FA-87401 / Collision detection broadphase / Open access

Fat margin is applied only to the upper corner · case 01

Jitter toward negative axes forces constant reinsertions.

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

ROOT CAUSE

The rebuilt min corner equals the tight min corner.

VERIFIED REPAIR

Subtract the margin from both minimum coordinates.

Unsuccessful approach: Half margin on the low side still makes the box asymmetric.

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], tight[1], 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 = [[[[[-3.4, -0.9, -2.5, 0.7], [-7.4, -12.9, 1.5, 4.7], [0.1, 0.2], 0.1, 1.0], [True, [-3.5, -1.0, -2.3, 1.0]]], [[[1.7, 2.9, 3.1, 4.2], [0.6, 0.9, 6.0, 6.2], [0.1, -1.0], 0.5, 4.0], [False, [0.6, 0.9, 6.0, 6.2]]], [[[2.8, 1.5, 4.5, 2.1], [1.8, -1.5, 5.5, 3.1], [0, 0.2], 0.2, 1.0], [True, [2.6, 1.3, 4.7, 2.5]]], [[[-3.1, 3.1, -1.7, 4.7], [-3.2, 4.0, -1.5, 5.8], [-0.1, -1.0], 0.1, 1.0], [True, [-3.3, 2.0, -1.6, 4.8]]], [[[-2.5, -4.5, -1.7, -2.2], [-4.7, -5.2, -1.5, -1.5], [1.0, 0.5], 0.2, 1.0], [False, [-4.7, -5.2, -1.5, -1.5]]], [[[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]]], [[[-0.3, 2.0, 2.2, 4.9], [-1.8, 0.9, 1.7, 5.3], [1.0, 0.1], 0.5, 1.0], [True, [-0.8, 1.5, 3.7, 5.5]]], [[[-2.6, 2.9, -0.8, 3.7], [-3.5, 0.9, 1.8, 7.7], [0.4, -1.0], 0.5, 2.0], [False, [-3.5, 0.9, 1.8, 7.7]]]], [[[[4.9, 4.1, 7.8, 6.9], [4.8, 3.4, 8.5, 6.6], [-0.1, 0.5], 0.1, 4.0], [True, [4.4, 4.0, 7.9, 9.0]]], [[[1.4, 3.8, 4.1, 6.8], [0.3, 2.1, 4.4, 7.5], [-0.1, 0.5], 0.2, 1.0], [False, [0.3, 2.1, 4.4, 7.5]]], [[[0.8, -0.3, 1.7, 1.2], [-0.3, -2.3, 2.1, 3.2], [0.1, -1.0], 0.5, 1.0], [False, [-0.3, -2.3, 2.1, 3.2]]], [[[-0.1, -0.3, 1.1, 1.0], [-0.8, -0.3, 1.1, 1.4], [0.1, -0.2], 0.1, 4.0], [False, [-0.8, -0.3, 1.1, 1.4]]], [[[1.0, -3.0, 1.6, -2.8], [0.0, -4.0, 2.6, -1.8], [0.1, 0.2], 0.1, 1.0], [True, [0.9, -3.1, 1.8, -2.5]]], [[[3.5, 4.1, 4.2, 5.4], [3.4, 3.4, 4.9, 5.0], [-0.1, 0.5], 0.1, 1.0], [True, [3.3, 4.0, 4.3, 6.0]]], [[[2.6, 1.8, 5.1, 3.0], [1.0, 2.6, 4.9, 4.4], [0.4, -1.0], 0.2, 1.0], [True, [2.4, 0.6, 5.7, 3.2]]], [[[4.2, 2.6, 6.0, 4.8], [4.7, 2.7, 7.2, 5.2], [-0.6, -0.2], 0.1, 4.0], [True, [1.7, 1.7, 6.1, 4.9]]]], [[[[-0.8, 2.6, 0.4, 4.2], [-1.4, 2.3, 1.0, 4.8], [0, 0], 0.1, 1.0], [False, [-1.4, 2.3, 1.0, 4.8]]], [[[0.9, 1.6, 3.2, 3.0], [-2.5, 1.3, 3.3, 4.2], [0.4, -0.2], 0.5, 2.0], [False, [-2.5, 1.3, 3.3, 4.2]]], [[[1.5, -4.8, 2.9, -2.8], [1.0, -4.0, 2.6, -1.6], [0.4, -1.0], 0.1, 4.0], [True, [1.4, -8.9, 4.6, -2.7]]], [[[-0.9, 0.5, 1.8, 2.4], [-1.9, -0.1, 1.5, 3.0], [0.4, 0], 0.1, 2.0], [True, [-1.0, 0.4, 2.7, 2.5]]], [[[-2.2, -4.2, -1.7, -3.8], [-2.8, -4.8, -1.1, -3.2], [0.1, 0.2], 0.1, 