FA-87421 / Collision detection broadphase / Open access

Vertical motion extension tests the x displacement sign · case 01

Bodies moving diagonally extend the wrong vertical side.

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

ROOT CAUSE

The y branch condition checks dx < 0.

VERIFIED REPAIR

Pick the y side from the sign of dy.

Unsuccessful approach: Using dy > 0 inverts the vertical choice.

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]
        if dx < 0:
            f[0] += dx
        else:
            f[2] += dx
        if dx < 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 = [[[[[0.3, -1.3, 1.2, 0.9], [-3.7, -1.9, 1.2, 1.8], [1.0, 0.1], 0.5, 4.0], [False, [-3.7, -1.9, 1.2, 1.8]]], [[[-1.6, -0.6, 0.2, 0.2], [-2.2, -2.4, 0.8, 0.8], [-0.1, 0.2], 0.1, 1.0], [False, [-2.2, -2.4, 0.8, 0.8]]], [[[-0.2, 2.0, 0.5, 3.9], [0.2, 2.0, 1.7, 4.7], [-0.6, -0.2], 0.1, 4.0], [True, [-2.7, 1.1, 0.6, 4.0]]], [[[-0.6, -0.2, 2.3, 1.7], [-0.2, -0.2, 3.1, 2.5], [-0.6, -0.2], 0.1, 1.0], [True, [-1.3, -0.5, 2.4, 1.8]]], [[[4.9, -4.6, 7.8, -3.4], [2.7, -4.0, 8.0, -1.2], [1.0, -1.0], 0.2, 2.0], [True, [4.7, -6.8, 10.0, -3.2]]], [[[-3.6, -3.3, -3.1, -2.6], [-5.6, -5.3, -1.1, -0.6], [-0.1, 0.2], 0.1, 1.0], [True, [-3.8, -3.4, -3.0, -2.3]]], [[[-3.5, -2.0, -2.1, -0.4], [-7.5, -4.0, -0.1, 3.6], [1.0, -1.0], 0.5, 1.0], [True, [-4.0, -3.5, -0.6, 0.1]]], [[[1.9, -0.7, 3.3, -0.1], [-2.1, -12.7, 7.3, 3.9], [-0.1, 0], 0.1, 1.0], [True, [1.7, -0.8, 3.4, 0.0]]]], [[[[-1.9, -3.8, 0.9, -2.8], [-3.1, -4.5, 0.1, -2.7], [1.0, 0.5], 0.1, 4.0], [True, [-2.0, -3.9, 5.0, -0.7]]], [[[3.2, 0.7, 5.9, 2.8], [2.7, 0.5, 7.0, 3.2], [0.1, 0], 0.2, 4.0], [False, [2.7, 0.5, 7.0, 3.2]]], [[[-5.3, -4.0, -2.3, -3.0], [-5.9, -4.4, -1.5, -2.8], [-0.6, 0], 0.2, 1.0], [False, [-5.9, -4.4, -1.5, -2.8]]], [[[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]]], [[[-1.7, -1.8, 0.6, 0.4], [-1.7, -2.1, 0.9, 0.9], [-0.1, 0.1], 0.1, 2.0], [False, [-1.7, -2.1, 0.9, 0.9]]], [[[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]]], [[[0.5, -1.7, 1.7, -0.3], [0.3, -1.6, 2.2, 0.1], [0.1, -0.2], 0.1, 4.0], [True, [0.4, -2.6, 2.2, -0.2]]], [[[4.7, -1.4, 7.7, -0.5], [4.2, -2.1, 7.9, -0.8], [-0.1, 0.5], 0.1, 1.0], [True, [4.5, -1.5, 7.8, 0.1]]]], [[[[3.0, -0.8, 3.5, 0.7], [2.7, -1.1, 3.8, 1.0], [0.1, 0.2], 0.1, 1.0], [False, [2.7, -1.1, 3.8, 1.0]]], [[[-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]]], [[[-0.5, -4.7, 0.5, -2.8], [-1.6, -5.1, 0.1, -2.0], [1.0, -0.2], 0.1, 4.0], [True, [-0.6, -5.6, 4.6, -2.7]]], [[[-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]]], [[[0.5, -1.4, 3.5, 