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FA-67861 / Traffic signal timing plans / Open access

Webster cycle length: the oversaturation guard only trips above Y = 1 · case 01

Webster cycle length returns a wrong result when the oversaturation guard only trips above Y = 1.

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

ROOT CAUSE

The guard uses the physical limit Y > 1, so plans with 0.9 <= Y <= 1 get absurdly long cycles instead of the oversaturated verdict.

VERIFIED REPAIR

Restore the oversaturation guard rule so that the step reads `if Y >= Fraction(9, 10):`.

Unsuccessful approach: A strict comparison misses the stipulated inclusive threshold at exactly Y = 0.9.

Case contract

Input {phases: per-phase lists of lane-group flows veh/h, sat: saturation flow per lane group, lost: lost seconds per phase, allred: extra all-red seconds per cycle, cmin, cmax}. Y is the sum over phases of the critical (largest) flow ratio; L = lost*phases + allred. If Y >= 0.9 return 'oversaturated'. Otherwise C0 = (1.5L + 5)/(1 - Y), rounded UP to a multiple of 5 s and clamped to [cmin, cmax]. Return {cycle, lost: L, y_milli: floor(1000Y)}.

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
from fractions import Fraction
import math
N = 1
observations = []
def solve(x):
    ph = x['phases']
    s = x['sat']
    Y = Fraction(0)
    for group in ph:
        Y += Fraction(max(group), s)
    L = x['lost'] * len(ph) + x['allred']
    if Y > 1:
        return 'oversaturated'
    c0 = (Fraction(3, 2) * L + 5) / (1 - Y)
    c = -(-c0 // 5) * 5
    c = max(x['cmin'], min(x['cmax'], int(c)))
    return {'cycle': c, 'lost': L, 'y_milli': int(Y * 1000)}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[({'phases': [[810], [810]], 'sat': 1800, 'lost': 4, 'allred': 0, 'cmin': 40, 'cmax': 180}, 'oversaturated'), ({'phases': [[90, 630], [450, 600], [180, 540]], 'sat': 1800, 'lost': 4, 'allred': 1, 'cmin': 60, 'cmax': 120}, 'oversaturated'), ({'phases': [[540, 450, 480], [390, 540]], 'sat': 1800, 'lost': 3, 'allred': 3, 'cmin': 40, 'cmax': 90}, {'cycle': 50, 'lost': 9, 'y_milli': 600}), ({'phases': [[150], [240, 510], [900], [690]], 'sat': 1800, 'lost': 3, 'allred': 4, 'cmin': 60, 'cmax': 120}, 'oversaturated'), ({'phases': [[720, 360], [540, 900]], 'sat': 1800, 'lost': 4, 'allred': 4, 'cmin': 60, 'cmax': 150}, 'oversaturated'), ({'phases': [[300, 600], [450]], 'sat': 1800, 'lost': 4, 'allred': 2, 'cmin': 40, 'cmax': 120}, {'cycle': 50, 'lost': 10, 'y_milli': 583}), ({'phases': [[330, 720, 390], [690, 840], [390], [750]], 