1.0], [True, [-2.3, -4.3, -1.5, -3.5]]], [[[2.4, 1.1, 3.8, 3.7], [2.4, 1.9, 4.1, 4.8], [-0.1, -1.0], 0.1, 1.0], [True, [2.2, 0.0, 3.9, 3.8]]], [[[-4.2, -4.4, -1.9, -2.9], [-4.9, -4.6, -1.9, -2.8], [0.1, 0.1], 0.1, 1.0], [False, [-4.9, -4.6, -1.9, -2.8]]], [[[-4.2, 0.1, -2.1, 2.4], [-3.7, -0.2, -0.9, 2.9], [-0.6, 0.1], 0.1, 1.0], [True, [-4.9, 0.0, -2.0, 2.6]]]], [[[[5.9, -0.6, 8.3, 0.4], [4.7, -1.2, 7.4, -0.0], [1.0, 0.5], 0.1, 1.0], [True, [5.8, -0.7, 9.4, 1.0]]], [[[-3.9, -0.3, -3.4, 1.0], [-4.9, -1.3, -2.4, 2.0], [-0.1, 0], 0.2, 1.0], [True, [-4.2, -0.5, -3.2, 1.2]]], [[[-2.4, 2.5, -1.2, 3.0], [-2.5, 1.8, -1.0, 2.7], [-0.1, 0.5], 0.1, 1.0], [True, [-2.6, 2.4, -1.1, 3.6]]], [[[-0.8, -3.1, 0.9, -1.9], [-4.8, -6.2, 2.9, -1.5], [1.0, 0.1], 0.5, 4.0], [False, [-4.8, -6.2, 2.9, -1.5]]], [[[-2.8, -2.5, -0.4, -1.1], [-3.9, -2.6, -1.3, -1.0], [1.0, 0], 0.1, 2.0], [True, [-2.9, -2.6, 1.7, -1.0]]], [[[3.9, -3.1, 4.8, -1.7], [2.9, -4.1, 5.8, -0.7], [0, 0.2], 0.2, 1.0], [False, [2.9, -4.1, 5.8, -0.7]]], [[[2.8, -3.8, 4.5, -3.3], [2.5, -4.7, 4.8, -3.0], [-0.1, 0], 0.1, 1.0], [False, [2.5, -4.7, 4.8, -3.0]]], [[[-4.3, 0.5, -3.8, 1.7], [-4.4, 0.1, -3.3, 1.9], [-0.1, 0], 0.2, 1.0], [False, [-4.4, 0.1, -3.3, 1.9]]]], [[[[-0.9, -1.1, 0.9, 0.0], [-1.2, -1.4, 1.2, 0.3], [-0.1, 0.2], 0.2, 1.0], [False, [-1.2, -1.4, 1.2, 0.3]]], [[[4.1, -3.3, 6.8, -0.9], [3.2, -4.3, 6.9, -0.4], [0.4, 0.5], 0.5, 1.0], [False, [3.2, -4.3, 6.9, -0.4]]], [[[1.3, 2.0, 3.9, 4.1], [1.1, 1.7, 4.3, 4.2], [0, 0.1], 0.2, 1.0], [False, [1.1, 1.7, 4.3, 4.2]]], [[[-3.1, 3.5, -2.4, 4.0], [-3.7, 1.7, -1.8, 4.6], [0, 0], 0.1, 1.0], [True, [-3.2, 3.4, -2.3, 4.1]]], [[[1.5, 2.3, 3.1, 4.3], [1.2, 3.1, 3.2, 5.4], [0.1, -1.0], 0.1, 1.0], [True, [1.4, 1.2, 3.3, 4.4]]], [[[-0.3, -4.5, 1.1, -3.4], [-4.3, -16.5, 5.1, 0.6], [0, 0.2], 0.1, 1.0], [True, [-0.4, -4.6, 1.2, -3.1]]], [[[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]]], [[[0.3, -3.8, 1.7, -3.3], [-1.7, -9.8, 3.7, -1.3], [0, 0], 0.2, 1.0], [True, [0.1, -4.0, 1.9, -3.1]]]]]
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	`[True, [-3.4, -0.9, -2.3, 1.0]]`	`[True, [-3.5, -1.0, -2.3, 1.0]]`	Failed
case 1	`[False, [0.6, 0.9, 6.0, 6.2]]`	`[False, [0.6, 0.9, 6.0, 6.2]]`	Passed
case 2	`[True, [2.8, 1.5, 4.7, 2.5]]`	`[True, [2.6, 1.3, 4.7, 2.5]]`	Failed
case 3	`[True, [-3.2, 2.1, -1.6, 4.8]]`	`[True, [-3.3, 2.0, -1.6, 4.8]]`	Failed
case 4	`[False, [-4.7, -5.2, -1.5, -1.5]]`	`[False, [-4.7, -5.2, -1.5, -1.5]]`	Passed
case 5	`[True, [1.8, 0.0, 3.7, 2.2]]`	`[True, [1.7, -0.1, 3.7, 2.2]]`	Failed
case 6	`[True, [-0.3, 2.0, 3.7, 5.5]]`	`[True, [-0.8, 1.5, 3.7, 5.5]]`	Failed
case 7	`[False, [-3.5, 0.9, 1.8, 7.7]]`	`[False, [-3.5, 0.9, 1.8, 7.7]]`	Passed