1.5], [0.4, -1.3, 3.7, 1.9], [-0.1, -0.2], 0.1, 2.0], [True, [0.2, -1.9, 3.6, 1.6]]], [[[-0.2, -4.9, 2.2, -3.1], [-1.1, -4.4, 2.3, -1.6], [0.4, -1.0], 0.5, 2.0], [True, [-0.7, -7.4, 3.5, -2.6]]], [[[-1.4, 3.0, -0.7, 3.7], [-1.4, 2.6, 0.5, 4.1], [-0.6, -0.2], 0.1, 4.0], [False, [-1.4, 2.6, 0.5, 4.1]]], [[[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]]]], [[[[-2.3, 3.3, 0.3, 5.0], [-2.9, 2.1, 1.1, 5.2], [-0.6, 0], 0.2, 1.0], [False, [-2.9, 2.1, 1.1, 5.2]]], [[[1.5, 5.0, 2.0, 6.9], [1.2, 4.1, 2.3, 7.2], [-0.1, 0.2], 0.1, 1.0], [False, [1.2, 4.1, 2.3, 7.2]]], [[[-3.2, 1.8, -0.6, 2.8], [-4.2, -1.0, -0.1, 6.0], [0, -0.2], 0.5, 4.0], [False, [-4.2, -1.0, -0.1, 6.0]]], [[[0.4, -3.3, 1.5, -0.5], [-0.2, -3.3, 2.3, -0.1], [-0.6, -0.2], 0.2, 4.0], [False, [-0.2, -3.3, 2.3, -0.1]]], [[[3.2, -4.6, 3.8, -3.6], [2.6, -4.6, 6.7, 0.4], [0.1, -1.0], 0.5, 1.0], [True, [2.7, -6.1, 4.4, -3.1]]], [[[-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]]], [[[0.3, 3.1, 0.6, 3.7], [-3.7, -8.9, 4.6, 7.7], [0.1, 0.2], 0.1, 1.0], [True, [0.2, 3.0, 0.8, 4.0]]], [[[-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]]]], [[[[-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]]], [[[2.1, 0.4, 3.6, 0.9], [1.5, -0.2, 4.2, 1.5], [0, 0.2], 0.1, 1.0], [False, [1.5, -0.2, 4.2, 1.5]]], [[[-0.7, 1.5, 0.8, 2.2], [-0.3, 2.3, 1.6, 3.6], [-0.6, -1.0], 0.2, 1.0], [True, [-1.5, 0.3, 1.0, 2.4]]], [[[5.4, -0.5, 6.0, 0.4], [4.8, 0.4, 6.2, 1.5], [0.4, -1.0], 0.1, 4.0], [True, [5.3, -4.6, 7.7, 0.5]]], [[[1.8, 2.4, 3.1, 4.2], [1.6, 1.7, 3.6, 4.3], [0.1, 0.1], 0.1, 2.0], [False, [1.6, 1.7, 3.6, 4.3]]], [[[4.4, 0.1, 6.7, 1.9], [4.2, -0.3, 7.9, 3.1], [0, 0], 0.2, 4.0], [False, [4.2, -0.3, 7.9, 3.1]]], [[[3.6, -5.7, 6.1, -4.5], [2.0, -4.9, 6.9, -3.3], [0.4, -1.0], 0.2, 2.0], [True, [3.4, -7.9, 7.1, -4.3]]], [[[2.8, -4.2, 4.8, -3.0], [-1.2, -16.2, 8.8, 1.0], [0.1, 0], 0.2, 1.0], [True, [2.6, -4.4, 5.1, -2.8]]]]]
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	`[False, [-3.7, -1.9, 1.2, 1.8]]`	`[False, [-3.7, -1.9, 1.2, 1.8]]`	Passed
case 1	`[True, [-1.8, -0.5, 0.3, 0.3]]`	`[False, [-2.2, -2.4, 0.8, 0.8]]`	Failed
case 2	`[True, [-2.7, 1.1, 0.6, 4.0]]`	`[True, [-2.7, 1.1, 0.6, 4.0]]`	Passed
case 3	`[True, [-1.3, -0.5, 2.4, 1.8]]`	`[True, [-1.3, -0.5, 2.4, 1.8]]`	Passed
case 4	`[True, [4.7, -4.8, 10.0, -5.2]]`	`[True, [4.7, -6.8, 10.0, -3.2]]`	Failed
case 5	`[True, [-3.8, -3.2, -3.0, -2.5]]`	`[True, [-3.8, -3.4, -3.0, -2.3]]`	Failed
case 6	`[True, [-4.0, -2.5, -0.6, -0.9]]`	`[True, [-4.0, -3.5, -0.6, 0.1]]`	Failed
case 7	`[True, [1.7, -0.8, 3.4, 0.0]]`	`[True, [1.7, -0.8, 3.4, 0.0]]`	Passed

