FAILURE MAP
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FA-87316 / Physics integrator stability / Open access

Energy loss is not treated as drift · case 01

Numerically dissipative integrators pass the monitor.

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

ROOT CAUSE

r is signed (E-E0)/E0.

THE FAILURE

r is signed (E-E0)/E0.

Unsuccessful approach: Flagging only losses misses energy gain.

Case contract

solve(states, k, m, tol, blowup): states [[x,v],...] of a spring integrator; E=0.5 m v^2+0.5 k x^2. Relative drift r=|E-E0|/E0 (absolute when E0=0). Scan in order: first state with E>blowup*E0 (E0>0) returns ["blowup", index, its r]. Otherwise ["drift", first index with r>tol, max r] or ["ok", -1, max r].

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(states, k, m, tol, blowup):
    def en(s):
        return 0.5 * m * s[1] * s[1] + 0.5 * k * s[0] * s[0]
    e0 = en(states[0])
    scale = e0 if e0 > 0 else 1.0
    worst = 0.0
    first_drift = -1
    for i, s in enumerate(states):
        e = en(s)
        if e0 > 0 and e > blowup * e0:
            return ['blowup', i, round(abs(e - e0) / scale, 6)]
        r = (e - e0) / scale
        if r > worst:
            worst = r
        if r > tol and first_drift < 0:
            first_drift = i
    if first_drift >= 0:
        return ['drift', first_drift, round(worst, 6)]
    return ['ok', -1, round(worst, 6)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[[[[0.642, -0.278], [0.5937, -0.2502], [0.5306, -0.2252], [0.4774, -0.2027], [0.4326, -0.1824], [0.3961, -0.1642]], 2.502, 2.772, 0.05, 2.0], ['drift', 1, 0.624807]], [[[[0.0, 0.0], [0.0023, 0.0], [0.008, 0.0], [0.0167, 0.0], [0.0239, 0.0]], 1.47, 2.583, 0.01, 2.0], ['ok', -1, 0.00042]], [[[[0.354, -0.856], [0.3699, -0.8731], [0.3842, -0.8906], [0.404, -0.9084], [0.4055, -0.9266], [0.422, -0.9451], [0.4415, -0.964], [0.4623, -0.9833], [0.4764, -1.0029]], 2.622, 2.687, 0.05, 1.5], ['drift', 2, 0.435375]], [[[[0.007, 0.342], [0.0094, 0.3488], [0.0178, 0.3558], [0.0276, 0.3629]], 3.958, 2.139, 0.1, 2.0], ['drift', 3, 0.137127]], [[[[0.77, -0.528], [0.7846, -0.5386], [0.8008, -0.5493], [0.8252, -0.5603]], 4.089, 2.468, 0.01, 1.5], ['drift', 1, 0.143558]], [[[[-0.506, -0.658], [-0.4427, -0.5922], [-0.4045, -0.533], [-0.3529, -0.4797], [-0.3127, -0.4317], [-0.2739, -0.3885], [-0.2412, -0.3497], [-0.2179, -0.3147], [-0.1951, -0.2832]], 2.054, 1.583, 0.01, 1.5], ['drift', 1, 0.830639]], [[[[-0.727, -0.401], [-0.7918, -0.4411], [-0.8566, -0.4852], [-0.9532, -0.5337], [-1.0294, -0.5871], [-1.1522, -0.6458], [-1.2399, -0.7104]], 3.173, 0.604, 0.01, 3.0], ['drift', 1, 1.921313]], [[[[-0.138, 0.988], [-0.1281, 0.988], [-0.1264, 0.988]], 2.839, 1.096, 0.1, 3.0], ['ok', -1, 0.007747]]], [[[[[-0.219, 0.241], [-0.2354, 0.2651], [-0.2595, 0.2916], [-0.2794, 