FA-87261 / Physics integrator stability / Open access

Sleeping bodies ignore incoming impulses · case 01

A sleeping crate hit by a kick stays frozen.

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

ROOT CAUSE

Asleep frames always continue without checking the kick.

VERIFIED REPAIR

Wake the body and reset its timer when a nonzero kick arrives.

Unsuccessful approach: Waking without resetting the timer puts the body straight back to sleep.

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:
            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 = [[[[[0.07, -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]], [[[-0.12, -5.54], -0.33, 0.5, 0.5, 0.015625, 8.0, 2.0, 0.3, 0.03125, [[1, 8, 2], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.853029, 2.384603, 1.618816, 0.0, False, -1]], [[[0.01, 0.0], 0.02, 20.0, 5.0, 0.0625, 8.0, 0.5, 0.3, 0.125, [[0, 0, 0], [0, 0, 0], [0, 0, -1], [0, 0, 0]]], [0.0, 0.0, -0.580499, 0.0, False, 1]], [[[0.01, -0.05], 1.96, 20.0, 0.5, 0.015625, 3.0, 2.0, 1.0, 0.03125, [[0, 0, 0], [-2, -3, 0], [0, 0, 0], [0, 0, 0], [5, 0, -1], [0, -3, -1], [0, 0, 0], [5, 8, 2], [0, 0, 0], [0, 1, -1]]], [1.25024, 1.974221, 0.858637, 0.0, False, -1]], [[[-0.42, 3.07], 0.58, 80.0, 40.0, 0.03125, 3.0, 2.0, 1.0, 0.09375, [[0, 0, 0], [0, 0, 0], [-2, 8, 0], [0, 0, 0], [0, 0, 0], [0, -3, 0], [1, 0, 0]]], [0.285714, 0.0, 0.0, 0.03125, False, 5]], [[[-0.04, -0.05], -0.23, 80.0, 5.0, 0.03125, 8.0, 2.0, 1.0, 0.0625, [[0, 0, 0], [0, 0, 0], [0, 1, -1], [0, 0, 0], [0, 0, 0], [5, 1, 0.5]]], [1.428571, 0.285714, 0.432432, 0.03125, False, 3]], [[[0.01, -0.01], 0.02, 80.0, 5.0, 0.0625, 3.0, 0.5, 0.3, 0.0625, [[5, 8, -1], [0, 0, 0], [0, 0, 2]]], [0.023194, 0.036991, 1.09037, 0.0, False, -1]], [[[0.02, -0.03], 0.99, 20.0, 40.0, 0.0625, 3.0, 0.5, 1.0, 0.0625, [[0, 0, 0], [0, 0, 0], [0, 8, 0.5], [0, 0, 0]]], [0.0, 1.333333, 0.040816, 0.0, False, 0]]], [[[[0.02, -0.03], 1.88, 20.0, 5.0, 0.0625, 3.0, 0.5, 1.0, 0.0625, [[-2, 0, 2], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [-2, 0, 0], [5, 0, 0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.0625, True, 8]], [[[-0.05, -0.0], 0.0, 0.5, 5.0, 0.015625, 8.0, 0.5, 0.3, 0.03125, [[0, 0, -1.5], [0, 0, 0], [0, 0, -1.5], [0, 0, 1.5], [0, 0, -1.5]]], [-0.048092, 0.0, -2.327574, 0.0, False, -1]], [[[0.01, -0.01], 0.0, 0.5, 5.0, 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], [0, 0, -0.5], [0, 0, -0.5], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, -0.769069, 0.0, False, 4]], [[[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]], [[[-0.05, -0.03], -1.75, 20.0, 40.0, 0.0625, 8.0, 0.5, 0.3, 0.0625, [[5, 0, 0.5], [0, 0, 0], [1, 0, 0.5], [0, 8, 0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0], [5, -3, 0]]], [2.222222, -1.333333, 0.0, 0.0, False, 6]], [[[-0.03, 0.06], 0.0, 0.5, 0.5, 0.03125, 8.0, 0.5, 1.0, 