FAILURE MAP
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FA-87276 / Physics integrator stability / Open access

Body sleeps only after strictly exceeding the required rest time · case 01

Bodies sleep one frame late relative to the contract.

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

ROOT CAUSE

The comparison is timer > sleep_time.

VERIFIED REPAIR

Sleep as soon as timer >= sleep_time.

Unsuccessful approach: Subtracting one frame from the requirement sleeps a frame early.

Case contract

solve(v, omega, lin_damp, ang_damp, dt, max_speed, sleep_lin, sleep_ang, sleep_time, kicks): per frame, a sleeping body wakes (timer reset) only when that frame's kick is nonzero, else it is skipped. Add the kick [dvx,dvy,domega], damp with 1/(1+dt*c) (linear and angular coefficients), clamp speed magnitude, then accumulate sleep time while |v|<sleep_lin and |omega|<sleep_ang (else reset). When timer>=sleep_time the body sleeps and velocities are zeroed. Return [vx, vy, omega, timer, asleep, frame index slept or -1].

Why this case matters

Game and robotics physics loops depend on integrator update order, step control and stabilization terms; a wrong decision point turns a stable simulation into drifting or exploding motion.

1 / The failure

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(v, omega, lin_damp, ang_damp, dt, max_speed, sleep_lin, sleep_ang, sleep_time, kicks):
    vx, vy = v
    w = omega
    timer = 0.0
    asleep = False
    slept_at = -1
    for f, (ax, ay, aw) in enumerate(kicks):
        if asleep:
            if ax or ay or aw:
                asleep = False
                timer = 0.0
            else:
                continue
        vx += ax
        vy += ay
        w += aw
        dl = 1.0 / (1.0 + dt * lin_damp)
        vx *= dl
        vy *= dl
        w *= 1.0 / (1.0 + dt * ang_damp)
        sp = math.hypot(vx, vy)
        if sp > max_speed:
            s = max_speed / sp
            vx *= s
            vy *= s
        if math.hypot(vx, vy) < sleep_lin and abs(w) < sleep_ang:
            timer += dt
        else:
            timer = 0.0
        if timer > sleep_time:
            asleep = True
            slept_at = f
            vx = vy = w = 0.0
    return [round(vx, 6), round(vy, 6), round(w, 6), round(timer, 6), asleep, slept_at]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[[[0.03, 0.06], 0.0, 2.0, 5.0, 0.0625, 8.0, 0.5, 0.3, 0.125, [[0, 0, 0], [0, 0, -1.5], [0, 0, 0], [0, 0, 1.5], [0, 0, 0], [0, 0, -1.5], [0, 0, 0]]], [0.013154, 0.026308, -0.658704, 0.0, False, -1]], [[[0.04, 0.03], 0.2, 2.0, 5.0, 0.015625, 3.0, 0.5, 1.0, 0.015625, [[0, 0, 0], [0, 0, 0], [0, -3, 0], [1, 0, 2], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.884187, -2.572181, 1.480313, 0.0, False, 0]], [[[0.07, -0.09], 0.0, 2.0, 0.5, 0.03125, 8.0, 0.5, 1.0, 0.09375, [[0, 0, -0.5], [0, 0, -0.5], [0, 0, 0], [0, 0, 0.5]]], [0.0, 0.0, 0.492308, 0.03125, False, 2]], [[[-0.01, -0.07], 0.0, 2.0, 0.5, 0.015625, 8.0, 0.5, 1.0, 0.03125, [[0, 0, 3.0], [0, 0, -3.0], [0, 0, 0], [0, 0, 3.0], [0, 0, -3.0], [0, 0, -3.0], [0, 0, 3.0]]], [0.0, 0.0, 0.000356, 0.015625, False, 2]], [[[-0.01, -0.04], 0.74, 20.0, 40.0, 0.0625, 8.0, 0.5, 1.0, 0.125, [[5, 0, 0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [-2, -3, 0]]], [-0.888889, -1.333333, 0.0, 0.0, False, 3]], [[[2.14, -0.12], 1.88, 80.0, 0.5, 0.015625, 8.0, 0.5, 0.3, 0.03125, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.007331, -0.000411, 1.780327, 0.0, False, -1]], [[[-0.02, 0.07], 0.0, 2.0, 5.0, 0.03125, 8.0, 0.5, 0.3, 0.0625, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0.5], [0, 