'sat': 1900, 'lost': 5, 'allred': 0, 'cmin': 40, 'cmax': 180}, 'oversaturated'), ({'phases': [[690], [570]], 'sat': 1900, 'lost': 5, 'allred': 1, 'cmin': 60, 'cmax': 150}, {'cycle': 65, 'lost': 11, 'y_milli': 663})], [({'phases': [[600], [780, 750], [900, 720, 150]], 'sat': 1800, 'lost': 2, 'allred': 1, 'cmin': 50, 'cmax': 180}, 'oversaturated'), ({'phases': [[450, 720, 750], [630, 270], [210], [210]], 'sat': 1900, 'lost': 4, 'allred': 4, 'cmin': 50, 'cmax': 180}, 'oversaturated'), ({'phases': [[90], [90], [90]], 'sat': 1800, 'lost': 3, 'allred': 0, 'cmin': 60, 'cmax': 120}, {'cycle': 60, 'lost': 9, 'y_milli': 150}), ({'phases': [[810], [810]], 'sat': 1800, 'lost': 4, 'allred': 0, 'cmin': 40, 'cmax': 180}, 'oversaturated'), ({'phases': [[540, 210, 210], [780], [240], [330]], 'sat': 1900, 'lost': 2, 'allred': 2, 'cmin': 50, 'cmax': 180}, 'oversaturated'), ({'phases': [[720, 360], [540, 900]], 'sat': 1800, 'lost': 4, 'allred': 4, 'cmin': 60, 'cmax': 150}, 'oversaturated'), ({'phases': [[570], [600, 210, 660], [210, 780, 240]], 'sat': 1900, 'lost': 2, 'allred': 2, 'cmin': 50, 'cmax': 120}, 'oversaturated'), ({'phases': [[90, 480], [420, 630]], 'sat': 1900, 'lost': 2, 'allred': 6, 'cmin': 60, 'cmax': 150}, {'cycle': 60, 'lost': 10, 'y_milli': 584})], [({'phases': [[900, 420, 210], [180, 150, 840], [780]], 'sat': 2000, 'lost': 2, 'allred': 0, 'cmin': 40, 'cmax': 120}, 'oversaturated'), ({'phases': [[900], [360, 450, 810]], 'sat': 1900, 'lost': 3, 'allred': 3, 'cmin': 60, 'cmax': 120}, 'oversaturated'), ({'phases': [[270], [750, 720, 330]], 'sat': 2000, 'lost': 3, 'allred': 4, 'cmin': 40, 'cmax': 120}, {'cycle': 45, 'lost': 10, 'y_milli': 510}), ({'phases': [[300, 600], [450]], 'sat': 1800, 'lost': 4, 'allred': 2, 'cmin': 40, 'cmax': 120}, {'cycle': 50, 'lost': 10, 'y_milli': 583}), ({'phases': [[750], [600], [150, 60, 60], [420]], 'sat': 2000, 'lost': 3, 'allred': 3, 'cmin': 40, 'cmax': 150}, 'oversaturated'), ({'phases': [[180, 780], [90, 900, 420]], 'sat': 1800, 'lost': 3, 'allred': 2, 'cmin': 40, 'cmax': 150}, 'oversaturated'), ({'phases': [[810], [810]], 'sat': 1800, 'lost': 4, 'allred': 0, 'cmin': 40, 'cmax': 180}, 'oversaturated'), ({'phases': [[90], [90], [90]], 'sat': 1800, 'lost': 3, 'allred': 0, 'cmin': 60, 'cmax': 120}, {'cycle': 60, 'lost': 9, 'y_milli': 150})], [({'phases': [[720, 360], [540, 900]], 'sat': 1800, 'lost': 4, 'allred': 4, 'cmin': 60, 'cmax': 150}, 'oversaturated'), ({'phases': [[90, 900, 810], [750, 540]], 'sat': 2000, 'lost': 5, 'allred': 0, 'cmin': 60, 'cmax': 150}, {'cycle': 115, 'lost': 10, 