0.0625, [[0, 0, 0], [0, 0, -0.5], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.0625, True, 1]], [[[-0.03, -0.03], 0.0, 0.5, 0.5, 0.0625, 8.0, 0.5, 1.0, 0.1875, [[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, 0], [0, 0, 0]]], [-0.023454, -0.023454, 7.253301, 0.0, False, -1]], [[[0.02, 0.02], -0.63, 80.0, 40.0, 0.015625, 8.0, 2.0, 1.0, 0.046875, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, -3, 0.5], [0, 0, 0]]], [0.0, -0.592593, 0.189349, 0.03125, False, 2]]], [[[[0.05, 0.06], 0.0, 0.5, 5.0, 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], [0, 0, -0.5], [0, 0, 0]]], [0.0, 0.0, -0.430162, 0.0, False, 4]], [[[-0.03, 0.08], 0.0, 2.0, 5.0, 0.015625, 8.0, 0.5, 1.0, 0.03125, [[0, 0, -0.5], [0, 0, 0.5], [0, 0, -0.5], [0, 0, -0.5], [0, 0, 0.5], [0, 0, 0], [0, 0, 0.5], [0, 0, -0.5]]], [0.0, 0.0, 0.0, 0.03125, True, 7]], [[[0.04, 0.1], 0.0, 2.0, 5.0, 0.015625, 8.0, 0.5, 1.0, 0.03125, [[0, 0, 0.5], [0, 0, 0.5], [0, 0, -0.5], [0, 0, 0.5], [0, 0, -0.5], [0, 0, -0.5], [0, 0, 0.5]]], [0.0, 0.0, 0.463768, 0.015625, False, 5]], [[[-0.01, 0.04], 1.03, 2.0, 0.5, 0.03125, 8.0, 0.5, 0.3, 0.0625, [[0, 0, 0], [0, 0, 0], [0, 0, 0]]], [-0.008337, 0.033348, 0.983189, 0.0, False, -1]], [[[0.09, 0.08], 0.0, 2.0, 5.0, 0.03125, 8.0, 0.5, 0.3, 0.0625, [[0, 0, 0.5], [0, 0, 0.5], [0, 0, 0], [0, 0, 0], [0, 0, -0.5], [0, 0, 0], [0, 0, 0.5], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.323456, 0.0, False, 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]], [[[0.05, -0.03], 0.0, 0.5, 5.0, 0.015625, 8.0, 0.5, 0.3, 0.046875, [[0, 0, -0.5], [0, 0, 0.5], [0, 0, -0.5], [0, 0, -0.5], [0, 0, -0.5], [0, 0, 0]]], [0.047719, -0.028631, -1.174357, 0.0, False, -1]], [[[0.09, 0.02], 0.0, 0.5, 5.0, 0.03125, 8.0, 0.5, 0.3, 0.0625, [[0, 0, 1.5], [0, 0, -1.5], [0, 0, -1.5], [0, 0, 1.5], [0, 0, 0], [0, 0, 1.5]]], [0.0, 0.0, 1.297297, 0.0, False, 4]]], [[[[0.06, 0.07], 0.0, 0.5, 5.0, 0.03125, 8.0, 0.5, 0.3, 0.09375, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, -3.0], [0, 0, 0], [0, 0, -3.0], [0, 0, 3.0]]], [0.0, 0.0, -1.327852, 0.0, False, 2]], [[[-0.05, -0.01], -0.3, 80.0, 40.0, 0.015625, 8.0, 2.0, 0.3, 0.015625, [[0, 0, 0], [0, 0, 0], [5, 0, -1], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.015625, True, 4]], [[[-0.0, 0.01], -1.88, 2.0, 40.0, 0.015625, 8.0, 2.0, 1.0, 0.015625, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [5, 8, 0]]], [4.239992, 6.783986, 0.0, 0.0, False, 1]], [[[0.04, -0.08], 0.0, 2.0, 5.0, 0.015625, 8.0, 0.5, 1.0, 0.046875, [[0, 0, 0], [0, 0, 0], [0, 0, -0.5], [0, 0, -0.5], [0, 0, 0.5], [0, 0, -0.5], [0, 0, 0], [0, 0, 0.5], [0, 0, -0.5]]], [0.0, 0.0, -0.033606, 0.03125, False, 5]], [[[3.71, -0.78], 1.01, 20.0, 40.0, 0.0625, 3.0, 0.5, 1.0, 0.0625, [[1, -3, 0], [0, -3, 2], [1, -3, 2], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.0625, True, 4]], [[[-5.26, 2.26], 