0.3208], [-0.2964, 0.3528], [-0.3284, 0.3881], [-0.3564, 0.4269]], 0.937, 2.683, 0.1, 3.0], ['blowup', 6, 2.028221]], [[[[-0.377, -0.929], [-0.3548, -0.9011], [-0.3496, -0.8741], [-0.3253, -0.8479], [-0.3166, -0.8224], [-0.2976, -0.7978]], 3.422, 0.967, 0.1, 1.5], ['drift', 2, 0.304614]], [[[[-0.274, -0.857], [-0.2679, -0.857], [-0.26, -0.857], [-0.2528, -0.857], [-0.2452, -0.857], [-0.2428, -0.857], [-0.2392, -0.857], [-0.2348, -0.857], [-0.2249, -0.857]], 3.816, 2.244, 0.1, 1.5], ['ok', -1, 0.048319]], [[[[0.098, -0.389], [0.1119, -0.4279], [0.1325, -0.4707], [0.1538, -0.5178], [0.1799, -0.5695], [0.203, -0.6265]], 1.475, 2.624, 0.01, 3.0], ['drift', 1, 1.652295]], [[[[0.303, 0.246], [0.3325, 0.2706], [0.3676, 0.2977], [0.4034, 0.3274], [0.4447, 0.3602], [0.5066, 0.3962]], 0.771, 1.949, 0.05, 2.0], ['blowup', 4, 1.147733]], [[[[0.0, 0.0], [0.0002, 0.0], [0.0055, 0.0], [0.0097, 0.0], [0.0174, 0.0], [0.0202, 0.0], [0.025, 0.0], [0.0315, 0.0], [0.0373, 0.0], [0.0427, 0.0]], 2.182, 1.732, 0.1, 2.0], ['ok', -1, 0.001989]], [[[[0.339, -0.79], [0.3312, -0.7663], [0.3266, -0.7433], [0.318, -0.721], [0.3149, -0.6994]], 1.641, 0.591, 0.01, 3.0], ['drift', 1, 0.189459]], [[[[-0.245, -0.092], [-0.247, -0.0938], [-0.2501, -0.0957], [-0.2553, -0.0976], [-0.253, -0.0996], [-0.2532, -0.1016]], 3.639, 1.24, 0.01, 1.5], ['drift', 1, 0.087664]]], [[[[[-0.602, -0.323], [-0.6548, -0.3553], [-0.7281, -0.3908], [-0.8042, -0.4299], [-0.8676, -0.4729], [-0.9515, -0.5202]], 4.781, 2.289, 0.05, 3.0], ['drift', 1, 1.509767]], [[[[-0.844, -0.85], [-0.8281, -0.85], [-0.8348, -0.85], [-0.8267, -0.85], [-0.8342, -0.85]], 1.842, 1.328, 0.01, 1.5], ['drift', 1, 0.023437]], [[[[0.983, 0.177], [1.0223, 0.1805], [1.0565, 0.1842], [1.0753, 0.1878], [1.1016, 0.1916], [1.126, 0.1954], [1.1604, 0.1993]], 2.096, 1.011, 0.01, 1.5], ['drift', 1, 0.39157]], [[[[0.846, 0.987], [0.8713, 1.0067], [0.9005, 1.0269], [0.9276, 1.0474], [0.9484, 1.0684]], 2.346, 2.182, 0.1, 3.0], ['drift', 2, 0.209251]], [[[[0.596, -0.74], [0.5494, -0.666], [0.496, -0.5994], [0.45, -0.5395], [0.4177, -0.4855], [0.3802, -0.437], [0.3542, -0.3933]], 2.077, 1.541, 0.05, 3.0], ['drift', 1, 0.684539]], [[[[0.0, 0.0], [0.0015, 0.0], [0.0069, 0.0], [0.0103, 0.0], [0.017, 0.0], [0.0223, 0.0], [0.0323, 0.0]], 4.193, 1.563, 0.05, 2.0], ['ok', -1, 0.002187]], [[[[0.494, 0.726], [0.4862, 0.7042], [0.4712, 0.6831], [0.4542, 0.6626]], 4.432, 1.484, 0.1, 1.5], ['drift', 2, 0.159841]], [[[[-0.61, -0.248], [-0.6209, -0.253], [-0.6338, -0.258], [-0.6283, -0.2632], [-0.6383, -0.2684], [-0.6504, -0.2738], [-0.6504, -0.2793], [-0.6669, -0.2849]], 3.89, 2.753, 0.05, 3.0], ['drift', 2, 0.208293]]], [[[[[-0.142, 0.767], [-0.1338, 0.7823], [-0.1303, 0.798], [-0.1279, 0.8139], [-0.1294, 0.8302], [-0.1206, 0.8468], [-0.1187, 0.8638], [-0.1125, 0.881]], 3.962, 