SHA-256 / 7c96c7dfa4d837b123f8fa3245710d5de2ca1cf1c537e4293b867038ade6c469

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 / 2, tight[1] - margin / 2, 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 = [[[[[-3.4, -0.9, -2.5, 0.7], [-7.4, -12.9, 1.5, 4.7], [0.1, 0.2], 0.1, 1.0], [True, [-3.5, -1.0, -2.3, 1.0]]], [[[1.7, 2.9, 3.1, 4.2], [0.6, 0.9, 6.0, 6.2], [0.1, -1.0], 0.5, 4.0], [False, [0.6, 0.9, 6.0, 6.2]]], [[[2.8, 1.5, 4.5, 2.1], [1.8, -1.5, 5.5, 3.1], [0, 0.2], 0.2, 1.0], [True, [2.6, 1.3, 4.7, 2.5]]], [[[-3.1, 3.1, -1.7, 4.7], [-3.2, 4.0, -1.5, 5.8], [-0.1, -1.0], 0.1, 1.0], [True, [-3.3, 2.0, -1.6, 4.8]]], [[[-2.5, -4.5, -1.7, -2.2], [-4.7, -5.2, -1.5, -1.5], [1.0, 0.5], 0.2, 1.0], [False, [-4.7, -5.2, -1.5, -1.5]]], [[[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]]], [[[-0.3, 2.0, 2.2, 4.9], [-1.8, 0.9, 1.7, 5.3], [1.0, 0.1], 0.5, 1.0], [True, [-0.8, 1.5, 3.7, 5.5]]], [[[-2.6, 2.9, -0.8, 3.7], [-3.5, 0.9, 1.8, 7.7], [0.4, -1.0], 0.5, 2.0], [False, [-3.5, 0.9, 1.8, 7.7]]]], [[[[4.9, 4.1, 7.8, 6.9], [4.8, 3.4, 8.5, 6.6], [-0.1, 0.5], 0.1, 4.0], [True, [4.4, 4.0, 7.9, 9.0]]], [[[1.4, 3.8, 4.1, 6.8], [0.3, 2.1, 4.4, 7.5], [-0.1, 0.5], 0.2, 1.0], [False, [0.3, 2.1, 4.4, 7.5]]], [[[0.8, -0.3, 1.7, 1.2], [-0.3, -2.3, 2.1, 3.2], [0.1, -1.0], 0.5, 1.0], [False, [-0.3, -2.3, 2.1, 3.2]]], [[[-0.1, -0.3, 1.1, 1.0], [-0.8, -0.3, 1.1, 1.4], [0.1, -0.2], 0.1, 4.0], [False, [-0.8, -0.3, 1.1, 1.4]]], [[[1.0, -3.0, 1.6, -2.8], [0.0, -4.0, 2.6, -1.8], [0.1, 0.2], 0.1, 1.0], [True, [0.9, -3.1, 1.8, -2.5]]], [[[3.5, 4.1, 4.2, 5.4], [3.4, 3.4, 4.9, 5.0], [-0.1, 0.5], 0.1, 1.0], [True, [3.3, 4.0, 4.3, 6.0]]], [[[2.6, 1.8, 5.1, 3.0], [1.0, 2.6, 4.9, 4.4], [0.4, -1.0], 0.2, 1.0], [True, [2.4, 0.6, 5.7, 3.2]]], [[[4.2, 2.6, 6.0, 4.8], [4.7, 2.7, 7.2, 5.2], [-0.6, -0.2], 0.1, 4.0], [True, [1.7, 1.7, 6.1, 4.9]]]], [[[[-0.8, 2.6, 0.4, 4.2], [-1.4, 2.3, 1.0, 4.8], [0, 0], 0.1, 1.0], [False, [-1.4, 2.3, 1.0, 4.8]]], [[[0.9, 1.6, 3.2, 3.0], [-2.5, 1.3, 3.3, 4.2], [0.4, -0.2], 0.5, 2.0], [False, [-2.5, 1.3, 3.3, 4.2]]], [[[1.5, -4.8, 2.9, -2.8], [1.0, -4.0, 2.6, -1.6], [0.4, -1.0], 0.1, 4.0], [True, [1.4, -8.9, 4.6, -2.7]]], [[[-0.9, 0.5, 1.8, 2.4], [-1.9, -0.1, 1.5, 3.0], [0.4, 0], 0.1, 2.0], [True, [-1.0, 0.4, 2.7, 2.5]]], [[[-2.2, -4.2, -1.7, -3.8], [-2.8, -4.8, -1.1, -3.2], [0.1, 0.2], 0.1, 1.0], [True, [-2.3, -4.3, -1.5, -3.5]]], [[[2.4, 1.1, 3.8, 3.7], [2.4, 1.9, 4.1, 4.8], [-0.1, -1.0], 0.1, 1.0], [True, [2.2, 0.0, 3.9, 3.8]]], [[[-4.2, -4.4, -1.9, -2.9], [-4.9, -4.6, -1.9, -2.8], [0.1, 