FA-87641 / Collision detection broadphase / Open access

Home cell is computed from the box centre · case 01

Neighbor search offsets assume the min corner and miss overlaps.

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

ROOT CAUSE

The home cell uses the centre point.

VERIFIED REPAIR

Anchor at the minimum corner.

Unsuccessful approach: Rounding the min corner instead of flooring picks the next cell half the time.

Case contract

solve(objs, base, levels): multi-level grid. Each [id,minx,miny,maxx,maxy] goes to the smallest level l (cell size base*2^l) whose cell size is >= the larger box extent, capped at levels-1; its home cell is floor(min corner / level cell size). Return sorted [[id, level, cx, cy]].

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(objs, base, levels):
    out = []
    for i, a, b, c, d in objs:
        ext = max(c - a, d - b)
        lvl = 0
        size = base
        while size < ext and lvl < levels - 1:
            size *= 2
            lvl += 1
        out.append([i, lvl, math.floor((a + c) / 2 / size), math.floor((b + d) / 2 / size)])
    out.sort()
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[[[[30, -8.0, 10.0, -1.0, 19.0], [14, -4.5, -6.5, -0.5, -1.5], [4, -7.5, 0.0, -0.5, 2.0], [17, 3.5, 9.5, 19.5, 10.5]], 1.0, 5], [[4, 3, -1, 0], [14, 3, -1, -1], [17, 4, 0, 0], [30, 4, -1, 0]]], [[[[13, 8.5, -0.5, 38.5, 4.5], [36, -4.0, 3.0, 3.0, 3.5]], 1.0, 3], [[13, 2, 2, -1], [36, 2, -1, 0]]], [[[[18, -3.0, 1.5, 27.0, 2.0], [25, -3.0, 8.5, 1.0, 10.5], [2, 2.0, 3.5, 2.5, 4.5], [32, 7.0, 2.5, 14.0, 11.5], [16, -8.5, 9.0, 21.5, 14.0]], 1.0, 4], [[2, 0, 2, 3], [16, 3, -2, 1], [18, 3, -1, 0], [25, 2, -1, 2], [32, 3, 0, 0]]], [[[[27, 6.5, -6.0, 7.5, -5.0], [17, -8.5, -9.5, 21.5, -7.5], [15, 10.0, 2.5, 11.0, 11.5], [31, 5.0, -9.0, 5.5, -7.0]], 1.0, 4], [[15, 3, 1, 0], [17, 3, -2, -2], [27, 0, 6, -6], [31, 1, 2, -5]]], [[[[36, 1.0, -10.0, 4.0, -9.5], [9, -7.0, -5.5, -4.0, 3.5], [31, 3.0, -10.0, 5.0, -8.0]], 1.0, 3], [[9, 2, -2, -2], [31, 1, 1, -5], [36, 2, 0, -3]]], [[[[37, 0.5, 