2.055, 0.1, 1.5], ['drift', 3, 0.276478]], [[[[0.533, -0.86], [0.535, -0.8342], [0.522, -0.8092]], 3.784, 2.389, 0.01, 1.5], ['drift', 1, 0.086734]], [[[[0.46, -0.857], [0.4146, -0.7713], [0.3847, -0.6942], [0.347, -0.6248], [0.313, -0.5623], [0.2833, -0.506], [0.2638, -0.4554], [0.2445, -0.4099]], 4.633, 2.893, 0.01, 1.5], ['drift', 1, 0.754263]], [[[[0.0, 0.0], [0.0095, 0.0], [0.0112, 0.0]], 4.453, 1.79, 0.1, 3.0], ['ok', -1, 0.000279]], [[[[0.0, 0.0], [0.0044, 0.0], [0.0106, 0.0], [0.0193, 0.0], [0.024, 0.0], [0.0241, 0.0], [0.03, 0.0], [0.0297, 0.0], [0.0363, 0.0]], 4.075, 1.166, 0.01, 2.0], ['ok', -1, 0.002685]], [[[[0.769, -0.203], [0.8009, -0.2071], [0.8291, -0.2112], [0.847, -0.2154], [0.8719, -0.2197]], 3.998, 0.622, 0.1, 2.0], ['drift', 2, 0.2843]], [[[[0.611, 0.179], [0.6286, 0.1826], [0.6327, 0.1862], [0.6452, 0.19]], 0.929, 1.354, 0.05, 3.0], ['drift', 1, 0.116371]], [[[[-0.944, -0.357], [-0.9235, -0.3463], [-0.9004, -0.3359], [-0.8797, -0.3258], [-0.8621, -0.316], [-0.8187, -0.3066], [-0.7942, -0.2974]], 0.792, 1.826, 0.1, 3.0], ['drift', 3, 0.295621]]], [[[[[0.803, 0.52], [0.7338, 0.468], [0.6728, 0.4212], [0.6205, 0.3791], [0.5593, 0.3412], [0.5062, 0.3071], [0.4563, 0.2763], [0.4139, 0.2487], [0.3713, 0.2238], [0.3301, 0.2015]], 0.955, 1.682, 0.05, 3.0], ['drift', 1, 0.839011]], [[[[0.0, 0.0], [0.0018, 0.0], [0.0028, 0.0], [0.0066, 0.0], [0.0144, 0.0]], 0.719, 1.234, 0.01, 2.0], ['ok', -1, 7.5e-05]], [[[[0.812, 0.7], [0.7824, 0.679], [0.7661, 0.6586], [0.7494, 0.6389], [0.7496, 0.6197], [0.7346, 0.6011]], 3.833, 2.927, 0.01, 2.0], ['drift', 1, 0.2109]], [[[[-0.612, 0.33], [-0.6277, 0.3366], [-0.6415, 0.3433], [-0.6394, 0.3502]], 2.324, 0.739, 0.01, 2.0], ['drift', 1, 0.097332]], [[[[-0.648, -0.612], [-0.7038, -0.6732], [-0.766, -0.7405], [-0.8245, -0.8146], [-0.9148, -0.896], [-1.0192, -0.9856], [-1.1118, -1.0842], [-1.2153, -1.1926]], 1.534, 1.581, 0.1, 3.0], ['blowup', 6, 2.037018]], [[[[-0.388, 0.367], [-0.3827, 0.3743], [-0.3809, 0.3818]], 4.434, 2.813, 0.05, 3.0], ['ok', -1, 0.006659]], [[[[0.788, 0.541], [0.8584, 0.5951], [0.9528, 0.6546], [1.0365, 0.7201], [1.1562, 0.7921], [1.2724, 0.8713]], 4.609, 2.968, 0.1, 3.0], ['drift', 1, 1.604181]], [[[[0.304, 0.926], [0.2951, 0.8982], [0.2913, 0.8713], [0.2845, 0.8451], [0.273, 0.8198]], 4.318, 0.794, 0.01, 2.0], ['drift', 1, 0.207843]]]]
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['ok', -1, 0.0]['drift', 1, 0.624807]Failed
case 1['ok', -1, 0.00042]['ok', -1, 0.00042]Passed
case 2['drift', 2, 0.435375]['drift', 2, 0.435375]Passed
case 3['drift', 3, 0.137127]['drift', 3, 0.137127]Passed
case 4['drift', 1, 0.143558]['drift', 1, 0.143558]Passed
case 5['ok', -1, 0.0]['drift', 1, 0.830639]Failed
case 6['drift', 1, 1.921313]['drift', 1, 1.921313]Passed
case 7['ok', -1, 0.0]['ok', -1, 0.007747]Failed

