FA-87406 / Collision detection broadphase / Open access

Displacement multiplier is applied to x only · case 01

Falling bodies escape their fat boxes while sideways movers are fine.

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

ROOT CAUSE

dy uses the raw displacement.

VERIFIED REPAIR

Scale both displacement components by mult.

Unsuccessful approach: Using |dy| always extends upward even for falling bodies.

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], 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 = [[[[[2.9, 1.2, 3.8, 3.0], [2.3, -0.6, 4.4, 3.6], [0, 0.2], 0.2, 1.0], [False, [2.3, -0.6, 4.4, 3.6]]], [[[-0.2, 3.1, 0.3, 5.0], [-0.2, 3.5, 1.0, 6.2], [-0.1, -1.0], 0.1, 1.0], [True, [-0.4, 2.0, 0.4, 5.1]]], [[[-0.8, -0.6, 0.7, 0.8], [-1.3, -0.2, 0.4, 2.4], [0.4, -1.0], 0.1, 4.0], [True, [-0.9, -4.7, 2.4, 0.9]]], [[[-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]]], [[[-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]]], [[[-2.1, 0.0, 0.0, 0.6], [-3.0, -3.1, 1.1, 1.5], [-0.1, 0.1], 0.5, 1.0], [False, [-3.0, -3.1, 1.1, 1.5]]], [[[5.8, 0.1, 8.4, 1.9], [4.6, 0.1, 7.6, 2.7], [1.0, -0.2], 0.1, 2.0], [True, [5.7, -0.4, 10.5, 2.0]]], [[[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]]]], [[[[-0.5, 3.7, 1.1, 4.6], [-1.3, 2.8, 1.9, 4.5], [0.4, 0.5], 0.2, 2.0], [True, [-0.7, 3.5, 2.1, 5.8]]], [[[4.0, 4.4, 6.7, 6.2], [3.1, 3.4, 6.8, 7.2], [0.4, 0], 0.5, 4.0], [False, [3.1, 3.4, 6.8, 7.2]]], [[[0.7, -1.0, 2.4, 1.6], [-1.3, -4.5, 1.9, 1.6], [1.0, 0.5], 0.5, 2.0], [True, [0.2, -1.5, 4.9, 3.1]]], [[[4.7, 3.5, 7.0, 4.8], [3.6, 4.4, 6.1, 5.9], [1.0, -1.0], 0.1, 4.0], [True, [4.6, -0.6, 11.1, 4.9]]], [[[-0.9, 5.1, 0.5, 6.7], [-0.5, 4.6, 2.3, 7.0], [-0.6, 0.1], 0.2, 1.0], [True, [-1.7, 4.9, 0.7, 7.0]]], [[[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]]], [[[-4.9, -1.4, -3.2, -0.2], [-5.5, -2.0, -2.6, 0.4], [0.1, 0.2], 0.1, 1.0], [False, [-5.5, -2.0, -2.6, 0.4]]], [[[-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]]]], [[[[-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]]], [[[-0.2, -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]]], [[[-2.3, 2.6, -1.4, 5.5], [-2.3, 3.0, -1.1, 6.6], [-0.1, -1.0], 0.1, 2.0], [True, [-2.6, 0.5, -1.3, 5.6]]], [[[1.8, 3.1, 3.1, 4.4], [-0.2, 2.0, 2.6, 5.3], [1.0, 0.1], 0.5, 2.0], [True, [1.3, 2.6, 5.6, 5.1]]], [[[1.7, -4.0, 2.2, -2.8], [0.6, -3.4, 2.5, -1.4], [-0.1, -1.0], 0.2, 2.0], [True, [1.3, -6.2, 