FAILURE MAP
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FA-87396 / Collision detection broadphase / Open access

Leftward motion extends the right side of the fat box · case 01

Proxies moving left escape their fat box immediately and churn the tree.

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

ROOT CAUSE

The x displacement is always added to maxx.

VERIFIED REPAIR

Negative displacement extends minx, positive extends maxx.

Unsuccessful approach: Subtracting a negative displacement from minx shrinks the box instead of extending it.

Case contract

solve(tight, fat, disp, margin, mult): dynamic-tree proxy update. If the stored fat box contains the new tight box (inclusive) and its area is at most 4x that of a freshly built fat box, keep it: [False, fat]. Otherwise rebuild: tight expanded by margin on all sides, then extended by mult*disp on the side the motion points to; return [True, rebuilt box rounded to 6].

Why this case matters

Broadphase stages decide which object pairs ever reach narrowphase; a wrong boundary, ordering or bookkeeping rule silently drops real contacts or floods the solver with false candidates.

1 / The failure

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(tight, fat, disp, margin, mult):
    def fatten():
        f = [tight[0] - margin, tight[1] - margin, tight[2] + margin, tight[3] + margin]
        dx, dy = mult * disp[0], mult * disp[1]
        f[2] += dx
        if dy < 0:
            f[1] += dy
        else:
            f[3] += dy
        return [round(c, 6) for c in f]
    def area(b):
        return (b[2] - b[0]) * (b[3] - b[1])
    inside = fat[0] <= tight[0] and fat[1] <= tight[1] and tight[2] <= fat[2] and tight[3] <= fat[3]
    fresh = fatten()
    if inside and area(fat) <= 4 * area(fresh):
        return [False, fat]
    return [True, fresh]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[[[-2.7, -2.8, -1.6, -1.1], [-4.9, -3.5, -2.2, -1.2], [1.0, 0.5], 0.2, 1.0], [True, [-2.9, -3.0, -0.4, -0.4]]], [[[1.9, 0.0, 3.6, 1.9], [-2.1, -4.0, 7.6, 5.9], [-0.1, 0.2], 0.1, 1.0], [True, [1.7, -0.1, 3.7, 2.2]]], [[[-1.8, -1.2, -0.2, 0.7], [-1.3, -1.3, 0.6, 0.8], [-0.6, 0], 0.1, 1.0], [True, [-2.5, -1.3, -0.1, 0.8]]], [[[-3.4, 2.2, -0.7, 2.8], [-6.3, -0.8, 