FA-68006 / Traffic signal timing plans / Open access

Volume-density added initial and gap reduction: variable initial is not floored at min green · case 01

Volume-density added initial and gap reduction returns a wrong result when variable initial is not floored at min green.

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ROOT CAUSE

The min/max nesting is inverted, so the variable initial jumps to max initial or beyond.

VERIFIED REPAIR

Restore the variable initial bounds rule so that the step reads `min(x['max_initial'], max(m,`.

Unsuccessful approach: Clamping at zero keeps the cap but lets few actuations produce an initial below min green.

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 = max(x['max_initial'], min(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_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': 9, 'added_per_act_tenths': 15, 'max_initial': 19, 'red_actuations': 11, 'initial_gap_tenths': 50, 'min_gap_tenths': 20, 'time_before_reduction': 12, 'time_to_reduce': 21, 'call': 13, 't': 11}, {'initial': 17, 'gap_tenths': 50}), ({'min_green': 7, 'added_per_act_tenths': 20, 'max_initial': 27, 'red_actuations': 2, 'initial_gap_tenths': 40, 'min_gap_tenths': 15, 'time_before_reduction': 5, 'time_to_reduce': 17, 'call': 15, 't': 60}, {'initial': 7, 'gap_tenths': 15}), ({'min_green': 10, 'added_per_act_tenths': 25, 'max_initial': 10, 'red_actuations': 3, 'initial_gap_tenths': 30, 'min_gap_tenths': 20, 'time_before_reduction': 14, 'time_to_reduce': 28, 'call': 5, 't': 59}, {'initial': 10, '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': 9, 'added_per_act_tenths': 20, 'max_initial': 28, 'red_actuations': 18, 'initial_gap_tenths': 50, 'min_gap_tenths': 10, 'time_before_reduction': 1, 'time_to_reduce': 8, 'call': -2, 't': 11}, {'initial': 28, 'gap_tenths': 10}), ({'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': 7, 'added_per_act_tenths': 25, 'max_initial': 27, 'red_actuations': 18, 'initial_gap_tenths': 35, 'min_gap_tenths': 20, 'time_before_reduction': 5, 'time_to_reduce': 6, 'call': 1, 't': 59}, {'initial': 27, 'gap_tenths': 20})], [({'min_green': 8, 'added_per_act_tenths': 25, 'max_initial': 20, 'red_actuations': 20, 'initial_gap_tenths': 50, 'min_gap_tenths': 20, 'time_before_reduction': 13, 'time_to_reduce': 6, 'call': 3, 't': 13}, {'initial': 20, 'gap_tenths': 50}), ({'min_green': 8, 'added_per_act_tenths': 25, 'max_initial': 10, 'red_actuations': 2, 'initial_gap_tenths': 40, 'min_gap_tenths': 10, 'time_before_reduction': 9, 'time_to_reduce': 22, 'call': 9, 't': 29}, {'initial': 8, 'gap_tenths': 25}), ({'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': 15, 'max_initial': 15, 'red_actuations': 14, 