2.4, -2.6]]], [[[-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]]], [[[-1.9, -1.2, -1.2, 0.1], [-2.2, -1.5, -0.9, 0.4], [0, 0.2], 0.1, 1.0], [False, [-2.2, -1.5, -0.9, 0.4]]], [[[-1.4, -5.6, -0.3, -2.6], [-1.0, -5.2, 0.9, -1.0], [-0.6, -1.0], 0.1, 4.0], [True, [-3.9, -9.7, -0.2, -2.5]]]], [[[[-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, -3.5, -0.3, -1.7], [-2.0, -3.7, -1.2, -1.6], [1.0, 0.1], 0.1, 4.0], [True, [-1.0, -3.6, 3.8, -1.2]]], [[[3.1, -0.7, 3.8, 1.2], [2.5, 0.1, 4.0, 2.3], [0.4, -1.0], 0.1, 4.0], [True, [3.0, -4.8, 5.5, 1.3]]], [[[3.6, 3.1, 6.4, 5.1], [2.5, 3.1, 5.6, 5.9], [1.0, -0.2], 0.1, 4.0], [True, [3.5, 2.2, 10.5, 5.2]]], [[[1.8, 4.2, 3.2, 4.7], [2.2, 4.0, 4.2, 5.9], [-0.6, 0], 0.2, 1.0], [True, [1.0, 4.0, 3.4, 4.9]]], [[[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]]], [[[3.7, 1.6, 4.9, 2.3], [3.4, 1.45, 5.2, 2.6], [0, 0], 0.1, 1.0], [False, [3.4, 1.45, 5.2, 2.6]]], [[[1.3, -0.6, 2.3, 2.4], [0.7, 0.2, 2.1, 3.8], [0.4, -1.0], 0.2, 1.0], [True, [1.1, -1.8, 2.9, 2.6]]]], [[[[0.9, 1.5, 3.5, 4.2], [-1.3, 0.6, 2.9, 4.9], [1.0, 0.5], 0.2, 1.0], [True, [0.7, 1.3, 4.7, 4.9]]], [[[2.3, -3.0, 3.5, -2.7], [2.0, -3.3, 3.8, -2.4], [0.1, 0.2], 0.2, 1.0], [False, [2.0, -3.3, 3.8, -2.4]]], [[[-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]]], [[[2.1, -0.9, 3.5, 1.2], [2.6, -1.1, 4.7, 1.7], [-0.6, 0.1], 0.1, 4.0], [True, [-0.4, -1.0, 3.6, 1.7]]], [[[1.7, -1.4, 3.5, 0.7], [-1.2, -0.9, 4.1, 2.2], [-0.1, -1.0], 0.5, 4.0], [True, [0.8, -5.9, 4.0, 1.2]]], [[[-0.9, -0.3, 0.4, 2.2], [-1.5, -1.3, 1.3, 4.7], [0.1, 0.5], 0.5, 1.0], [False, [-1.5, -1.3, 1.3, 4.7]]], [[[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]]], [[[0.3, -2.3, 2.4, -1.5], [-1.1, -3.6, 1.6, -1.2], [1.0, 0.1], 0.2, 4.0], [True, [0.1, -2.5, 6.6, -0.9]]]]]
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, [2.3, -0.6, 4.4, 3.6]]`	`[False, [2.3, -0.6, 4.4, 3.6]]`	Passed
case 1	`[True, [-0.4, 2.0, 0.4, 5.1]]`	`[True, [-0.4, 2.0, 0.4, 5.1]]`	Passed
case 2	`[True, [-0.9, -1.7, 2.4, 0.9]]`	`[True, [-0.9, -4.7, 2.4, 0.9]]`	Failed
case 3	`[True, [-2.7, 1.7, 0.6, 4.0]]`	`[True, [-2.7, 1.1, 0.6, 4.0]]`	Failed
case 4	`[False, [-1.8, -4.0, -0.3, -0.7]]`	`[False, [-1.8, -4.0, -0.3, -0.7]]`	Passed
case 5	`[False, [-3.0, -3.1, 1.1, 1.5]]`	`[False, [-3.0, -3.1, 1.1, 1.5]]`	Passed
case 6	`[True, [5.7, -0.2, 10.5, 2.0]]`	`[True, [5.7, -0.4, 10.5, 2.0]]`	Failed
case 7	`[True, [4.7, -5.8, 10.0, -3.2]]`	`[True, [4.7, -6.8, 10.0, -3.2]]`	Failed