0, 0.5]]], [0.0, 0.0, 0.806428, 0.0, False, 1]], [[[-0.0, 0.04], -1.42, 0.5, 40.0, 0.0625, 8.0, 0.5, 1.0, 0.0625, [[0, 1, 0.5], [0, 0, 0.5], [-2, -3, -1], [0, 0, 0], [0, 1, -1]]], [-1.823636, -0.874067, -0.307458, 0.0, False, -1]]], [[[[0.01, -0.0], -0.96, 80.0, 5.0, 0.03125, 8.0, 2.0, 1.0, 0.0625, [[0, 8, 0.5], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.0625, True, 2]], [[[0.03, 0.01], 0.0, 2.0, 5.0, 0.0625, 8.0, 0.5, 1.0, 0.125, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 3.0], [0, 0, 3.0], [0, 0, -3.0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.125, True, 6]], [[[-0.01, -0.02], -1.79, 2.0, 40.0, 0.015625, 3.0, 0.5, 0.3, 0.03125, [[0, 0, -1], [0, 0, 0], [5, 1, 2], [1, 8, 2], [1, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [1.68995, 2.044541, 0.140151, 0.0, False, -1]], [[[-2.24, -3.75], -1.0, 20.0, 0.5, 0.015625, 3.0, 2.0, 0.3, 0.046875, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [-2, 0, 2], [1, 1, 0.5]]], [-0.57379, 0.469444, 1.532879, 0.0, False, -1]], [[[3.68, -0.77], 1.93, 2.0, 5.0, 0.0625, 8.0, 0.5, 0.3, 0.0625, [[0, 8, 2], [0, 1, 0], [0, 0, 0], [0, 0, 0], [1, 8, -1], [0, 8, 0.5], [-2, -3, 0], [0, 0, 0]]], [-0.8094, 3.903439, 0.330434, 0.0, False, -1]], [[[0.03, -0.02], -1.31, 80.0, 40.0, 0.0625, 8.0, 2.0, 0.3, 0.0625, [[0, 0, 0], [0, 0, 0], [0, 0, -1], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.0625, True, 2]], [[[-0.04, -0.04], -1.97, 80.0, 0.5, 0.015625, 8.0, 0.5, 1.0, 0.046875, [[5, 1, 0], [0, 0, 0], [-2, 0, 0.5], [0, 0, 0], [0, 8, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [5, -3, 2]]], [2.218727, -1.193952, 0.621244, 0.0, False, -1]], [[[4.19, 1.85], -0.69, 80.0, 0.5, 0.015625, 8.0, 0.5, 1.0, 0.015625, [[0, 1, 0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 1, 0.5], [-2, 1, -1]]], [-0.888889, 0.444444, -0.992248, 0.0, False, 4]]], [[[[-0.05, -0.07], 0.0, 2.0, 0.5, 0.015625, 8.0, 0.5, 0.3, 0.03125, [[0, 0, -0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0.5], [0, 0, -0.5], [0, 0, 0], [0, 0, 0.5], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.03125, True, 7]], [[[4.02, -0.48], -0.66, 2.0, 5.0, 0.03125, 3.0, 0.5, 1.0, 0.0625, [[0, 0, 0], [1, -3, 0.5], [0, 0, 0]]], [2.158391, -1.820348, -0.052966, 0.0, False, -1]], [[[0.04, 0.0], 1.58, 80.0, 5.0, 0.015625, 8.0, 2.0, 0.3, 0.046875, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, -3, 0], [0, 0, 0], [1, 0, -1], [-2, 8, -1], [0, 0, 0], [5, 0, 2]]], [2.085685, 0.67921, 1.119786, 0.0, False, -1]], [[[0.18, 0.67], -0.31, 0.5, 5.0, 0.03125, 3.0, 2.0, 0.3, 0.0625, [[0, 0, 0], [0, 0, -1], [0, -3, 2], [0, 0, 0], [1, 1, -1], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.0625, True, 5]], [[[0.09, -0.1], 0.0, 0.5, 0.5, 0.03125, 8.0, 0.5, 1.0, 0.0625, [[0, 0, 0], [0, 0, 1.5], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.082005, -0.091117, 1.388111, 0.0, False, -1]], [[[-4.16, 4.12], -1.07, 80.0, 40.0, 0.03125, 3.0, 0.5, 0.3, 0.0625, [[0, 0, 0], [0, 0, 2], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 1, -1], [0, 0, 0]]], [0.0, 0.081633, -0.197531, 0.03125, False, 4]], [[[0.04, -0.02], -1.17, 20.0, 5.0, 0.0625, 3.0, 0.5, 1.0, 0.125, [[0, 0, -1], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.125, True, 3]], [[[0.01, -0.0], 0.7, 0.5, 0.5, 0.0625, 8.0, 2.0, 1.0, 0.1875, [[0, 0, 0], [0, 0, 0], [1, 8, 0.5], [5, -3, 2]]], [5.797639, 4.613407, 3.028481, 0.0, False, -1]]], [[[[-0.03, -0.0], 0.97, 2.0, 5.0, 0.015625, 8.0, 0.5, 1.0, 0.015625, [[0, 0, 0], [0, 0, 0], [0, 1, 0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [5, 8, 0]]], [3.941435, 