0.01, 2.0, 40.0, 0.03125, 8.0, 0.5, 1.0, 0.09375, [[0, 0, 0], [0, 0, 2], [-2, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [-4.918004, 1.478447, 0.015449, 0.0, False, -1]], [[[0.08, 0.03], 0.0, 2.0, 0.5, 0.0625, 8.0, 0.5, 1.0, 0.1875, [[0, 0, 0], [0, 0, 0], [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, -1.5]]], [0.027715, 0.010393, -0.008837, 0.0625, False, -1]], [[[-0.05, 0.02], 0.0, 0.5, 5.0, 0.015625, 8.0, 0.5, 1.0, 0.03125, [[0, 0, 0], [0, 0, 0], [0, 0, 0.5], [0, 0, -0.5], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.03125, True, 3]]], [[[[0.06, 0.05], 0.0, 2.0, 5.0, 0.03125, 8.0, 0.5, 1.0, 0.0625, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0.5], [0, 0, 0.5], [0, 0, -0.5], [0, 0, 0], [0, 0, 0.5]]], [0.0, 0.0, 0.432432, 0.03125, False, 6]], [[[-0.0, 0.0], -1.06, 2.0, 5.0, 0.0625, 3.0, 2.0, 1.0, 0.1875, [[0, 0, 0], [-2, 1, 0.5], [0, 0, 0], [0, 0, 0], [1, 8, 2], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.261341, 2.090725, 0.673958, 0.0, False, 2]], [[[-0.03, -0.03], 0.71, 80.0, 40.0, 0.0625, 3.0, 0.5, 0.3, 0.1875, [[0, 0, 0], [0, 0, -1], [0, 0, 0], [0, 0, 0], [-2, 0, 0.5]]], [-0.333333, 0.0, 0.142857, 0.0625, False, 2]], [[[0.08, -0.08], 0.0, 0.5, 0.5, 0.0625, 8.0, 0.5, 1.0, 0.125, [[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, 0.125, True, 5]], [[[-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]], [[[-0.03, -0.01], 1.59, 80.0, 40.0, 0.03125, 8.0, 0.5, 1.0, 0.0625, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 1, 0.5], [1, -3, -1], [-2, 0, 0], [0, 0, 0]]], [-0.139942, -0.063307, -0.068282, 0.03125, False, 1]], [[[-0.01, 0.03], -1.06, 2.0, 40.0, 0.03125, 3.0, 2.0, 1.0, 0.03125, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.03125, True, 0]], [[[0.24, 4.31], -1.09, 0.5, 40.0, 0.0625, 8.0, 2.0, 1.0, 0.0625, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 8, 0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.133785, 7.293316, 0.003163, 0.0, False, -1]]]]
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 fixture	Actual	Expected	Outcome
case 0	`[0.0, 0.0, 0.0, 0.09375, True, 2]`	`[0.0, 0.0, 0.492308, 0.03125, False, 2]`	Failed
case 1	`[0.853029, 2.384603, 1.618816, 0.0, False, -1]`	`[0.853029, 2.384603, 1.618816, 0.0, False, -1]`	Passed
case 2	`[0.0, 0.0, 0.0, 0.125, True, 1]`	`[0.0, 0.0, -0.580499, 0.0, False, 1]`	Failed
case 3	`[1.25024, 1.974221, 0.858637, 0.0, False, -1]`	`[1.25024, 1.974221, 0.858637, 0.0, False, -1]`	Passed
case 4	`[0.0, 0.0, 0.0, 0.09375, True, 5]`	`[0.285714, 0.0, 0.0, 0.03125, False, 5]`	Failed
case 5	`[0.0, 0.0, 0.0, 0.0625, True, 1]`	`[1.428571, 0.285714, 0.432432, 0.03125, False, 3]`	Failed
case 6	`[0.023194, 0.036991, 1.09037, 0.0, False, -1]`	`[0.023194, 0.036991, 1.09037, 0.0, False, -1]`	Passed
case 7	`[0.0, 0.0, 0.0, 0.0625, True, 0]`	`[0.0, 1.333333, 0.040816, 0.0, False, 0]`	Failed

