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FA-67846 / Traffic signal timing plans / Open access

Webster cycle length: lost time is counted once per cycle instead of once per phase · case 01

Webster cycle length returns a wrong result when lost time is counted once per cycle instead of once per phase.

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

ROOT CAUSE

The per-phase start-up and clearance lost time is added only once, underestimating L for multi-phase plans.

VERIFIED REPAIR

Restore the total lost time rule so that the step reads `x['lost'] * len(ph) + x['allred']`.

Unsuccessful approach: Counting phases minus one still omits the lost time of one phase change in the ring.

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'] + 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': [[540, 750, 300], [360, 120], [300, 60, 900], [840]], 'sat': 1800, 'lost': 2, 'allred': 5, 'cmin': 40, 'cmax': 90}, 'oversaturated'), ({'phases': [[810], [810]], 'sat': 1800, 'lost': 4, 'allred': 0, 'cmin': 40, 'cmax': 180}, 'oversaturated'), ({'phases': [[810, 690], [840], [630]], 'sat': 1800, 'lost': 3, 'allred': 0, 'cmin': 50, 'cmax': 90}, 'oversaturated'), ({'phases': [[300, 600], [450]], 'sat': 1800, 'lost': 4, 'allred': 2, 'cmin': 40, 'cmax': 120}, {'cycle': 50, 'lost': 10, 'y_milli': 583}), ({'phases': [[90], [90], [90]], 'sat': 1800, 'lost': 3, 'allred': 0, 'cmin': 60, 'cmax': 120}, {'cycle': 60, 'lost': 9, 'y_milli': 150}), ({'phases': [[540, 600, 690], [420]], 'sat': 1900, 'lost': 4, 'allred': 1, 'cmin': 60, 'cmax': 180}, {'cycle': 60, 'lost': 9, 'y_milli': 584}), ({'phases': [[540, 900], [330, 780], [150], [510, 720]], 'sat': 2000, 'lost': 5, 'allred': 0, 'cmin': 60, 'cmax': 150}, 'oversaturated'), ({'phases': [[390, 450, 660], [750, 240], [240]], 'sat': 1900, 'lost': 3, 'allred': 0, 'cmin': 40, 'cmax': 180}, {'cycle': 145, 'lost': 9, 'y_milli': 868})], [({'phases': [[420], [750, 900]], 'sat': 1800, 'lost': 5, 'allred': 0, 'cmin': 60, 'cmax': 90}, {'cycle': 75, 'lost': 10, 'y_milli': 733}), ({'phases': [[510], [600, 570, 180], [450, 60], [300]], 'sat': 1900, 'lost': 3, 'allred': 4, 'cmin': 50, 'cmax': 150}, 'oversaturated'), ({'phases': [[480, 