6.961687, 0.295315, 0.0, False, 0]], [[[3.82, 5.03], 0.39, 2.0, 5.0, 0.03125, 3.0, 2.0, 1.0, 0.03125, [[0, 0, 0], [0, 0, 0], [0, -3, 0], [0, 0, 0], [-2, -3, 0.5], [0, 0, 0]]], [-1.566212, -2.349318, 0.373996, 0.0, False, 2]], [[[-2.34, -1.3], 0.07, 80.0, 5.0, 0.0625, 8.0, 0.5, 0.3, 0.1875, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.1875, True, 2]], [[[-0.04, 0.1], 0.0, 0.5, 0.5, 0.015625, 8.0, 0.5, 0.3, 0.03125, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, -1.5]]], [0.0, 0.0, -1.488372, 0.0, False, 1]], [[[-0.04, -0.04], 0.45, 20.0, 40.0, 0.0625, 3.0, 0.5, 0.3, 0.0625, [[0, 1, -1], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.0625, True, 0]], [[[5.83, 2.38], -1.72, 80.0, 5.0, 0.015625, 8.0, 0.5, 1.0, 0.03125, [[0, 0, 0], [0, 0, 0], [1, 0, 2]]], [0.956269, 0.208944, 0.482545, 0.0, False, -1]], [[[-0.05, -0.02], 1.89, 0.5, 40.0, 0.0625, 3.0, 2.0, 0.3, 0.1875, [[0, 0, 0], [5, 0, -1], [1, 1, -1], [0, 0, 0], [1, 0, 2]]], [2.951277, 0.538484, 0.54504, 0.0, False, -1]], [[[-0.01, 0.0], 0.0, 0.5, 0.5, 0.0625, 8.0, 0.5, 1.0, 0.125, [[0, 0, 1.5], [0, 0, -1.5], [0, 0, -1.5], [0, 0, 1.5], [0, 0, 1.5], [0, 0, 0], [0, 0, 0]]], [-0.008062, 0.0, 1.370126, 0.0, False, -1]]], [[[[0.03, -0.04], -1.19, 2.0, 5.0, 0.0625, 3.0, 0.5, 1.0, 0.0625, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [5, -3, 2]]], [2.572479, -1.543487, 1.52381, 0.0, False, 0]], [[[-3.48, 1.74], 1.67, 20.0, 40.0, 0.0625, 3.0, 2.0, 1.0, 0.1875, [[1, -3, 0.5], [0, -3, 0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.1875, True, 2]], [[[0.45, -2.24], -0.91, 0.5, 0.5, 0.015625, 8.0, 2.0, 0.3, 0.046875, [[1, -3, 2], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [5, 0, 0], [0, 0, 0], [0, 0, 0], [5, 0, 0]]], [7.339549, -3.182927, 1.008391, 0.0, False, -1]], [[[0.04, 0.03], 0.6, 2.0, 0.5, 0.015625, 3.0, 2.0, 0.3, 0.015625, [[0, 0, 0], [0, 0, 0], [0, 1, -1], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.030324, 0.82896, -0.387568, 0.0, False, -1]], [[[-4.0, -0.28], -1.66, 20.0, 0.5, 0.0625, 8.0, 0.5, 1.0, 0.125, [[-2, 8, 2], [0, 0, 0], [-2, 0, 2], [0, 0, 0], [0, 0, 0]]], [-0.279632, 0.133877, 2.11515, 0.0, False, -1]], [[[-4.04, -5.1], 0.88, 80.0, 40.0, 0.0625, 8.0, 0.5, 1.0, 0.0625, [[0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.0625, True, 1]], [[[0.02, 0.01], 0.18, 20.0, 40.0, 0.03125, 8.0, 2.0, 0.3, 0.0625, [[0, 0, 0], [0, 0, 0], [-2, -3, 2], [-2, 0, 2], [0, 0, 0], [0, 0, 0], [0, 8, 2]]], [-0.463332, 4.658316, 1.001609, 0.0, False, 1]], [[[0.05, -0.01], 0.0, 0.5, 0.5, 0.0625, 8.0, 0.5, 1.0, 0.1875, [[0, 0, 0.5], [0, 0, -0.5], [0, 0, -0.5], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.1875, True, 2]]]]
for i, (args, expected) in enumerate(fixtures[N-1]):
    check("case %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
case 0[0.013154, 0.026308, -0.658704, 0.0, False, -1][0.013154, 0.026308, -0.658704, 0.0, False, -1]Passed
case 1[0.884187, -2.572181, 1.480313, 0.0, False, 1][0.884187, -2.572181, 1.480313, 0.0, False, 0]Failed
case 2[0.0, 0.0, 0.0, 0.125, True, 3][0.0, 0.0, 0.492308, 0.03125, False, 2]Failed
case 3[-0.008062, -0.056435, -0.021839, 0.015625, False, -1][0.0, 0.0, 0.000356, 0.015625, False, 2]Failed
case 4[-0.888889, -1.333333, 0.0, 0.0, False, 4][-0.888889, -1.333333, 0.0, 0.0, False, 3]Failed
case 5[0.007331, -0.000411, 1.780327, 0.0, False, -1][0.007331, -0.000411, 1.780327, 0.0, False, -1]Passed
case 6[0.0, 0.0, 0.806428, 0.0, False, 2][0.0, 0.0, 0.806428, 0.0, False, 1]Failed
case 7[-1.823636, -0.874067, -0.307458, 0.0, False, -1][-1.823636, -0.874067, -0.307458, 0.0, False, -1]Passed

