FAILURE MAP
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FA-87271 / Physics integrator stability / Open access

Falling asleep does not zero velocities · case 01

Sleeping bodies report residual motion and wake-up comparisons drift.

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

ROOT CAUSE

The zeroing of vx, vy and omega on sleep is missing.

THE FAILURE

The zeroing of vx, vy and omega on sleep is missing.

Unsuccessful approach: Zeroing only linear velocity keeps residual spin.

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
    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, -0.0], 0.0, 2.0, 5.0, 0.03125, 8.0, 0.5, 1.0, 0.0625, [[0, 0, 3.0], [0, 0, 3.0], [0, 0, 3.0], [0, 0, 3.0], [0, 0, 0], [0, 0, 0]]], [0.020852, 0.0, 6.326342, 0.0, False, -1]], [[[0.07, -0.02], 0.0, 2.0, 5.0, 0.015625, 8.0, 0.5, 0.3, 0.046875, [[0, 0, 0], [0, 0, 0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0.5], [0, 0, 0]]], [0.058199, -0.016628, 0.773423, 0.0, False, -1]], [[[-0.04, 0.04], -0.28, 80.0, 40.0, 0.0625, 3.0, 0.5, 0.3, 0.0625, [[0, 0, 0], [0, 0, 0], [1, 8, -1], [0, 0, 0], [-2, 0, 0.5], [0, 0, 0], [0, 8, -1], [0, 0, 0], [0, -3, -1], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.0625, True, 9]], [[[-0.01, -0.02], -0.81, 20.0, 0.5, 0.015625, 8.0, 2.0, 1.0, 0.03125, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [-2, -3, 0.5], [0, 0, 0]]], [-1.160998, -1.741497, 0.492278, 0.0, False, 1]], [[[0.04, -0.03], 0.0, 0.5, 0.5, 0.03125, 8.0, 0.5, 1.0, 0.09375, [[0, 0, -1.5], [0, 0, -1.5], [0, 0, 0], [0, 0, -1.5], [0, 0, 0], [0, 0, 0]]], [0.036447, -0.027335, -4.186696, 0.0, False, -1]], [[[5.83, -5.96], 1.87, 20.0, 40.0, 0.0625, 8.0, 2.0, 1.0, 0.1875, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [1, 1, 0], [1, 0, 0.5]]], [0.444444, 0.0, 0.142857, 0.0625, False, 3]], [[[-1.08, -1.72], -1.45, 20.0, 0.5, 0.03125, 8.0, 0.5, 1.0, 0.09375, [[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], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.09375, True, 4]], [[[-0.02, 0.03], -1.96, 20.0, 0.5, 0.015625, 8.0, 2.0, 0.3, 0.03125, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [5, 8, 2], [-2, 0, -1], [0, 0, 0], [0, 0, 0], [1, 8, 2], [5, 0, 2]]], [4.81969, 6.010948, 3.087279, 0.0, False, -1]]], [[[[-0.02, -0.03], -1.37, 2.0, 0.5, 0.03125, 8.0, 2.0, 0.3, 0.03125, [[0, 0, 0], [0, 0, 0], [5, 0, 0.5], [0, 0, 0], [-2, 1, 2], [0, 8, 2], [0, 0, 0]]], [1.858205, 7.296514, 3.081645, 0.0, False, -1]], [[[0.81, -0.69], -1.88, 2.0, 40.0, 0.03125, 3.0, 2.0, 0.3, 0.03125, [[1, 0, -1], [5, 8, 0.5], [0, 0, 0], [0, 0, 0], [5, 1, -1], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [-2, 0, -1]]], [0.148227, 0.886167, -0.45268, 0.0, False, -1]], [[[0.03, 0.05], -0.24, 20.0, 40.0, 0.03125, 3.0, 0.5, 0.3, 0.09375, [[0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.09375, True, 2]], [[[-0.04, 0.01], -0.55, 2.0, 5.0, 0.0625, 3.0, 2.0, 1.0, 