SHA-256 / a3af616de268973fe4bc540688a54485d109fdf0e17d9ae287c1790d236b762a

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
            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 = [[[[[0.07, -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]], [[[-0.12, -5.54], -0.33, 0.5, 0.5, 0.015625, 8.0, 2.0, 0.3, 0.03125, [[1, 8, 2], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.853029, 2.384603, 1.618816, 0.0, False, -1]], [[[0.01, 0.0], 0.02, 20.0, 5.0, 0.0625, 8.0, 0.5, 0.3, 0.125, [[0, 0, 0], [0, 0, 0], [0, 0, -1], [0, 0, 0]]], [0.0, 0.0, -0.580499, 0.0, False, 1]], [[[0.01, -0.05], 1.96, 20.0, 0.5, 0.015625, 3.0, 2.0, 1.0, 0.03125, [[0, 0, 0], [-2, -3, 0], [0, 0, 0], [0, 0, 0], [5, 0, -1], [0, -3, -1], [0, 0, 0], [5, 8, 2], [0, 0, 0], [0, 1, -1]]], [1.25024, 1.974221, 0.858637, 0.0, False, -1]], [[[-0.42, 3.07], 0.58, 80.0, 40.0, 0.03125, 3.0, 2.0, 1.0, 0.09375, [[0, 0, 0], [0, 0, 0], [-2, 8, 0], [0, 0, 0], [0, 0, 0], [0, -3, 0], [1, 0, 0]]], [0.285714, 0.0, 0.0, 0.03125, False, 5]], [[[-0.04, -0.05], -0.23, 80.0, 5.0, 0.03125, 8.0, 2.0, 1.0, 0.0625, [[0, 0, 0], [0, 0, 0], [0, 1, -1], [0, 0, 0], [0, 0, 0], [5, 1, 0.5]]], [1.428571, 0.285714, 0.432432, 0.03125, False, 3]], [[[0.01, -0.01], 0.02, 80.0, 5.0, 0.0625, 3.0, 0.5, 0.3, 0.0625, [[5, 8, -1], [0, 0, 0], [0, 0, 2]]], [0.023194, 0.036991, 1.09037, 0.0, False, -1]], [[[0.02, -0.03], 0.99, 20.0, 40.0, 0.0625, 3.0, 0.5, 1.0, 0.0625, [[0, 0, 0], [0, 0, 0], [0, 8, 0.5], [0, 0, 0]]], [0.0, 1.333333, 0.040816, 0.0, False, 0]]], [[[[0.02, -0.03], 1.88, 20.0, 5.0, 0.0625, 3.0, 0.5, 1.0, 0.0625, [[-2, 0, 2], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [-2, 0, 0], [5, 0, 0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.0625, True, 8]], [[[-0.05, -0.0], 0.0, 0.5, 5.0, 0.015625, 8.0, 0.5, 0.3, 0.03125, [[0, 0, -1.5], [0, 0, 0], [0, 0, -1.5], [0, 0, 1.5], [0, 0, -1.5]]], [-0.048092, 0.0, -2.327574, 0.0, False, -1]], [[[0.01, -0.01], 0.0, 0.5, 5.0, 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], [0, 0, -0.5], [0, 0, -0.5], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, -0.769069, 0.0, False, 4]], [[[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]], [[[-0.05, -0.03], -1.75, 20.0, 40.0, 0.0625, 8.0, 0.5, 0.3, 0.0625, [[5, 0, 0.5], [0, 0, 0], [1, 0, 0.5], [0, 8, 0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0], [5, -3, 0]]], [2.222222, -1.333333, 0.0, 0.0, False, 6]], [[[-0.03, 0.06], 0.0, 0.5, 0.5, 0.03125, 8.0, 0.5, 1.0, 0.0625, [[0, 0, 0], [0, 0, -0.5], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.0625, True, 1]], [[[-0.03, -0.03], 0.0, 0.5, 0.5, 0.0625, 8.0, 0.5, 1.0, 0.1875, [[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, 0], [0, 0, 0]]], [-0.023454, -0.023454, 7.253301, 0.0, False, -1]], [[[0.02, 0.02], -0.63, 80.0, 40.0, 0.015625, 8.0, 2.0, 1.0, 0.046875, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, -3, 0.5], [0, 0, 0]]], [0.0, -0.592593, 0.189349, 0.03125, False, 2]]], [[[[0.05, 0.06], 0.0, 0.5, 5.0, 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], [0, 0, -0.5], [0, 0, 0]]], [0.0, 0.0, -0.430162, 0.0, False, 4]], [[[-0.03, 0.08], 0.0, 2.0, 5.0, 0.015625, 8.0, 0.5, 1.0, 0.03125, [[0, 0, -0.5], [0, 0, 0.5], [0, 0, -0.5], [0, 0, -0.5], [0, 0, 0.5], [0, 0, 0], [0, 0, 0.5], [0, 0, -0.5]]], [0.0, 0.0, 0.0, 0.03125, True, 7]], [[[0.04, 0.1], 0.0, 2.0, 5.0, 0.015625, 8.0, 0.5, 1.0, 0.03125, [[0, 0, 0.5], [0, 0, 0.5], [0, 0, -0.5], [0, 0, 0.5], [0, 0, -0.5], [0, 0, -0.5], [0, 0, 0.5]]], [0.0, 0.0, 0.463768, 0.015625, False, 5]], [[[-0.01, 0.04], 1.03, 2.0, 0.5, 0.03125, 8.0, 0.5, 0.3, 0.0625, [[0, 0, 0], [0, 0, 0], [0, 0, 0]]], [-0.008337, 0.033348, 0.983189, 0.0, False, -1]], [[[0.09, 0.08], 0.0, 2.0, 5.0, 0.03125, 8.0, 0.5, 0.3, 0.0625, [[0, 0, 0.5], [0, 0, 0.5], [0, 0, 0], [0, 0, 0], [0, 0, -0.5], [0, 0, 0], [0, 0, 0.5], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.323456, 0.0, False, 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]], [[[0.05, -0.03], 0.0, 0.5, 5.0, 0.015625, 8.0, 0.5, 0.3, 0.046875, [[0, 0, -0.5], [0, 0, 0.5], [0, 0, -0.5], [0, 0, -0.5], [0, 