SHA-256 / 4e2650245a6d65be4ac1729b48a641211e4cdb89af67aa76d31340f01fbd605e

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(v, omega, lin_damp, ang_damp, dt, max_speed, sleep_lin, sleep_ang, sleep_time, kicks):
    vx, vy = v
    w = omega
    timer = 0.0
    asleep = False
    slept_at = -1
    for f, (ax, ay, aw) in enumerate(kicks):
        if asleep:
            if ax or ay or aw:
                asleep = False
                timer = 0.0
            else:
                continue
        vx += ax
        vy += ay
        w += aw
        dl = 1.0 / (1.0 + dt * lin_damp)
        vx *= dl
        vy *= dl
        w *= 1.0 / (1.0 + dt * ang_damp)
        sp = math.hypot(vx, vy)
        if sp > max_speed:
            s = max_speed / sp
            vx *= s
            vy *= s
        if math.hypot(vx, vy) < sleep_lin and abs(w) < sleep_ang:
            timer += dt
        else:
            timer = 0.0
        if timer >= sleep_time - dt:
            asleep = True
            slept_at = f
            vx = vy = w = 0.0
    return [round(vx, 6), round(vy, 6), round(w, 6), round(timer, 6), asleep, slept_at]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[[[0.03, 0.06], 0.0, 2.0, 5.0, 0.0625, 8.0, 0.5, 0.3, 0.125, [[0, 0, 0], [0, 0, -1.5], [0, 0, 0], [0, 0, 1.5], [0, 0, 0], [0, 0, -1.5], [0, 0, 0]]], [0.013154, 0.026308, -0.658704, 0.0, False, -1]], [[[0.04, 0.03], 0.2, 2.0, 5.0, 0.015625, 3.0, 0.5, 1.0, 0.015625, [[0, 0, 0], [0, 0, 0], [0, -3, 0], [1, 0, 2], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.884187, -2.572181, 1.480313, 0.0, False, 0]], [[[0.07, -0.09], 0.0, 2.0, 0.5, 0.03125, 8.0, 0.5, 1.0, 0.09375, [[0, 0, -0.5], [0, 0, -0.5], [0, 0, 0], [0, 0, 0.5]]], [0.0, 0.0, 0.492308, 0.03125, False, 2]], [[[-0.01, -0.07], 0.0, 2.0, 0.5, 0.015625, 8.0, 0.5, 1.0, 0.03125, [[0, 0, 3.0], [0, 0, -3.0], [0, 0, 0], [0, 0, 3.0], [0, 0, -3.0], [0, 0, -3.0], [0, 0, 3.0]]], [0.0, 0.0, 0.000356, 0.015625, False, 2]], [[[-0.01, -0.04], 0.74, 20.0, 40.0, 0.0625, 8.0, 0.5, 1.0, 0.125, [[5, 0, 0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [-2, -3, 0]]], [-0.888889, -1.333333, 0.0, 0.0, False, 3]], [[[2.14, -0.12], 1.88, 80.0, 0.5, 0.015625, 8.0, 0.5, 0.3, 0.03125, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.007331, -0.000411, 1.780327, 0.0, False, -1]], [[[-0.02, 0.07], 0.0, 2.0, 5.0, 0.03125, 8.0, 0.5, 0.3, 0.0625, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0.5], [0, 0, 0.5]]], [0.0, 0.0, 0.806428, 0.0, False, 1]], [[[-0.0, 0.04], -1.42, 0.5, 40.0, 0.0625, 8.0, 0.5, 1.0, 0.0625, [[0, 1, 0.5], [0, 0, 0.5], [-2, -3, -1], [0, 0, 0], [0, 1, -1]]], [-1.823636, -0.874067, -0.307458, 0.0, False, -1]]], [[[[0.01, -0.0], -0.96, 80.0, 5.0, 0.03125, 8.0, 2.0, 1.0, 0.0625, [[0, 8, 0.5], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.0625, True, 2]], [[[0.03, 0.01], 0.0, 2.0, 5.0, 0.0625, 8.0, 0.5, 1.0, 0.125, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 3.0], [0, 0, 3.0], [0, 0, -3.0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.125, True, 6]], [[[-0.01, -0.02], -1.79, 2.0, 40.0, 0.015625, 3.0, 0.5, 0.3, 0.03125, [[0, 0, -1], [0, 0, 0], [5, 1, 2], [1, 8, 2], [1, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [1.68995, 2.044541, 0.140151, 0.0, False, -1]], [[[-2.24, -3.75], -1.0, 20.0, 0.5, 0.015625, 3.0, 2.0, 0.3, 0.046875, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [-2, 0, 2], [1, 1, 0.5]]], [-0.57379, 0.469444, 1.532879, 0.0, False, -1]], [[[3.68, -0.77], 1.93, 2.0, 5.0, 0.0625, 8.0, 0.5, 0.3, 0.0625, [[0, 8, 2], [0, 1, 0], [0, 0, 0], [0, 0, 0], [1, 8, -1], [0, 8, 0.5], [-2, -3, 0], [0, 0, 0]]], [-0.8094, 3.903439, 0.330434, 0.0, False, -1]], [[[0.03, -0.02], -1.31, 80.0, 40.0, 0.0625, 8.0, 2.0, 0.3, 0.0625, [[0, 0, 0], [0, 0, 0], [0, 0, -1], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.0625, True, 2]], [[[-0.04, -0.04], -1.97, 80.0, 0.5, 0.015625, 8.0, 0.5, 1.0, 0.046875, [[5, 1, 0], [0, 0, 0], [-2, 0, 0.5], [0, 0, 0], [0, 8, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [5, -3, 2]]], [2.218727, -1.193952, 0.621244, 0.0, False, -1]], [[[4.19, 1.85], -0.69, 80.0, 0.5, 0.015625, 8.0, 0.5, 1.0, 0.015625, [[0, 1, 0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 1, 0.5], [-2, 1, -1]]], [-0.888889, 0.444444, -0.992248, 0.0, False, 4]]], [[[[-0.05, -0.07], 0.0, 2.0, 0.5, 0.015625, 8.0, 0.5, 0.3, 0.03125, [[0, 0, -0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0.5], [0, 0, -0.5], [0, 0, 0], [0, 0, 0.5], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.03125, True, 7]], [[[4.02, -0.48], -0.66, 2.0, 5.0, 0.03125, 3.0, 0.5, 1.0, 0.0625, [[0, 0, 0], [1, -3, 0.5], [0, 0, 0]]], [2.158391, -1.820348, -0.052966, 0.0, False, -1]], [[[0.04, 0.0], 1.58, 80.0, 5.0, 0.015625, 8.0, 2.0, 0.3, 