'initial_gap_tenths': 50, 'min_gap_tenths': 15, 'time_before_reduction': 15, 'time_to_reduce': 12, 'call': -1, 't': 23}, {'initial': 15, 'gap_tenths': 27}), ({'min_green': 9, 'added_per_act_tenths': 15, 'max_initial': 24, 'red_actuations': 0, 'initial_gap_tenths': 30, 'min_gap_tenths': 20, 'time_before_reduction': 11, 'time_to_reduce': 25, 'call': 10, 't': 6}, {'initial': 9, 'gap_tenths': 30}), ({'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': 9, 'added_per_act_tenths': 20, 'max_initial': 10, 'red_actuations': 6, 'initial_gap_tenths': 40, 'min_gap_tenths': 10, 'time_before_reduction': 1, 'time_to_reduce': 25, 'call': -1, 't': 52}, {'initial': 10, 'gap_tenths': 10})], [({'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': 9, 'added_per_act_tenths': 25, 'max_initial': 11, 'red_actuations': 18, 'initial_gap_tenths': 30, 'min_gap_tenths': 20, 'time_before_reduction': 12, 'time_to_reduce': 17, 'call': 2, 't': 46}, {'initial': 11, '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': 8, 'added_per_act_tenths': 25, 'max_initial': 27, 'red_actuations': 2, 'initial_gap_tenths': 30, 'min_gap_tenths': 15, 'time_before_reduction': 2, 'time_to_reduce': 21, 'call': 10, 't': 4}, {'initial': 8, 'gap_tenths': 30}), ({'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': 6, 'added_per_act_tenths': 20, 'max_initial': 24, 'red_actuations': 2, 'initial_gap_tenths': 35, 'min_gap_tenths': 20, 'time_before_reduction': 11, 'time_to_reduce': 8, 'call': -2, 't': 26}, {'initial': 6, 'gap_tenths': 20}), ({'min_green': 8, 'added_per_act_tenths': 20, 'max_initial': 12, 'red_actuations': 20, 'initial_gap_tenths': 40, 'min_gap_tenths': 20, 'time_before_reduction': 10, 'time_to_reduce': 24, 'call': 14, 't': 35}, {'initial': 12, 'gap_tenths': 31}), ({'min_green': 4, 'added_per_act_tenths': 15, 'max_initial': 29, 'red_actuations': 3, 'initial_gap_tenths': 40, 'min_gap_tenths': 10, 'time_before_reduction': 12, 'time_to_reduce': 13, 'call': -2, 't': 48}, {'initial': 5, 'gap_tenths': 10})], [({'min_green': 5, 'added_per_act_tenths': 20, 'max_initial': 25, 'red_actuations': 16, 'initial_gap_tenths': 35, 'min_gap_tenths': 15, 'time_before_reduction': 13, 'time_to_reduce': 29, 'call': -4, 't': 16}, {'initial': 25, 'gap_tenths': 33}), ({'min_green': 7, 'added_per_act_tenths': 10, 'max_initial': 11, 'red_actuations': 0, 'initial_gap_tenths': 50, 'min_gap_tenths': 15, 'time_before_reduction': 12, 'time_to_reduce': 6, 'call': 1, 't': 28}, {'initial': 7, 'gap_tenths': 15}), ({'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': 10, 'added_per_act_tenths': 20, 'max_initial': 18, 'red_actuations': 12, 'initial_gap_tenths': 30, 'min_gap_tenths': 15, 'time_before_reduction': 6, 'time_to_reduce': 