SHA-256 / ff516d0549cb904f4a336656632f99c922f0fb8b57d679b3ce3348a36f308774

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 * abs(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 = [[[[[2.9, 1.2, 3.8, 3.0], [2.3, -0.6, 4.4, 3.6], [0, 0.2], 0.2, 1.0], [False, [2.3, -0.6, 4.4, 3.6]]], [[[-0.2, 3.1, 0.3, 5.0], [-0.2, 3.5, 1.0, 6.2], [-0.1, -1.0], 0.1, 1.0], [True, [-0.4, 2.0, 0.4, 5.1]]], [[[-0.8, -0.6, 0.7, 0.8], [-1.3, -0.2, 0.4, 2.4], [0.4, -1.0], 0.1, 4.0], [True, [-0.9, -4.7, 2.4, 0.9]]], [[[-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]]], [[[-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]]], [[[-2.1, 0.0, 0.0, 0.6], [-3.0, -3.1, 1.1, 1.5], [-0.1, 0.1], 0.5, 1.0], [False, [-3.0, -3.1, 1.1, 1.5]]], [[[5.8, 0.1, 8.4, 1.9], [4.6, 0.1, 7.6, 2.7], [1.0, -0.2], 0.1, 2.0], [True, [5.7, -0.4, 10.5, 2.0]]], [[[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]]]], [[[[-0.5, 3.7, 1.1, 4.6], [-1.3, 2.8, 1.9, 4.5], [0.4, 0.5], 0.2, 2.0], [True, [-0.7, 3.5, 2.1, 5.8]]], [[[4.0, 4.4, 6.7, 6.2], [3.1, 3.4, 6.8, 7.2], [0.4, 0], 0.5, 4.0], [False, [3.1, 3.4, 6.8, 7.2]]], [[[0.7, -1.0, 2.4, 1.6], [-1.3, -4.5, 1.9, 1.6], [1.0, 0.5], 0.5, 2.0], [True, [0.2, -1.5, 4.9, 3.1]]], [[[4.7, 3.5, 7.0, 4.8], [3.6, 4.4, 6.1, 5.9], [1.0, -1.0], 0.1, 4.0], [True, [4.6, -0.6, 11.1, 4.9]]], [[[-0.9, 5.1, 0.5, 6.7], [-0.5, 4.6, 2.3, 7.0], [-0.6, 0.1], 0.2, 1.0], [True, [-1.7, 4.9, 0.7, 7.0]]], [[[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]]], [[[-4.9, -1.4, -3.2, -0.2], [-5.5, -2.0, -2.6, 0.4], [0.1, 0.2], 0.1, 1.0], [False, [-5.5, -2.0, -2.6, 0.4]]], [[[-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]]]], [[[[-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]]], [[[-0.2, -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]]], [[[-2.3, 2.6, -1.4, 5.5], [-2.3, 3.0, -1.1, 6.6], [-0.1, -1.0], 0.1, 2.0], [True, [-2.6, 0.5, -1.3, 5.6]]], [[[1.8, 3.1, 3.1, 4.4], [-0.2, 2.0, 2.6, 5.3], [1.0, 0.1], 0.5, 2.0], [True, [1.3, 2.6, 5.6, 5.1]]], [[[1.7, -4.0, 2.2, -2.8], [0.6, -3.4, 2.5, -1.4], [-0.1, -1.0], 0.2, 2.0], [True, [1.3, -6.2, 2.4, -2.6]]], [[[-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]]], [[[-1.9, -1.2, -1.2, 0.1], [-2.2, -1.5, -0.9, 0.4], [0, 0.2], 0.1, 1.0], [False, [-2.2, -1.5, -0.9, 