0.046875, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, -3, 0], [0, 0, 0], [1, 0, -1], [-2, 8, -1], [0, 0, 0], [5, 0, 2]]], [2.085685, 0.67921, 1.119786, 0.0, False, -1]], [[[0.18, 0.67], -0.31, 0.5, 5.0, 0.03125, 3.0, 2.0, 0.3, 0.0625, [[0, 0, 0], [0, 0, -1], [0, -3, 2], [0, 0, 0], [1, 1, -1], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.0625, True, 5]], [[[0.09, -0.1], 0.0, 0.5, 0.5, 0.03125, 8.0, 0.5, 1.0, 0.0625, [[0, 0, 0], [0, 0, 1.5], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.082005, -0.091117, 1.388111, 0.0, False, -1]], [[[-4.16, 4.12], -1.07, 80.0, 40.0, 0.03125, 3.0, 0.5, 0.3, 0.0625, [[0, 0, 0], [0, 0, 2], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 1, -1], [0, 0, 0]]], [0.0, 0.081633, -0.197531, 0.03125, False, 4]], [[[0.04, -0.02], -1.17, 20.0, 5.0, 0.0625, 3.0, 0.5, 1.0, 0.125, [[0, 0, -1], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.125, True, 3]], [[[0.01, -0.0], 0.7, 0.5, 0.5, 0.0625, 8.0, 2.0, 1.0, 0.1875, [[0, 0, 0], [0, 0, 0], [1, 8, 0.5], [5, -3, 2]]], [5.797639, 4.613407, 3.028481, 0.0, False, -1]]], [[[[-0.03, -0.0], 0.97, 2.0, 5.0, 0.015625, 8.0, 0.5, 1.0, 0.015625, [[0, 0, 0], [0, 0, 0], [0, 1, 0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [5, 8, 0]]], [3.941435, 6.961687, 0.295315, 0.0, False, 0]], [[[3.82, 5.03], 0.39, 2.0, 5.0, 0.03125, 3.0, 2.0, 1.0, 0.03125, [[0, 0, 0], [0, 0, 0], [0, -3, 0], [0, 0, 0], [-2, -3, 0.5], [0, 0, 0]]], [-1.566212, -2.349318, 0.373996, 0.0, False, 2]], [[[-2.34, -1.3], 0.07, 80.0, 5.0, 0.0625, 8.0, 0.5, 0.3, 0.1875, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.1875, True, 2]], [[[-0.04, 0.1], 0.0, 0.5, 0.5, 0.015625, 8.0, 0.5, 0.3, 0.03125, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, -1.5]]], [0.0, 0.0, -1.488372, 0.0, False, 1]], [[[-0.04, -0.04], 0.45, 20.0, 40.0, 0.0625, 3.0, 0.5, 0.3, 0.0625, [[0, 1, -1], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.0625, True, 0]], [[[5.83, 2.38], -1.72, 80.0, 5.0, 0.015625, 8.0, 0.5, 1.0, 0.03125, [[0, 0, 0], [0, 0, 0], [1, 0, 2]]], [0.956269, 0.208944, 0.482545, 0.0, False, -1]], [[[-0.05, -0.02], 1.89, 0.5, 40.0, 0.0625, 3.0, 2.0, 0.3, 0.1875, [[0, 0, 0], [5, 0, -1], [1, 1, -1], [0, 0, 0], [1, 0, 2]]], [2.951277, 0.538484, 0.54504, 0.0, False, -1]], [[[-0.01, 0.0], 0.0, 0.5, 0.5, 0.0625, 8.0, 0.5, 1.0, 0.125, [[0, 0, 1.5], [0, 0, -1.5], [0, 0, -1.5], [0, 0, 1.5], [0, 0, 1.5], [0, 0, 0], [0, 0, 0]]], [-0.008062, 0.0, 1.370126, 0.0, False, -1]]], [[[[0.03, -0.04], -1.19, 2.0, 5.0, 0.0625, 3.0, 0.5, 1.0, 0.0625, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [5, -3, 2]]], [2.572479, -1.543487, 1.52381, 0.0, False, 0]], [[[-3.48, 1.74], 1.67, 20.0, 40.0, 0.0625, 3.0, 2.0, 1.0, 0.1875, [[1, -3, 0.5], [0, -3, 0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.1875, True, 2]], [[[0.45, -2.24], -0.91, 0.5, 0.5, 0.015625, 8.0, 2.0, 0.3, 0.046875, [[1, -3, 2], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [5, 0, 0], [0, 0, 0], [0, 0, 0], [5, 0, 0]]], [7.339549, -3.182927, 1.008391, 0.0, False, -1]], [[[0.04, 0.03], 0.6, 2.0, 0.5, 0.015625, 3.0, 2.0, 0.3, 0.015625, [[0, 0, 0], [0, 0, 0], [0, 1, -1], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.030324, 0.82896, -0.387568, 0.0, False, -1]], [[[-4.0, -0.28], -1.66, 20.0, 0.5, 0.0625, 8.0, 0.5, 1.0, 0.125, [[-2, 8, 2], [0, 0, 0], [-2, 0, 2], [0, 0, 0], [0, 0, 0]]], [-0.279632, 0.133877, 2.11515, 0.0, False, -1]], [[[-4.04, -5.1], 0.88, 80.0, 40.0, 0.0625, 8.0, 0.5, 1.0, 0.0625, [[0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.0625, True, 1]], [[[0.02, 0.01], 0.18, 20.0, 40.0, 0.03125, 8.0, 2.0, 0.3, 0.0625, [[0, 0, 0], [0, 0, 0], [-2, -3, 2], [-2, 0, 2], [0, 0, 0], [0, 0, 0], [0, 8, 2]]], [-0.463332, 4.658316, 1.001609, 0.0, False, 1]], [[[0.05, -0.01], 0.0, 0.5, 0.5, 0.0625, 8.0, 0.5, 1.0, 0.1875, [[0, 0, 0.5], [0, 0, -0.5], [0, 0, -0.5], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.1875, True, 2]]]]
for i, (args, expected) in enumerate(fixtures[N-1]):
    check("case %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
case 0[0.0, 0.0, -0.658704, 0.0, False, 0][0.013154, 0.026308, -0.658704, 0.0, False, -1]Failed
case 1[0.0, 0.0, 0.0, 0.0, True, 3][0.884187, -2.572181, 1.480313, 0.0, False, 0]Failed
case 2[0.0, 0.0, 0.492308, 0.03125, False, 1][0.0, 0.0, 0.492308, 0.03125, False, 2]Failed
case 3[0.0, 0.0, 0.0, 0.015625, True, 6][0.0, 0.0, 0.000356, 0.015625, False, 2]Failed
case 4[-0.888889, -1.333333, 0.0, 0.0, False, 2][-0.888889, -1.333333, 0.0, 0.0, False, 3]Failed
case 5[0.007331, -0.000411, 1.780327, 0.0, False, -1][0.007331, -0.000411, 1.780327, 0.0, False, -1]Passed
case 6[0.0, 0.0, 0.806428, 0.0, False, 0][0.0, 0.0, 0.806428, 0.0, False, 1]Failed
case 7[0.0, 0.0, 0.0, 0.0, True, 4][-1.823636, -0.874067, -0.307458, 0.0, False, -1]Failed