24, 'call': -2, 't': 33}, {'initial': 18, 'gap_tenths': 15}), ({'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': 21, 'red_actuations': 0, 'initial_gap_tenths': 50, 'min_gap_tenths': 15, 'time_before_reduction': 6, 'time_to_reduce': 29, 'call': 13, 't': 51}, {'initial': 6, 'gap_tenths': 15}), ({'min_green': 9, 'added_per_act_tenths': 25, 'max_initial': 20, 'red_actuations': 9, 'initial_gap_tenths': 35, 'min_gap_tenths': 10, 'time_before_reduction': 2, 'time_to_reduce': 27, 'call': 12, 't': 31}, {'initial': 20, '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': 4, 'added_per_act_tenths': 25, 'max_initial': 15, 'red_actuations': 1, 'initial_gap_tenths': 35, 'min_gap_tenths': 20, 'time_before_reduction': 8, 'time_to_reduce': 21, 'call': 9, 't': 44}, {'initial': 4, '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': 5, 'added_per_act_tenths': 20, 'max_initial': 27, 'red_actuations': 1, 'initial_gap_tenths': 50, 'min_gap_tenths': 15, 'time_before_reduction': 2, 'time_to_reduce': 5, 'call': -4, 't': 31}, {'initial': 5, 'gap_tenths': 15}), ({'min_green': 5, 'added_per_act_tenths': 25, 'max_initial': 10, 'red_actuations': 18, 'initial_gap_tenths': 35, 'min_gap_tenths': 15, 'time_before_reduction': 14, 'time_to_reduce': 22, 'call': -2, 't': 11}, {'initial': 10, 'gap_tenths': 35}), ({'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': 17, 'red_actuations': 20, 'initial_gap_tenths': 50, 'min_gap_tenths': 15, 'time_before_reduction': 1, 'time_to_reduce': 12, 'call': -3, 't': 60}, {'initial': 17, 'gap_tenths': 15}), ({'min_green': 5, 'added_per_act_tenths': 25, 'max_initial': 22, 'red_actuations': 19, 'initial_gap_tenths': 40, 'min_gap_tenths': 15, 'time_before_reduction': 2, 'time_to_reduce': 23, 'call': 12, 't': 12}, {'initial': 22, 'gap_tenths': 40})]]
for i, (args, expected) in enumerate(fixtures[N-1]):
    check('timing oracle' + ' %d' % i, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
timing oracle 0	`{'gap_tenths': 50, 'initial': 19}`	`{'gap_tenths': 50, 'initial': 17}`	Failed
timing oracle 1	`{'gap_tenths': 15, 'initial': 27}`	`{'gap_tenths': 15, 'initial': 7}`	Failed
timing oracle 2	`{'gap_tenths': 20, 'initial': 10}`	`{'gap_tenths': 20, 'initial': 10}`	Passed
timing oracle 3	`{'gap_tenths': 20, 'initial': 25}`	`{'gap_tenths': 20, 'initial': 8}`	Failed
timing oracle 4	`{'gap_tenths': 10, 'initial': 28}`	`{'gap_tenths': 10, 'initial': 28}`	Passed
timing oracle 5	`{'gap_tenths': 31, 'initial': 20}`	`{'gap_tenths': 31, 'initial': 11}`	Failed
timing oracle 6	`{'gap_tenths': 28, 'initial': 12}`	`{'gap_tenths': 28, 'initial': 12}`	Passed
timing oracle 7	`{'gap_tenths': 20, 'initial': 27}`	`{'gap_tenths': 20, 'initial': 27}`	Passed