0, -0.5], [0, 0, 0]]], [0.047719, -0.028631, -1.174357, 0.0, False, -1]], [[[0.09, 0.02], 0.0, 0.5, 5.0, 0.03125, 8.0, 0.5, 0.3, 0.0625, [[0, 0, 1.5], [0, 0, -1.5], [0, 0, -1.5], [0, 0, 1.5], [0, 0, 0], [0, 0, 1.5]]], [0.0, 0.0, 1.297297, 0.0, False, 4]]], [[[[0.06, 0.07], 0.0, 0.5, 5.0, 0.03125, 8.0, 0.5, 0.3, 0.09375, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, -3.0], [0, 0, 0], [0, 0, -3.0], [0, 0, 3.0]]], [0.0, 0.0, -1.327852, 0.0, False, 2]], [[[-0.05, -0.01], -0.3, 80.0, 40.0, 0.015625, 8.0, 2.0, 0.3, 0.015625, [[0, 0, 0], [0, 0, 0], [5, 0, -1], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.015625, True, 4]], [[[-0.0, 0.01], -1.88, 2.0, 40.0, 0.015625, 8.0, 2.0, 1.0, 0.015625, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [5, 8, 0]]], [4.239992, 6.783986, 0.0, 0.0, False, 1]], [[[0.04, -0.08], 0.0, 2.0, 5.0, 0.015625, 8.0, 0.5, 1.0, 0.046875, [[0, 0, 0], [0, 0, 0], [0, 0, -0.5], [0, 0, -0.5], [0, 0, 0.5], [0, 0, -0.5], [0, 0, 0], [0, 0, 0.5], [0, 0, -0.5]]], [0.0, 0.0, -0.033606, 0.03125, False, 5]], [[[3.71, -0.78], 1.01, 20.0, 40.0, 0.0625, 3.0, 0.5, 1.0, 0.0625, [[1, -3, 0], [0, -3, 2], [1, -3, 2], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.0625, True, 4]], [[[-5.26, 2.26], 0.01, 2.0, 40.0, 0.03125, 8.0, 0.5, 1.0, 0.09375, [[0, 0, 0], [0, 0, 2], [-2, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [-4.918004, 1.478447, 0.015449, 0.0, False, -1]], [[[0.08, 0.03], 0.0, 2.0, 0.5, 0.0625, 8.0, 0.5, 1.0, 0.1875, [[0, 0, 0], [0, 0, 0], [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, -1.5]]], [0.027715, 0.010393, -0.008837, 0.0625, False, -1]], [[[-0.05, 0.02], 0.0, 0.5, 5.0, 0.015625, 8.0, 0.5, 1.0, 0.03125, [[0, 0, 0], [0, 0, 0], [0, 0, 0.5], [0, 0, -0.5], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.03125, True, 3]]], [[[[0.06, 0.05], 0.0, 2.0, 5.0, 0.03125, 8.0, 0.5, 1.0, 0.0625, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0.5], [0, 0, 0.5], [0, 0, -0.5], [0, 0, 0], [0, 0, 0.5]]], [0.0, 0.0, 0.432432, 0.03125, False, 6]], [[[-0.0, 0.0], -1.06, 2.0, 5.0, 0.0625, 3.0, 2.0, 1.0, 0.1875, [[0, 0, 0], [-2, 1, 0.5], [0, 0, 0], [0, 0, 0], [1, 8, 2], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.261341, 2.090725, 0.673958, 0.0, False, 2]], [[[-0.03, -0.03], 0.71, 80.0, 40.0, 0.0625, 3.0, 0.5, 0.3, 0.1875, [[0, 0, 0], [0, 0, -1], [0, 0, 0], [0, 0, 0], [-2, 0, 0.5]]], [-0.333333, 0.0, 0.142857, 0.0625, False, 2]], [[[0.08, -0.08], 0.0, 0.5, 0.5, 0.0625, 8.0, 0.5, 1.0, 0.125, [[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, 0.125, True, 5]], [[[-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]], [[[-0.03, -0.01], 1.59, 80.0, 40.0, 0.03125, 8.0, 0.5, 1.0, 0.0625, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 1, 0.5], [1, -3, -1], [-2, 0, 0], [0, 0, 0]]], [-0.139942, -0.063307, -0.068282, 0.03125, False, 1]], [[[-0.01, 0.03], -1.06, 2.0, 40.0, 0.03125, 3.0, 2.0, 1.0, 0.03125, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.03125, True, 0]], [[[0.24, 4.31], -1.09, 0.5, 40.0, 0.0625, 8.0, 2.0, 1.0, 0.0625, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 8, 0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.133785, 7.293316, 0.003163, 0.0, False, -1]]]]
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 fixture	Actual	Expected	Outcome
case 0	`[0.0, 0.0, 0.0, 0.125, True, 3]`	`[0.0, 0.0, 0.492308, 0.03125, False, 2]`	Failed
case 1	`[0.853029, 2.384603, 1.618816, 0.0, False, -1]`	`[0.853029, 2.384603, 1.618816, 0.0, False, -1]`	Passed
case 2	`[0.0, 0.0, -0.580499, 0.0, False, 1]`	`[0.0, 0.0, -0.580499, 0.0, False, 1]`	Passed
case 3	`[1.25024, 1.974221, 0.858637, 0.0, False, -1]`	`[1.25024, 1.974221, 0.858637, 0.0, False, -1]`	Passed
case 4	`[0.0, 0.0, 0.0, 0.125, True, 6]`	`[0.285714, 0.0, 0.0, 0.03125, False, 5]`	Failed
case 5	`[0.0, 0.0, 0.0, 0.125, True, 5]`	`[1.428571, 0.285714, 0.432432, 0.03125, False, 3]`	Failed
case 6	`[0.023194, 0.036991, 1.09037, 0.0, False, -1]`	`[0.023194, 0.036991, 1.09037, 0.0, False, -1]`	Passed
case 7	`[0.0, 1.333333, 0.040816, 0.0, False, 0]`	`[0.0, 1.333333, 0.040816, 0.0, False, 0]`	Passed