SHA-256 / 6cc1481c85226d8966d1a1b807d17c5fb3c193ea00b3391b7e628a6320995941

3 / The verified repair

Exit 0
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(v, omega, lin_damp, ang_damp, dt, max_speed, sleep_lin, sleep_ang, sleep_time, kicks):
    vx, vy = v
    w = omega
    timer = 0.0
    asleep = False
    slept_at = -1
    for f, (ax, ay, aw) in enumerate(kicks):
        if asleep:
            if ax or ay or aw:
                asleep = False
                timer = 0.0
            else:
                continue
        vx += ax
        vy += ay
        w += aw
        dl = 1.0 / (1.0 + dt * lin_damp)
        vx *= dl
        vy *= dl
        w *= 1.0 / (1.0 + dt * ang_damp)
        sp = math.hypot(vx, vy)
        if sp > max_speed:
            s = max_speed / sp
            vx *= s
            vy *= s
        if math.hypot(vx, vy) < sleep_lin and abs(w) < sleep_ang:
            timer += dt
        else:
            timer = 0.0
        if timer >= sleep_time:
            asleep = True
            slept_at = f
            vx = vy = w = 0.0
    return [round(vx, 6), round(vy, 6), round(w, 6), round(timer, 6), asleep, slept_at]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[[[0.03, 0.06], 0.0, 2.0, 5.0, 0.0625, 8.0, 0.5, 0.3, 0.125, [[0, 0, 0], [0, 0, -1.5], [0, 0, 0], [0, 0, 1.5], [0, 0, 0], [0, 0, -1.5], [0, 0, 0]]], [0.013154, 0.026308, -0.658704, 0.0, False, -1]], [[[0.04, 0.03], 0.2, 2.0, 5.0, 0.015625, 3.0, 0.5, 1.0, 0.015625, [[0, 0, 0], [0, 0, 0], [0, -3, 0], [1, 0, 2], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.884187, -2.572181, 1.480313, 0.0, False, 0]], [[[0.07, -0.09], 0.0, 2.0, 0.5, 0.03125, 8.0, 0.5, 1.0, 0.09375, [[0, 0, -0.5], [0, 0, -0.5], [0, 0, 0], [0, 0, 0.5]]], [0.0, 0.0, 0.492308, 0.03125, False, 2]], [[[-0.01, -0.07], 0.0, 2.0, 0.5, 0.015625, 8.0, 0.5, 1.0, 0.03125, [[0, 0, 3.0], [0, 0, -3.0], [0, 0, 0], [0, 0, 3.0], [0, 0, -3.0], [0, 0, -3.0], [0, 0, 3.0]]], [0.0, 0.0, 0.000356, 0.015625, False, 2]], [[[-0.01, -0.04], 0.74, 20.0, 40.0, 0.0625, 8.0, 0.5, 1.0, 0.125, [[5, 0, 0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [-2, -3, 0]]], [-0.888889, -1.333333, 0.0, 0.0, False, 3]], [[[2.14, -0.12], 1.88, 80.0, 0.5, 0.015625, 8.0, 0.5, 0.3, 0.03125, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.007331, -0.000411, 1.780327, 0.0, False, -1]], [[[-0.02, 0.07], 0.0, 2.0, 5.0, 0.03125, 8.0, 0.5, 0.3, 0.0625, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0.5], [0, 0, 0.5]]], [0.0, 0.0, 0.806428, 0.0, False, 1]], [[[-0.0, 0.04], -1.42, 0.5, 40.0, 0.0625, 8.0, 0.5, 1.0, 0.0625, [[0, 1, 0.5], [0, 0, 0.5], [-2, -3, -1], [0, 0, 0], [0, 1, -1]]], [-1.823636, -0.874067, -0.307458, 0.0, False, -1]]], [[[[0.01, -0.0], -0.96, 80.0, 5.0, 0.03125, 8.0, 2.0, 1.0, 0.0625, [[0, 8, 0.5], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.0625, True, 2]], [[[0.03, 0.01], 0.0, 2.0, 5.0, 0.0625, 8.0, 0.5, 1.0, 0.125, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 3.0], [0, 0, 3.0], [0, 0, -3.0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.125, True, 6]], [[[-0.01, -0.02], -1.79, 2.0, 40.0, 0.015625, 3.0, 0.5, 0.3, 0.03125, [[0, 0, -1], [0, 0, 0], [5, 1, 2], [1, 8, 2], [1, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [1.68995, 2.044541, 0.140151, 0.0, False, -1]], [[[-2.24, -3.75], -1.0, 20.0, 0.5, 0.015625, 3.0, 2.0, 0.3, 