0.4]]], [[[-1.4, -5.6, -0.3, -2.6], [-1.0, -5.2, 0.9, -1.0], [-0.6, -1.0], 0.1, 4.0], [True, [-3.9, -9.7, -0.2, -2.5]]]], [[[[-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, -3.5, -0.3, -1.7], [-2.0, -3.7, -1.2, -1.6], [1.0, 0.1], 0.1, 4.0], [True, [-1.0, -3.6, 3.8, -1.2]]], [[[3.1, -0.7, 3.8, 1.2], [2.5, 0.1, 4.0, 2.3], [0.4, -1.0], 0.1, 4.0], [True, [3.0, -4.8, 5.5, 1.3]]], [[[3.6, 3.1, 6.4, 5.1], [2.5, 3.1, 5.6, 5.9], [1.0, -0.2], 0.1, 4.0], [True, [3.5, 2.2, 10.5, 5.2]]], [[[1.8, 4.2, 3.2, 4.7], [2.2, 4.0, 4.2, 5.9], [-0.6, 0], 0.2, 1.0], [True, [1.0, 4.0, 3.4, 4.9]]], [[[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]]], [[[3.7, 1.6, 4.9, 2.3], [3.4, 1.45, 5.2, 2.6], [0, 0], 0.1, 1.0], [False, [3.4, 1.45, 5.2, 2.6]]], [[[1.3, -0.6, 2.3, 2.4], [0.7, 0.2, 2.1, 3.8], [0.4, -1.0], 0.2, 1.0], [True, [1.1, -1.8, 2.9, 2.6]]]], [[[[0.9, 1.5, 3.5, 4.2], [-1.3, 0.6, 2.9, 4.9], [1.0, 0.5], 0.2, 1.0], [True, [0.7, 1.3, 4.7, 4.9]]], [[[2.3, -3.0, 3.5, -2.7], [2.0, -3.3, 3.8, -2.4], [0.1, 0.2], 0.2, 1.0], [False, [2.0, -3.3, 3.8, -2.4]]], [[[-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]]], [[[2.1, -0.9, 3.5, 1.2], [2.6, -1.1, 4.7, 1.7], [-0.6, 0.1], 0.1, 4.0], [True, [-0.4, -1.0, 3.6, 1.7]]], [[[1.7, -1.4, 3.5, 0.7], [-1.2, -0.9, 4.1, 2.2], [-0.1, -1.0], 0.5, 4.0], [True, [0.8, -5.9, 4.0, 1.2]]], [[[-0.9, -0.3, 0.4, 2.2], [-1.5, -1.3, 1.3, 4.7], [0.1, 0.5], 0.5, 1.0], [False, [-1.5, -1.3, 1.3, 4.7]]], [[[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]]], [[[0.3, -2.3, 2.4, -1.5], [-1.1, -3.6, 1.6, -1.2], [1.0, 0.1], 0.2, 4.0], [True, [0.1, -2.5, 6.6, -0.9]]]]]
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, [2.3, -0.6, 4.4, 3.6]]`	`[False, [2.3, -0.6, 4.4, 3.6]]`	Passed
case 1	`[True, [-0.4, 3.0, 0.4, 6.1]]`	`[True, [-0.4, 2.0, 0.4, 5.1]]`	Failed
case 2	`[True, [-0.9, -0.7, 2.4, 4.9]]`	`[True, [-0.9, -4.7, 2.4, 0.9]]`	Failed
case 3	`[True, [-2.7, 1.9, 0.6, 4.8]]`	`[True, [-2.7, 1.1, 0.6, 4.0]]`	Failed
case 4	`[False, [-1.8, -4.0, -0.3, -0.7]]`	`[False, [-1.8, -4.0, -0.3, -0.7]]`	Passed
case 5	`[False, [-3.0, -3.1, 1.1, 1.5]]`	`[False, [-3.0, -3.1, 1.1, 1.5]]`	Passed
case 6	`[True, [5.7, 0.0, 10.5, 2.4]]`	`[True, [5.7, -0.4, 10.5, 2.0]]`	Failed
case 7	`[True, [4.7, -4.8, 10.0, -1.2]]`	`[True, [4.7, -6.8, 10.0, -3.2]]`	Failed