SHA-256 / 8d9ec7ee037ae9df4f8ac69ec1e91e179304e523fc0a37c9340deef80e5c9a25

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 = [[[[[0.07, -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]], [[[-0.12, -5.54], -0.33, 0.5, 0.5, 0.015625, 8.0, 2.0, 0.3, 0.03125, [[1, 8, 2], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.853029, 2.384603, 1.618816, 0.0, False, -1]], [[[0.01, 0.0], 0.02, 20.0, 5.0, 0.0625, 8.0, 0.5, 0.3, 0.125, [[0, 0, 0], [0, 0, 0], [0, 0, -1], [0, 0, 0]]], [0.0, 0.0, -0.580499, 0.0, False, 1]], [[[0.01, -0.05], 1.96, 20.0, 0.5, 0.015625, 3.0, 2.0, 1.0, 0.03125, [[0, 0, 0], [-2, -3, 0], [0, 0, 0], [0, 0, 0], [5, 0, -1], [0, -3, -1], [0, 0, 0], [5, 8, 2], [0, 0, 0], [0, 1, -1]]], [1.25024, 1.974221, 0.858637, 0.0, False, -1]], [[[-0.42, 3.07], 0.58, 80.0, 40.0, 0.03125, 3.0, 2.0, 1.0, 0.09375, [[0, 0, 0], [0, 0, 0], [-2, 8, 0], [0, 0, 0], [0, 0, 0], [0, -3, 0], [1, 0, 0]]], [0.285714, 0.0, 0.0, 0.03125, False, 5]], [[[-0.04, -0.05], -0.23, 80.0, 5.0, 0.03125, 8.0, 2.0, 1.0, 0.0625, [[0, 0, 0], [0, 0, 0], [0, 1, -1], [0, 0, 0], [0, 0, 0], [5, 1, 0.5]]], [1.428571, 0.285714, 0.432432, 0.03125, False, 3]], [[[0.01, -0.01], 0.02, 80.0, 5.0, 0.0625, 3.0, 0.5, 0.3, 0.0625, [[5, 8, -1], [0, 0, 0], [0, 0, 2]]], [0.023194, 0.036991, 1.09037, 0.0, False, -1]], [[[0.02, -0.03], 0.99, 20.0, 40.0, 0.0625, 3.0, 0.5, 1.0, 0.0625, [[0, 0, 0], [0, 0, 0], [0, 8, 0.5], [0, 0, 0]]], [0.0, 1.333333, 0.040816, 0.0, False, 0]]], [[[[0.02, -0.03], 1.88, 20.0, 5.0, 0.0625, 3.0, 0.5, 1.0, 0.0625, [[-2, 0, 2], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [-2, 0, 0], [5, 0, 0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.0625, True, 8]], [[[-0.05, -0.0], 0.0, 0.5, 5.0, 0.015625, 8.0, 0.5, 0.3, 0.03125, [[0, 0, -1.5], [0, 0, 0], [0, 0, -1.5], [0, 0, 1.5], [0, 0, -1.5]]], [-0.048092, 0.0, -2.327574, 0.0, False, -1]], [[[0.01, -0.01], 0.0, 0.5, 5.0, 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], [0, 0, -0.5], [0, 0, -0.5], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, -0.769069, 0.0, False, 4]], [[[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]], [[[-0.05, -0.03], -1.75, 20.0, 40.0, 0.0625, 8.0, 0.5, 0.3, 0.0625, [[5, 0, 0.5], [0, 0, 0], [1, 0, 0.5], [0, 8, 0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0], [5, -3, 0]]], [2.222222, -1.333333, 0.0, 0.0, False, 6]], [[[-0.03, 0.06], 0.0, 0.5, 0.5, 0.03125, 8.0, 0.5, 1.0, 0.0625, [[0, 0, 0], [0, 0, -0.5], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.0625, True, 1]], [[[-0.03, -0.03], 0.0, 0.5, 0.5, 0.0625, 8.0, 0.5, 1.0, 0.1875, [[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, 0], [0, 0, 0]]], [-0.023454, -0.023454, 7.253301, 0.0, False, -1]], [[[0.02, 0.02], -0.63, 80.0, 40.0, 0.015625, 8.0, 2.0, 1.0, 0.046875, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, -3, 