0.1], 0.1, 1.0], [False, [-4.9, -4.6, -1.9, -2.8]]], [[[-4.2, 0.1, -2.1, 2.4], [-3.7, -0.2, -0.9, 2.9], [-0.6, 0.1], 0.1, 1.0], [True, [-4.9, 0.0, -2.0, 2.6]]]], [[[[5.9, -0.6, 8.3, 0.4], [4.7, -1.2, 7.4, -0.0], [1.0, 0.5], 0.1, 1.0], [True, [5.8, -0.7, 9.4, 1.0]]], [[[-3.9, -0.3, -3.4, 1.0], [-4.9, -1.3, -2.4, 2.0], [-0.1, 0], 0.2, 1.0], [True, [-4.2, -0.5, -3.2, 1.2]]], [[[-2.4, 2.5, -1.2, 3.0], [-2.5, 1.8, -1.0, 2.7], [-0.1, 0.5], 0.1, 1.0], [True, [-2.6, 2.4, -1.1, 3.6]]], [[[-0.8, -3.1, 0.9, -1.9], [-4.8, -6.2, 2.9, -1.5], [1.0, 0.1], 0.5, 4.0], [False, [-4.8, -6.2, 2.9, -1.5]]], [[[-2.8, -2.5, -0.4, -1.1], [-3.9, -2.6, -1.3, -1.0], [1.0, 0], 0.1, 2.0], [True, [-2.9, -2.6, 1.7, -1.0]]], [[[3.9, -3.1, 4.8, -1.7], [2.9, -4.1, 5.8, -0.7], [0, 0.2], 0.2, 1.0], [False, [2.9, -4.1, 5.8, -0.7]]], [[[2.8, -3.8, 4.5, -3.3], [2.5, -4.7, 4.8, -3.0], [-0.1, 0], 0.1, 1.0], [False, [2.5, -4.7, 4.8, -3.0]]], [[[-4.3, 0.5, -3.8, 1.7], [-4.4, 0.1, -3.3, 1.9], [-0.1, 0], 0.2, 1.0], [False, [-4.4, 0.1, -3.3, 1.9]]]], [[[[-0.9, -1.1, 0.9, 0.0], [-1.2, -1.4, 1.2, 0.3], [-0.1, 0.2], 0.2, 1.0], [False, [-1.2, -1.4, 1.2, 0.3]]], [[[4.1, -3.3, 6.8, -0.9], [3.2, -4.3, 6.9, -0.4], [0.4, 0.5], 0.5, 1.0], [False, [3.2, -4.3, 6.9, -0.4]]], [[[1.3, 2.0, 3.9, 4.1], [1.1, 1.7, 4.3, 4.2], [0, 0.1], 0.2, 1.0], [False, [1.1, 1.7, 4.3, 4.2]]], [[[-3.1, 3.5, -2.4, 4.0], [-3.7, 1.7, -1.8, 4.6], [0, 0], 0.1, 1.0], [True, [-3.2, 3.4, -2.3, 4.1]]], [[[1.5, 2.3, 3.1, 4.3], [1.2, 3.1, 3.2, 5.4], [0.1, -1.0], 0.1, 1.0], [True, [1.4, 1.2, 3.3, 4.4]]], [[[-0.3, -4.5, 1.1, -3.4], [-4.3, -16.5, 5.1, 0.6], [0, 0.2], 0.1, 1.0], [True, [-0.4, -4.6, 1.2, -3.1]]], [[[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]]], [[[0.3, -3.8, 1.7, -3.3], [-1.7, -9.8, 3.7, -1.3], [0, 0], 0.2, 1.0], [True, [0.1, -4.0, 1.9, -3.1]]]]]
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	`[True, [-3.45, -0.95, -2.3, 1.0]]`	`[True, [-3.5, -1.0, -2.3, 1.0]]`	Failed
case 1	`[False, [0.6, 0.9, 6.0, 6.2]]`	`[False, [0.6, 0.9, 6.0, 6.2]]`	Passed
case 2	`[True, [2.7, 1.4, 4.7, 2.5]]`	`[True, [2.6, 1.3, 4.7, 2.5]]`	Failed
case 3	`[True, [-3.25, 2.05, -1.6, 4.8]]`	`[True, [-3.3, 2.0, -1.6, 4.8]]`	Failed
case 4	`[False, [-4.7, -5.2, -1.5, -1.5]]`	`[False, [-4.7, -5.2, -1.5, -1.5]]`	Passed
case 5	`[True, [1.75, -0.05, 3.7, 2.2]]`	`[True, [1.7, -0.1, 3.7, 2.2]]`	Failed
case 6	`[True, [-0.55, 1.75, 3.7, 5.5]]`	`[True, [-0.8, 1.5, 3.7, 5.5]]`	Failed
case 7	`[False, [-3.5, 0.9, 1.8, 7.7]]`	`[False, [-3.5, 0.9, 1.8, 7.7]]`	Passed