2.4, 3.8], [-0.1, 0], 0.5, 4.0], [True, [-4.3, 1.7, -0.2, 3.3]]], [[[-4.0, 2.9, -2.1, 3.2], [-4.3, 2.6, -1.8, 3.5], [0, 0], 0.1, 1.0], [False, [-4.3, 2.6, -1.8, 3.5]]], [[[-1.3, 4.3, 0.2, 5.2], [-1.9, 2.5, 0.8, 5.8], [-0.1, 0], 0.1, 1.0], [True, [-1.5, 4.2, 0.3, 5.3]]], [[[-1.7, -2.8, -0.8, -1.1], [-1.8, -4.0, -0.3, -0.7], [-0.1, 0], 0.2, 4.0], [False, [-1.8, -4.0, -0.3, -0.7]]], [[[-0.2, 0.4, 0.5, 0.8], [-1.2, -0.1, 1.5, 1.8], [-0.1, 0.2], 0.1, 1.0], [True, [-0.4, 0.3, 0.6, 1.1]]]], [[[[-3.6, 4.9, -0.8, 7.8], [-4.0, 3.6, 0.4, 7.9], [0, 0.1], 0.2, 1.0], [False, [-4.0, 3.6, 0.4, 7.9]]], [[[-5.3, 1.1, -3.8, 2.4], [-4.9, 0.9, -3.0, 3.0], [-0.6, 0], 0.1, 2.0], [True, [-6.6, 1.0, -3.7, 2.5]]], [[[2.6, -0.5, 4.4, 1.4], [3.0, -1.7, 5.2, 2.6], [-0.6, 0], 0.2, 4.0], [True, [0.0, -0.7, 4.6, 1.6]]], [[[-4.1, 1.1, -3.3, 2.1], [-7.0, 1.6, -2.2, 6.1], [-0.1, -1.0], 0.5, 1.0], [True, [-4.7, -0.4, -2.8, 2.6]]], [[[2.1, 1.6, 2.8, 3.0], [1.5, -0.2, 3.4, 3.6], [0, 0], 0.1, 1.0], [True, [2.0, 1.5, 2.9, 3.1]]], [[[2.0, 3.8, 2.9, 5.5], [1.8, 3.2, 3.4, 5.7], [0.1, 0], 0.1, 1.0], [False, [1.8, 3.2, 3.4, 5.7]]], [[[2.9, 0.7, 5.9, 3.4], [3.3, 0.4, 6.7, 3.7], [-0.6, 0.1], 0.2, 2.0], [True, [1.5, 0.5, 6.1, 3.8]]], [[[3.1, -3.4, 3.7, -2.5], [3.5, -4.1, 4.5, -2.0], [-0.6, 0.1], 0.1, 1.0], [True, [2.4, -3.5, 3.8, -2.3]]]], [[[[-5.0, 2.9, -4.0, 3.6], [-5.3, 2.0, -3.7, 3.9], [0, 0], 0.2, 1.0], [False, [-5.3, 2.0, -3.7, 3.9]]], [[[1.1, 2.3, 3.5, 5.1], [1.1, 2.7, 4.2, 6.7], [-0.6, -1.0], 0.1, 4.0], [True, [-1.4, -1.8, 3.6, 5.2]]], [[[2.4, 1.8, 3.0, 3.7], [1.8, 0.8, 4.8, 4.1], [-0.6, -0.2], 0.2, 2.0], [False, [1.8, 0.8, 4.8, 4.1]]], [[[-1.1, -4.2, 0.4, -2.3], [-1.7, -6.0, 1.0, -1.7], [0, 0.2], 0.2, 1.0], [False, [-1.7, -6.0, 1.0, -1.7]]], [[[-1.1, -0.2, -0.3, 1.7], [-3.5, -3.7, 1.3, 1.7], [-0.6, 0.5], 0.5, 1.0], [False, [-3.5, -3.7, 1.3, 1.7]]], [[[2.5, 2.5, 4.3, 3.2], [2.9, 1.9, 5.1, 3.8], [-0.6, 0], 0.1, 4.0], [True, [0.0, 2.4, 4.4, 3.3]]], [[[-2.7, -2.3, -1.0, -0.7], [-3.7, -3.3, -0.0, 0.3], [0, 0], 0.2, 1.0], [False, [-3.7, -3.3, -0.0, 0.3]]], [[[-4.3, -1.2, -2.9, -0.1], [-4.3, -1.6, -1.7, 0.2], [-0.6, -0.2], 0.1, 2.0], [False, [-4.3, -1.6, -1.7, 0.2]]]], [[[[-2.1, -5.0, 0.3, -2.4], [-1.7, -4.2, 1.1, -1.2], [-0.6, -1.0], 0.2, 