'y_milli': 825}), ({'phases': [[90], [90], [90]], 'sat': 1800, 'lost': 3, 'allred': 0, 'cmin': 60, 'cmax': 120}, {'cycle': 60, 'lost': 9, 'y_milli': 150}), ({'phases': [[720, 510], [300, 750]], 'sat': 1800, 'lost': 5, 'allred': 2, 'cmin': 40, 'cmax': 90}, {'cycle': 90, 'lost': 12, 'y_milli': 816}), ({'phases': [[360], [630, 750], [750]], 'sat': 2000, 'lost': 3, 'allred': 1, 'cmin': 40, 'cmax': 90}, 'oversaturated'), ({'phases': [[360], [360, 510, 630], [570, 840], [840]], 'sat': 1800, 'lost': 5, 'allred': 2, 'cmin': 40, 'cmax': 120}, 'oversaturated'), ({'phases': [[300], [630]], 'sat': 1800, 'lost': 4, 'allred': 3, 'cmin': 40, 'cmax': 120}, {'cycle': 45, 'lost': 11, 'y_milli': 516}), ({'phases': [[810], [810]], 'sat': 1800, 'lost': 4, 'allred': 0, 'cmin': 40, 'cmax': 180}, 'oversaturated')], [({'phases': [[330, 840, 90], [60, 180], [720]], 'sat': 1800, 'lost': 4, 'allred': 2, 'cmin': 40, 'cmax': 180}, 'oversaturated'), ({'phases': [[810], [810]], 'sat': 1800, 'lost': 4, 'allred': 0, 'cmin': 40, 'cmax': 180}, 'oversaturated'), ({'phases': [[690, 420], [150]], 'sat': 1800, 'lost': 5, 'allred': 4, 'cmin': 60, 'cmax': 150}, {'cycle': 60, 'lost': 14, 'y_milli': 466}), ({'phases': [[450, 120, 480], [600], [630, 90, 780], [900, 720, 510]], 'sat': 1800, 'lost': 2, 'allred': 4, 'cmin': 50, 'cmax': 180}, 'oversaturated'), ({'phases': [[720, 360], [540, 900]], 'sat': 1800, 'lost': 4, 'allred': 4, 'cmin': 60, 'cmax': 150}, 'oversaturated'), ({'phases': [[840, 840], [900, 90, 180], [570], [330, 270]], 'sat': 2000, 'lost': 2, 'allred': 2, 'cmin': 50, 'cmax': 150}, 'oversaturated'), ({'phases': [[150, 420], [690, 180, 180], [570, 390]], 'sat': 1900, 'lost': 5, 'allred': 0, 'cmin': 60, 'cmax': 180}, {'cycle': 180, 'lost': 15, 'y_milli': 884}), ({'phases': [[90], [90], [90]], 'sat': 1800, 'lost': 3, 'allred': 0, 'cmin': 60, 'cmax': 120}, {'cycle': 60, 'lost': 9, 'y_milli': 150})]]
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': 170, 'lost': 8, 'y_milli': 900}oversaturatedFailed
timing oracle 1{'cycle': 120, 'lost': 13, 'y_milli': 983}oversaturatedFailed
timing oracle 2{'cycle': 50, 'lost': 9, 'y_milli': 600}{'cycle': 50, 'lost': 9, 'y_milli': 600}Passed
timing oracle 3oversaturatedoversaturatedPassed
timing oracle 4{'cycle': 150, 'lost': 12, 'y_milli': 900}oversaturatedFailed
timing oracle 5{'cycle': 50, 'lost': 10, 'y_milli': 583}{'cycle': 50, 'lost': 10, 'y_milli': 583}Passed
timing oracle 6oversaturatedoversaturatedPassed
timing oracle 7{'cycle': 65, 'lost': 11, 'y_milli': 663}{'cycle': 65, 'lost': 11, 'y_milli': 663}Passed