SHA-256 / 423448e8f02c7e0741bc869ad9a5c49427e519c9e09da38f2887078815194acf

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 = [[[[[2.9, 1.2, 3.8, 3.0], [2.3, -0.6, 4.4, 3.6], [0, 0.2], 0.2, 1.0], [False, [2.3, -0.6, 4.4, 3.6]]], [[[-0.2, 3.1, 0.3, 5.0], [-0.2, 3.5, 1.0, 6.2], [-0.1, -1.0], 0.1, 1.0], [True, [-0.4, 2.0, 0.4, 5.1]]], [[[-0.8, -0.6, 0.7, 0.8], [-1.3, -0.2, 0.4, 2.4], [0.4, -1.0], 0.1, 4.0], [True, [-0.9, -4.7, 2.4, 0.9]]], [[[-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]]], [[[-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]]], [[[-2.1, 0.0, 0.0, 0.6], [-3.0, -3.1, 1.1, 1.5], [-0.1, 0.1], 0.5, 1.0], [False, [-3.0, -3.1, 1.1, 1.5]]], [[[5.8, 0.1, 8.4, 1.9], [4.6, 0.1, 7.6, 2.7], [1.0, -0.2], 0.1, 2.0], [True, [5.7, -0.4, 10.5, 2.0]]], [[[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]]]], [[[[-0.5, 3.7, 1.1, 4.6], [-1.3, 2.8, 1.9, 4.5], [0.4, 0.5], 0.2, 2.0], [True, [-0.7, 3.5, 2.1, 5.8]]], [[[4.0, 4.4, 6.7, 6.2], [3.1, 3.4, 6.8, 7.2], [0.4, 0], 0.5, 4.0], [False, [3.1, 3.4, 6.8, 7.2]]], [[[0.7, -1.0, 2.4, 1.6], [-1.3, -4.5, 1.9, 1.6], [1.0, 0.5], 0.5, 2.0], [True, [0.2, -1.5, 4.9, 3.1]]], [[[4.7, 3.5, 7.0, 4.8], [3.6, 4.4, 6.1, 5.9], [1.0, -1.0], 0.1, 4.0], [True, [4.6, -0.6, 11.1, 4.9]]], [[[-0.9, 5.1, 0.5, 6.7], [-0.5, 4.6, 2.3, 7.0], [-0.6, 0.1], 0.2, 1.0], [True, [-1.7, 4.9, 0.7, 7.0]]], [[[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]]], [[[-4.9, -1.4, -3.2, -0.2], [-5.5, -2.0, -2.6, 0.4], [0.1, 0.2], 0.1, 1.0], [False, [-5.5, -2.0, -2.6, 0.4]]], [[[-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]]]], [[[[-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]]], [[[-0.2, -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]]], [[[-2.3, 2.6, -1.4, 5.5], [-2.3, 3.0, -1.1, 6.6], [-0.1, -1.0], 0.1, 2.0], [True, [-2.6, 0.5, -1.3, 5.6]]], [[[1.8, 3.1, 3.1, 4.4], [-0.2, 2.0, 2.6, 5.3], [1.0, 0.1], 0.5, 2.0], [True, [1.3, 2.6, 5.6, 5.1]]], [[[1.7, -4.0, 2.2, -2.8], [0.6, -3.4, 2.5, -1.4], [-0.1, -1.0], 0.2, 2.0], [True, [1.3, -6.2, 2.4, -2.6]]], [[[-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]]], [[[-1.9, -1.2, -1.2, 0.1], [-2.2, -1.5, -0.9, 0.4], [0, 0.2], 0.1, 1.0], [False, [-2.2, -1.5, -0.9, 0.4]]], [[[-1.4, -5.6, -0.3, -2.6], [-1.0, -5.2, 0.9, -1.0], [-0.6, -1.0], 0.1, 4.0], [True, [-3.9, -9.7, -0.2, -2.5]]]], [[[[-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, -3.5, -0.3, -1.7], [-2.0, -3.7, -1.2, -1.6], [1.0, 