SHA-256 / 7ea613bfd9a5173adc6baec08a9582d1db11eea0e190b593ca10caca13c26402

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 = [[[[[0.3, -1.3, 1.2, 0.9], [-3.7, -1.9, 1.2, 1.8], [1.0, 0.1], 0.5, 4.0], [False, [-3.7, -1.9, 1.2, 1.8]]], [[[-1.6, -0.6, 0.2, 0.2], [-2.2, -2.4, 0.8, 0.8], [-0.1, 0.2], 0.1, 1.0], [False, [-2.2, -2.4, 0.8, 0.8]]], [[[-0.2, 2.0, 0.5, 3.9], [0.2, 2.0, 1.7, 4.7], [-0.6, -0.2], 0.1, 4.0], [True, [-2.7, 1.1, 0.6, 4.0]]], [[[-0.6, -0.2, 2.3, 1.7], [-0.2, -0.2, 3.1, 2.5], [-0.6, -0.2], 0.1, 1.0], [True, [-1.3, -0.5, 2.4, 1.8]]], [[[4.9, -4.6, 7.8, -3.4], [2.7, -4.0, 8.0, -1.2], [1.0, -1.0], 0.2, 2.0], [True, [4.7, -6.8, 10.0, -3.2]]], [[[-3.6, -3.3, -3.1, -2.6], [-5.6, -5.3, -1.1, -0.6], [-0.1, 0.2], 0.1, 1.0], [True, [-3.8, -3.4, -3.0, -2.3]]], [[[-3.5, -2.0, -2.1, -0.4], [-7.5, -4.0, -0.1, 3.6], [1.0, -1.0], 0.5, 1.0], [True, [-4.0, -3.5, -0.6, 0.1]]], [[[1.9, -0.7, 3.3, -0.1], [-2.1, -12.7, 7.3, 3.9], [-0.1, 0], 0.1, 1.0], [True, [1.7, -0.8, 3.4, 0.0]]]], [[[[-1.9, -3.8, 0.9, -2.8], [-3.1, -4.5, 0.1, -2.7], [1.0, 0.5], 0.1, 4.0], [True, [-2.0, -3.9, 5.0, -0.7]]], [[[3.2, 0.7, 5.9, 2.8], [2.7, 0.5, 7.0, 3.2], [0.1, 0], 0.2, 4.0], [False, [2.7, 0.5, 7.0, 3.2]]], [[[-5.3, -4.0, -2.3, -3.0], [-5.9, -4.4, -1.5, -2.8], [-0.6, 0], 0.2, 1.0], [False, [-5.9, -4.4, -1.5, -2.8]]], [[[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]]], [[[-1.7, -1.8, 0.6, 0.4], [-1.7, -2.1, 0.9, 0.9], [-0.1, 0.1], 0.1, 2.0], [False, [-1.7, -2.1, 0.9, 0.9]]], [[[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]]], [[[0.5, -1.7, 1.7, -0.3], [0.3, -1.6, 2.2, 0.1], [0.1, -0.2], 0.1, 4.0], [True, [0.4, -2.6, 2.2, -0.2]]], [[[4.7, -1.4, 7.7, -0.5], [4.2, -2.1, 7.9, -0.8], [-0.1, 0.5], 0.1, 1.0], [True, [4.5, -1.5, 7.8, 0.1]]]], [[[[3.0, -0.8, 3.5, 0.7], [2.7, -1.1, 3.8, 1.0], [0.1, 0.2], 0.1, 1.0], [False, [2.7, -1.1, 3.8, 1.0]]], [[[-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]]], [[[-0.5, -4.7, 0.5, -2.8], [-1.6, -5.1, 0.1, -2.0], [1.0, -0.2], 0.1, 4.0], [True, [-0.6, -5.6, 4.6, -2.7]]], [[[-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]]], [[[0.5, -1.4, 3.5, 1.5], [0.4, -1.3, 3.7, 1.9], [-0.1, -0.2], 0.1, 2.0], [True, [0.2, -1.9, 3.6, 1.6]]], [[[-0.2, -4.9, 2.2, -3.1], [-1.1, -4.4, 2.3, -1.6], [0.4, -1.0], 0.5, 2.0], [True, [-0.7, -7.4, 3.5, -2.6]]], [[[-1.4, 3.0, -0.7, 3.7], [-1.4, 2.6, 0.5, 