SHA-256 / 2ccf5155a1374a151434732471325e85e3ee406a3350d6e53a2f6ad8aea736a6

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
import math
N = 1
observations = []
def solve(x):
    ph = x['phases']
    s = x['sat']
    Y = Fraction(0)
    for group in ph:
        Y += Fraction(max(group), s)
    L = x['lost'] * len(ph) + x['allred']
    if Y > Fraction(9, 10):
        return 'oversaturated'
    c0 = (Fraction(3, 2) * L + 5) / (1 - Y)
    c = -(-c0 // 5) * 5
    c = max(x['cmin'], min(x['cmax'], int(c)))
    return {'cycle': c, 'lost': L, 'y_milli': int(Y * 1000)}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[({'phases': [[810], [810]], 'sat': 1800, 'lost': 4, 'allred': 0, 'cmin': 40, 'cmax': 180}, 'oversaturated'), ({'phases': [[90, 630], [450, 600], [180, 540]], 'sat': 1800, 'lost': 4, 'allred': 1, 'cmin': 60, 'cmax': 120}, 'oversaturated'), ({'phases': [[540, 450, 480], [390, 540]], 'sat': 1800, 'lost': 3, 'allred': 3, 'cmin': 40, 'cmax': 90}, {'cycle': 50, 'lost': 9, 'y_milli': 600}), ({'phases': [[150], [240, 510], [900], [690]], 'sat': 1800, 'lost': 3, 'allred': 4, 'cmin': 60, 'cmax': 120}, 'oversaturated'), ({'phases': [[720, 360], [540, 900]], 'sat': 1800, 'lost': 4, 'allred': 4, 'cmin': 60, 'cmax': 150}, 'oversaturated'), ({'phases': [[300, 600], [450]], 'sat': 1800, 'lost': 4, 'allred': 2, 'cmin': 40, 'cmax': 120}, {'cycle': 50, 'lost': 10, 'y_milli': 583}), ({'phases': [[330, 720, 390], [690, 840], [390], [750]], 'sat': 1900, 'lost': 5, 'allred': 0, 'cmin': 40, 'cmax': 180}, 'oversaturated'), ({'phases': [[690], [570]], 'sat': 1900, 'lost': 5, 'allred': 1, 'cmin': 60, 'cmax': 150}, {'cycle': 65, 'lost': 11, 'y_milli': 663})], [({'phases': [[600], [780, 750], [900, 720, 150]], 'sat': 1800, 'lost': 2, 'allred': 1, 'cmin': 50, 'cmax': 180}, 'oversaturated'), ({'phases': [[450, 720, 750], [630, 270], [210], [210]], 'sat': 1900, 'lost': 4, 'allred': 4, 'cmin': 50, 'cmax': 180}, 'oversaturated'), ({'phases': [[90], [90], [90]], 'sat': 1800, 'lost': 3, 'allred': 0, 'cmin': 60, 'cmax': 120}, {'cycle': 60, 'lost': 9, 'y_milli': 150}), ({'phases': [[810], [810]], 'sat': 1800, 'lost': 4, 'allred': 0, 'cmin': 40, 'cmax': 180}, 'oversaturated'), ({'phases': [[540, 210, 210], [780], [240], [330]], 'sat': 1900, 'lost': 2, 'allred': 2, 'cmin': 50, 'cmax': 180}, 'oversaturated'), ({'phases': [[720, 360], [540, 900]], 'sat': 1800, 'lost': 4, 'allred': 4, 'cmin': 60, 'cmax': 150}, 'oversaturated'), ({'phases': [[570], [600, 210, 660], [210, 780, 240]], 'sat': 1900, 'lost': 2, 'allred': 2, 'cmin': 50, 'cmax': 120}, 'oversaturated'), ({'phases': [[90, 480], [420, 630]], 'sat': 1900, 'lost': 2, 'allred': 6, 'cmin': 60, 'cmax': 150}, {'cycle': 60, 'lost': 10, 'y_milli': 584})], [({'phases': [[900, 420, 210], [180, 150, 840], [780]], 'sat': 2000, 'lost': 2, 'allred': 0, 'cmin': 40, 'cmax': 120}, 'oversaturated'), ({'phases': [[900], [360, 450, 810]], 'sat': 1900, 'lost': 3, 'allred': 3, 'cmin': 60, 'cmax': 120}, 'oversaturated'), ({'phases': [[270], [750, 720, 330]], 'sat': 2000, 'lost': 3, 'allred': 4, 'cmin': 40, 'cmax': 120}, {'cycle': 45, 'lost': 10, 'y_milli': 510}), ({'phases': [[300, 600], [450]], 'sat': 1800, 'lost': 4, 'allred': 2, 'cmin': 40, 'cmax': 120}, {'cycle': 50, 'lost': 10, 'y_milli': 