540], [360]], 'sat': 1900, 'lost': 3, 'allred': 4, 'cmin': 40, 'cmax': 120}, {'cycle': 40, 'lost': 10, 'y_milli': 473}), ({'phases': [[810], [810]], 'sat': 1800, 'lost': 4, 'allred': 0, 'cmin': 40, 'cmax': 180}, 'oversaturated'), ({'phases': [[510, 90, 420], [510], [90, 840], [750, 240, 150]], 'sat': 1800, 'lost': 2, 'allred': 4, 'cmin': 60, 'cmax': 120}, 'oversaturated'), ({'phases': [[300, 600], [450]], 'sat': 1800, 'lost': 4, 'allred': 2, 'cmin': 40, 'cmax': 120}, {'cycle': 50, 'lost': 10, 'y_milli': 583}), ({'phases': [[780], [900, 630]], 'sat': 1800, 'lost': 2, 'allred': 6, 'cmin': 40, 'cmax': 150}, 'oversaturated'), ({'phases': [[720, 360], [540, 900]], 'sat': 1800, 'lost': 4, 'allred': 4, 'cmin': 60, 'cmax': 150}, 'oversaturated')], [({'phases': [[270], [630], [690, 330, 420]], 'sat': 1800, 'lost': 3, 'allred': 2, 'cmin': 40, 'cmax': 180}, {'cycle': 180, 'lost': 11, 'y_milli': 883}), ({'phases': [[870, 570, 480], [690, 270, 300], [540, 840, 240], [420, 570]], 'sat': 1800, 'lost': 5, 'allred': 4, 'cmin': 60, 'cmax': 90}, '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': [[750, 390, 480], [900, 330, 60], [780, 840, 660]], 'sat': 1900, 'lost': 5, 'allred': 2, 'cmin': 40, 'cmax': 150}, 'oversaturated'), ({'phases': [[210], [330, 210], [900], [450]], 'sat': 1800, 'lost': 4, 'allred': 2, 'cmin': 50, 'cmax': 120}, 'oversaturated'), ({'phases': [[300, 600], [450]], 'sat': 1800, 'lost': 4, 'allred': 2, 'cmin': 40, 'cmax': 120}, {'cycle': 50, 'lost': 10, 'y_milli': 583}), ({'phases': [[210], [120, 60, 300]], 'sat': 1800, 'lost': 2, 'allred': 1, 'cmin': 50, 'cmax': 180}, {'cycle': 50, 'lost': 5, 'y_milli': 283})], [({'phases': [[270], [210, 420, 540]], 'sat': 1800, 'lost': 3, 'allred': 0, 'cmin': 40, 'cmax': 120}, {'cycle': 40, 'lost': 6, 'y_milli': 450}), ({'phases': [[180, 120, 690], [480], [90, 480, 510], [480, 300, 630]], 'sat': 1800, 'lost': 3, 'allred': 2, 'cmin': 40, 'cmax': 90}, 'oversaturated'), ({'phases': [[90], [90], [90]], 'sat': 1800, 'lost': 3, 'allred': 0, 'cmin': 60, 'cmax': 120}, {'cycle': 60, 'lost': 9, 'y_milli': 150}), ({'phases': [[330, 690, 270], [660], [420, 480, 600]], 'sat': 1800, 'lost': 3, 'allred': 4, 