap_tenths': 20}), ({'min_green': 8, 'added_per_act_tenths': 20, 'max_initial': 12, 'red_actuations': 9, 'initial_gap_tenths': 35, 'min_gap_tenths': 15, 'time_before_reduction': 5, 'time_to_reduce': 20, 'call': -4, 't': 12}, {'initial': 12, 'gap_tenths': 28}), ({'min_green': 5, 'added_per_act_tenths': 20, 'max_initial': 14, 'red_actuations': 3, 'initial_gap_tenths': 40, 'min_gap_tenths': 10, 'time_before_reduction': 15, 'time_to_reduce': 10, 'call': 14, 't': 39}, {'initial': 6, 'gap_tenths': 10}), ({'min_green': 8, 'added_per_act_tenths': 10, 'max_initial': 12, 'red_actuations': 14, 'initial_gap_tenths': 40, 'min_gap_tenths': 15, 'time_before_reduction': 5, 'time_to_reduce': 11, 'call': 7, 't': 49}, {'initial': 12, 'gap_tenths': 15}), ({'min_green': 5, 'added_per_act_tenths': 15, 'max_initial': 16, 'red_actuations': 9, 'initial_gap_tenths': 35, 'min_gap_tenths': 20, 'time_before_reduction': 3, 'time_to_reduce': 25, 'call': 1, 't': 20}, {'initial': 14, 'gap_tenths': 26})], [({'min_green': 6, 'added_per_act_tenths': 25, 'max_initial': 25, 'red_actuations': 3, 'initial_gap_tenths': 50, 'min_gap_tenths': 20, 'time_before_reduction': 8, 'time_to_reduce': 12, 'call': 0, 't': 40}, {'initial': 8, 'gap_tenths': 20}), ({'min_green': 5, 'added_per_act_tenths': 15, 'max_initial': 20, 'red_actuations': 7, 'initial_gap_tenths': 40, 'min_gap_tenths': 20, 'time_before_reduction': 10, 'time_to_reduce': 15, 'call': 3, 't': 20}, {'initial': 11, 'gap_tenths': 31}), ({'min_green': 8, 'added_per_act_tenths': 20, 'max_initial': 12, 'red_actuations': 9, 'initial_gap_tenths': 35, 'min_gap_tenths': 15, 'time_before_reduction': 5, 'time_to_reduce': 20, 'call': -4, 't': 12}, {'initial': 12, 'gap_tenths': 28}), ({'min_green': 4, 'added_per_act_tenths': 20, 'max_initial': 10, 'red_actuations': 13, 'initial_gap_tenths': 40, 'min_gap_tenths': 20, 'time_before_reduction': 10, 'time_to_reduce': 21, 'call': 5, 't': 13}, {'initial': 10, 'gap_tenths': 40}), ({'min_green': 10, 'added_per_act_tenths': 25, 'max_initial': 28, 'red_actuations': 18, 'initial_gap_tenths': 30, 'min_gap_tenths': 10, 'time_before_reduction': 3, 'time_to_reduce': 30, 'call': 14, 't': 33}, {'initial': 28, 'gap_tenths': 20}), ({'min_green': 9, 'added_per_act_tenths': 10, 'max_initial': 19, 'red_actuations': 0, 'initial_gap_tenths': 30, 'min_gap_tenths': 10, 'time_before_reduction': 7, 'time_to_reduce': 20, 'call': 2, 't': 38}, {'initial': 9, 'gap_tenths': 10}), ({'min_green': 7, 'added_per_act_tenths': 15, 'max_initial': 19, 'red_actuations': 9, 'initial_gap_tenths': 50, 'min_gap_tenths': 10, 'time_before_reduction': 5, 'time_to_reduce': 15, 'call': 9, 't': 26}, {'initial': 14, 'gap_tenths': 18}), ({'min_green': 5, 'added_per_act_tenths': 20, 'max_initial': 10, 'red_actuations': 7, 'initial_gap_tenths': 40, 'min_gap_tenths': 10, 'time_before_reduction': 12, 'time_to_reduce': 9, 'call': 12, 't': 31}, {'initial': 10, 'gap_tenths': 17})], [({'min_green': 8, 'added_per_act_tenths': 20, 'max_initial': 12, 'red_actuations': 9, 'initial_gap_tenths': 35, 'min_gap_tenths': 15, 'time_before_reduction': 5, 'time_to_reduce': 20, 'call': -4, 't': 12}, {'initial': 12, 'gap_tenths': 28}), ({'min_green': 6, 'added_per_act_tenths': 20, 'max_initial': 26, 'red_actuations': 2, 'initial_gap_tenths': 35, 'min_gap_tenths': 20, 'time_before_reduction': 3, 'time_to_reduce': 14, 'call': 12, 't': 28}, {'initial': 6, 'gap_tenths': 22}), ({'min_green': 8, 'added_per_act_tenths': 25, 'max_initial': 24, 'red_actuations': 0, 'initial_gap_tenths': 30, 'min_gap_tenths': 15, 'time_before_reduction': 14, 'time_to_reduce': 27, 'call': 1, 't': 34}, {'initial': 8, 'gap_tenths': 20}), ({'min_green': 6, 'added_per_act_tenths': 25, 'max_initial': 25, 'red_actuations': 3, 'initial_gap_tenths': 50, 'min_gap_tenths': 20, 'time_before_reduction': 8, 'time_to_reduce': 12, 'call': 0, 't': 40}, {'initial': 8, 'gap_tenths': 