0.5], [0, 0, 0]]], [0.0, -0.592593, 0.189349, 0.03125, False, 2]]], [[[[0.05, 0.06], 0.0, 0.5, 5.0, 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], [0, 0, -0.5], [0, 0, 0]]], [0.0, 0.0, -0.430162, 0.0, False, 4]], [[[-0.03, 0.08], 0.0, 2.0, 5.0, 0.015625, 8.0, 0.5, 1.0, 0.03125, [[0, 0, -0.5], [0, 0, 0.5], [0, 0, -0.5], [0, 0, -0.5], [0, 0, 0.5], [0, 0, 0], [0, 0, 0.5], [0, 0, -0.5]]], [0.0, 0.0, 0.0, 0.03125, True, 7]], [[[0.04, 0.1], 0.0, 2.0, 5.0, 0.015625, 8.0, 0.5, 1.0, 0.03125, [[0, 0, 0.5], [0, 0, 0.5], [0, 0, -0.5], [0, 0, 0.5], [0, 0, -0.5], [0, 0, -0.5], [0, 0, 0.5]]], [0.0, 0.0, 0.463768, 0.015625, False, 5]], [[[-0.01, 0.04], 1.03, 2.0, 0.5, 0.03125, 8.0, 0.5, 0.3, 0.0625, [[0, 0, 0], [0, 0, 0], [0, 0, 0]]], [-0.008337, 0.033348, 0.983189, 0.0, False, -1]], [[[0.09, 0.08], 0.0, 2.0, 5.0, 0.03125, 8.0, 0.5, 0.3, 0.0625, [[0, 0, 0.5], [0, 0, 0.5], [0, 0, 0], [0, 0, 0], [0, 0, -0.5], [0, 0, 0], [0, 0, 0.5], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.323456, 0.0, False, 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]], [[[0.05, -0.03], 0.0, 0.5, 5.0, 0.015625, 8.0, 0.5, 0.3, 0.046875, [[0, 0, -0.5], [0, 0, 0.5], [0, 0, -0.5], [0, 0, -0.5], [0, 0, -0.5], [0, 0, 0]]], [0.047719, -0.028631, -1.174357, 0.0, False, -1]], [[[0.09, 0.02], 0.0, 0.5, 5.0, 0.03125, 8.0, 0.5, 0.3, 0.0625, [[0, 0, 1.5], [0, 0, -1.5], [0, 0, -1.5], [0, 0, 1.5], [0, 0, 0], [0, 0, 1.5]]], [0.0, 0.0, 1.297297, 0.0, False, 4]]], [[[[0.06, 0.07], 0.0, 0.5, 5.0, 0.03125, 8.0, 0.5, 0.3, 0.09375, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, -3.0], [0, 0, 0], [0, 0, -3.0], [0, 0, 3.0]]], [0.0, 0.0, -1.327852, 0.0, False, 2]], [[[-0.05, -0.01], -0.3, 80.0, 40.0, 0.015625, 8.0, 2.0, 0.3, 0.015625, [[0, 0, 0], [0, 0, 0], [5, 0, -1], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.015625, True, 4]], [[[-0.0, 0.01], -1.88, 2.0, 40.0, 0.015625, 8.0, 2.0, 1.0, 0.015625, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [5, 8, 0]]], [4.239992, 6.783986, 0.0, 0.0, False, 1]], [[[0.04, -0.08], 0.0, 2.0, 5.0, 0.015625, 8.0, 0.5, 1.0, 0.046875, [[0, 0, 0], [0, 0, 0], [0, 0, -0.5], [0, 0, -0.5], [0, 0, 0.5], [0, 0, -0.5], [0, 0, 0], [0, 0, 0.5], [0, 0, -0.5]]], [0.0, 0.0, -0.033606, 0.03125, False, 5]], [[[3.71, -0.78], 1.01, 20.0, 40.0, 0.0625, 3.0, 0.5, 1.0, 0.0625, [[1, -3, 0], [0, -3, 2], [1, -3, 2], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.0625, True, 4]], [[[-5.26, 2.26], 0.01, 2.0, 40.0, 0.03125, 8.0, 0.5, 1.0, 0.09375, [[0, 0, 0], [0, 0, 2], [-2, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [-4.918004, 1.478447, 0.015449, 0.0, False, -1]], [[[0.08, 0.03], 0.0, 2.0, 0.5, 0.0625, 8.0, 0.5, 1.0, 0.1875, [[0, 0, 0], [0, 0, 0], [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, -1.5]]], [0.027715, 