4.1], [-0.6, -0.2], 0.1, 4.0], [False, [-1.4, 2.6, 0.5, 4.1]]], [[[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]]]], [[[[-2.3, 3.3, 0.3, 5.0], [-2.9, 2.1, 1.1, 5.2], [-0.6, 0], 0.2, 1.0], [False, [-2.9, 2.1, 1.1, 5.2]]], [[[1.5, 5.0, 2.0, 6.9], [1.2, 4.1, 2.3, 7.2], [-0.1, 0.2], 0.1, 1.0], [False, [1.2, 4.1, 2.3, 7.2]]], [[[-3.2, 1.8, -0.6, 2.8], [-4.2, -1.0, -0.1, 6.0], [0, -0.2], 0.5, 4.0], [False, [-4.2, -1.0, -0.1, 6.0]]], [[[0.4, -3.3, 1.5, -0.5], [-0.2, -3.3, 2.3, -0.1], [-0.6, -0.2], 0.2, 4.0], [False, [-0.2, -3.3, 2.3, -0.1]]], [[[3.2, -4.6, 3.8, -3.6], [2.6, -4.6, 6.7, 0.4], [0.1, -1.0], 0.5, 1.0], [True, [2.7, -6.1, 4.4, -3.1]]], [[[-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]]], [[[0.3, 3.1, 0.6, 3.7], [-3.7, -8.9, 4.6, 7.7], [0.1, 0.2], 0.1, 1.0], [True, [0.2, 3.0, 0.8, 4.0]]], [[[-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]]]], [[[[-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]]], [[[2.1, 0.4, 3.6, 0.9], [1.5, -0.2, 4.2, 1.5], [0, 0.2], 0.1, 1.0], [False, [1.5, -0.2, 4.2, 1.5]]], [[[-0.7, 1.5, 0.8, 2.2], [-0.3, 2.3, 1.6, 3.6], [-0.6, -1.0], 0.2, 1.0], [True, [-1.5, 0.3, 1.0, 2.4]]], [[[5.4, -0.5, 6.0, 0.4], [4.8, 0.4, 6.2, 1.5], [0.4, -1.0], 0.1, 4.0], [True, [5.3, -4.6, 7.7, 0.5]]], [[[1.8, 2.4, 3.1, 4.2], [1.6, 1.7, 3.6, 4.3], [0.1, 0.1], 0.1, 2.0], [False, [1.6, 1.7, 3.6, 4.3]]], [[[4.4, 0.1, 6.7, 1.9], [4.2, -0.3, 7.9, 3.1], [0, 0], 0.2, 4.0], [False, [4.2, -0.3, 7.9, 3.1]]], [[[3.6, -5.7, 6.1, -4.5], [2.0, -4.9, 6.9, -3.3], [0.4, -1.0], 0.2, 2.0], [True, [3.4, -7.9, 7.1, -4.3]]], [[[2.8, -4.2, 4.8, -3.0], [-1.2, -16.2, 8.8, 1.0], [0.1, 0], 0.2, 1.0], [True, [2.6, -4.4, 5.1, -2.8]]]]]
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	`[False, [-3.7, -1.9, 1.2, 1.8]]`	`[False, [-3.7, -1.9, 1.2, 1.8]]`	Passed
case 1	`[True, [-1.8, -0.5, 0.3, 0.3]]`	`[False, [-2.2, -2.4, 0.8, 0.8]]`	Failed
case 2	`[True, [-2.7, 1.9, 0.6, 3.2]]`	`[True, [-2.7, 1.1, 0.6, 4.0]]`	Failed
case 3	`[True, [-1.3, -0.3, 2.4, 1.6]]`	`[True, [-1.3, -0.5, 2.4, 1.8]]`	Failed
case 4	`[True, [4.7, -4.8, 10.0, -5.2]]`	`[True, [4.7, -6.8, 10.0, -3.2]]`	Failed
case 5	`[True, [-3.8, -3.2, -3.0, -2.5]]`	`[True, [-3.8, -3.4, -3.0, -2.3]]`	Failed
case 6	`[True, [-4.0, -2.5, -0.6, -0.9]]`	`[True, [-4.0, -3.5, -0.6, 0.1]]`	Failed
case 7	`[True, [1.7, -0.8, 3.4, 0.0]]`	`[True, [1.7, -0.8, 3.4, 0.0]]`	Passed