583}), ({'phases': [[750], [600], [150, 60, 60], [420]], 'sat': 2000, 'lost': 3, 'allred': 3, 'cmin': 40, 'cmax': 150}, 'oversaturated'), ({'phases': [[180, 780], [90, 900, 420]], 'sat': 1800, 'lost': 3, 'allred': 2, 'cmin': 40, 'cmax': 150}, 'oversaturated'), ({'phases': [[810], [810]], 'sat': 1800, 'lost': 4, 'allred': 0, 'cmin': 40, 'cmax': 180}, 'oversaturated'), ({'phases': [[90], [90], [90]], 'sat': 1800, 'lost': 3, 'allred': 0, 'cmin': 60, 'cmax': 120}, {'cycle': 60, 'lost': 9, 'y_milli': 150})], [({'phases': [[720, 360], [540, 900]], 'sat': 1800, 'lost': 4, 'allred': 4, 'cmin': 60, 'cmax': 150}, 'oversaturated'), ({'phases': [[90, 900, 810], [750, 540]], 'sat': 2000, 'lost': 5, 'allred': 0, 'cmin': 60, 'cmax': 150}, {'cycle': 115, 'lost': 10, 'y_milli': 825}), ({'phases': [[90], [90], [90]], 'sat': 1800, 'lost': 3, 'allred': 0, 'cmin': 60, 'cmax': 120}, {'cycle': 60, 'lost': 9, 'y_milli': 150}), ({'phases': [[720, 510], [300, 750]], 'sat': 1800, 'lost': 5, 'allred': 2, 'cmin': 40, 'cmax': 90}, {'cycle': 90, 'lost': 12, 'y_milli': 816}), ({'phases': [[360], [630, 750], [750]], 'sat': 2000, 'lost': 3, 'allred': 1, 'cmin': 40, 'cmax': 90}, 'oversaturated'), ({'phases': [[360], [360, 510, 630], [570, 840], [840]], 'sat': 1800, 'lost': 5, 'allred': 2, 'cmin': 40, 'cmax': 120}, 'oversaturated'), ({'phases': [[300], [630]], 'sat': 1800, 'lost': 4, 'allred': 3, 'cmin': 40, 'cmax': 120}, {'cycle': 45, 'lost': 11, 'y_milli': 516}), ({'phases': [[810], [810]], 'sat': 1800, 'lost': 4, 'allred': 0, 'cmin': 40, 'cmax': 180}, 'oversaturated')], [({'phases': [[330, 840, 90], [60, 180], [720]], 'sat': 1800, 'lost': 4, 'allred': 2, 'cmin': 40, 'cmax': 180}, 'oversaturated'), ({'phases': [[810], [810]], 'sat': 1800, 'lost': 4, 'allred': 0, 'cmin': 40, 'cmax': 180}, 'oversaturated'), ({'phases': [[690, 420], [150]], 'sat': 1800, 'lost': 5, 'allred': 4, 'cmin': 60, 'cmax': 150}, {'cycle': 60, 'lost': 14, 'y_milli': 466}), ({'phases': [[450, 120, 480], [600], [630, 90, 780], [900, 720, 510]], 'sat': 1800, 'lost': 2, 'allred': 4, 'cmin': 50, 'cmax': 180}, 'oversaturated'), ({'phases': [[720, 360], [540, 900]], 'sat': 1800, 'lost': 4, 'allred': 4, 'cmin': 60, 'cmax': 150}, 'oversaturated'), ({'phases': [[840, 840], [900, 90, 180], [570], [330, 270]], 'sat': 2000, 'lost': 2, 'allred': 2, 'cmin': 50, 'cmax': 150}, 'oversaturated'), ({'phases': [[150, 420], [690, 180, 180], [570, 390]], 'sat': 1900, 'lost': 5, 'allred': 0, 'cmin': 60, 'cmax': 180}, {'cycle': 180, 'lost': 15, 'y_milli': 884}), ({'phases': [[90], [90], [90]], 'sat': 1800, 'lost': 3, 'allred': 0, 'cmin': 60, 'cmax': 120}, {'cycle': 60, 'lost': 9, 'y_milli': 150})]]
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': 170, 'lost': 8, 'y_milli': 900}oversaturatedFailed
timing oracle 1oversaturatedoversaturatedPassed
timing oracle 2{'cycle': 50, 'lost': 9, 'y_milli': 600}{'cycle': 50, 'lost': 9, 'y_milli': 600}Passed
timing oracle 3oversaturatedoversaturatedPassed
timing oracle 4{'cycle': 150, 'lost': 12, 'y_milli': 900}oversaturatedFailed
timing oracle 5{'cycle': 50, 'lost': 10, 'y_milli': 583}{'cycle': 50, 'lost': 10, 'y_milli': 583}Passed
timing oracle 6oversaturatedoversaturatedPassed
timing oracle 7{'cycle': 65, 'lost': 11, 'y_milli': 663}{'cycle': 65, 'lost': 11, 'y_milli': 663}Passed