0.1], 0.1, 4.0], [True, [-1.0, -3.6, 3.8, -1.2]]], [[[3.1, -0.7, 3.8, 1.2], [2.5, 0.1, 4.0, 2.3], [0.4, -1.0], 0.1, 4.0], [True, [3.0, -4.8, 5.5, 1.3]]], [[[3.6, 3.1, 6.4, 5.1], [2.5, 3.1, 5.6, 5.9], [1.0, -0.2], 0.1, 4.0], [True, [3.5, 2.2, 10.5, 5.2]]], [[[1.8, 4.2, 3.2, 4.7], [2.2, 4.0, 4.2, 5.9], [-0.6, 0], 0.2, 1.0], [True, [1.0, 4.0, 3.4, 4.9]]], [[[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]]], [[[3.7, 1.6, 4.9, 2.3], [3.4, 1.45, 5.2, 2.6], [0, 0], 0.1, 1.0], [False, [3.4, 1.45, 5.2, 2.6]]], [[[1.3, -0.6, 2.3, 2.4], [0.7, 0.2, 2.1, 3.8], [0.4, -1.0], 0.2, 1.0], [True, [1.1, -1.8, 2.9, 2.6]]]], [[[[0.9, 1.5, 3.5, 4.2], [-1.3, 0.6, 2.9, 4.9], [1.0, 0.5], 0.2, 1.0], [True, [0.7, 1.3, 4.7, 4.9]]], [[[2.3, -3.0, 3.5, -2.7], [2.0, -3.3, 3.8, -2.4], [0.1, 0.2], 0.2, 1.0], [False, [2.0, -3.3, 3.8, -2.4]]], [[[-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]]], [[[2.1, -0.9, 3.5, 1.2], [2.6, -1.1, 4.7, 1.7], [-0.6, 0.1], 0.1, 4.0], [True, [-0.4, -1.0, 3.6, 1.7]]], [[[1.7, -1.4, 3.5, 0.7], [-1.2, -0.9, 4.1, 2.2], [-0.1, -1.0], 0.5, 4.0], [True, [0.8, -5.9, 4.0, 1.2]]], [[[-0.9, -0.3, 0.4, 2.2], [-1.5, -1.3, 1.3, 4.7], [0.1, 0.5], 0.5, 1.0], [False, [-1.5, -1.3, 1.3, 4.7]]], [[[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]]], [[[0.3, -2.3, 2.4, -1.5], [-1.1, -3.6, 1.6, -1.2], [1.0, 0.1], 0.2, 4.0], [True, [0.1, -2.5, 6.6, -0.9]]]]]
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, [2.3, -0.6, 4.4, 3.6]]`	`[False, [2.3, -0.6, 4.4, 3.6]]`	Passed
case 1	`[True, [-0.4, 2.0, 0.4, 5.1]]`	`[True, [-0.4, 2.0, 0.4, 5.1]]`	Passed
case 2	`[True, [-0.9, -4.7, 2.4, 0.9]]`	`[True, [-0.9, -4.7, 2.4, 0.9]]`	Passed
case 3	`[True, [-2.7, 1.1, 0.6, 4.0]]`	`[True, [-2.7, 1.1, 0.6, 4.0]]`	Passed
case 4	`[False, [-1.8, -4.0, -0.3, -0.7]]`	`[False, [-1.8, -4.0, -0.3, -0.7]]`	Passed
case 5	`[False, [-3.0, -3.1, 1.1, 1.5]]`	`[False, [-3.0, -3.1, 1.1, 1.5]]`	Passed
case 6	`[True, [5.7, -0.4, 10.5, 2.0]]`	`[True, [5.7, -0.4, 10.5, 2.0]]`	Passed
case 7	`[True, [4.7, -6.8, 10.0, -3.2]]`	`[True, [4.7, -6.8, 10.0, -3.2]]`	Passed

SHA-256 / 5bbce8743987d3358bafb262af1258fb9cebd59c059a0b9c18d9a279a400eaeb

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 2026-09-29T14:50:58.512829+00:00.

Case digest / 3f732d971cdd05a7f07c122d02b833d61b1d7c1a00a4d2bfc0b992cb0de8d25f