SHA-256 / b809f291ebe53c10149350e76a176c375e1c86eb58774d5e6db10379fb05e42e

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 = [[[[[0.3, -1.3, 1.2, 0.9], [-3.7, -1.9, 1.2, 1.8], [1.0, 0.1], 0.5, 4.0], [False, [-3.7, -1.9, 1.2, 1.8]]], [[[-1.6, -0.6, 0.2, 0.2], [-2.2, -2.4, 0.8, 0.8], [-0.1, 0.2], 0.1, 1.0], [False, [-2.2, -2.4, 0.8, 0.8]]], [[[-0.2, 2.0, 0.5, 3.9], [0.2, 2.0, 1.7, 4.7], [-0.6, -0.2], 0.1, 4.0], [True, [-2.7, 1.1, 0.6, 4.0]]], [[[-0.6, -0.2, 2.3, 1.7], [-0.2, -0.2, 3.1, 2.5], [-0.6, -0.2], 0.1, 1.0], [True, [-1.3, -0.5, 2.4, 1.8]]], [[[4.9, -4.6, 7.8, -3.4], [2.7, -4.0, 8.0, -1.2], [1.0, -1.0], 0.2, 2.0], [True, [4.7, -6.8, 10.0, -3.2]]], [[[-3.6, -3.3, -3.1, -2.6], [-5.6, -5.3, -1.1, -0.6], [-0.1, 0.2], 0.1, 1.0], [True, [-3.8, -3.4, -3.0, -2.3]]], [[[-3.5, -2.0, -2.1, -0.4], [-7.5, -4.0, -0.1, 3.6], [1.0, -1.0], 0.5, 1.0], [True, [-4.0, -3.5, -0.6, 0.1]]], [[[1.9, -0.7, 3.3, -0.1], [-2.1, -12.7, 7.3, 3.9], [-0.1, 0], 0.1, 1.0], [True, [1.7, -0.8, 3.4, 0.0]]]], [[[[-1.9, -3.8, 0.9, -2.8], [-3.1, -4.5, 0.1, -2.7], [1.0, 0.5], 0.1, 4.0], [True, [-2.0, -3.9, 5.0, -0.7]]], [[[3.2, 0.7, 5.9, 2.8], [2.7, 0.5, 7.0, 3.2], [0.1, 0], 0.2, 4.0], [False, [2.7, 0.5, 7.0, 3.2]]], [[[-5.3, -4.0, -2.3, -3.0], [-5.9, -4.4, -1.5, -2.8], [-0.6, 0], 0.2, 1.0], [False, [-5.9, -4.4, -1.5, -2.8]]], [[[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]]], [[[-1.7, -1.8, 0.6, 0.4], [-1.7, -2.1, 0.9, 0.9], [-0.1, 0.1], 0.1, 2.0], [False, [-1.7, -2.1, 0.9, 0.9]]], [[[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]]], [[[0.5, -1.7, 1.7, -0.3], [0.3, -1.6, 2.2, 0.1], [0.1, -0.2], 0.1, 4.0], [True, [0.4, -2.6, 2.2, -0.2]]], [[[4.7, -1.4, 7.7, -0.5], [4.2, -2.1, 7.9, -0.8], [-0.1, 0.5], 0.1, 1.0], [True, [4.5, -1.5, 7.8, 0.1]]]], [[[[3.0, -0.8, 3.5, 0.7], [2.7, -1.1, 3.8, 1.0], [0.1, 0.2], 0.1, 1.0], [False, [2.7, -1.1, 3.8, 1.0]]], [[[-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]]], [[[-0.5, -4.7, 0.5, -2.8], [-1.6, -5.1, 0.1, -2.0], [1.0, -0.2], 0.1, 4.0], [True, [-0.6, -5.6, 4.6, -2.7]]], [[[-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]]], [[[0.5, -1.4, 3.5, 1.5], [0.4, -1.3, 3.7, 1.9], [-0.1, -0.2], 0.1, 2.0], [True, [0.2, -1.9, 3.6, 1.6]]], [[[-0.2, -4.9, 2.2, -3.1], [-1.1, -4.4, 2.3, -1.6], [0.4, -1.0], 0.5, 2.0], [True, [-0.7, -7.4, 3.5, -2.6]]], [[[-1.4, 3.0, -0.7, 3.7], [-1.4, 2.6, 0.5, 4.1], [-0.6, -0.2], 0.1, 4.0], [False, [-1.4, 2.6, 0.5, 4.1]]], [[[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]]]], [[[[-2.3, 