SHA-256 / 8f4b449a412a432eca1aebdc5d0f24e06793b05bda43e89244e12f74913ce4a5

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(0, -(-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_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': 9, 'added_per_act_tenths': 15, 'max_initial': 19, 'red_actuations': 11, 'initial_gap_tenths': 50, 'min_gap_tenths': 20, 'time_before_reduction': 12, 'time_to_reduce': 21, 'call': 13, 't': 11}, {'initial': 17, 'gap_tenths': 50}), ({'min_green': 7, 'added_per_act_tenths': 20, 'max_initial': 27, 'red_actuations': 2, 'initial_gap_tenths': 40, 'min_gap_tenths': 15, 'time_before_reduction': 5, 'time_to_reduce': 17, 'call': 15, 't': 60}, {'initial': 7, 'gap_tenths': 15}), ({'min_green': 10, 'added_per_act_tenths': 25, 'max_initial': 10, 'red_actuations': 3, 'initial_gap_tenths': 30, 'min_gap_tenths': 20, 'time_before_reduction': 14, 'time_to_reduce': 28, 'call': 5, 't': 59}, {'initial': 10, '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': 9, 'added_per_act_tenths': 20, 'max_initial': 28, 'red_actuations': 18, 'initial_gap_tenths': 50, 'min_gap_tenths': 10, 'time_before_reduction': 1, 'time_to_reduce': 8, 'call': -2, 't': 11}, {'initial': 28, 'gap_tenths': 10}), ({'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': 7, 'added_per_act_tenths': 25, 'max_initial': 27, 'red_actuations': 18, 'initial_gap_tenths': 35, 'min_gap_tenths': 20, 'time_before_reduction': 5, 'time_to_reduce': 6, 'call': 1, 't': 59}, {'initial': 27, 'gap_tenths': 20})], [({'min_green': 8, 'added_per_act_tenths': 25, 'max_initial': 20, 'red_actuations': 20, 'initial_gap_tenths': 50, 'min_gap_tenths': 20, 'time_before_reduction': 13, 'time_to_reduce': 6, 'call': 3, 't': 13}, {'initial': 20, 'gap_tenths': 50}), ({'min_green': 8, 'added_per_act_tenths': 25, 'max_initial': 10, 'red_actuations': 2, 'initial_gap_tenths': 40, 'min_gap_tenths': 10, 'time_before_reduction': 9, 'time_to_reduce': 22, 'call': 9, 't': 29}, {'initial': 8, 'gap_tenths': 25}), ({'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': 15, 'max_initial': 15, 'red_actuations': 14, 'initial_gap_tenths': 50, 'min_gap_tenths': 15, 'time_before_reduction': 15, 'time_to_reduce': 12, 'call': -1, 't': 23}, {'initial': 15, 'gap_tenths': 27}), ({'min_green': 9, 'added_per_act_tenths': 15, 'max_initial': 24, 'red_actuations': 0, 'initial_gap_tenths': 30, 'min_gap_tenths': 20, 'time_before_reduction': 11, 'time_to_reduce': 25, 'call': 10, 't': 6}, {'initial': 9, 'gap_tenths': 30}), ({'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': 9, 'added_per_act_tenths': 20, 'max_initial': 10, 'red_actuations': 6, 'initial_gap_tenths': 40, 'min_gap_tenths': 10, 'time_before_reduction': 1, 'time_to_reduce': 25, 'call': -1, 't': 52}, {'initial': 10, 'gap_tenths': 10})], [({'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': 9, 'added_per_act_tenths': 25, 'max_initial': 11, 'red_actuations': 18, 'initial_gap_tenths': 30, 'min_gap_tenths': 20, 'time_before_reduction': 12, 'time_to_reduce': 17, 'call': 2, 't': 46}, {'initial': 11, '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': 8, 'added_per_act_tenths': 25, 'max_initial': 27, 'red_actuations': 2, 'initial_gap_tenths': 30, 'min_gap_tenths': 15, 'time_before_reduction': 2, 'time_to_reduce': 21, 'call': 10, 't': 4}, {'initial': 8, 'gap_tenths': 30}), ({'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': 6, 'added_per_act_tenths': 20, 'max_initial': 24, 'red_actuations': 2, 'initial_gap_tenths': 35, 'min_gap_tenths': 20, 'time_before_reduction': 11, 'time_to_reduce': 8, 'call': -2, 't': 26}, {'initial': 6, 'gap_tenths': 20}), ({'min_green': 8, 'added_per_act_tenths': 20, 'max_initial': 12, 'red_actuations': 20, 'initial_gap_tenths': 40, 'min_gap_tenths': 20, 