7.5, 7.5, 8.0], [8, 0.5, -9.0, 30.5, -5.0], [10, -6.5, 1.5, -3.5, 6.5]], 1.0, 5], [[8, 4, 0, -1], [10, 3, -1, 0], [37, 3, 0, 0]]], [[[[37, 9.0, -9.5, 17.0, -0.5], [1, 7.5, 3.0, 14.5, 7.0], [18, 8.5, 3.0, 12.5, 7.0], [20, -1.0, 10.0, 15.0, 11.0], [3, -3.0, -1.0, -2.5, 0.0]], 2.0, 5], [[1, 2, 0, 0], [3, 0, -2, -1], [18, 1, 2, 0], [20, 3, -1, 0], [37, 3, 0, -1]]], [[[[20, -4.0, -9.0, 3.0, -8.5], [16, -7.0, 1.5, -6.0, 2.0]], 2.0, 5], [[16, 0, -4, 0], [20, 2, -1, -2]]]], [[[[[7, 8.0, 2.5, 16.0, 4.5], [20, 7.5, 5.5, 11.5, 14.5], [25, -4.0, -10.0, 3.0, -9.0], [1, 0.5, -0.5, 4.5, 0.0]], 2.0, 5], [[1, 1, 0, -1], [7, 2, 1, 0], [20, 3, 0, 0], [25, 2, -1, -2]]], [[[[28, -6.5, 5.0, 23.5, 7.0], [2, -1.0, 3.5, 7.0, 4.5], [33, 5.5, 5.5, 9.5, 9.5], [39, 10.0, -8.0, 11.0, -7.0], [36, 8.5, -9.0, 16.5, -8.5], [10, -2.0, -6.5, 28.0, -6.0], [37, 6.5, -7.5, 22.5, -5.5]], 1.0, 2], [[2, 1, -1, 1], [10, 1, -1, -4], [28, 1, -4, 2], [33, 1, 2, 2], [36, 1, 4, -5], [37, 1, 3, -4], [39, 0, 10, -8]]], [[[[4, -4.5, 1.5, -2.5, 6.5], [12, 4.5, 0.0, 8.5, 1.0]], 2.0, 4], [[4, 2, -1, 0], [12, 1, 1, 0]]], [[[[27, -5.0, 1.0, 11.0, 1.5], [25, -9.5, -2.0, -1.5, 2.0], [2, -4.0, -5.0, -2.0, -1.0], [4, -7.5, 5.0, 8.5, 14.0], [28, -2.0, 7.0, 1.0, 11.0], [1, 10.0, 7.0, 17.0, 11.0]], 2.0, 3], [[1, 2, 1, 0], [2, 1, -1, -2], [4, 2, -1, 0], [25, 2, -2, -1], [27, 2, -1, 0], [28, 1, -1, 1]]], [[[[20, 2.5, -4.0, 3.0, 0.0], [1, -3.0, 2.5, 4.0, 6.5], [13, -4.0, -3.5, 4.0, -3.0], [35, -4.0, -1.0, 3.0, 8.0]], 1.0, 3], [[1, 2, -1, 0], [13, 2, -1, -1], [20, 2, 0, -1], [35, 2, -1, -1]]], [[[[16, -10.0, -5.5, -8.0, -5.0], [6, -7.5, -3.5, -7.0, -1.5]], 1.0, 5], [[6, 1, -4, -2], [16, 1, -5, -3]]], [[[[10, -2.5, 7.5, -2.0, 8.5], [25, 10.0, 2.0, 40.0, 6.0], [11, -5.5, 7.5, -1.5, 8.0]], 2.0, 2], [[10, 0, -2, 3], [11, 1, -2, 1], [25, 1, 2, 0]]], [[[[21, -9.0, -1.0, -2.0, 8.0], [20, -7.5, 2.0, -6.5, 2.5], [36, 6.5, -7.5, 14.5, -7.0], [17, 5.0, 2.0, 6.0, 4.0]], 1.0, 3], [[17, 1, 2, 1], [20, 0, -8, 2], [21, 2, -3, -1], [36, 2, 1, -2]]]], [[[[[15, 7.5, -4.5, 11.5, 0.5], [3, -4.5, 6.5, 