3.3, 0.3, 5.0], [-2.9, 2.1, 1.1, 5.2], [-0.6, 0], 0.2, 1.0], [False, [-2.9, 2.1, 1.1, 5.2]]], [[[1.5, 5.0, 2.0, 6.9], [1.2, 4.1, 2.3, 7.2], [-0.1, 0.2], 0.1, 1.0], [False, [1.2, 4.1, 2.3, 7.2]]], [[[-3.2, 1.8, -0.6, 2.8], [-4.2, -1.0, -0.1, 6.0], [0, -0.2], 0.5, 4.0], [False, [-4.2, -1.0, -0.1, 6.0]]], [[[0.4, -3.3, 1.5, -0.5], [-0.2, -3.3, 2.3, -0.1], [-0.6, -0.2], 0.2, 4.0], [False, [-0.2, -3.3, 2.3, -0.1]]], [[[3.2, -4.6, 3.8, -3.6], [2.6, -4.6, 6.7, 0.4], [0.1, -1.0], 0.5, 1.0], [True, [2.7, -6.1, 4.4, -3.1]]], [[[-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]]], [[[0.3, 3.1, 0.6, 3.7], [-3.7, -8.9, 4.6, 7.7], [0.1, 0.2], 0.1, 1.0], [True, [0.2, 3.0, 0.8, 4.0]]], [[[-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]]]], [[[[-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]]], [[[2.1, 0.4, 3.6, 0.9], [1.5, -0.2, 4.2, 1.5], [0, 0.2], 0.1, 1.0], [False, [1.5, -0.2, 4.2, 1.5]]], [[[-0.7, 1.5, 0.8, 2.2], [-0.3, 2.3, 1.6, 3.6], [-0.6, -1.0], 0.2, 1.0], [True, [-1.5, 0.3, 1.0, 2.4]]], [[[5.4, -0.5, 6.0, 0.4], [4.8, 0.4, 6.2, 1.5], [0.4, -1.0], 0.1, 4.0], [True, [5.3, -4.6, 7.7, 0.5]]], [[[1.8, 2.4, 3.1, 4.2], [1.6, 1.7, 3.6, 4.3], [0.1, 0.1], 0.1, 2.0], [False, [1.6, 1.7, 3.6, 4.3]]], [[[4.4, 0.1, 6.7, 1.9], [4.2, -0.3, 7.9, 3.1], [0, 0], 0.2, 4.0], [False, [4.2, -0.3, 7.9, 3.1]]], [[[3.6, -5.7, 6.1, -4.5], [2.0, -4.9, 6.9, -3.3], [0.4, -1.0], 0.2, 2.0], [True, [3.4, -7.9, 7.1, -4.3]]], [[[2.8, -4.2, 4.8, -3.0], [-1.2, -16.2, 8.8, 1.0], [0.1, 0], 0.2, 1.0], [True, [2.6, -4.4, 5.1, -2.8]]]]]
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	`[False, [-3.7, -1.9, 1.2, 1.8]]`	`[False, [-3.7, -1.9, 1.2, 1.8]]`	Passed
case 1	`[False, [-2.2, -2.4, 0.8, 0.8]]`	`[False, [-2.2, -2.4, 0.8, 0.8]]`	Passed
case 2	`[True, [-2.7, 1.1, 0.6, 4.0]]`	`[True, [-2.7, 1.1, 0.6, 4.0]]`	Passed
case 3	`[True, [-1.3, -0.5, 2.4, 1.8]]`	`[True, [-1.3, -0.5, 2.4, 1.8]]`	Passed
case 4	`[True, [4.7, -6.8, 10.0, -3.2]]`	`[True, [4.7, -6.8, 10.0, -3.2]]`	Passed
case 5	`[True, [-3.8, -3.4, -3.0, -2.3]]`	`[True, [-3.8, -3.4, -3.0, -2.3]]`	Passed
case 6	`[True, [-4.0, -3.5, -0.6, 0.1]]`	`[True, [-4.0, -3.5, -0.6, 0.1]]`	Passed
case 7	`[True, [1.7, -0.8, 3.4, 0.0]]`	`[True, [1.7, -0.8, 3.4, 0.0]]`	Passed

SHA-256 / c1756376254147fc7d993443b563a3c2848ecc4433df58b22b793d2b561e578c

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 2026-09-29T14:50:58.602775+00:00.

Case digest / 70268215dfd3e8a826605849380840f2a3b4b177b198305e03b467c2eff345e5