SHA-256 / 9943178acc8dfa27007d4b72f05576abbac252a3b911463fd7b8136018a11cec

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 = [[[[[-3.4, -0.9, -2.5, 0.7], [-7.4, -12.9, 1.5, 4.7], [0.1, 0.2], 0.1, 1.0], [True, [-3.5, -1.0, -2.3, 1.0]]], [[[1.7, 2.9, 3.1, 4.2], [0.6, 0.9, 6.0, 6.2], [0.1, -1.0], 0.5, 4.0], [False, [0.6, 0.9, 6.0, 6.2]]], [[[2.8, 1.5, 4.5, 2.1], [1.8, -1.5, 5.5, 3.1], [0, 0.2], 0.2, 1.0], [True, [2.6, 1.3, 4.7, 2.5]]], [[[-3.1, 3.1, -1.7, 4.7], [-3.2, 4.0, -1.5, 5.8], [-0.1, -1.0], 0.1, 1.0], [True, [-3.3, 2.0, -1.6, 4.8]]], [[[-2.5, -4.5, -1.7, -2.2], [-4.7, -5.2, -1.5, -1.5], [1.0, 0.5], 0.2, 1.0], [False, [-4.7, -5.2, -1.5, -1.5]]], [[[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]]], [[[-0.3, 2.0, 2.2, 4.9], [-1.8, 0.9, 1.7, 5.3], [1.0, 0.1], 0.5, 1.0], [True, [-0.8, 1.5, 3.7, 5.5]]], [[[-2.6, 2.9, -0.8, 3.7], [-3.5, 0.9, 1.8, 7.7], [0.4, -1.0], 0.5, 2.0], [False, [-3.5, 0.9, 1.8, 7.7]]]], [[[[4.9, 4.1, 7.8, 6.9], [4.8, 3.4, 8.5, 6.6], [-0.1, 0.5], 0.1, 4.0], [True, [4.4, 4.0, 7.9, 9.0]]], [[[1.4, 3.8, 4.1, 6.8], [0.3, 2.1, 4.4, 7.5], [-0.1, 0.5], 0.2, 1.0], [False, [0.3, 2.1, 4.4, 7.5]]], [[[0.8, -0.3, 1.7, 1.2], [-0.3, -2.3, 2.1, 3.2], [0.1, -1.0], 0.5, 1.0], [False, [-0.3, -2.3, 2.1, 3.2]]], [[[-0.1, -0.3, 1.1, 1.0], [-0.8, -0.3, 1.1, 1.4], [0.1, -0.2], 0.1, 4.0], [False, [-0.8, -0.3, 1.1, 1.4]]], [[[1.0, -3.0, 1.6, -2.8], [0.0, -4.0, 2.6, -1.8], [0.1, 0.2], 0.1, 1.0], [True, [0.9, -3.1, 1.8, -2.5]]], [[[3.5, 4.1, 4.2, 5.4], [3.4, 3.4, 4.9, 5.0], [-0.1, 0.5], 0.1, 1.0], [True, [3.3, 4.0, 4.3, 6.0]]], [[[2.6, 1.8, 5.1, 3.0], [1.0, 2.6, 4.9, 4.4], [0.4, -1.0], 0.2, 1.0], [True, [2.4, 0.6, 5.7, 3.2]]], [[[4.2, 2.6, 6.0, 4.8], [4.7, 2.7, 7.2, 5.2], [-0.6, -0.2], 0.1, 