'cmin': 40, 'cmax': 90}, 'oversaturated'), ({'phases': [[840, 420], [510], [900, 600]], 'sat': 1900, 'lost': 2, 'allred': 2, 'cmin': 50, 'cmax': 90}, 'oversaturated'), ({'phases': [[720, 360], [540, 900]], 'sat': 1800, 'lost': 4, 'allred': 4, 'cmin': 60, 'cmax': 150}, 'oversaturated'), ({'phases': [[210], [900, 510, 750], [180, 840, 900], [420, 210]], 'sat': 1800, 'lost': 3, 'allred': 3, 'cmin': 40, 'cmax': 180}, 'oversaturated'), ({'phases': [[300, 600], [450]], 'sat': 1800, 'lost': 4, 'allred': 2, 'cmin': 40, 'cmax': 120}, {'cycle': 50, 'lost': 10, 'y_milli': 583})], [({'phases': [[690, 390], [300, 690], [390, 810]], 'sat': 1800, 'lost': 3, 'allred': 2, 'cmin': 50, 'cmax': 120}, 'oversaturated'), ({'phases': [[660], [180], [690]], 'sat': 2000, 'lost': 4, 'allred': 5, 'cmin': 50, 'cmax': 150}, {'cycle': 130, 'lost': 17, 'y_milli': 765}), ({'phases': [[480, 900, 870], [600, 570, 870], [810]], 'sat': 1900, 'lost': 5, 'allred': 5, 'cmin': 50, 'cmax': 120}, 'oversaturated'), ({'phases': [[300, 600], [450]], 'sat': 1800, 'lost': 4, 'allred': 2, 'cmin': 40, 'cmax': 120}, {'cycle': 50, 'lost': 10, 'y_milli': 583}), ({'phases': [[510], [360, 660]], 'sat': 1800, 'lost': 3, 'allred': 6, 'cmin': 50, 'cmax': 120}, {'cycle': 70, 'lost': 12, 'y_milli': 650}), ({'phases': [[90], [90], [90]], 'sat': 1800, 'lost': 3, 'allred': 0, 'cmin': 60, 'cmax': 120}, {'cycle': 60, 'lost': 9, 'y_milli': 150}), ({'phases': [[900, 630, 450], [510, 720, 480]], 'sat': 1800, 'lost': 2, 'allred': 0, 'cmin': 40, 'cmax': 120}, 'oversaturated'), ({'phases': [[810], [810]], 'sat': 1800, 'lost': 4, 'allred': 0, 'cmin': 40, 'cmax': 180}, 'oversaturated')]]
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 2oversaturatedoversaturatedPassed
timing oracle 3{'cycle': 40, 'lost': 6, 'y_milli': 583}{'cycle': 50, 'lost': 10, 'y_milli': 583}Failed
timing oracle 4{'cycle': 60, 'lost': 3, 'y_milli': 150}{'cycle': 60, 'lost': 9, 'y_milli': 150}Failed
timing oracle 5{'cycle': 60, 'lost': 5, 'y_milli': 584}{'cycle': 60, 'lost': 9, 'y_milli': 584}Failed
timing oracle 6oversaturatedoversaturatedPassed
timing oracle 7{'cycle': 75, 'lost': 3, 'y_milli': 868}{'cycle': 145, 'lost': 9, 'y_milli': 868}Failed