0.125, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 1, 0.5], [0, 0, 2], [5, 8, 0.5], [0, 0, 0]]], [1.318477, 2.317915, 1.343309, 0.0, False, 1]], [[[0.63, 0.72], -1.08, 20.0, 0.5, 0.0625, 3.0, 2.0, 1.0, 0.1875, [[0, 0, 0], [0, 0, 0], [5, 0, 2], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.1875, True, 8]], [[[-1.82, -3.97], -1.03, 0.5, 40.0, 0.0625, 3.0, 2.0, 0.3, 0.1875, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 8, 0.5], [0, 0, 0]]], [-0.541146, 2.858316, 0.040771, 0.0, False, -1]], [[[0.01, 0.07], 0.0, 2.0, 0.5, 0.015625, 8.0, 0.5, 1.0, 0.046875, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, -3.0], [0, 0, 3.0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.046875, True, 6]], [[[0.04, 0.05], -1.81, 20.0, 40.0, 0.0625, 3.0, 2.0, 1.0, 0.1875, [[5, 0, 0.5], [0, 0, 0], [1, -3, -1], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [1, 1, 0], [0, 8, 0]]], [0.157676, 2.995853, 0.0, 0.0, False, 3]]], [[[[-1.13, 2.26], 0.9, 0.5, 5.0, 0.0625, 3.0, 2.0, 0.3, 0.1875, [[0, 0, 0], [0, 0, -1], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [-0.911026, 1.822052, -0.061479, 0.0, False, -1]], [[[0.01, -0.05], 0.0, 0.5, 5.0, 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, 0], [0, 0, 0], [0, 0, 3.0]]], [0.0, 0.0, 4.853834, 0.0, False, 2]], [[[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]], [[[-0.05, 0.02], -0.33, 20.0, 5.0, 0.0625, 8.0, 0.5, 0.3, 0.1875, [[0, -3, 0.5], [5, 1, 2], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.038365, -0.002501, 0.416569, 0.0, False, -1]], [[[-0.43, 5.53], 1.03, 80.0, 5.0, 0.03125, 8.0, 0.5, 1.0, 0.0625, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.0625, True, 2]], [[[0.08, -0.01], 0.0, 0.5, 5.0, 0.03125, 8.0, 0.5, 1.0, 0.09375, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, -1.5], [0, 0, -1.5], [0, 0, 1.5], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.09375, True, 8]], [[[0.03, 0.03], -0.45, 80.0, 40.0, 0.03125, 3.0, 2.0, 1.0, 0.09375, [[5, 8, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.09375, True, 3]], [[[0.05, -0.06], 0.0, 0.5, 5.0, 0.03125, 8.0, 0.5, 0.3, 0.0625, [[0, 0, 0], [0, 0, 0], [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, 1.5]]], [0.0, 0.0, 0.17531, 0.03125, False, 6]]], [[[[-0.1, 0.04], 0.0, 0.5, 5.0, 0.03125, 8.0, 0.5, 1.0, 0.09375, [[0, 0, -3.0], [0, 0, -3.0], [0, 0, 0], [0, 0, 3.0]]], [-0.093987, 0.037595, -1.024612, 0.0, False, -1]], [[[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]], [[[0.09, 0.04], 0.0, 0.5, 5.0, 0.0625, 8.0, 0.5, 0.3, 0.1875, [[0, 0, 1.5], [0, 0, -1.5], [0, 0, 0], [0, 0, 1.5], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.07256, 0.032249, 0.435606, 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]], [[[-0.05, -0.03], 1.51, 0.5, 0.5, 0.03125, 3.0, 2.0, 0.3, 0.03125, [[0, 0, 0], [0, 0, 0], [5, 1, 0], [0, 1, 0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [2.524203, 1.35238, 1.824634, 0.0, False, -1]], [[[-0.0, 