SHA-256 / 3b5642fe6346292bf5369e25e942eff8aacf4adce3784a238dc75905ea22fbdf

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(states, k, m, tol, blowup):
    def en(s):
        return 0.5 * m * s[1] * s[1] + 0.5 * k * s[0] * s[0]
    e0 = en(states[0])
    scale = e0 if e0 > 0 else 1.0
    worst = 0.0
    first_drift = -1
    for i, s in enumerate(states):
        e = en(s)
        if e0 > 0 and e > blowup * e0:
            return ['blowup', i, round(abs(e - e0) / scale, 6)]
        r = max(0.0, e0 - e) / scale
        if r > worst:
            worst = r
        if r > tol and first_drift < 0:
            first_drift = i
    if first_drift >= 0:
        return ['drift', first_drift, round(worst, 6)]
    return ['ok', -1, round(worst, 6)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[[[[0.642, -0.278], [0.5937, -0.2502], [0.5306, -0.2252], [0.4774, -0.2027], [0.4326, -0.1824], [0.3961, -0.1642]], 2.502, 2.772, 0.05, 2.0], ['drift', 1, 0.624807]], [[[[0.0, 0.0], [0.0023, 0.0], [0.008, 0.0], [0.0167, 0.0], [0.0239, 0.0]], 1.47, 2.583, 0.01, 2.0], ['ok', -1, 0.00042]], [[[[0.354, -0.856], [0.3699, -0.8731], [0.3842, -0.8906], [0.404, -0.9084], [0.4055, -0.9266], [0.422, -0.9451], [0.4415, -0.964], [0.4623, -0.9833], [0.4764, -1.0029]], 2.622, 2.687, 0.05, 1.5], ['drift', 2, 0.435375]], [[[[0.007, 0.342], [0.0094, 0.3488], [0.0178, 0.3558], [0.0276, 0.3629]], 3.958, 2.139, 0.1, 2.0], ['drift', 3, 0.137127]], [[[[0.77, -0.528], [0.7846, -0.5386], [0.8008, -0.5493], [0.8252, -0.5603]], 4.089, 2.468, 0.01, 1.5], ['drift', 1, 0.143558]], [[[[-0.506, -0.658], [-0.4427, -0.5922], [-0.4045, -0.533], [-0.3529, -0.4797], [-0.3127, -0.4317], [-0.2739, -0.3885], [-0.2412, -0.3497], [-0.2179, -0.3147], [-0.1951, -0.2832]], 2.054, 1.583, 0.01, 1.5], ['drift', 1, 0.830639]], [[[[-0.727, -0.401], [-0.7918, -0.4411], [-0.8566, -0.4852], [-0.9532, -0.5337], [-1.0294, -0.5871], [-1.1522, -0.6458], [-1.2399, -0.7104]], 3.173, 0.604, 0.01, 3.0], ['drift', 1, 1.921313]], [[[[-0.138, 0.988], [-0.1281, 0.988], [-0.1264, 0.988]], 2.839, 1.096, 0.1, 3.0], ['ok', -1, 0.007747]]], [[[[[-0.219, 0.241], [-0.2354, 0.2651], [-0.2595, 0.2916], [-0.2794, 0.3208], [-0.2964, 0.3528], [-0.3284, 0.3881], [-0.3564, 0.4269]], 0.937, 2.683, 0.1, 3.0], ['blowup', 6, 2.028221]], [[[[-0.377, -0.929], [-0.3548, -0.9011], [-0.3496, -0.8741], [-0.3253, -0.8479], [-0.3166, -0.8224], [-0.2976, -0.7978]], 3.422, 0.967, 0.1, 1.5], ['drift', 2, 0.304614]], [[[[-0.274, -0.857], [-0.2679, -0.857], [-0.26, -0.857], [-0.2528, -0.857], [-0.2452, -0.857], [-0.2428, -0.857], [-0.2392, -0.857], [-0.2348, -0.857], [-0.2249, -0.857]], 3.816, 2.244, 0.1, 1.5], ['ok', -1, 