SHA-256 / 36496920972ab6d3607af230c642fc719473ee9c1976ba25d7e4abc00de8b743

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) - 1) + 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': [[540, 750, 300], [360, 120], [300, 60, 900], [840]], 'sat': 1800, 'lost': 2, 'allred': 5, 'cmin': 40, 'cmax': 90}, 'oversaturated'), ({'phases': [[810], [810]], 'sat': 1800, 'lost': 4, 'allred': 0, 'cmin': 40, 'cmax': 180}, 'oversaturated'), ({'phases': [[810, 690], [840], [630]], 'sat': 1800, 'lost': 3, 'allred': 0, 'cmin': 50, 'cmax': 90}, 'oversaturated'), ({'phases': [[300, 600], [450]], 'sat': 1800, 'lost': 4, 'allred': 2, 'cmin': 40, 'cmax': 120}, {'cycle': 50, 'lost': 10, 'y_milli': 583}), ({'phases': [[90], [90], [90]], 'sat': 1800, 'lost': 3, 'allred': 0, 'cmin': 60, 'cmax': 120}, {'cycle': 60, 'lost': 9, 'y_milli': 150}), ({'phases': [[540, 600, 690], [420]], 'sat': 1900, 'lost': 4, 'allred': 1, 'cmin': 60, 'cmax': 180}, {'cycle': 60, 'lost': 9, 'y_milli': 584}), ({'phases': [[540, 900], [330, 780], [150], [510, 720]], 'sat': 2000, 'lost': 5, 'allred': 0, 'cmin': 60, 'cmax': 150}, 'oversaturated'), ({'phases': [[390, 450, 660], [750, 240], [240]], 'sat': 1900, 'lost': 3, 'allred': 0, 'cmin': 40, 'cmax': 180}, {'cycle': 145, 'lost': 9, 'y_milli': 868})], [({'phases': [[420], [750, 900]], 'sat': 1800, 'lost': 5, 'allred': 0, 'cmin': 60, 'cmax': 90}, {'cycle': 75, 'lost': 10, 'y_milli': 733}), ({'phases': [[510], [600, 570, 180], [450, 60], [300]], 'sat': 1900, 'lost': 3, 'allred': 4, 'cmin': 50, 'cmax': 150}, 'oversaturated'), ({'phases': [[480, 540], [360]], 'sat': 1900, 'lost': 3, 'allred': 4, 'cmin': 40, 'cmax': 120}, {'cycle': 40, 'lost': 10, 'y_milli': 473}), ({'phases': [[810], [810]], 'sat': 1800, 'lost': 4, 'allred': 0, 'cmin': 40, 'cmax': 180}, 'oversaturated'), ({'phases': [[510, 90, 420], [510], [90, 840], [750, 240, 150]], 'sat': 1800, 'lost': 2, 'allred': 4, 'cmin': 60, 'cmax': 120}, 'oversaturated'), ({'phases': [[300, 600], [450]], 'sat': 1800, 'lost': 4, 'allred': 2, 'cmin': 40, 'cmax': 120}, {'cycle': 50, 'lost': 10, 'y_milli': 583}), ({'phases': [[780], [900, 630]], 'sat': 1800, 'lost': 2, 'allred': 6, 'cmin': 40, 'cmax': 150}, 'oversaturated'), ({'phases': [[720, 360], [540, 900]], 'sat': 1800, 'lost': 4, 'allred': 4, 'cmin': 60, 'cmax': 150}, 'oversaturated')], [({'phases': [[270], [630], [690, 330, 420]], 'sat': 1800, 'lost': 3, 'allred': 2, 'cmin': 40, 'cmax': 180}, {'cycle': 180, 'lost': 11, 'y_milli': 883}), ({'phases': [[870, 570, 480], [690, 270, 300], [540, 840, 240], [420, 570]], 'sat': 1800, 'lost': 5, 'allred': 4, 'cmin': 60, 'cmax': 90}, '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': [[750, 390, 480], [900, 330, 60], [780, 840, 660]], 'sat': 1900, 'lost': 5, 'allred': 2, 'cmin': 40, 'cmax': 150}, 'oversaturated'), ({'phases': [[210], [330, 210], [900], [450]], 'sat': 1800, 'lost': 4, 'allred': 2, 'cmin': 50, 'cmax': 120}, 'oversaturated'), ({'phases': [[300, 600], [450]], 