2.0], [True, [-3.5, -7.2, 0.5, -2.2]]], [[[-0.4, 3.7, 2.0, 5.4], [-0.8, 2.9, 5.6, 6.1], [-0.6, -0.2], 0.5, 4.0], [False, [-0.8, 2.9, 5.6, 6.1]]], [[[-4.4, -0.8, -3.4, 0.6], [-7.3, -4.3, -0.3, 3.1], [-0.1, 0.5], 0.5, 4.0], [True, [-5.3, -1.3, -2.9, 3.1]]], [[[-2.1, 2.7, -0.9, 4.6], [-3.1, -0.3, 0.1, 5.6], [0.1, 0], 0.1, 1.0], [True, [-2.2, 2.6, -0.7, 4.7]]], [[[-0.6, -4.6, 1.1, -3.7], [-1.5, -4.1, 1.2, -1.7], [0.4, -1.0], 0.5, 1.0], [True, [-1.1, -6.1, 2.0, -3.2]]], [[[2.7, 0.6, 3.1, 2.2], [-1.3, -1.4, 7.1, 6.2], [0, 0], 0.1, 1.0], [True, [2.6, 0.5, 3.2, 2.3]]], [[[-4.7, 1.6, -3.6, 3.6], [-4.6, 1.1, -2.0, 4.6], [-0.6, 0], 0.5, 1.0], [True, [-5.8, 1.1, -3.1, 4.1]]], [[[-0.9, -2.7, 0.9, -2.0], [-3.8, -3.7, 2.0, 1.0], [-0.1, 0], 0.5, 4.0], [True, [-1.8, -3.2, 1.4, -1.5]]]], [[[[3.7, 1.3, 6.2, 4.0], [3.4, 1.3, 6.5, 4.6], [-0.1, -0.2], 0.2, 1.0], [False, [3.4, 1.3, 6.5, 4.6]]], [[[-4.3, 4.5, -2.1, 5.9], [-5.6, 3.3, -1.8, 7.1], [0.1, 0], 0.2, 1.0], [False, [-5.6, 3.3, -1.8, 7.1]]], [[[2.3, 1.4, 3.5, 2.3], [0.3, -0.6, 5.5, 4.3], [0.1, 0], 0.2, 1.0], [True, [2.1, 1.2, 3.8, 2.5]]], [[[-4.6, -2.3, -3.4, 0.4], [-5.1, -3.5, -2.3, 0.8], [0.1, 0], 0.2, 1.0], [False, [-5.1, -3.5, -2.3, 0.8]]], [[[3.0, 3.8, 4.7, 5.0], [3.2, 2.6, 5.7, 6.2], [-0.6, 0], 0.2, 2.0], [True, [1.6, 3.6, 4.9, 5.2]]], [[[0.7, 2.5, 2.0, 3.2], [-0.3, 2.0, 3.0, 4.2], [-0.1, 0.2], 0.1, 1.0], [True, [0.5, 2.4, 2.1, 3.5]]], [[[-5.5, 2.6, -4.1, 5.4], [-5.1, 2.4, -3.3, 5.4], [-0.6, 0.1], 0.1, 1.0], [True, [-6.2, 2.5, -4.0, 5.6]]], [[[-4.0, 1.4, -2.1, 2.9], [-5.1, 0.7, -1.8, 2.6], [-0.1, 0.5], 0.2, 4.0], [True, [-4.6, 1.2, -1.9, 5.1]]]]]
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[True, [-2.9, -3.0, -0.4, -0.4]][True, [-2.9, -3.0, -0.4, -0.4]]Passed
case 1[True, [1.8, -0.1, 3.6, 2.2]][True, [1.7, -0.1, 3.7, 2.2]]Failed
case 2[True, [-1.9, -1.3, -0.7, 0.8]][True, [-2.5, -1.3, -0.1, 0.8]]Failed
case 3[True, [-3.9, 1.7, -0.6, 3.3]][True, [-4.3, 1.7, -0.2, 3.3]]Failed
case 4[False, [-4.3, 2.6, -1.8, 3.5]][False, [-4.3, 2.6, -1.8, 3.5]]Passed
case 5[True, [-1.4, 4.2, 0.2, 5.3]][True, [-1.5, 4.2, 0.3, 5.3]]Failed
case 6[False, [-1.8, -4.0, -0.3, -0.7]][False, [-1.8, -4.0, -0.3, -0.7]]Passed
case 7[True, [-0.3, 0.3, 0.5, 1.1]][True, [-0.4, 0.3, 0.6, 1.1]]Failed