SHA-256 / 4f8ef5ec37eb443b792a66c081b466c4fda20ccf1e7f60b32e168aff16451de4

3 / The verified repair

Exit 0
"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
import math
N = 1
observations = []
def solve(x):
    ph = x['phases']
    s = x['sat']
    Y = Fraction(0)
    for group in ph:
        Y += Fraction(max(group), s)
    L = x['lost'] * len(ph) + x['allred']
    if Y >= Fraction(9, 10):
        return 'oversaturated'
    c0 = (Fraction(3, 2) * L + 5) / (1 - Y)
    c = -(-c0 // 5) * 5
    c = max(x['cmin'], min(x['cmax'], int(c)))
    return {'cycle': c, 'lost': L, 'y_milli': int(Y * 1000)}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[({'phases': [[810], [810]], 'sat': 1800, 'lost': 4, 'allred': 0, 'cmin': 40, 'cmax': 180}, 'oversaturated'), ({'phases': [[90, 630], [450, 600], [180, 540]], 'sat': 1800, 'lost': 4, 'allred': 1, 'cmin': 60, 'cmax': 120}, 'oversaturated'), ({'phases': [[540, 450, 480], [390, 540]], 'sat': 1800, 'lost': 3, 'allred': 3, 'cmin': 40, 'cmax': 90}, {'cycle': 50, 'lost': 9, 'y_milli': 600}), ({'phases': [[150], [240, 510], [900], [690]], 'sat': 1800, 'lost': 3, 'allred': 4, 'cmin': 60, 'cmax': 120}, 'oversaturated'), ({'phases': [[720, 360], [540, 900]], 'sat': 1800, 'lost': 4, 'allred': 4, 'cmin': 60, 'cmax': 150}, 'oversaturated'), ({'phases': [[300, 600], [450]], 'sat': 1800, 'lost': 4, 'allred': 2, 'cmin': 40, 'cmax': 120}, {'cycle': 50, 'lost': 10, 'y_milli': 583}), ({'phases': [[330, 720, 390], [690, 840], [390], [750]], 'sat': 1900, 'lost': 5, 'allred': 0, 'cmin': 40, 'cmax': 180}, 'oversaturated'), ({'phases': [[690], [570]], 'sat': 1900, 'lost': 5, 'allred': 1, 'cmin': 60, 'cmax': 150}, {'cycle': 65, 'lost': 11, 'y_milli': 663})], [({'phases': [[600], [780, 750], [900, 720, 150]], 'sat': 1800, 'lost': 2, 'allred': 1, 'cmin': 50, 'cmax': 180}, 'oversaturated'), ({'phases': [[450, 720, 750], [630, 270], [210], [210]], 'sat': 1900, 'lost': 4, 'allred': 4, 'cmin': 50, 'cmax': 180}, 'oversaturated'), ({'phases': [[90], [90], [90]], 'sat': 1800, 'lost': 3, 'allred': 0, 'cmin': 60, 'cmax': 120}, {'cycle': 60, 'lost': 9, 'y_milli': 150}), ({'phases': [[810], [810]], 'sat': 1800, 'lost': 4, 'allred': 0, 'cmin': 40, 'cmax': 180}, 'oversaturated'), ({'phases': [[540, 210, 210], [780], [240], [330]], 'sat': 1900, 'lost': 2, 'allred': 2, 'cmin': 50, 'cmax': 180}, 'oversaturated'), ({'phases': [[720, 360], [540, 900]], 'sat': 1800, 'lost': 4, 'allred': 4, 'cmin': 60, 'cmax': 150}, 'oversaturated'), ({'phases': [[570], [600, 210, 660], [210, 780, 240]], 'sat': 1900, 'lost': 2, 'allred': 2, 'cmin': 50, 'cmax': 120}, 'oversaturated'), ({'phases': [[90, 480], [420, 630]], 'sat': 1900, 'lost': 2, 'allred': 6, 'cmin': 60, 'cmax': 150}, {'cycle': 60, 'lost': 10, 'y_milli': 584})], [({'phases': [[900, 420, 210], [180, 150, 840], [780]], 'sat': 2000, 'lost': 2, 'allred': 0, 'cmin': 40, 'cmax': 120}, 'oversaturated'), ({'phases': [[900], [360, 450, 810]], 'sat': 1900, 'lost': 3, 'allred': 3, 'cmin': 60, 'cmax': 120}, 'oversaturated'), ({'phases': [[270], [750, 720, 330]], 'sat': 2000, 'lost': 3, 'allred': 4, 'cmin': 40, 'cmax': 120}, {'cycle': 45, 'lost': 10, 'y_milli': 510}), ({'phases': [[300, 600], [450]], 'sat': 1800, 'lost': 4, 'allred': 2, 'cmin': 40, 'cmax': 120}, {'cycle': 50, 'lost': 10, 'y_milli': 583}), ({'phases': [[750], [600], [150, 60, 60], [420]], 'sat': 2000, 'lost': 3, 'allred': 3, 'cmin': 