'sat': 1800, 'lost': 4, 'allred': 2, 'cmin': 40, 'cmax': 120}, {'cycle': 50, 'lost': 10, 'y_milli': 583}), ({'phases': [[210], [120, 60, 300]], 'sat': 1800, 'lost': 2, 'allred': 1, 'cmin': 50, 'cmax': 180}, {'cycle': 50, 'lost': 5, 'y_milli': 283})], [({'phases': [[270], [210, 420, 540]], 'sat': 1800, 'lost': 3, 'allred': 0, 'cmin': 40, 'cmax': 120}, {'cycle': 40, 'lost': 6, 'y_milli': 450}), ({'phases': [[180, 120, 690], [480], [90, 480, 510], [480, 300, 630]], 'sat': 1800, 'lost': 3, 'allred': 2, 'cmin': 40, 'cmax': 90}, 'oversaturated'), ({'phases': [[90], [90], [90]], 'sat': 1800, 'lost': 3, 'allred': 0, 'cmin': 60, 'cmax': 120}, {'cycle': 60, 'lost': 9, 'y_milli': 150}), ({'phases': [[330, 690, 270], [660], [420, 480, 600]], 'sat': 1800, 'lost': 3, 'allred': 4, 'cmin': 40, 'cmax': 90}, 'oversaturated'), ({'phases': [[840, 420], [510], [900, 600]], 'sat': 1900, 'lost': 2, 'allred': 2, 'cmin': 50, 'cmax': 90}, 'oversaturated'), ({'phases': [[720, 360], [540, 900]], 'sat': 1800, 'lost': 4, 'allred': 4, 'cmin': 60, 'cmax': 150}, 'oversaturated'), ({'phases': [[210], [900, 510, 750], [180, 840, 900], [420, 210]], 'sat': 1800, 'lost': 3, 'allred': 3, 'cmin': 40, 'cmax': 180}, 'oversaturated'), ({'phases': [[300, 600], [450]], 'sat': 1800, 'lost': 4, 'allred': 2, 'cmin': 40, 'cmax': 120}, {'cycle': 50, 'lost': 10, 'y_milli': 583})], [({'phases': [[690, 390], [300, 690], [390, 810]], 'sat': 1800, 'lost': 3, 'allred': 2, 'cmin': 50, 'cmax': 120}, 'oversaturated'), ({'phases': [[660], [180], [690]], 'sat': 2000, 'lost': 4, 'allred': 5, 'cmin': 50, 'cmax': 150}, {'cycle': 130, 'lost': 17, 'y_milli': 765}), ({'phases': [[480, 900, 870], [600, 570, 870], [810]], 'sat': 1900, 'lost': 5, 'allred': 5, 'cmin': 50, 'cmax': 120}, 'oversaturated'), ({'phases': [[300, 600], [450]], 'sat': 1800, 'lost': 4, 'allred': 2, 'cmin': 40, 'cmax': 120}, {'cycle': 50, 'lost': 10, 'y_milli': 583}), ({'phases': [[510], [360, 660]], 'sat': 1800, 'lost': 3, 'allred': 6, 'cmin': 50, 'cmax': 120}, {'cycle': 70, 'lost': 12, 'y_milli': 650}), ({'phases': [[90], [90], [90]], 'sat': 1800, 'lost': 3, 'allred': 0, 'cmin': 60, 'cmax': 120}, {'cycle': 60, 'lost': 9, 'y_milli': 150}), ({'phases': [[900, 630, 450], [510, 720, 480]], 'sat': 1800, 'lost': 2, 'allred': 0, 'cmin': 40, 'cmax': 120}, 'oversaturated'), ({'phases': [[810], [810]], 'sat': 1800, 'lost': 4, 'allred': 0, 'cmin': 40, 'cmax': 180}, 'oversaturated')]]
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 2oversaturatedoversaturatedPassed
timing oracle 3{'cycle': 40, 'lost': 6, 'y_milli': 583}{'cycle': 50, 'lost': 10, 'y_milli': 583}Failed
timing oracle 4{'cycle': 60, 'lost': 6, 'y_milli': 150}{'cycle': 60, 'lost': 9, 'y_milli': 150}Failed
timing oracle 5{'cycle': 60, 'lost': 5, 'y_milli': 584}{'cycle': 60, 'lost': 9, 'y_milli': 584}Failed
timing oracle 6oversaturatedoversaturatedPassed
timing oracle 7{'cycle': 110, 'lost': 6, 'y_milli': 868}{'cycle': 145, 'lost': 9, 'y_milli': 868}Failed