SHA-256 / 1b14899017d9ca789fd7ba6bb197c59677bb65560145d6c8a960b8716de1ab93

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(tight, fat, disp, margin, mult):
    def fatten():
        f = [tight[0] - margin, tight[1] - margin, tight[2] + margin, tight[3] + margin]
        dx, dy = mult * disp[0], mult * disp[1]
        if dx < 0:
            f[0] -= dx
        else:
            f[2] += dx
        if dy < 0:
            f[1] += dy
        else:
            f[3] += dy
        return [round(c, 6) for c in f]
    def area(b):
        return (b[2] - b[0]) * (b[3] - b[1])
    inside = fat[0] <= tight[0] and fat[1] <= tight[1] and tight[2] <= fat[2] and tight[3] <= fat[3]
    fresh = fatten()
    if inside and area(fat) <= 4 * area(fresh):
        return [False, fat]
    return [True, fresh]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[[[-2.7, -2.8, -1.6, -1.1], [-4.9, -3.5, -2.2, -1.2], [1.0, 0.5], 0.2, 1.0], [True, [-2.9, -3.0, -0.4, -0.4]]], [[[1.9, 0.0, 3.6, 1.9], [-2.1, -4.0, 7.6, 5.9], [-0.1, 0.2], 0.1, 1.0], [True, [1.7, -0.1, 3.7, 2.2]]], [[[-1.8, -1.2, -0.2, 0.7], [-1.3, -1.3, 0.6, 0.8], [-0.6, 0], 0.1, 1.0], [True, [-2.5, -1.3, -0.1, 0.8]]], [[[-3.4, 2.2, -0.7, 2.8], [-6.3, -0.8, 2.4, 3.8], [-0.1, 0], 0.5, 4.0], [True, [-4.3, 1.7, -0.2, 3.3]]], [[[-4.0, 2.9, -2.1, 3.2], [-4.3, 2.6, -1.8, 3.5], [0, 0], 0.1, 1.0], [False, [-4.3, 2.6, -1.8, 3.5]]], [[[-1.3, 4.3, 0.2, 5.2], [-1.9, 2.5, 0.8, 5.8], [-0.1, 0], 0.1, 1.0], [True, [-1.5, 4.2, 0.3, 5.3]]], [[[-1.7, -2.8, -0.8, -1.1], [-1.8, -4.0, -0.3, -0.7], [-0.1, 0], 0.2, 4.0], [False, [-1.8, -4.0, -0.3, -0.7]]], [[[-0.2, 0.4, 0.5, 0.8], [-1.2, -0.1, 1.5, 1.8], [-0.1, 0.2], 0.1, 1.0], [True, [-0.4, 0.3, 0.6, 1.1]]]], [[[[-3.6, 4.9, -0.8, 7.8], [-4.0, 3.6, 0.4, 7.9], [0, 0.1], 0.2, 1.0], [False, [-4.0, 3.6, 0.4, 7.9]]], [[[-5.3, 1.1, -3.8, 2.4], [-4.9, 0.9, -3.0, 3.0], [-0.6, 0], 0.1, 2.0], [True, [-6.6, 1.0, -3.7, 2.5]]], [[[2.6, -0.5, 4.4, 1.4], [3.0, -1.7, 5.2, 2.6], [-0.6, 0], 0.2, 4.0], [True, [0.0, -0.7, 4.6, 1.6]]], [[[-4.1, 1.1, -3.3, 2.1], [-7.0, 1.6, -2.2, 6.1], [-0.1, -1.0], 0.5, 1.0], [True, [-4.7, -0.4, -2.8, 2.6]]], [[[2.1, 1.6, 2.8, 3.0], [1.5, -0.2, 3.4, 3.6], [0, 0], 0.1, 1.0], [True, [2.0, 1.5, 2.9, 3.1]]], [[[2.0, 3.8, 2.9, 5.5], [1.8, 3.2, 3.4, 5.7], [0.1, 0], 0.1, 1.0], [False, [1.8, 3.2, 3.4, 5.7]]], [[[2.9, 0.7, 5.9, 3.4], [3.3, 0.4, 6.7, 3.7], [-0.6, 0.1], 0.2, 2.0], [True, [1.5, 0.5, 6.1, 3.8]]], [[[3.1, -3.4, 3.7, -2.5], [3.5, -4.1, 4.5, -2.0], [-0.6, 0.1], 0.1, 1.0], [True, [2.4, -3.5, 3.8, -2.3]]]], [[[[-5.0, 2.9, -4.0, 3.6], [-5.3, 2.0, -3.7, 3.9], [0, 0], 0.2, 1.0], [False, [-5.3, 2.0, -3.7, 3.9]]], [[[1.1, 2.3, 3.5, 5.1], [1.1, 2.7, 4.2, 6.7], [-0.6, -1.0], 0.1, 4.0], [True, [-1.4, -1.8, 3.6, 5.2]]], [[[2.4, 1.8, 3.0, 3.7], [1.8, 0.8, 4.8, 4.1], [-0.6, -0.2], 0.2, 2.0], [False, [1.8, 0.8, 4.8, 4.1]]], [[[-1.1, -4.2, 