'time_before_reduction': 10, 'time_to_reduce': 24, 'call': 14, 't': 35}, {'initial': 12, 'gap_tenths': 31}), ({'min_green': 4, 'added_per_act_tenths': 15, 'max_initial': 29, 'red_actuations': 3, 'initial_gap_tenths': 40, 'min_gap_tenths': 10, 'time_before_reduction': 12, 'time_to_reduce': 13, 'call': -2, 't': 48}, {'initial': 5, 'gap_tenths': 10})], [({'min_green': 5, 'added_per_act_tenths': 20, 'max_initial': 25, 'red_actuations': 16, 'initial_gap_tenths': 35, 'min_gap_tenths': 15, 'time_before_reduction': 13, 'time_to_reduce': 29, 'call': -4, 't': 16}, {'initial': 25, 'gap_tenths': 33}), ({'min_green': 7, 'added_per_act_tenths': 10, 'max_initial': 11, 'red_actuations': 0, 'initial_gap_tenths': 50, 'min_gap_tenths': 15, 'time_before_reduction': 12, 'time_to_reduce': 6, 'call': 1, 't': 28}, {'initial': 7, 'gap_tenths': 15}), ({'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': 10, 'added_per_act_tenths': 20, 'max_initial': 18, 'red_actuations': 12, 'initial_gap_tenths': 30, 'min_gap_tenths': 15, 'time_before_reduction': 6, 'time_to_reduce': 24, 'call': -2, 't': 33}, {'initial': 18, 'gap_tenths': 15}), ({'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': 21, 'red_actuations': 0, 'initial_gap_tenths': 50, 'min_gap_tenths': 15, 'time_before_reduction': 6, 'time_to_reduce': 29, 'call': 13, 't': 51}, {'initial': 6, 'gap_tenths': 15}), ({'min_green': 9, 'added_per_act_tenths': 25, 'max_initial': 20, 'red_actuations': 9, 'initial_gap_tenths': 35, 'min_gap_tenths': 10, 'time_before_reduction': 2, 'time_to_reduce': 27, 'call': 12, 't': 31}, {'initial': 20, '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': 4, 'added_per_act_tenths': 25, 'max_initial': 15, 'red_actuations': 1, 'initial_gap_tenths': 35, 'min_gap_tenths': 20, 'time_before_reduction': 8, 'time_to_reduce': 21, 'call': 9, 't': 44}, {'initial': 4, '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': 5, 'added_per_act_tenths': 20, 'max_initial': 27, 'red_actuations': 1, 'initial_gap_tenths': 50, 'min_gap_tenths': 15, 'time_before_reduction': 2, 'time_to_reduce': 5, 'call': -4, 't': 31}, {'initial': 5, 'gap_tenths': 15}), ({'min_green': 5, 'added_per_act_tenths': 25, 'max_initial': 10, 'red_actuations': 18, 'initial_gap_tenths': 35, 'min_gap_tenths': 15, 'time_before_reduction': 14, 'time_to_reduce': 22, 'call': -2, 't': 11}, {'initial': 10, 'gap_tenths': 35}), ({'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': 17, 'red_actuations': 20, 'initial_gap_tenths': 50, 'min_gap_tenths': 15, 'time_before_reduction': 1, 'time_to_reduce': 12, 'call': -3, 't': 60}, {'initial': 17, 'gap_tenths': 15}), ({'min_green': 5, 'added_per_act_tenths': 25, 'max_initial': 22, 'red_actuations': 19, 'initial_gap_tenths': 40, 'min_gap_tenths': 15, 'time_before_reduction': 2, 'time_to_reduce': 23, 'call': 12, 't': 12}, {'initial': 22, 'gap_tenths': 40})]]
for i, (args, expected) in enumerate(fixtures[N-1]):
    check('timing oracle' + ' %d' % i, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
timing oracle 0	`{'gap_tenths': 50, 'initial': 17}`	`{'gap_tenths': 50, 'initial': 17}`	Passed
timing oracle 1	`{'gap_tenths': 15, 'initial': 4}`	`{'gap_tenths': 15, 'initial': 7}`	Failed
timing oracle 2	`{'gap_tenths': 20, 'initial': 8}`	`{'gap_tenths': 20, 'initial': 10}`	Failed
timing oracle 3	`{'gap_tenths': 20, 'initial': 8}`	`{'gap_tenths': 20, 'initial': 8}`	Passed
timing oracle 4	`{'gap_tenths': 10, 'initial': 28}`	`{'gap_tenths': 10, 'initial': 28}`	Passed
timing oracle 5	`{'gap_tenths': 31, 'initial': 11}`	`{'gap_tenths': 31, 'initial': 11}`	Passed
timing oracle 6	`{'gap_tenths': 28, 'initial': 12}`	`{'gap_tenths': 28, 'initial': 12}`	Passed
timing oracle 7	`{'gap_tenths': 20, 'initial': 27}`	`{'gap_tenths': 20, 'initial': 27}`	Passed