0.07], 0.0, 0.5, 0.5, 0.015625, 8.0, 0.5, 1.0, 0.046875, [[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]]], [0.0, 0.065775, -5.817074, 0.0, False, -1]], [[[-0.04, -0.07], 0.0, 0.5, 0.5, 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], [0, 0, 0]]], [0.0, 0.0, -0.477276, 0.0, False, 1]], [[[1.67, 5.72], 0.16, 80.0, 40.0, 0.03125, 8.0, 0.5, 0.3, 0.03125, [[0, 0, 0], [-2, 0, 0.5], [0, 0, 0], [0, -3, -1], [0, 0, 0], [-2, -3, -1], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, -3, -1]]], [0.0, -0.857143, -0.444444, 0.0, False, 6]]], [[[[-0.04, -0.02], 1.89, 20.0, 40.0, 0.0625, 3.0, 0.5, 1.0, 0.125, [[0, 0, -1], [0, 0, 0], [0, 0, 0], [0, 0, 0], [-2, -3, -1], [-2, 0, 0.5]]], [-1.283951, -0.592593, 0.061224, 0.0, False, 1]], [[[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]], [[[-0.04, -0.04], -0.84, 2.0, 40.0, 0.0625, 3.0, 2.0, 1.0, 0.0625, [[1, 8, 0], [0, 0, 0], [1, 1, 0.5], [1, 1, 0.5], [0, 0, 0], [-2, -3, 0.5], [0, 0, 0], [5, 1, -1], [0, 0, 0], [0, 0, 0]]], [2.324339, 0.464868, -0.023324, 0.0, False, 5]], [[[-2.6, 4.32], -1.06, 2.0, 5.0, 0.03125, 8.0, 2.0, 0.3, 0.03125, [[0, 0, 0], [0, 0, 2], [0, 0, 0], [0, 0, 0], [0, 8, -1], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [-1.041672, 5.81551, -0.125229, 0.0, False, -1]], [[[-0.01, 0.03], -0.14, 0.5, 0.5, 0.0625, 3.0, 0.5, 1.0, 0.0625, [[0, 0, 0], [1, 1, -1], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0.5], [0, 0, 0]]], [0.806218, 0.806218, -0.336061, 0.0, False, 0]], [[[-1.37, -4.17], -0.34, 20.0, 0.5, 0.03125, 8.0, 2.0, 1.0, 0.0625, [[-2, 8, 2], [-2, 0, 0], [1, 0, -1], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 1, -1], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.0625, True, 8]], [[[1.67, -3.47], 0.96, 0.5, 0.5, 0.015625, 3.0, 0.5, 1.0, 0.015625, [[0, 0, 0], [0, 0, 0], [5, -3, 2]]], [2.226277, -2.010893, 2.922343, 0.0, False, -1]], [[[0.04, -0.02], -0.56, 20.0, 5.0, 0.03125, 3.0, 2.0, 0.3, 0.0625, [[0, 0, 0], [-2, 8, 0], [1, -3, 2], [0, 0, 0], [0, 1, 0.5]]], [0.065203, 0.594939, 1.45528, 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 fixtureActualExpectedOutcome
case 0[0.020852, 0.0, 6.326342, 0.0, False, -1][0.020852, 0.0, 6.326342, 0.0, False, -1]Passed
case 1[0.058199, -0.016628, 0.773423, 0.0, False, -1][0.058199, -0.016628, 0.773423, 0.0, False, -1]Passed
case 2[-0.000254, -0.077132, -0.087512, 0.0625, True, 9][0.0, 0.0, 0.0, 0.0625, True, 9]Failed
case 3[-1.164368, -1.748236, -0.292896, 0.0, False, 1][-1.160998, -1.741497, 0.492278, 0.0, False, 1]Failed
case 4[0.036447, -0.027335, -4.186696, 0.0, False, -1][0.036447, -0.027335, -4.186696, 0.0, False, -1]Passed
case 5[0.743076, 0.094175, 0.146418, 0.0625, False, 3][0.444444, 0.0, 0.142857, 0.0625, False, 3]Failed
case 6[-0.095314, 0.081249, -0.864565, 0.09375, True, 4][0.0, 0.0, 0.0, 0.09375, True, 4]Failed
case 7[4.81969, 6.010948, 3.087279, 0.0, False, -1][4.81969, 6.010948, 3.087279, 0.0, False, -1]Passed