0.4, -2.3], [-1.7, -6.0, 1.0, -1.7], [0, 0.2], 0.2, 1.0], [False, [-1.7, -6.0, 1.0, -1.7]]], [[[-1.1, -0.2, -0.3, 1.7], [-3.5, -3.7, 1.3, 1.7], [-0.6, 0.5], 0.5, 1.0], [False, [-3.5, -3.7, 1.3, 1.7]]], [[[2.5, 2.5, 4.3, 3.2], [2.9, 1.9, 5.1, 3.8], [-0.6, 0], 0.1, 4.0], [True, [0.0, 2.4, 4.4, 3.3]]], [[[-2.7, -2.3, -1.0, -0.7], [-3.7, -3.3, -0.0, 0.3], [0, 0], 0.2, 1.0], [False, [-3.7, -3.3, -0.0, 0.3]]], [[[-4.3, -1.2, -2.9, -0.1], [-4.3, -1.6, -1.7, 0.2], [-0.6, -0.2], 0.1, 2.0], [False, [-4.3, -1.6, -1.7, 0.2]]]], [[[[-2.1, -5.0, 0.3, -2.4], [-1.7, -4.2, 1.1, -1.2], [-0.6, -1.0], 0.2, 2.0], [True, [-3.5, -7.2, 0.5, -2.2]]], [[[-0.4, 3.7, 2.0, 5.4], [-0.8, 2.9, 5.6, 6.1], [-0.6, -0.2], 0.5, 4.0], [False, [-0.8, 2.9, 5.6, 6.1]]], [[[-4.4, -0.8, -3.4, 0.6], [-7.3, -4.3, -0.3, 3.1], [-0.1, 0.5], 0.5, 4.0], [True, [-5.3, -1.3, -2.9, 3.1]]], [[[-2.1, 2.7, -0.9, 4.6], [-3.1, -0.3, 0.1, 5.6], [0.1, 0], 0.1, 1.0], [True, [-2.2, 2.6, -0.7, 4.7]]], [[[-0.6, -4.6, 1.1, -3.7], [-1.5, -4.1, 1.2, -1.7], [0.4, -1.0], 0.5, 1.0], [True, [-1.1, -6.1, 2.0, -3.2]]], [[[2.7, 0.6, 3.1, 2.2], [-1.3, -1.4, 7.1, 6.2], [0, 0], 0.1, 1.0], [True, [2.6, 0.5, 3.2, 2.3]]], [[[-4.7, 1.6, -3.6, 3.6], [-4.6, 1.1, -2.0, 4.6], [-0.6, 0], 0.5, 1.0], [True, [-5.8, 1.1, -3.1, 4.1]]], [[[-0.9, -2.7, 0.9, -2.0], [-3.8, -3.7, 2.0, 1.0], [-0.1, 0], 0.5, 4.0], [True, [-1.8, -3.2, 1.4, -1.5]]]], [[[[3.7, 1.3, 6.2, 4.0], [3.4, 1.3, 6.5, 4.6], [-0.1, -0.2], 0.2, 1.0], [False, [3.4, 1.3, 6.5, 4.6]]], [[[-4.3, 4.5, -2.1, 5.9], [-5.6, 3.3, -1.8, 7.1], [0.1, 0], 0.2, 1.0], [False, [-5.6, 3.3, -1.8, 7.1]]], [[[2.3, 1.4, 3.5, 2.3], [0.3, -0.6, 5.5, 4.3], [0.1, 0], 0.2, 1.0], [True, [2.1, 1.2, 3.8, 2.5]]], [[[-4.6, -2.3, -3.4, 0.4], [-5.1, -3.5, -2.3, 0.8], [0.1, 0], 0.2, 1.0], [False, [-5.1, -3.5, -2.3, 0.8]]], [[[3.0, 3.8, 4.7, 5.0], [3.2, 2.6, 5.7, 6.2], [-0.6, 0], 0.2, 2.0], [True, [1.6, 3.6, 4.9, 5.2]]], [[[0.7, 2.5, 2.0, 3.2], [-0.3, 2.0, 3.0, 4.2], [-0.1, 0.2], 0.1, 1.0], [True, [0.5, 2.4, 2.1, 3.5]]], [[[-5.5, 2.6, -4.1, 5.4], [-5.1, 2.4, -3.3, 5.4], [-0.6, 0.1], 0.1, 1.0], [True, [-6.2, 2.5, -4.0, 5.6]]], [[[-4.0, 1.4, -2.1, 2.9], [-5.1, 0.7, -1.8, 2.6], [-0.1, 0.5], 0.2, 4.0], [True, [-4.6, 1.2, -1.9, 5.1]]]]]
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[True, [-2.9, -3.0, -0.4, -0.4]][True, [-2.9, -3.0, -0.4, -0.4]]Passed
case 1[True, [1.9, -0.1, 3.7, 2.2]][True, [1.7, -0.1, 3.7, 2.2]]Failed
case 2[True, [-1.3, -1.3, -0.1, 0.8]][True, [-2.5, -1.3, -0.1, 0.8]]Failed
case 3[True, [-3.5, 1.7, -0.2, 3.3]][True, [-4.3, 1.7, -0.2, 3.3]]Failed
case 4[False, [-4.3, 2.6, -1.8, 3.5]][False, [-4.3, 2.6, -1.8, 3.5]]Passed
case 5[True, [-1.3, 4.2, 0.3, 5.3]][True, [-1.5, 4.2, 0.3, 5.3]]Failed
case 6[False, [-1.8, -4.0, -0.3, -0.7]][False, [-1.8, -4.0, -0.3, -0.7]]Passed
case 7[True, [-0.2, 0.3, 0.6, 1.1]][True, [-0.4, 0.3, 0.6, 1.1]]Failed