4.0], [True, [1.7, 1.7, 6.1, 4.9]]]], [[[[-0.8, 2.6, 0.4, 4.2], [-1.4, 2.3, 1.0, 4.8], [0, 0], 0.1, 1.0], [False, [-1.4, 2.3, 1.0, 4.8]]], [[[0.9, 1.6, 3.2, 3.0], [-2.5, 1.3, 3.3, 4.2], [0.4, -0.2], 0.5, 2.0], [False, [-2.5, 1.3, 3.3, 4.2]]], [[[1.5, -4.8, 2.9, -2.8], [1.0, -4.0, 2.6, -1.6], [0.4, -1.0], 0.1, 4.0], [True, [1.4, -8.9, 4.6, -2.7]]], [[[-0.9, 0.5, 1.8, 2.4], [-1.9, -0.1, 1.5, 3.0], [0.4, 0], 0.1, 2.0], [True, [-1.0, 0.4, 2.7, 2.5]]], [[[-2.2, -4.2, -1.7, -3.8], [-2.8, -4.8, -1.1, -3.2], [0.1, 0.2], 0.1, 1.0], [True, [-2.3, -4.3, -1.5, -3.5]]], [[[2.4, 1.1, 3.8, 3.7], [2.4, 1.9, 4.1, 4.8], [-0.1, -1.0], 0.1, 1.0], [True, [2.2, 0.0, 3.9, 3.8]]], [[[-4.2, -4.4, -1.9, -2.9], [-4.9, -4.6, -1.9, -2.8], [0.1, 0.1], 0.1, 1.0], [False, [-4.9, -4.6, -1.9, -2.8]]], [[[-4.2, 0.1, -2.1, 2.4], [-3.7, -0.2, -0.9, 2.9], [-0.6, 0.1], 0.1, 1.0], [True, [-4.9, 0.0, -2.0, 2.6]]]], [[[[5.9, -0.6, 8.3, 0.4], [4.7, -1.2, 7.4, -0.0], [1.0, 0.5], 0.1, 1.0], [True, [5.8, -0.7, 9.4, 1.0]]], [[[-3.9, -0.3, -3.4, 1.0], [-4.9, -1.3, -2.4, 2.0], [-0.1, 0], 0.2, 1.0], [True, [-4.2, -0.5, -3.2, 1.2]]], [[[-2.4, 2.5, -1.2, 3.0], [-2.5, 1.8, -1.0, 2.7], [-0.1, 0.5], 0.1, 1.0], [True, [-2.6, 2.4, -1.1, 3.6]]], [[[-0.8, -3.1, 0.9, -1.9], [-4.8, -6.2, 2.9, -1.5], [1.0, 0.1], 0.5, 4.0], [False, [-4.8, -6.2, 2.9, -1.5]]], [[[-2.8, -2.5, -0.4, -1.1], [-3.9, -2.6, -1.3, -1.0], [1.0, 0], 0.1, 2.0], [True, [-2.9, -2.6, 1.7, -1.0]]], [[[3.9, -3.1, 4.8, -1.7], [2.9, -4.1, 5.8, -0.7], [0, 0.2], 0.2, 1.0], [False, [2.9, -4.1, 5.8, -0.7]]], [[[2.8, -3.8, 4.5, -3.3], [2.5, -4.7, 4.8, -3.0], [-0.1, 0], 0.1, 1.0], [False, [2.5, -4.7, 4.8, -3.0]]], [[[-4.3, 0.5, -3.8, 1.7], [-4.4, 0.1, -3.3, 1.9], [-0.1, 0], 0.2, 1.0], [False, [-4.4, 0.1, -3.3, 