0.048319]], [[[[0.098, -0.389], [0.1119, -0.4279], [0.1325, -0.4707], [0.1538, -0.5178], [0.1799, -0.5695], [0.203, -0.6265]], 1.475, 2.624, 0.01, 3.0], ['drift', 1, 1.652295]], [[[[0.303, 0.246], [0.3325, 0.2706], [0.3676, 0.2977], [0.4034, 0.3274], [0.4447, 0.3602], [0.5066, 0.3962]], 0.771, 1.949, 0.05, 2.0], ['blowup', 4, 1.147733]], [[[[0.0, 0.0], [0.0002, 0.0], [0.0055, 0.0], [0.0097, 0.0], [0.0174, 0.0], [0.0202, 0.0], [0.025, 0.0], [0.0315, 0.0], [0.0373, 0.0], [0.0427, 0.0]], 2.182, 1.732, 0.1, 2.0], ['ok', -1, 0.001989]], [[[[0.339, -0.79], [0.3312, -0.7663], [0.3266, -0.7433], [0.318, -0.721], [0.3149, -0.6994]], 1.641, 0.591, 0.01, 3.0], ['drift', 1, 0.189459]], [[[[-0.245, -0.092], [-0.247, -0.0938], [-0.2501, -0.0957], [-0.2553, -0.0976], [-0.253, -0.0996], [-0.2532, -0.1016]], 3.639, 1.24, 0.01, 1.5], ['drift', 1, 0.087664]]], [[[[[-0.602, -0.323], [-0.6548, -0.3553], [-0.7281, -0.3908], [-0.8042, -0.4299], [-0.8676, -0.4729], [-0.9515, -0.5202]], 4.781, 2.289, 0.05, 3.0], ['drift', 1, 1.509767]], [[[[-0.844, -0.85], [-0.8281, -0.85], [-0.8348, -0.85], [-0.8267, -0.85], [-0.8342, -0.85]], 1.842, 1.328, 0.01, 1.5], ['drift', 1, 0.023437]], [[[[0.983, 0.177], [1.0223, 0.1805], [1.0565, 0.1842], [1.0753, 0.1878], [1.1016, 0.1916], [1.126, 0.1954], [1.1604, 0.1993]], 2.096, 1.011, 0.01, 1.5], ['drift', 1, 0.39157]], [[[[0.846, 0.987], [0.8713, 1.0067], [0.9005, 1.0269], [0.9276, 1.0474], [0.9484, 1.0684]], 2.346, 2.182, 0.1, 3.0], ['drift', 2, 0.209251]], [[[[0.596, -0.74], [0.5494, -0.666], [0.496, -0.5994], [0.45, -0.5395], [0.4177, -0.4855], [0.3802, -0.437], [0.3542, -0.3933]], 2.077, 1.541, 0.05, 3.0], ['drift', 1, 0.684539]], [[[[0.0, 0.0], [0.0015, 0.0], [0.0069, 0.0], [0.0103, 0.0], [0.017, 0.0], [0.0223, 0.0], [0.0323, 0.0]], 4.193, 1.563, 0.05, 2.0], ['ok', -1, 0.002187]], [[[[0.494, 0.726], [0.4862, 0.7042], [0.4712, 0.6831], [0.4542, 0.6626]], 4.432, 1.484, 0.1, 1.5], ['drift', 2, 0.159841]], [[[[-0.61, -0.248], [-0.6209, -0.253], [-0.6338, -0.258], [-0.6283, -0.2632], [-0.6383, -0.2684], [-0.6504, -0.2738], [-0.6504, -0.2793], [-0.6669, -0.2849]], 3.89, 2.753, 0.05, 3.0], ['drift', 2, 0.208293]]], [[[[[-0.142, 0.767], [-0.1338, 0.7823], [-0.1303, 0.798], [-0.1279, 0.8139], [-0.1294, 0.8302], [-0.1206, 0.8468], [-0.1187, 0.8638], [-0.1125, 0.881]], 3.962, 2.055, 0.1, 1.5], ['drift', 3, 0.276478]], [[[[0.533, -0.86], [0.535, -0.8342], [0.522, -0.8092]], 3.784, 2.389, 0.01, 1.5], ['drift', 1, 0.086734]], [[[[0.46, -0.857], [0.4146, -0.7713], [0.3847, -0.6942], [0.347, -0.6248], [0.313, -0.5623], [0.2833, -0.506], [0.2638, -0.4554], [0.2445, -0.4099]], 4.633, 2.893, 0.01, 1.5], ['drift', 1, 0.754263]], [[[[0.0, 0.0], [0.0095, 