11.5, 10.5], [8, 8.0, -2.0, 10.0, -1.0], [10, -6.5, -3.0, -2.5, 6.0], [17, -8.5, 9.0, -1.5, 14.0], [34, -6.0, 9.0, -3.0, 18.0], [39, 5.0, -8.5, 9.0, -7.5], [28, 0.5, 0.0, 7.5, 0.5]], 2.0, 3], [[3, 2, -1, 0], [8, 0, 4, -1], [10, 2, -1, -1], [15, 2, 0, -1], [17, 2, -2, 1], [28, 2, 0, 0], [34, 2, -1, 1], [39, 1, 1, -3]]], [[[[34, -9.5, -9.0, -5.5, 0.0], [16, -7.0, -1.5, -6.0, -1.0]], 2.0, 3], [[16, 0, -4, -1], [34, 2, -2, -2]]], [[[[7, -8.0, -9.0, -1.0, -8.5], [10, 3.0, -9.0, 6.0, -5.0], [3, -5.5, -8.0, -2.5, -3.0]], 1.0, 4], [[3, 3, -1, -1], [7, 3, -1, -2], [10, 2, 0, -3]]], [[[[14, -8.5, 1.0, -7.5, 5.0], [8, -2.5, 5.0, -1.5, 9.0], [10, -7.5, 6.0, -6.5, 10.0], [25, -7.5, 0.5, 0.5, 2.5], [38, -8.5, -7.5, -0.5, -5.5], [5, 0.5, -9.0, 30.5, -4.0], [12, -6.5, -8.0, 9.5, -7.0], [4, -6.0, -3.0, -5.0, -1.0]], 1.0, 5], [[4, 1, -3, -2], [5, 4, 0, -1], [8, 2, -1, 1], [10, 2, -2, 1], [12, 4, -1, -1], [14, 2, -3, 0], [25, 3, -1, 0], [38, 3, -2, -1]]], [[[[27, 6.0, 3.0, 8.0, 4.0], [2, -1.0, 3.0, 6.0, 3.5], [19, -0.5, -5.0, 1.5, 0.0], [23, -7.5, -9.0, 0.5, -5.0], [3, 7.0, -6.0, 11.0, -1.0]], 2.0, 3], [[2, 2, -1, 0], [3, 2, 0, -1], [19, 2, -1, -1], [23, 2, -1, -2], [27, 0, 3, 1]]], [[[[5, -3.0, 1.5, 1.0, 5.5], [24, -1.5, -10.0, 6.5, -1.0], [19, 1.0, 7.5, 2.0, 11.5], [17, -4.5, 3.5, -4.0, 5.5], [7, 5.5, 10.0, 21.5, 19.0]], 1.0, 2], [[5, 1, -2, 0], [7, 1, 2, 5], [17, 1, -3, 1], [19, 1, 0, 3], [24, 1, -1, -5]]], [[[[20, -3.5, 1.0, -3.0, 10.0], [11, 0.0, 2.5, 4.0, 4.5]], 1.0, 4], [[11, 2, 0, 0], [20, 3, -1, 0]]], [[[[17, -1.0, -3.5, 3.0, 0.5], [31, -3.0, 2.0, -2.0, 11.0], [27, 8.5, 1.5, 12.5, 10.5], [20, 9.0, 6.0, 25.0, 7.0], [13, -2.0, -6.5, 6.0, -1.5], [19, -1.5, 6.0, 28.5, 6.5], [9, 9.0, 10.0, 39.0, 10.5]], 2.0, 2], [[9, 1, 2, 2], [13, 1, -1, -2], [17, 1, -1, -1], [19, 1, -1, 1], [20, 1, 2, 1], [27, 1, 2, 0], [31, 1, -1, 0]]]], [[[[[16, -9.5, -7.5, -7.5, -7.0], [29, -0.5, -10.0, 0.0, -8.0]], 2.0, 4], [[16, 0, -5, -4], [29, 0, -1, -5]]], [[[[19, -9.5, -0.5, -8.5, 0.0], [25, 6.0, -9.0, 7.0, -8.5]], 2.0, 2], [[19, 0, -5, -1], [25, 0, 