1.9]]]], [[[[-0.9, -1.1, 0.9, 0.0], [-1.2, -1.4, 1.2, 0.3], [-0.1, 0.2], 0.2, 1.0], [False, [-1.2, -1.4, 1.2, 0.3]]], [[[4.1, -3.3, 6.8, -0.9], [3.2, -4.3, 6.9, -0.4], [0.4, 0.5], 0.5, 1.0], [False, [3.2, -4.3, 6.9, -0.4]]], [[[1.3, 2.0, 3.9, 4.1], [1.1, 1.7, 4.3, 4.2], [0, 0.1], 0.2, 1.0], [False, [1.1, 1.7, 4.3, 4.2]]], [[[-3.1, 3.5, -2.4, 4.0], [-3.7, 1.7, -1.8, 4.6], [0, 0], 0.1, 1.0], [True, [-3.2, 3.4, -2.3, 4.1]]], [[[1.5, 2.3, 3.1, 4.3], [1.2, 3.1, 3.2, 5.4], [0.1, -1.0], 0.1, 1.0], [True, [1.4, 1.2, 3.3, 4.4]]], [[[-0.3, -4.5, 1.1, -3.4], [-4.3, -16.5, 5.1, 0.6], [0, 0.2], 0.1, 1.0], [True, [-0.4, -4.6, 1.2, -3.1]]], [[[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]]], [[[0.3, -3.8, 1.7, -3.3], [-1.7, -9.8, 3.7, -1.3], [0, 0], 0.2, 1.0], [True, [0.1, -4.0, 1.9, -3.1]]]]]
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	`[True, [-3.5, -1.0, -2.3, 1.0]]`	`[True, [-3.5, -1.0, -2.3, 1.0]]`	Passed
case 1	`[False, [0.6, 0.9, 6.0, 6.2]]`	`[False, [0.6, 0.9, 6.0, 6.2]]`	Passed
case 2	`[True, [2.6, 1.3, 4.7, 2.5]]`	`[True, [2.6, 1.3, 4.7, 2.5]]`	Passed
case 3	`[True, [-3.3, 2.0, -1.6, 4.8]]`	`[True, [-3.3, 2.0, -1.6, 4.8]]`	Passed
case 4	`[False, [-4.7, -5.2, -1.5, -1.5]]`	`[False, [-4.7, -5.2, -1.5, -1.5]]`	Passed
case 5	`[True, [1.7, -0.1, 3.7, 2.2]]`	`[True, [1.7, -0.1, 3.7, 2.2]]`	Passed
case 6	`[True, [-0.8, 1.5, 3.7, 5.5]]`	`[True, [-0.8, 1.5, 3.7, 5.5]]`	Passed
case 7	`[False, [-3.5, 0.9, 1.8, 7.7]]`	`[False, [-3.5, 0.9, 1.8, 7.7]]`	Passed

SHA-256 / f76f7d5289517d9f5de4a682df6d653b1cd5488b57ffb6cb4aea8c76bc144dd8

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 2026-09-29T14:50:58.512237+00:00.

Case digest / 24f50f96eeea50fd564f60f5410b5f464d553bcb971eeec60a0eb4ab2cefff86