0.0], [0.0112, 0.0]], 4.453, 1.79, 0.1, 3.0], ['ok', -1, 0.000279]], [[[[0.0, 0.0], [0.0044, 0.0], [0.0106, 0.0], [0.0193, 0.0], [0.024, 0.0], [0.0241, 0.0], [0.03, 0.0], [0.0297, 0.0], [0.0363, 0.0]], 4.075, 1.166, 0.01, 2.0], ['ok', -1, 0.002685]], [[[[0.769, -0.203], [0.8009, -0.2071], [0.8291, -0.2112], [0.847, -0.2154], [0.8719, -0.2197]], 3.998, 0.622, 0.1, 2.0], ['drift', 2, 0.2843]], [[[[0.611, 0.179], [0.6286, 0.1826], [0.6327, 0.1862], [0.6452, 0.19]], 0.929, 1.354, 0.05, 3.0], ['drift', 1, 0.116371]], [[[[-0.944, -0.357], [-0.9235, -0.3463], [-0.9004, -0.3359], [-0.8797, -0.3258], [-0.8621, -0.316], [-0.8187, -0.3066], [-0.7942, -0.2974]], 0.792, 1.826, 0.1, 3.0], ['drift', 3, 0.295621]]], [[[[[0.803, 0.52], [0.7338, 0.468], [0.6728, 0.4212], [0.6205, 0.3791], [0.5593, 0.3412], [0.5062, 0.3071], [0.4563, 0.2763], [0.4139, 0.2487], [0.3713, 0.2238], [0.3301, 0.2015]], 0.955, 1.682, 0.05, 3.0], ['drift', 1, 0.839011]], [[[[0.0, 0.0], [0.0018, 0.0], [0.0028, 0.0], [0.0066, 0.0], [0.0144, 0.0]], 0.719, 1.234, 0.01, 2.0], ['ok', -1, 7.5e-05]], [[[[0.812, 0.7], [0.7824, 0.679], [0.7661, 0.6586], [0.7494, 0.6389], [0.7496, 0.6197], [0.7346, 0.6011]], 3.833, 2.927, 0.01, 2.0], ['drift', 1, 0.2109]], [[[[-0.612, 0.33], [-0.6277, 0.3366], [-0.6415, 0.3433], [-0.6394, 0.3502]], 2.324, 0.739, 0.01, 2.0], ['drift', 1, 0.097332]], [[[[-0.648, -0.612], [-0.7038, -0.6732], [-0.766, -0.7405], [-0.8245, -0.8146], [-0.9148, -0.896], [-1.0192, -0.9856], [-1.1118, -1.0842], [-1.2153, -1.1926]], 1.534, 1.581, 0.1, 3.0], ['blowup', 6, 2.037018]], [[[[-0.388, 0.367], [-0.3827, 0.3743], [-0.3809, 0.3818]], 4.434, 2.813, 0.05, 3.0], ['ok', -1, 0.006659]], [[[[0.788, 0.541], [0.8584, 0.5951], [0.9528, 0.6546], [1.0365, 0.7201], [1.1562, 0.7921], [1.2724, 0.8713]], 4.609, 2.968, 0.1, 3.0], ['drift', 1, 1.604181]], [[[[0.304, 0.926], [0.2951, 0.8982], [0.2913, 0.8713], [0.2845, 0.8451], [0.273, 0.8198]], 4.318, 0.794, 0.01, 2.0], ['drift', 1, 0.207843]]]]
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['drift', 1, 0.624807]['drift', 1, 0.624807]Passed
case 1['ok', -1, 0.0]['ok', -1, 0.00042]Failed
case 2['ok', -1, 0.0]['drift', 2, 0.435375]Failed
case 3['ok', -1, 0.0]['drift', 3, 0.137127]Failed
case 4['ok', -1, 0.0]['drift', 1, 0.143558]Failed
case 5['drift', 1, 0.830639]['drift', 1, 0.830639]Passed
case 6['ok', -1, 0.0]['drift', 1, 1.921313]Failed
case 7['ok', -1, 0.007747]['ok', -1, 0.007747]Passed

SHA-256 / fc7ff21f293f772dceb1db363aba9eb779b1762bf8e54d3de9afa36cebd4042e

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 2026-09-29T14:50:57.714696+00:00.

Case digest / 59f6050a54b122818eba68e14bc0c82f85d53363037466b0182363fc25214908