SHA-256 / 0ef25afa2fe4e4254cc6110a8943b56a5dafddf966bb910a87ce07465602448e

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:
            asleep = True
            slept_at = f
            vx = vy = 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, -0.0], 0.0, 2.0, 5.0, 0.03125, 8.0, 0.5, 1.0, 0.0625, [[0, 0, 3.0], [0, 0, 3.0], [0, 0, 3.0], [0, 0, 3.0], [0, 0, 0], [0, 0, 0]]], [0.020852, 0.0, 6.326342, 0.0, False, -1]], [[[0.07, -0.02], 0.0, 2.0, 5.0, 0.015625, 8.0, 0.5, 0.3, 0.046875, [[0, 0, 0], [0, 0, 0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0.5], [0, 0, 0]]], [0.058199, -0.016628, 0.773423, 0.0, False, -1]], [[[-0.04, 0.04], -0.28, 80.0, 40.0, 0.0625, 3.0, 0.5, 0.3, 0.0625, [[0, 0, 0], [0, 0, 0], [1, 8, -1], [0, 0, 0], [-2, 0, 0.5], [0, 0, 0], [0, 8, -1], [0, 0, 0], [0, -3, -1], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.0625, True, 9]], [[[-0.01, -0.02], -0.81, 20.0, 0.5, 0.015625, 8.0, 2.0, 1.0, 0.03125, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [-2, -3, 0.5], [0, 0, 0]]], [-1.160998, -1.741497, 0.492278, 0.0, False, 1]], [[[0.04, -0.03], 0.0, 0.5, 0.5, 0.03125, 8.0, 0.5, 1.0, 0.09375, [[0, 0, -1.5], [0, 0, -1.5], [0, 0, 0], [0, 0, -1.5], [0, 0, 0], [0, 0, 0]]], [0.036447, -0.027335, -4.186696, 0.0, False, -1]], [[[5.83, -5.96], 1.87, 20.0, 40.0, 0.0625, 8.0, 2.0, 1.0, 0.1875, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [1, 1, 0], [1, 0, 0.5]]], [0.444444, 0.0, 0.142857, 0.0625, False, 3]], [[[-1.08, -1.72], -1.45, 20.0, 0.5, 0.03125, 8.0, 0.5, 1.0, 0.09375, [[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], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.09375, True, 4]], [[[-0.02, 0.03], -1.96, 20.0, 0.5, 0.015625, 8.0, 2.0, 0.3, 0.03125, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [5, 8, 2], [-2, 0, -1], [0, 0, 0], [0, 0, 0], [1, 8, 2], [5, 0, 2]]], [4.81969, 6.010948, 3.087279, 0.0, False, -1]]], [[[[-0.02, -0.03], -1.37, 2.0, 0.5, 0.03125, 8.0, 2.0, 0.3, 0.03125, [[0, 0, 0], [0, 0, 0], [5, 0, 0.5], [0, 0, 0], [-2, 1, 2], [0, 8, 2], [0, 0, 0]]], [1.858205, 7.296514, 3.081645, 0.0, False, -1]], [[[0.81, -0.69], -1.88, 2.0, 40.0, 0.03125, 3.0, 2.0, 0.3, 0.03125, [[1, 0, -1], [5, 8, 0.5], [0, 0, 0], [0, 0, 0], [5, 1, -1], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [-2, 0, -1]]], [0.148227, 0.886167, -0.45268, 0.0, False, -1]], [[[0.03, 0.05], -0.24, 20.0, 40.0, 0.03125, 3.0, 0.5, 0.3, 0.09375, [[0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.09375, True, 2]], [[[-0.04, 0.01], -0.55, 2.0, 5.0, 0.0625, 3.0, 2.0, 1.0, 0.125, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 1, 0.5], [0, 0, 2], [5, 8, 0.5], [0, 0, 0]]], [1.318477, 2.317915, 1.343309, 0.0, False, 1]], [[[0.63, 0.72], -1.08, 20.0, 0.5, 0.0625, 3.0, 2.0, 1.0, 0.1875, [[0, 0, 0], [0, 0, 0], [5, 0, 2], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.1875, True, 8]], [[[-1.82, -3.97], -1.03, 0.5, 40.0, 0.0625, 3.0, 2.0, 0.3, 