SHA-256 / e005376f24d281674960a4af763408aa32846aee4171bc2a986ccb213c823bce

3 / The verified repair

Exit 0
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(tight, fat, disp, margin, mult):
    def fatten():
        f = [tight[0] - margin, tight[1] - margin, tight[2] + margin, tight[3] + margin]
        dx, dy = mult * disp[0], mult * disp[1]
        if dx < 0:
            f[0] += dx
        else:
            f[2] += dx
        if dy < 0:
            f[1] += dy
        else:
            f[3] += dy
        return [round(c, 6) for c in f]
    def area(b):
        return (b[2] - b[0]) * (b[3] - b[1])
    inside = fat[0] <= tight[0] and fat[1] <= tight[1] and tight[2] <= fat[2] and tight[3] <= fat[3]
    fresh = fatten()
    if inside and area(fat) <= 4 * area(fresh):
        return [False, fat]
    return [True, fresh]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[[[-2.7, -2.8, -1.6, -1.1], [-4.9, -3.5, -2.2, -1.2], [1.0, 0.5], 0.2, 1.0], [True, [-2.9, -3.0, -0.4, -0.4]]], [[[1.9, 0.0, 3.6, 1.9], [-2.1, -4.0, 7.6, 5.9], [-0.1, 0.2], 0.1, 1.0], [True, [1.7, -0.1, 3.7, 2.2]]], [[[-1.8, -1.2, -0.2, 0.7], [-1.3, -1.3, 0.6, 0.8], [-0.6, 0], 0.1, 1.0], [True, [-2.5, -1.3, -0.1, 0.8]]], [[[-3.4, 2.2, -0.7, 2.8], [-6.3, -0.8, 2.4, 3.8], [-0.1, 0], 0.5, 4.0], [True, [-4.3, 1.7, -0.2, 3.3]]], [[[-4.0, 2.9, -2.1, 3.2], [-4.3, 2.6, -1.8, 3.5], [0, 0], 0.1, 1.0], [False, [-4.3, 2.6, -1.8, 3.5]]], [[[-1.3, 4.3, 0.2, 5.2], [-1.9, 2.5, 0.8, 5.8], [-0.1, 0], 0.1, 1.0], [True, [-1.5, 4.2, 0.3, 5.3]]], [[[-1.7, -2.8, -0.8, -1.1], [-1.8, -4.0, -0.3, -0.7], [-0.1, 0], 0.2, 4.0], [False, [-1.8, -4.0, -0.3, -0.7]]], [[[-0.2, 0.4, 0.5, 0.8], [-1.2, -0.1, 1.5, 1.8], [-0.1, 0.2], 0.1, 1.0], [True, [-0.4, 0.3, 0.6, 1.1]]]], [[[[-3.6, 4.9, -0.8, 7.8], [-4.0, 3.6, 0.4, 7.9], [0, 0.1], 0.2, 1.0], [False, [-4.0, 3.6, 0.4, 7.9]]], [[[-5.3, 1.1, -3.8, 2.4], [-4.9, 0.9, -3.0, 3.0], [-0.6, 0], 0.1, 2.0], [True, [-6.6, 1.0, -3.7, 2.5]]], [[[2.6, -0.5, 4.4, 1.4], [3.0, -1.7, 5.2, 2.6], [-0.6, 0], 0.2, 4.0], [True, [0.0, -0.7, 4.6, 