0.010393, -0.008837, 0.0625, False, -1]], [[[-0.05, 0.02], 0.0, 0.5, 5.0, 0.015625, 8.0, 0.5, 1.0, 0.03125, [[0, 0, 0], [0, 0, 0], [0, 0, 0.5], [0, 0, -0.5], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.03125, True, 3]]], [[[[0.06, 0.05], 0.0, 2.0, 5.0, 0.03125, 8.0, 0.5, 1.0, 0.0625, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0.5], [0, 0, 0.5], [0, 0, -0.5], [0, 0, 0], [0, 0, 0.5]]], [0.0, 0.0, 0.432432, 0.03125, False, 6]], [[[-0.0, 0.0], -1.06, 2.0, 5.0, 0.0625, 3.0, 2.0, 1.0, 0.1875, [[0, 0, 0], [-2, 1, 0.5], [0, 0, 0], [0, 0, 0], [1, 8, 2], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.261341, 2.090725, 0.673958, 0.0, False, 2]], [[[-0.03, -0.03], 0.71, 80.0, 40.0, 0.0625, 3.0, 0.5, 0.3, 0.1875, [[0, 0, 0], [0, 0, -1], [0, 0, 0], [0, 0, 0], [-2, 0, 0.5]]], [-0.333333, 0.0, 0.142857, 0.0625, False, 2]], [[[0.08, -0.08], 0.0, 0.5, 0.5, 0.0625, 8.0, 0.5, 1.0, 0.125, [[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, 0.125, True, 5]], [[[-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]], [[[-0.03, -0.01], 1.59, 80.0, 40.0, 0.03125, 8.0, 0.5, 1.0, 0.0625, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 1, 0.5], [1, -3, -1], [-2, 0, 0], [0, 0, 0]]], [-0.139942, -0.063307, -0.068282, 0.03125, False, 1]], [[[-0.01, 0.03], -1.06, 2.0, 40.0, 0.03125, 3.0, 2.0, 1.0, 0.03125, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.03125, True, 0]], [[[0.24, 4.31], -1.09, 0.5, 40.0, 0.0625, 8.0, 2.0, 1.0, 0.0625, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 8, 0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.133785, 7.293316, 0.003163, 0.0, False, -1]]]]
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 fixture	Actual	Expected	Outcome
case 0	`[0.0, 0.0, 0.492308, 0.03125, False, 2]`	`[0.0, 0.0, 0.492308, 0.03125, False, 2]`	Passed
case 1	`[0.853029, 2.384603, 1.618816, 0.0, False, -1]`	`[0.853029, 2.384603, 1.618816, 0.0, False, -1]`	Passed
case 2	`[0.0, 0.0, -0.580499, 0.0, False, 1]`	`[0.0, 0.0, -0.580499, 0.0, False, 1]`	Passed
case 3	`[1.25024, 1.974221, 0.858637, 0.0, False, -1]`	`[1.25024, 1.974221, 0.858637, 0.0, False, -1]`	Passed
case 4	`[0.285714, 0.0, 0.0, 0.03125, False, 5]`	`[0.285714, 0.0, 0.0, 0.03125, False, 5]`	Passed
case 5	`[1.428571, 0.285714, 0.432432, 0.03125, False, 3]`	`[1.428571, 0.285714, 0.432432, 0.03125, False, 3]`	Passed
case 6	`[0.023194, 0.036991, 1.09037, 0.0, False, -1]`	`[0.023194, 0.036991, 1.09037, 0.0, False, -1]`	Passed
case 7	`[0.0, 1.333333, 0.040816, 0.0, False, 0]`	`[0.0, 1.333333, 0.040816, 0.0, False, 0]`	Passed

SHA-256 / db58ea8e8aacad5347be6ab55f7799edf759af0b948e35a004e224d015d79d3b

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 2026-09-29T14:50:57.208504+00:00.

Case digest / bd47dd7c7607cbb2f7cafd14b67f8cf176b2142a317344b5e38ee9241a2b9d71