0.1875, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 8, 0.5], [0, 0, 0]]], [-0.541146, 2.858316, 0.040771, 0.0, False, -1]], [[[0.01, 0.07], 0.0, 2.0, 0.5, 0.015625, 8.0, 0.5, 1.0, 0.046875, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, -3.0], [0, 0, 3.0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.046875, True, 6]], [[[0.04, 0.05], -1.81, 20.0, 40.0, 0.0625, 3.0, 2.0, 1.0, 0.1875, [[5, 0, 0.5], [0, 0, 0], [1, -3, -1], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [1, 1, 0], [0, 8, 0]]], [0.157676, 2.995853, 0.0, 0.0, False, 3]]], [[[[-1.13, 2.26], 0.9, 0.5, 5.0, 0.0625, 3.0, 2.0, 0.3, 0.1875, [[0, 0, 0], [0, 0, -1], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [-0.911026, 1.822052, -0.061479, 0.0, False, -1]], [[[0.01, -0.05], 0.0, 0.5, 5.0, 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, 0], [0, 0, 0], [0, 0, 3.0]]], [0.0, 0.0, 4.853834, 0.0, False, 2]], [[[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]], [[[-0.05, 0.02], -0.33, 20.0, 5.0, 0.0625, 8.0, 0.5, 0.3, 0.1875, [[0, -3, 0.5], [5, 1, 2], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.038365, -0.002501, 0.416569, 0.0, False, -1]], [[[-0.43, 5.53], 1.03, 80.0, 5.0, 0.03125, 8.0, 0.5, 1.0, 0.0625, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.0625, True, 2]], [[[0.08, -0.01], 0.0, 0.5, 5.0, 0.03125, 8.0, 0.5, 1.0, 0.09375, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, -1.5], [0, 0, -1.5], [0, 0, 1.5], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.09375, True, 8]], [[[0.03, 0.03], -0.45, 80.0, 40.0, 0.03125, 3.0, 2.0, 1.0, 0.09375, [[5, 8, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.09375, True, 3]], [[[0.05, -0.06], 0.0, 0.5, 5.0, 0.03125, 8.0, 0.5, 0.3, 0.0625, [[0, 0, 0], [0, 0, 0], [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, 1.5]]], [0.0, 0.0, 0.17531, 0.03125, False, 6]]], [[[[-0.1, 0.04], 0.0, 0.5, 5.0, 0.03125, 8.0, 0.5, 1.0, 0.09375, [[0, 0, -3.0], [0, 0, -3.0], [0, 0, 0], [0, 0, 3.0]]], [-0.093987, 0.037595, -1.024612, 0.0, False, -1]], [[[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]], [[[0.09, 0.04], 0.0, 0.5, 5.0, 0.0625, 8.0, 0.5, 0.3, 0.1875, [[0, 0, 1.5], [0, 0, -1.5], [0, 0, 0], [0, 0, 1.5], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.07256, 0.032249, 0.435606, 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]], [[[-0.05, -0.03], 1.51, 0.5, 0.5, 0.03125, 3.0, 2.0, 0.3, 0.03125, [[0, 0, 0], [0, 0, 0], [5, 1, 0], [0, 1, 0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [2.524203, 1.35238, 1.824634, 0.0, False, -1]], [[[-0.0, 0.07], 0.0, 0.5, 0.5, 0.015625, 8.0, 0.5, 1.0, 0.046875, [[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]]], [0.0, 0.065775, -5.817074, 0.0, False, -1]], [[[-0.04, -0.07], 0.0, 0.5, 0.5, 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], [0, 0, 0]]], [0.0, 0.0, -0.477276, 0.0, False, 1]], [[[1.67, 5.72], 0.16, 80.0, 40.0, 0.03125, 8.0, 0.5, 0.3, 0.03125, [[0, 