0.046875, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [-2, 0, 2], [1, 1, 0.5]]], [-0.57379, 0.469444, 1.532879, 0.0, False, -1]], [[[3.68, -0.77], 1.93, 2.0, 5.0, 0.0625, 8.0, 0.5, 0.3, 0.0625, [[0, 8, 2], [0, 1, 0], [0, 0, 0], [0, 0, 0], [1, 8, -1], [0, 8, 0.5], [-2, -3, 0], [0, 0, 0]]], [-0.8094, 3.903439, 0.330434, 0.0, False, -1]], [[[0.03, -0.02], -1.31, 80.0, 40.0, 0.0625, 8.0, 2.0, 0.3, 0.0625, [[0, 0, 0], [0, 0, 0], [0, 0, -1], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.0625, True, 2]], [[[-0.04, -0.04], -1.97, 80.0, 0.5, 0.015625, 8.0, 0.5, 1.0, 0.046875, [[5, 1, 0], [0, 0, 0], [-2, 0, 0.5], [0, 0, 0], [0, 8, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [5, -3, 2]]], [2.218727, -1.193952, 0.621244, 0.0, False, -1]], [[[4.19, 1.85], -0.69, 80.0, 0.5, 0.015625, 8.0, 0.5, 1.0, 0.015625, [[0, 1, 0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 1, 0.5], [-2, 1, -1]]], [-0.888889, 0.444444, -0.992248, 0.0, False, 4]]], [[[[-0.05, -0.07], 0.0, 2.0, 0.5, 0.015625, 8.0, 0.5, 0.3, 0.03125, [[0, 0, -0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0.5], [0, 0, -0.5], [0, 0, 0], [0, 0, 0.5], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.03125, True, 7]], [[[4.02, -0.48], -0.66, 2.0, 5.0, 0.03125, 3.0, 0.5, 1.0, 0.0625, [[0, 0, 0], [1, -3, 0.5], [0, 0, 0]]], [2.158391, -1.820348, -0.052966, 0.0, False, -1]], [[[0.04, 0.0], 1.58, 80.0, 5.0, 0.015625, 8.0, 2.0, 0.3, 0.046875, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, -3, 0], [0, 0, 0], [1, 0, -1], [-2, 8, -1], [0, 0, 0], [5, 0, 2]]], [2.085685, 0.67921, 1.119786, 0.0, False, -1]], [[[0.18, 0.67], -0.31, 0.5, 5.0, 0.03125, 3.0, 2.0, 0.3, 0.0625, [[0, 0, 0], [0, 0, -1], [0, -3, 2], [0, 0, 0], [1, 1, -1], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.0625, True, 5]], [[[0.09, -0.1], 0.0, 0.5, 0.5, 0.03125, 8.0, 0.5, 1.0, 0.0625, [[0, 0, 0], [0, 0, 1.5], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.082005, -0.091117, 1.388111, 0.0, False, -1]], [[[-4.16, 4.12], -1.07, 80.0, 40.0, 0.03125, 3.0, 0.5, 0.3, 0.0625, [[0, 0, 0], [0, 0, 2], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 1, -1], [0, 0, 0]]], [0.0, 0.081633, -0.197531, 0.03125, False, 4]], [[[0.04, -0.02], -1.17, 20.0, 5.0, 0.0625, 3.0, 0.5, 1.0, 0.125, [[0, 0, -1], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.125, True, 3]], [[[0.01, -0.0], 0.7, 0.5, 0.5, 0.0625, 8.0, 2.0, 1.0, 0.1875, [[0, 0, 0], [0, 0, 0], [1, 8, 0.5], [5, -3, 2]]], [5.797639, 4.613407, 3.028481, 0.0, False, -1]]], [[[[-0.03, -0.0], 0.97, 2.0, 5.0, 0.015625, 8.0, 0.5, 1.0, 0.015625, [[0, 0, 0], [0, 0, 0], [0, 1, 0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [5, 8, 0]]], [3.941435, 6.961687, 0.295315, 0.0, False, 0]], [[[3.82, 5.03], 0.39, 2.0, 5.0, 0.03125, 3.0, 2.0, 1.0, 0.03125, [[0, 0, 0], [0, 0, 0], [0, -3, 0], [0, 0, 0], [-2, -3, 0.5], [0, 0, 0]]], [-1.566212, -2.349318, 0.373996, 0.0, False, 2]], [[[-2.34, -1.3], 0.07, 80.0, 5.0, 0.0625, 8.0, 0.5, 0.3, 0.1875, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.1875, True, 2]], [[[-0.04, 0.1], 0.0, 0.5, 0.5, 0.015625, 8.0, 0.5, 0.3, 0.03125, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, -1.5]]], [0.0, 0.0, -1.488372, 0.0, False, 1]], [[[-0.04, -0.04], 0.45, 20.0, 40.0, 0.0625, 3.0, 0.5, 0.3, 0.0625, [[0, 1, -1], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.0625, True, 