3, -5]]], [[[[13, 1.5, 1.5, 17.5, 5.5], [2, 5.0, 10.0, 8.0, 19.0], [33, -3.5, -2.0, 12.5, 7.0], [12, 8.5, -5.0, 10.5, -3.0]], 1.0, 4], [[2, 3, 0, 1], [12, 1, 4, -3], [13, 3, 0, 0], [33, 3, -1, -1]]], [[[[3, 6.0, -5.0, 6.5, 0.0], [22, 6.0, 10.0, 8.0, 15.0], [30, -1.5, 1.0, 6.5, 5.0], [39, -3.5, -1.0, 0.5, -0.5], [1, -10.0, -1.0, -6.0, 8.0], [12, -5.5, -2.0, -2.5, 0.0]], 2.0, 4], [[1, 3, -1, -1], [3, 2, 0, -1], [12, 1, -2, -1], [22, 2, 0, 1], [30, 2, -1, 0], [39, 1, -1, -1]]], [[[[25, 8.0, 8.0, 24.0, 12.0], [29, -1.0, 7.0, 3.0, 7.5], [24, 2.0, 2.0, 4.0, 3.0]], 2.0, 4], [[24, 0, 1, 1], [25, 3, 0, 0], [29, 1, -1, 1]]], [[[[16, -5.0, 1.5, -1.0, 10.5], [34, 6.5, 3.0, 22.5, 3.5], [17, -10.0, -6.5, -6.0, 2.5], [4, -1.0, 6.0, 0.0, 7.0], [24, -7.5, 9.0, -3.5, 10.0], [1, -5.5, -4.5, -3.5, 0.5], [2, 2.5, 5.5, 18.5, 7.5]], 2.0, 4], [[1, 2, -1, -1], [2, 3, 0, 0], [4, 0, -1, 3], [16, 3, -1, 0], [17, 3, -1, -1], [24, 1, -2, 2], [34, 3, 0, 0]]], [[[[23, -6.5, 4.5, -4.5, 9.5], [4, 4.0, 8.5, 12.0, 12.5], [5, -6.0, -3.5, 1.0, 1.5], [7, -4.5, -2.0, 11.5, -1.5], [11, -1.0, 0.5, 1.0, 9.5], [15, -1.5, 3.5, 14.5, 5.5], [17, 8.5, -1.0, 11.5, 4.0]], 1.0, 5], [[4, 3, 0, 1], [5, 3, -1, -1], [7, 4, -1, -1], [11, 4, -1, 0], [15, 4, -1, 0], [17, 3, 1, -1], [23, 3, -1, 0]]], [[[[6, 5.5, -4.5, 7.5, -0.5], [14, -6.0, 6.5, -5.0, 11.5], [34, -0.5, -5.5, 29.5, -0.5], [23, 1.0, 9.0, 8.0, 10.0], [32, 1.0, -6.5, 4.0, -2.5]], 2.0, 2], [[6, 1, 1, -2], [14, 1, -2, 1], [23, 1, 0, 2], [32, 1, 0, -2], [34, 1, -1, -2]]]], [[[[[25, 8.5, 6.0, 10.5, 15.0], [27, -0.5, 1.5, 2.5, 5.5], [12, -7.0, 8.0, -4.0, 12.0], [23, 9.0, -5.0, 13.0, -1.0], [7, 7.0, 2.5, 14.0, 6.5], [8, -5.5, 5.5, 24.5, 6.0], [32, -8.5, -9.5, 21.5, -4.5], [31, -5.0, -8.5, -4.0, -3.5], [10, 8.0, 2.5, 24.0, 3.5]], 2.0, 3], [[7, 2, 0, 0], [8, 2, -1, 0], [10, 2, 1, 0], [12, 1, -2, 2], [23, 1, 2, -2], [25, 2, 1, 0], [27, 1, -1, 0], [31, 2, -1, -2], [32, 2, -2, -2]]], [[[[39, 1.0, -1.5, 9.0, -0.5], [35, 9.5, 8.5, 10.0, 9.0], [37, -6.5, -6.0, -2.5, -5.5], [32, -10.0, -3.5, -9.0, 0.5], [34, 1.5, 1.5, 8.5, 5.5], [21, -4.5, 