40, 'cmax': 150}, 'oversaturated'), ({'phases': [[180, 780], [90, 900, 420]], 'sat': 1800, 'lost': 3, 'allred': 2, 'cmin': 40, 'cmax': 150}, 'oversaturated'), ({'phases': [[810], [810]], 'sat': 1800, 'lost': 4, 'allred': 0, 'cmin': 40, 'cmax': 180}, 'oversaturated'), ({'phases': [[90], [90], [90]], 'sat': 1800, 'lost': 3, 'allred': 0, 'cmin': 60, 'cmax': 120}, {'cycle': 60, 'lost': 9, 'y_milli': 150})], [({'phases': [[720, 360], [540, 900]], 'sat': 1800, 'lost': 4, 'allred': 4, 'cmin': 60, 'cmax': 150}, 'oversaturated'), ({'phases': [[90, 900, 810], [750, 540]], 'sat': 2000, 'lost': 5, 'allred': 0, 'cmin': 60, 'cmax': 150}, {'cycle': 115, 'lost': 10, 'y_milli': 825}), ({'phases': [[90], [90], [90]], 'sat': 1800, 'lost': 3, 'allred': 0, 'cmin': 60, 'cmax': 120}, {'cycle': 60, 'lost': 9, 'y_milli': 150}), ({'phases': [[720, 510], [300, 750]], 'sat': 1800, 'lost': 5, 'allred': 2, 'cmin': 40, 'cmax': 90}, {'cycle': 90, 'lost': 12, 'y_milli': 816}), ({'phases': [[360], [630, 750], [750]], 'sat': 2000, 'lost': 3, 'allred': 1, 'cmin': 40, 'cmax': 90}, 'oversaturated'), ({'phases': [[360], [360, 510, 630], [570, 840], [840]], 'sat': 1800, 'lost': 5, 'allred': 2, 'cmin': 40, 'cmax': 120}, 'oversaturated'), ({'phases': [[300], [630]], 'sat': 1800, 'lost': 4, 'allred': 3, 'cmin': 40, 'cmax': 120}, {'cycle': 45, 'lost': 11, 'y_milli': 516}), ({'phases': [[810], [810]], 'sat': 1800, 'lost': 4, 'allred': 0, 'cmin': 40, 'cmax': 180}, 'oversaturated')], [({'phases': [[330, 840, 90], [60, 180], [720]], 'sat': 1800, 'lost': 4, 'allred': 2, 'cmin': 40, 'cmax': 180}, 'oversaturated'), ({'phases': [[810], [810]], 'sat': 1800, 'lost': 4, 'allred': 0, 'cmin': 40, 'cmax': 180}, 'oversaturated'), ({'phases': [[690, 420], [150]], 'sat': 1800, 'lost': 5, 'allred': 4, 'cmin': 60, 'cmax': 150}, {'cycle': 60, 'lost': 14, 'y_milli': 466}), ({'phases': [[450, 120, 480], [600], [630, 90, 780], [900, 720, 510]], 'sat': 1800, 'lost': 2, 'allred': 4, 'cmin': 50, 'cmax': 180}, 'oversaturated'), ({'phases': [[720, 360], [540, 900]], 'sat': 1800, 'lost': 4, 'allred': 4, 'cmin': 60, 'cmax': 150}, 'oversaturated'), ({'phases': [[840, 840], [900, 90, 180], [570], [330, 270]], 'sat': 2000, 'lost': 2, 'allred': 2, 'cmin': 50, 'cmax': 150}, 'oversaturated'), ({'phases': [[150, 420], [690, 180, 180], [570, 390]], 'sat': 1900, 'lost': 5, 'allred': 0, 'cmin': 60, 'cmax': 180}, {'cycle': 180, 'lost': 15, 'y_milli': 884}), ({'phases': [[90], [90], [90]], 'sat': 1800, 'lost': 3, 'allred': 0, 'cmin': 60, 'cmax': 120}, {'cycle': 60, 'lost': 9, 'y_milli': 150})]]
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 0oversaturatedoversaturatedPassed
timing oracle 1oversaturatedoversaturatedPassed
timing oracle 2{'cycle': 50, 'lost': 9, 'y_milli': 600}{'cycle': 50, 'lost': 9, 'y_milli': 600}Passed
timing oracle 3oversaturatedoversaturatedPassed
timing oracle 4oversaturatedoversaturatedPassed
timing oracle 5{'cycle': 50, 'lost': 10, 'y_milli': 583}{'cycle': 50, 'lost': 10, 'y_milli': 583}Passed
timing oracle 6oversaturatedoversaturatedPassed
timing oracle 7{'cycle': 65, 'lost': 11, 'y_milli': 663}{'cycle': 65, 'lost': 11, 'y_milli': 663}Passed

SHA-256 / 4e509fe004dab1cff1cdf07e11558ee7cc2767c9cf1fdabd511c0044843cae04

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 2026-09-29T14:47:56.834364+00:00.

Case digest / 07bfd45e4dd6ed93760fbc93292be1c2063cd15c5d4bb124c957a1c1ff6c499d