1.6]]], [[[-4.1, 1.1, -3.3, 2.1], [-7.0, 1.6, -2.2, 6.1], [-0.1, -1.0], 0.5, 1.0], [True, [-4.7, -0.4, -2.8, 2.6]]], [[[2.1, 1.6, 2.8, 3.0], [1.5, -0.2, 3.4, 3.6], [0, 0], 0.1, 1.0], [True, [2.0, 1.5, 2.9, 3.1]]], [[[2.0, 3.8, 2.9, 5.5], [1.8, 3.2, 3.4, 5.7], [0.1, 0], 0.1, 1.0], [False, [1.8, 3.2, 3.4, 5.7]]], [[[2.9, 0.7, 5.9, 3.4], [3.3, 0.4, 6.7, 3.7], [-0.6, 0.1], 0.2, 2.0], [True, [1.5, 0.5, 6.1, 3.8]]], [[[3.1, -3.4, 3.7, -2.5], [3.5, -4.1, 4.5, -2.0], [-0.6, 0.1], 0.1, 1.0], [True, [2.4, -3.5, 3.8, -2.3]]]], [[[[-5.0, 2.9, -4.0, 3.6], [-5.3, 2.0, -3.7, 3.9], [0, 0], 0.2, 1.0], [False, [-5.3, 2.0, -3.7, 3.9]]], [[[1.1, 2.3, 3.5, 5.1], [1.1, 2.7, 4.2, 6.7], [-0.6, -1.0], 0.1, 4.0], [True, [-1.4, -1.8, 3.6, 5.2]]], [[[2.4, 1.8, 3.0, 3.7], [1.8, 0.8, 4.8, 4.1], [-0.6, -0.2], 0.2, 2.0], [False, [1.8, 0.8, 4.8, 4.1]]], [[[-1.1, -4.2, 0.4, -2.3], [-1.7, -6.0, 1.0, -1.7], [0, 0.2], 0.2, 1.0], [False, [-1.7, -6.0, 1.0, -1.7]]], [[[-1.1, -0.2, -0.3, 1.7], [-3.5, -3.7, 1.3, 1.7], [-0.6, 0.5], 0.5, 1.0], [False, [-3.5, -3.7, 1.3, 1.7]]], [[[2.5, 2.5, 4.3, 3.2], [2.9, 1.9, 5.1, 3.8], [-0.6, 0], 0.1, 4.0], [True, [0.0, 2.4, 4.4, 3.3]]], [[[-2.7, -2.3, -1.0, -0.7], [-3.7, -3.3, -0.0, 0.3], [0, 0], 0.2, 1.0], [False, [-3.7, -3.3, -0.0, 0.3]]], [[[-4.3, -1.2, -2.9, -0.1], [-4.3, -1.6, -1.7, 0.2], [-0.6, -0.2], 0.1, 2.0], [False, [-4.3, -1.6, -1.7, 0.2]]]], [[[[-2.1, -5.0, 0.3, -2.4], [-1.7, -4.2, 1.1, -1.2], [-0.6, -1.0], 0.2, 2.0], [True, [-3.5, -7.2, 0.5, -2.2]]], [[[-0.4, 3.7, 2.0, 5.4], [-0.8, 2.9, 5.6, 6.1], [-0.6, -0.2], 0.5, 4.0], [False, [-0.8, 2.9, 5.6, 6.1]]], [[[-4.4, -0.8, -3.4, 0.6], [-7.3, -4.3, -0.3, 3.1], [-0.1, 0.5], 0.5, 4.0], [True, [-5.3, -1.3, -2.9, 3.1]]], [[[-2.1, 2.7, -0.9, 4.6], [-3.1, -0.3, 0.1, 5.6], [0.1, 0], 0.1, 1.0], [True, [-2.2, 2.6, -0.7, 4.7]]], [[[-0.6, -4.6, 1.1, -3.7], [-1.5, -4.1, 1.2, -1.7], [0.4, -1.0], 0.5, 1.0], [True, [-1.1, -6.1, 2.0, -3.2]]], [[[2.7, 0.6, 3.1, 2.2], [-1.3, -1.4, 7.1, 6.2], [0, 0], 0.1, 1.0], [True, [2.6, 0.5, 3.2, 2.3]]], [[[-4.7, 1.6, -3.6, 3.6], [-4.6, 