SHA-256 / de904d8ccc8244706b57435223e5e3dff807e8cfe0fbe6e773f78d32bdd720c3

3 / The verified repair

Exit 0

"""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_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': 9, 'added_per_act_tenths': 15, 'max_initial': 19, 'red_actuations': 11, 'initial_gap_tenths': 50, 'min_gap_tenths': 20, 'time_before_reduction': 12, 'time_to_reduce': 21, 'call': 13, 't': 11}, {'initial': 17, 'gap_tenths': 50}), ({'min_green': 7, 'added_per_act_tenths': 20, 'max_initial': 27, 'red_actuations': 2, 'initial_gap_tenths': 40, 'min_gap_tenths': 15, 'time_before_reduction': 5, 'time_to_reduce': 17, 'call': 15, 't': 60}, {'initial': 7, 'gap_tenths': 15}), ({'min_green': 10, 'added_per_act_tenths': 25, 'max_initial': 10, 'red_actuations': 3, 'initial_gap_tenths': 30, 'min_gap_tenths': 20, 'time_before_reduction': 14, 'time_to_reduce': 28, 'call': 5, 't': 59}, {'initial': 10, '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': 9, 'added_per_act_tenths': 20, 'max_initial': 28, 'red_actuations': 18, 'initial_gap_tenths': 50, 'min_gap_tenths': 10, 'time_before_reduction': 1, 'time_to_reduce': 8, 'call': -2, 't': 11}, {'initial': 28, 'gap_tenths': 10}), ({'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': 7, 'added_per_act_tenths': 25, 'max_initial': 27, 'red_actuations': 18, 'initial_gap_tenths': 35, 'min_gap_tenths': 20, 'time_before_reduction': 5, 'time_to_reduce': 6, 'call': 1, 't': 59}, {'initial': 27, 'gap_tenths': 20})], [({'min_green': 8, 'added_per_act_tenths': 25, 'max_initial': 20, 'red_actuations': 20, 'initial_gap_tenths': 50, 'min_gap_tenths': 20, 'time_before_reduction': 13, 'time_to_reduce': 6, 'call': 3, 't': 13}, {'initial': 20, 'gap_tenths': 50}), ({'min_green': 8, 'added_per_act_tenths': 25, 'max_initial': 10, 'red_actuations': 2, 'initial_gap_tenths': 40, 'min_gap_tenths': 10, 'time_before_reduction': 9, 'time_to_reduce': 22, 'call': 9, 't': 29}, {'initial': 8, 'gap_tenths': 25}), ({'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': 15, 'max_initial': 15, 'red_actuations': 14, 'initial_gap_tenths': 50, 'min_gap_tenths': 15, 'time_before_reduction': 15, 'time_to_reduce': 12, 'call': -1, 't': 23}, {'initial': 15, 'gap_tenths': 27}), ({'min_green': 9, 'added_per_act_tenths': 15, 'max_initial': 24, 'red_actuations': 0, 'initial_gap_tenths': 30, 'min_gap_tenths': 20, 'time_before_reduction': 11, 'time_to_reduce': 25, 'call': 10, 't': 6}, {'initial': 9, 'gap_tenths': 30}), ({'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': 9, 'added_per_act_tenths': 20, 'max_initial': 10, 'red_actuations': 6, 'initial_gap_tenths': 40, 'min_gap_tenths': 10, 'time_before_reduction': 1, 'time_to_reduce': 25, 'call': -1, 't': 52}, {'initial': 10, 'gap_tenths': 10})], [({'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': 9, 'added_per_act_tenths': 25, 'max_initial': 11, 'red_actuations': 18, 'initial_gap_tenths': 30, 'min_gap_tenths': 20, 'time_before_reduction': 12, 'time_to_reduce': 17, 'call': 2, 't': 46}, {'initial': 11, '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': 8, 'added_per_act_tenths': 25, 'max_initial': 27, 'red_actuations': 2, 'initial_gap_tenths': 30, 'min_gap_tenths': 15, 'time_before_reduction': 2, 'time_to_reduce': 21, 'call': 10, 't': 4}, {'initial': 8, 'gap_tenths': 30}), ({'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': 6, 'added_per_act_tenths': 20, 'max_initial': 24, 'red_actuations': 2, 'initial_gap_tenths': 35, 'min_gap_tenths': 20, 'time_before_reduction': 11, 'time_to_reduce': 8, 'call': -2, 't': 26}, {'initial': 6, 'gap_tenths': 20}), ({'min_green': 8, 'added_per_act_tenths': 20, 'max_initial': 12, 'red_actuations': 20, 'initial_gap_tenths': 40, 'min_gap_tenths': 20, 'time_before_reduction': 10, 'time_to_reduce': 24, 'call': 14, 't': 35}, {'initial': 12, 'gap_tenths': 31}), ({'min_green': 4, 