SHA-256 / 4650d0cb7032e5847040a7a4fba6a4b900b5745fb0e8bf0790da69d4405984e4

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': [[540, 750, 300], [360, 120], [300, 60, 900], [840]], 'sat': 1800, 'lost': 2, 'allred': 5, 'cmin': 40, 'cmax': 90}, 'oversaturated'), ({'phases': [[810], [810]], 'sat': 1800, 'lost': 4, 'allred': 0, 'cmin': 40, 'cmax': 180}, 'oversaturated'), ({'phases': [[810, 690], [840], [630]], 'sat': 1800, 'lost': 3, 'allred': 0, 'cmin': 50, 'cmax': 90}, 'oversaturated'), ({'phases': [[300, 600], [450]], 'sat': 1800, 'lost': 4, 'allred': 2, 'cmin': 40, 'cmax': 120}, {'cycle': 50, 'lost': 10, 'y_milli': 583}), ({'phases': [[90], [90], [90]], 'sat': 1800, 'lost': 3, 'allred': 0, 'cmin': 60, 'cmax': 120}, {'cycle': 60, 'lost': 9, 'y_milli': 150}), ({'phases': [[540, 600, 690], [420]], 'sat': 1900, 'lost': 4, 'allred': 1, 'cmin': 60, 'cmax': 180}, {'cycle': 60, 'lost': 9, 'y_milli': 584}), ({'phases': [[540, 900], [330, 780], [150], [510, 720]], 'sat': 2000, 'lost': 5, 'allred': 0, 'cmin': 60, 'cmax': 150}, 'oversaturated'), ({'phases': [[390, 450, 660], [750, 240], [240]], 'sat': 1900, 'lost': 3, 'allred': 0, 'cmin': 40, 'cmax': 180}, {'cycle': 145, 'lost': 9, 'y_milli': 868})], [({'phases': [[420], [750, 900]], 'sat': 1800, 'lost': 5, 'allred': 0, 'cmin': 60, 'cmax': 90}, {'cycle': 75, 'lost': 10, 'y_milli': 733}), ({'phases': [[510], [600, 570, 180], [450, 60], [300]], 'sat': 1900, 'lost': 3, 'allred': 4, 'cmin': 50, 'cmax': 150}, 'oversaturated'), ({'phases': [[480, 540], [360]], 'sat': 1900, 'lost': 3, 'allred': 4, 'cmin': 40, 'cmax': 120}, {'cycle': 40, 'lost': 10, 'y_milli': 473}), ({'phases': [[810], [810]], 'sat': 1800, 'lost': 4, 'allred': 0, 'cmin': 40, 'cmax': 180}, 'oversaturated'), ({'phases': [[510, 90, 420], [510], [90, 840], [750, 240, 150]], 'sat': 1800, 'lost': 2, 'allred': 4, 'cmin': 60, 'cmax': 120}, 'oversaturated'), ({'phases': [[300, 600], [450]], 'sat': 1800, 'lost': 4, 'allred': 2, 'cmin': 40, 'cmax': 120}, {'cycle': 50, 'lost': 10, 'y_milli': 583}), ({'phases': [[780], [900, 630]], 'sat': 1800, 'lost': 2, 'allred': 6, 'cmin': 40, 'cmax': 150}, 'oversaturated'), ({'phases': [[720, 360], [540, 900]], 'sat': 1800, 'lost': 4, 'allred': 4, 'cmin': 60, 'cmax': 150}, 'oversaturated')], [({'phases': [[270], [630], [690, 330, 420]], 'sat': 1800, 'lost': 3, 'allred': 2, 'cmin': 40, 'cmax': 180}, {'cycle': 180, 'lost': 11, 'y_milli': 883}), ({'phases': [[870, 570, 480], [690, 270, 300], [540, 840, 240], [420, 570]], 'sat': 1800, 'lost': 5, 'allred': 4, 'cmin': 60, 'cmax': 90}, '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': [[750, 390, 480], [900, 330, 60], [780, 840, 660]], 'sat': 1900, 'lost': 5, 'allred': 2, 'cmin': 40, 'cmax': 150}, 'oversaturated'), ({'phases': [[210], [330, 210], [900], [450]], 'sat': 1800, 'lost': 4, 'allred': 2, 'cmin': 50, 'cmax': 120}, 'oversaturated'), ({'phases': [[300, 600], [450]], 'sat': 1800, 'lost': 4, 'allred': 2, 'cmin': 40, 'cmax': 120}, {'cycle': 50, 'lost': 10, 'y_milli': 583}), ({'phases': [[210], [120, 60, 300]], 'sat': 1800, 