1.1, -2.0, 4.6], [-0.6, 0], 0.5, 1.0], [True, [-5.8, 1.1, -3.1, 4.1]]], [[[-0.9, -2.7, 0.9, -2.0], [-3.8, -3.7, 2.0, 1.0], [-0.1, 0], 0.5, 4.0], [True, [-1.8, -3.2, 1.4, -1.5]]]], [[[[3.7, 1.3, 6.2, 4.0], [3.4, 1.3, 6.5, 4.6], [-0.1, -0.2], 0.2, 1.0], [False, [3.4, 1.3, 6.5, 4.6]]], [[[-4.3, 4.5, -2.1, 5.9], [-5.6, 3.3, -1.8, 7.1], [0.1, 0], 0.2, 1.0], [False, [-5.6, 3.3, -1.8, 7.1]]], [[[2.3, 1.4, 3.5, 2.3], [0.3, -0.6, 5.5, 4.3], [0.1, 0], 0.2, 1.0], [True, [2.1, 1.2, 3.8, 2.5]]], [[[-4.6, -2.3, -3.4, 0.4], [-5.1, -3.5, -2.3, 0.8], [0.1, 0], 0.2, 1.0], [False, [-5.1, -3.5, -2.3, 0.8]]], [[[3.0, 3.8, 4.7, 5.0], [3.2, 2.6, 5.7, 6.2], [-0.6, 0], 0.2, 2.0], [True, [1.6, 3.6, 4.9, 5.2]]], [[[0.7, 2.5, 2.0, 3.2], [-0.3, 2.0, 3.0, 4.2], [-0.1, 0.2], 0.1, 1.0], [True, [0.5, 2.4, 2.1, 3.5]]], [[[-5.5, 2.6, -4.1, 5.4], [-5.1, 2.4, -3.3, 5.4], [-0.6, 0.1], 0.1, 1.0], [True, [-6.2, 2.5, -4.0, 5.6]]], [[[-4.0, 1.4, -2.1, 2.9], [-5.1, 0.7, -1.8, 2.6], [-0.1, 0.5], 0.2, 4.0], [True, [-4.6, 1.2, -1.9, 5.1]]]]]
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[True, [-2.9, -3.0, -0.4, -0.4]][True, [-2.9, -3.0, -0.4, -0.4]]Passed
case 1[True, [1.7, -0.1, 3.7, 2.2]][True, [1.7, -0.1, 3.7, 2.2]]Passed
case 2[True, [-2.5, -1.3, -0.1, 0.8]][True, [-2.5, -1.3, -0.1, 0.8]]Passed
case 3[True, [-4.3, 1.7, -0.2, 3.3]][True, [-4.3, 1.7, -0.2, 3.3]]Passed
case 4[False, [-4.3, 2.6, -1.8, 3.5]][False, [-4.3, 2.6, -1.8, 3.5]]Passed
case 5[True, [-1.5, 4.2, 0.3, 5.3]][True, [-1.5, 4.2, 0.3, 5.3]]Passed
case 6[False, [-1.8, -4.0, -0.3, -0.7]][False, [-1.8, -4.0, -0.3, -0.7]]Passed
case 7[True, [-0.4, 0.3, 0.6, 1.1]][True, [-0.4, 0.3, 0.6, 1.1]]Passed

SHA-256 / 7c8b8d9ebbc5b6346345e486067158b6552ebc73520376fec410030043dfe019

Verification & scope

A deterministic bounded teaching model with stipulated toy conventions; not a production physics engine or spatial index. 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 2026-09-29T14:50:58.383496+00:00.

Case digest / abe12a9bf73b57b13cb50840f0a00c42e6a84500e185109219e2ca5afb8fac10