20}), ({'min_green': 7, 'added_per_act_tenths': 10, 'max_initial': 29, 'red_actuations': 1, 'initial_gap_tenths': 35, 'min_gap_tenths': 10, 'time_before_reduction': 1, 'time_to_reduce': 21, 'call': 14, 't': 30}, {'initial': 7, 'gap_tenths': 18}), ({'min_green': 8, 'added_per_act_tenths': 25, 'max_initial': 28, 'red_actuations': 14, 'initial_gap_tenths': 40, 'min_gap_tenths': 10, 'time_before_reduction': 15, 'time_to_reduce': 30, 'call': 10, 't': 56}, {'initial': 28, 'gap_tenths': 10}), ({'min_green': 8, 'added_per_act_tenths': 20, 'max_initial': 30, 'red_actuations': 12, 'initial_gap_tenths': 40, 'min_gap_tenths': 20, 'time_before_reduction': 11, 'time_to_reduce': 25, 'call': -2, 't': 12}, {'initial': 24, 'gap_tenths': 40}), ({'min_green': 5, 'added_per_act_tenths': 15, 'max_initial': 20, 'red_actuations': 7, 'initial_gap_tenths': 40, 'min_gap_tenths': 20, 'time_before_reduction': 10, 'time_to_reduce': 15, 'call': 3, 't': 20}, {'initial': 11, 'gap_tenths': 31})], [({'min_green': 4, 'added_per_act_tenths': 25, 'max_initial': 20, 'red_actuations': 9, 'initial_gap_tenths': 40, 'min_gap_tenths': 20, 'time_before_reduction': 6, 'time_to_reduce': 23, 'call': 2, 't': 17}, {'initial': 20, 'gap_tenths': 33}), ({'min_green': 5, 'added_per_act_tenths': 25, 'max_initial': 13, 'red_actuations': 11, 'initial_gap_tenths': 50, 'min_gap_tenths': 20, 'time_before_reduction': 8, 'time_to_reduce': 16, 'call': 6, 't': 27}, {'initial': 13, 'gap_tenths': 26}), ({'min_green': 4, 'added_per_act_tenths': 15, 'max_initial': 17, 'red_actuations': 7, 'initial_gap_tenths': 40, 'min_gap_tenths': 20, 'time_before_reduction': 14, 'time_to_reduce': 8, 'call': 3, 't': 50}, {'initial': 11, 'gap_tenths': 20}), ({'min_green': 5, 'added_per_act_tenths': 15, 'max_initial': 20, 'red_actuations': 7, 'initial_gap_tenths': 40, 'min_gap_tenths': 20, 'time_before_reduction': 10, 'time_to_reduce': 15, 'call': 3, 't': 20}, {'initial': 11, 'gap_tenths': 31}), ({'min_green': 6, 'added_per_act_tenths': 25, 'max_initial': 25, 'red_actuations': 3, 'initial_gap_tenths': 50, 'min_gap_tenths': 20, 'time_before_reduction': 8, 'time_to_reduce': 12, 'call': 0, 't': 40}, {'initial': 8, 'gap_tenths': 20}), ({'min_green': 8, 'added_per_act_tenths': 20, 'max_initial': 12, 'red_actuations': 9, 'initial_gap_tenths': 35, 'min_gap_tenths': 15, 'time_before_reduction': 5, 'time_to_reduce': 20, 'call': -4, 't': 12}, {'initial': 12, 'gap_tenths': 28}), ({'min_green': 6, 'added_per_act_tenths': 25, 'max_initial': 16, 'red_actuations': 4, 'initial_gap_tenths': 50, 'min_gap_tenths': 15, 'time_before_reduction': 10, 'time_to_reduce': 22, 'call': 5, 't': 28}, {'initial': 10, 'gap_tenths': 30}), ({'min_green': 8, 'added_per_act_tenths': 25, 'max_initial': 23, 'red_actuations': 3, 'initial_gap_tenths': 50, 'min_gap_tenths': 10, 'time_before_reduction': 3, 'time_to_reduce': 30, 'call': 3, 't': 53}, {'initial': 8, 'gap_tenths': 10})]]
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_tenths': 10, 'initial': 14}{'gap_tenths': 10, 'initial': 14}Passed
timing oracle 1{'gap_tenths': 50, 'initial': 6}{'gap_tenths': 50, 'initial': 6}Passed
timing oracle 2{'gap_tenths': 20, 'initial': 17}{'gap_tenths': 20, 'initial': 17}Passed
timing oracle 3{'gap_tenths': 20, 'initial': 16}{'gap_tenths': 26, 'initial': 16}Failed
timing oracle 4{'gap_tenths': 20, 'initial': 8}{'gap_tenths': 20, 'initial': 8}Passed
timing oracle 5{'gap_tenths': 20, 'initial': 11}{'gap_tenths': 31, 'initial': 11}Failed
timing oracle 6{'gap_tenths': 20, 'initial': 27}{'gap_tenths': 34, 'initial': 27}Failed
timing oracle 7{'gap_tenths': 28, 'initial': 12}{'gap_tenths': 28, 'initial': 12}Passed

SHA-256 / c53c8d1682f078ff4cd4824ce2ee75e7a8e85aa6b85bf91303fcae2705e298c5

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 2026-09-29T14:47:58.332376+00:00.

Case digest / 80cf24a339457352adf5b36f233733924aa9ad8f2892625a1b1068205a8c06a5