0, 0], [-2, 0, 0.5], [0, 0, 0], [0, -3, -1], [0, 0, 0], [-2, -3, -1], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, -3, -1]]], [0.0, -0.857143, -0.444444, 0.0, False, 6]]], [[[[-0.04, -0.02], 1.89, 20.0, 40.0, 0.0625, 3.0, 0.5, 1.0, 0.125, [[0, 0, -1], [0, 0, 0], [0, 0, 0], [0, 0, 0], [-2, -3, -1], [-2, 0, 0.5]]], [-1.283951, -0.592593, 0.061224, 0.0, False, 1]], [[[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]], [[[-0.04, -0.04], -0.84, 2.0, 40.0, 0.0625, 3.0, 2.0, 1.0, 0.0625, [[1, 8, 0], [0, 0, 0], [1, 1, 0.5], [1, 1, 0.5], [0, 0, 0], [-2, -3, 0.5], [0, 0, 0], [5, 1, -1], [0, 0, 0], [0, 0, 0]]], [2.324339, 0.464868, -0.023324, 0.0, False, 5]], [[[-2.6, 4.32], -1.06, 2.0, 5.0, 0.03125, 8.0, 2.0, 0.3, 0.03125, [[0, 0, 0], [0, 0, 2], [0, 0, 0], [0, 0, 0], [0, 8, -1], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [-1.041672, 5.81551, -0.125229, 0.0, False, -1]], [[[-0.01, 0.03], -0.14, 0.5, 0.5, 0.0625, 3.0, 0.5, 1.0, 0.0625, [[0, 0, 0], [1, 1, -1], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0.5], [0, 0, 0]]], [0.806218, 0.806218, -0.336061, 0.0, False, 0]], [[[-1.37, -4.17], -0.34, 20.0, 0.5, 0.03125, 8.0, 2.0, 1.0, 0.0625, [[-2, 8, 2], [-2, 0, 0], [1, 0, -1], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 1, -1], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.0625, True, 8]], [[[1.67, -3.47], 0.96, 0.5, 0.5, 0.015625, 3.0, 0.5, 1.0, 0.015625, [[0, 0, 0], [0, 0, 0], [5, -3, 2]]], [2.226277, -2.010893, 2.922343, 0.0, False, -1]], [[[0.04, -0.02], -0.56, 20.0, 5.0, 0.03125, 3.0, 2.0, 0.3, 0.0625, [[0, 0, 0], [-2, 8, 0], [1, -3, 2], [0, 0, 0], [0, 1, 0.5]]], [0.065203, 0.594939, 1.45528, 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 fixtureActualExpectedOutcome
case 0[0.020852, 0.0, 6.326342, 0.0, False, -1][0.020852, 0.0, 6.326342, 0.0, False, -1]Passed
case 1[0.058199, -0.016628, 0.773423, 0.0, False, -1][0.058199, -0.016628, 0.773423, 0.0, False, -1]Passed
case 2[0.0, 0.0, -0.087512, 0.0625, True, 9][0.0, 0.0, 0.0, 0.0625, True, 9]Failed
case 3[-1.160998, -1.741497, -0.292896, 0.0, False, 1][-1.160998, -1.741497, 0.492278, 0.0, False, 1]Failed
case 4[0.036447, -0.027335, -4.186696, 0.0, False, -1][0.036447, -0.027335, -4.186696, 0.0, False, -1]Passed
case 5[0.444444, 0.0, 0.146418, 0.0625, False, 3][0.444444, 0.0, 0.142857, 0.0625, False, 3]Failed
case 6[0.0, 0.0, -0.864565, 0.09375, True, 4][0.0, 0.0, 0.0, 0.09375, True, 4]Failed
case 7[4.81969, 6.010948, 3.087279, 0.0, False, -1][4.81969, 6.010948, 3.087279, 0.0, False, -1]Passed

SHA-256 / ed171b8f44df9cb00a717d402995714c47005c62a29c633159024f9a54aab104

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 8 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

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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 2026-09-29T14:50:57.219315+00:00.

Case digest / f3a993dfcacff7fd70774130d5c27470692d48a120050e351e9784cba958e01a