'added_per_act_tenths': 15, 'max_initial': 29, 'red_actuations': 3, 'initial_gap_tenths': 40, 'min_gap_tenths': 10, 'time_before_reduction': 12, 'time_to_reduce': 13, 'call': -2, 't': 48}, {'initial': 5, 'gap_tenths': 10})], [({'min_green': 5, 'added_per_act_tenths': 20, 'max_initial': 25, 'red_actuations': 16, 'initial_gap_tenths': 35, 'min_gap_tenths': 15, 'time_before_reduction': 13, 'time_to_reduce': 29, 'call': -4, 't': 16}, {'initial': 25, 'gap_tenths': 33}), ({'min_green': 7, 'added_per_act_tenths': 10, 'max_initial': 11, 'red_actuations': 0, 'initial_gap_tenths': 50, 'min_gap_tenths': 15, 'time_before_reduction': 12, 'time_to_reduce': 6, 'call': 1, 't': 28}, {'initial': 7, 'gap_tenths': 15}), ({'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': 10, 'added_per_act_tenths': 20, 'max_initial': 18, 'red_actuations': 12, 'initial_gap_tenths': 30, 'min_gap_tenths': 15, 'time_before_reduction': 6, 'time_to_reduce': 24, 'call': -2, 't': 33}, {'initial': 18, 'gap_tenths': 15}), ({'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': 21, 'red_actuations': 0, 'initial_gap_tenths': 50, 'min_gap_tenths': 15, 'time_before_reduction': 6, 'time_to_reduce': 29, 'call': 13, 't': 51}, {'initial': 6, 'gap_tenths': 15}), ({'min_green': 9, 'added_per_act_tenths': 25, 'max_initial': 20, 'red_actuations': 9, 'initial_gap_tenths': 35, 'min_gap_tenths': 10, 'time_before_reduction': 2, 'time_to_reduce': 27, 'call': 12, 't': 31}, {'initial': 20, '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': 4, 'added_per_act_tenths': 25, 'max_initial': 15, 'red_actuations': 1, 'initial_gap_tenths': 35, 'min_gap_tenths': 20, 'time_before_reduction': 8, 'time_to_reduce': 21, 'call': 9, 't': 44}, {'initial': 4, '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': 5, 'added_per_act_tenths': 20, 'max_initial': 27, 'red_actuations': 1, 'initial_gap_tenths': 50, 'min_gap_tenths': 15, 'time_before_reduction': 2, 'time_to_reduce': 5, 'call': -4, 't': 31}, {'initial': 5, 'gap_tenths': 15}), ({'min_green': 5, 'added_per_act_tenths': 25, 'max_initial': 10, 'red_actuations': 18, 'initial_gap_tenths': 35, 'min_gap_tenths': 15, 'time_before_reduction': 14, 'time_to_reduce': 22, 'call': -2, 't': 11}, {'initial': 10, 'gap_tenths': 35}), ({'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': 17, 'red_actuations': 20, 'initial_gap_tenths': 50, 'min_gap_tenths': 15, 'time_before_reduction': 1, 'time_to_reduce': 12, 'call': -3, 't': 60}, {'initial': 17, 'gap_tenths': 15}), ({'min_green': 5, 'added_per_act_tenths': 25, 'max_initial': 22, 'red_actuations': 19, 'initial_gap_tenths': 40, 'min_gap_tenths': 15, 'time_before_reduction': 2, 'time_to_reduce': 23, 'call': 12, 't': 12}, {'initial': 22, 'gap_tenths': 40})]]
for i, (args, expected) in enumerate(fixtures[N-1]):
    check('timing oracle' + ' %d' % i, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
timing oracle 0	`{'gap_tenths': 50, 'initial': 17}`	`{'gap_tenths': 50, 'initial': 17}`	Passed
timing oracle 1	`{'gap_tenths': 15, 'initial': 7}`	`{'gap_tenths': 15, 'initial': 7}`	Passed
timing oracle 2	`{'gap_tenths': 20, 'initial': 10}`	`{'gap_tenths': 20, 'initial': 10}`	Passed
timing oracle 3	`{'gap_tenths': 20, 'initial': 8}`	`{'gap_tenths': 20, 'initial': 8}`	Passed
timing oracle 4	`{'gap_tenths': 10, 'initial': 28}`	`{'gap_tenths': 10, 'initial': 28}`	Passed
timing oracle 5	`{'gap_tenths': 31, 'initial': 11}`	`{'gap_tenths': 31, 'initial': 11}`	Passed
timing oracle 6	`{'gap_tenths': 28, 'initial': 12}`	`{'gap_tenths': 28, 'initial': 12}`	Passed
timing oracle 7	`{'gap_tenths': 20, 'initial': 27}`	`{'gap_tenths': 20, 'initial': 27}`	Passed

SHA-256 / 7b4d70f46330cb4e830d7ab6c5e9122ece344687afeb97b30c215b86cc74c066

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 2026-09-29T14:47:58.254734+00:00.

Case digest / 2fee26a4849f9d794a241cdfeba4225ef9c0e2f2855c573e6cd78ad31a045e06