0]], [[[5.83, 2.38], -1.72, 80.0, 5.0, 0.015625, 8.0, 0.5, 1.0, 0.03125, [[0, 0, 0], [0, 0, 0], [1, 0, 2]]], [0.956269, 0.208944, 0.482545, 0.0, False, -1]], [[[-0.05, -0.02], 1.89, 0.5, 40.0, 0.0625, 3.0, 2.0, 0.3, 0.1875, [[0, 0, 0], [5, 0, -1], [1, 1, -1], [0, 0, 0], [1, 0, 2]]], [2.951277, 0.538484, 0.54504, 0.0, False, -1]], [[[-0.01, 0.0], 0.0, 0.5, 0.5, 0.0625, 8.0, 0.5, 1.0, 0.125, [[0, 0, 1.5], [0, 0, -1.5], [0, 0, -1.5], [0, 0, 1.5], [0, 0, 1.5], [0, 0, 0], [0, 0, 0]]], [-0.008062, 0.0, 1.370126, 0.0, False, -1]]], [[[[0.03, -0.04], -1.19, 2.0, 5.0, 0.0625, 3.0, 0.5, 1.0, 0.0625, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [5, -3, 2]]], [2.572479, -1.543487, 1.52381, 0.0, False, 0]], [[[-3.48, 1.74], 1.67, 20.0, 40.0, 0.0625, 3.0, 2.0, 1.0, 0.1875, [[1, -3, 0.5], [0, -3, 0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.1875, True, 2]], [[[0.45, -2.24], -0.91, 0.5, 0.5, 0.015625, 8.0, 2.0, 0.3, 0.046875, [[1, -3, 2], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [5, 0, 0], [0, 0, 0], [0, 0, 0], [5, 0, 0]]], [7.339549, -3.182927, 1.008391, 0.0, False, -1]], [[[0.04, 0.03], 0.6, 2.0, 0.5, 0.015625, 3.0, 2.0, 0.3, 0.015625, [[0, 0, 0], [0, 0, 0], [0, 1, -1], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.030324, 0.82896, -0.387568, 0.0, False, -1]], [[[-4.0, -0.28], -1.66, 20.0, 0.5, 0.0625, 8.0, 0.5, 1.0, 0.125, [[-2, 8, 2], [0, 0, 0], [-2, 0, 2], [0, 0, 0], [0, 0, 0]]], [-0.279632, 0.133877, 2.11515, 0.0, False, -1]], [[[-4.04, -5.1], 0.88, 80.0, 40.0, 0.0625, 8.0, 0.5, 1.0, 0.0625, [[0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.0625, True, 1]], [[[0.02, 0.01], 0.18, 20.0, 40.0, 0.03125, 8.0, 2.0, 0.3, 0.0625, [[0, 0, 0], [0, 0, 0], [-2, -3, 2], [-2, 0, 2], [0, 0, 0], [0, 0, 0], [0, 8, 2]]], [-0.463332, 4.658316, 1.001609, 0.0, False, 1]], [[[0.05, -0.01], 0.0, 0.5, 0.5, 0.0625, 8.0, 0.5, 1.0, 0.1875, [[0, 0, 0.5], [0, 0, -0.5], [0, 0, -0.5], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.1875, True, 2]]]]
for i, (args, expected) in enumerate(fixtures[N-1]):
    check("case %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
case 0[0.013154, 0.026308, -0.658704, 0.0, False, -1][0.013154, 0.026308, -0.658704, 0.0, False, -1]Passed
case 1[0.884187, -2.572181, 1.480313, 0.0, False, 0][0.884187, -2.572181, 1.480313, 0.0, False, 0]Passed
case 2[0.0, 0.0, 0.492308, 0.03125, False, 2][0.0, 0.0, 0.492308, 0.03125, False, 2]Passed
case 3[0.0, 0.0, 0.000356, 0.015625, False, 2][0.0, 0.0, 0.000356, 0.015625, False, 2]Passed
case 4[-0.888889, -1.333333, 0.0, 0.0, False, 3][-0.888889, -1.333333, 0.0, 0.0, False, 3]Passed
case 5[0.007331, -0.000411, 1.780327, 0.0, False, -1][0.007331, -0.000411, 1.780327, 0.0, False, -1]Passed
case 6[0.0, 0.0, 0.806428, 0.0, False, 1][0.0, 0.0, 0.806428, 0.0, False, 1]Passed
case 7[-1.823636, -0.874067, -0.307458, 0.0, False, -1][-1.823636, -0.874067, -0.307458, 0.0, False, -1]Passed

SHA-256 / 52202281c58bf4552dc5acb95238e86ebc2aa5f3063690854272f327382e64e5

Verification & scope

A deterministic bounded teaching model with stipulated toy conventions and rounded float output; not a production physics engine or a proof of numerical stability. 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 2026-09-29T14:50:57.302276+00:00.

Case digest / d6e51de29b067ecd6bf590a8628f219e85add2e16fda5d0c1464e481dffb174b