'lost': 2, 'allred': 1, 'cmin': 50, 'cmax': 180}, {'cycle': 50, 'lost': 5, 'y_milli': 283})], [({'phases': [[270], [210, 420, 540]], 'sat': 1800, 'lost': 3, 'allred': 0, 'cmin': 40, 'cmax': 120}, {'cycle': 40, 'lost': 6, 'y_milli': 450}), ({'phases': [[180, 120, 690], [480], [90, 480, 510], [480, 300, 630]], 'sat': 1800, 'lost': 3, 'allred': 2, 'cmin': 40, 'cmax': 90}, 'oversaturated'), ({'phases': [[90], [90], [90]], 'sat': 1800, 'lost': 3, 'allred': 0, 'cmin': 60, 'cmax': 120}, {'cycle': 60, 'lost': 9, 'y_milli': 150}), ({'phases': [[330, 690, 270], [660], [420, 480, 600]], 'sat': 1800, 'lost': 3, 'allred': 4, 'cmin': 40, 'cmax': 90}, 'oversaturated'), ({'phases': [[840, 420], [510], [900, 600]], 'sat': 1900, 'lost': 2, 'allred': 2, 'cmin': 50, 'cmax': 90}, 'oversaturated'), ({'phases': [[720, 360], [540, 900]], 'sat': 1800, 'lost': 4, 'allred': 4, 'cmin': 60, 'cmax': 150}, 'oversaturated'), ({'phases': [[210], [900, 510, 750], [180, 840, 900], [420, 210]], 'sat': 1800, 'lost': 3, 'allred': 3, 'cmin': 40, 'cmax': 180}, 'oversaturated'), ({'phases': [[300, 600], [450]], 'sat': 1800, 'lost': 4, 'allred': 2, 'cmin': 40, 'cmax': 120}, {'cycle': 50, 'lost': 10, 'y_milli': 583})], [({'phases': [[690, 390], [300, 690], [390, 810]], 'sat': 1800, 'lost': 3, 'allred': 2, 'cmin': 50, 'cmax': 120}, 'oversaturated'), ({'phases': [[660], [180], [690]], 'sat': 2000, 'lost': 4, 'allred': 5, 'cmin': 50, 'cmax': 150}, {'cycle': 130, 'lost': 17, 'y_milli': 765}), ({'phases': [[480, 900, 870], [600, 570, 870], [810]], 'sat': 1900, 'lost': 5, 'allred': 5, 'cmin': 50, 'cmax': 120}, 'oversaturated'), ({'phases': [[300, 600], [450]], 'sat': 1800, 'lost': 4, 'allred': 2, 'cmin': 40, 'cmax': 120}, {'cycle': 50, 'lost': 10, 'y_milli': 583}), ({'phases': [[510], [360, 660]], 'sat': 1800, 'lost': 3, 'allred': 6, 'cmin': 50, 'cmax': 120}, {'cycle': 70, 'lost': 12, 'y_milli': 650}), ({'phases': [[90], [90], [90]], 'sat': 1800, 'lost': 3, 'allred': 0, 'cmin': 60, 'cmax': 120}, {'cycle': 60, 'lost': 9, 'y_milli': 150}), ({'phases': [[900, 630, 450], [510, 720, 480]], 'sat': 1800, 'lost': 2, 'allred': 0, 'cmin': 40, 'cmax': 120}, 'oversaturated'), ({'phases': [[810], [810]], 'sat': 1800, 'lost': 4, 'allred': 0, 'cmin': 40, 'cmax': 180}, 'oversaturated')]]
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 2oversaturatedoversaturatedPassed
timing oracle 3{'cycle': 50, 'lost': 10, 'y_milli': 583}{'cycle': 50, 'lost': 10, 'y_milli': 583}Passed
timing oracle 4{'cycle': 60, 'lost': 9, 'y_milli': 150}{'cycle': 60, 'lost': 9, 'y_milli': 150}Passed
timing oracle 5{'cycle': 60, 'lost': 9, 'y_milli': 584}{'cycle': 60, 'lost': 9, 'y_milli': 584}Passed
timing oracle 6oversaturatedoversaturatedPassed
timing oracle 7{'cycle': 145, 'lost': 9, 'y_milli': 868}{'cycle': 145, 'lost': 9, 'y_milli': 868}Passed

SHA-256 / 8702703c51970f12818e91092c655d12f798be1a7a1fc9ae23c74ffe331666f2

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 2026-09-29T14:47:56.584316+00:00.

Case digest / 68ed186474ad9a13445ae2972c7cfc3343043796e3adfc192862bc9ce1cf84d0