4.5, -4.0, 5.5], [36, -4.5, -5.0, 25.5, 0.0]], 1.0, 2], [[21, 0, -5, 4], [32, 1, -5, -2], [34, 1, 0, 0], [35, 0, 9, 8], [36, 1, -3, -3], [37, 1, -4, -3], [39, 1, 0, -1]]], [[[[11, 6.0, -6.0, 10.0, -2.0], [24, -1.5, -5.0, -1.0, -4.5], [13, 2.0, 1.5, 10.0, 6.5], [35, -3.0, -10.0, 27.0, -9.5], [25, 8.5, -1.0, 12.5, 3.0]], 1.0, 3], [[11, 2, 1, -2], [13, 2, 0, 0], [24, 0, -2, -5], [25, 2, 2, -1], [35, 2, -1, -3]]], [[[[7, 4.5, 1.5, 11.5, 2.5], [37, 2.0, 3.5, 10.0, 4.5], [2, 4.0, -5.5, 5.0, 3.5], [5, -7.0, 10.0, 0.0, 14.0], [33, 6.0, -6.5, 14.0, 2.5], [30, 0.0, 0.0, 2.0, 9.0], [38, -1.0, -5.5, 1.0, -3.5], [10, -7.5, -9.0, 0.5, -5.0], [28, -0.5, 2.5, 15.5, 4.5]], 1.0, 5], [[2, 4, 0, -1], [5, 3, -1, 1], [7, 3, 0, 0], [10, 3, -1, -2], [28, 4, -1, 0], [30, 4, 0, 0], [33, 4, 0, -1], [37, 3, 0, 0], [38, 1, -1, -3]]], [[[[24, -8.5, 1.5, 21.5, 2.5], [29, 5.0, -8.5, 12.0, -6.5], [39, -6.0, 7.5, -2.0, 12.5]], 1.0, 5], [[24, 4, -1, 0], [29, 3, 0, -2], [39, 3, -1, 0]]], [[[[31, -10.0, 1.5, 6.0, 10.5], [28, 3.5, 3.5, 7.5, 8.5], [13, 6.0, 6.0, 8.0, 10.0], [20, 7.0, 3.5, 8.0, 8.5], [19, 7.5, -3.0, 14.5, 6.0], [8, 9.5, 9.0, 12.5, 11.0], [32, 7.0, 9.5, 9.0, 10.0], [9, -4.5, 3.0, -4.0, 8.0], [14, 9.5, -2.0, 10.0, -1.5], [4, 8.0, -2.5, 11.0, -2.0]], 1.0, 5], [[4, 2, 2, -1], [8, 2, 2, 2], [9, 3, -1, 0], [13, 2, 1, 1], [14, 0, 9, -2], [19, 4, 0, -1], [20, 3, 0, 0], [28, 3, 0, 0], [31, 4, -1, 0], [32, 1, 3, 4]]], [[[[28, -2.0, 0.0, 14.0, 9.0], [34, 4.5, 0.5, 5.5, 4.5], [14, 6.5, -10.0, 9.5, -9.5], [20, -0.5, -6.0, 15.5, 3.0], [31, -9.5, 5.5, -1.5, 6.0], [4, -1.5, 9.0, 5.5, 9.5], [23, -4.5, -5.5, 25.5, -3.5]], 1.0, 4], [[4, 3, -1, 1], [14, 2, 1, -3], [20, 3, -1, -1], [23, 3, -1, -1], [28, 3, -1, 0], [31, 3, -2, 0], [34, 2, 1, 0]]], [[[[24, 10.0, 2.5, 26.0, 11.5], [1, -7.5, -10.0, 0.5, -9.0], [4, 0.0, 6.0, 4.0, 8.0], [17, -0.5, 5.0, 7.5, 14.0], [32, 3.5, -1.5, 19.5, -0.5]], 2.0, 4], [[1, 2, -1, -2], [4, 1, 0, 1], [17, 3, -1, 0], [24, 3, 0, 0], [32, 3, 0, -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	`[[4, 3, -1, 0], [14, 3, -1, -1], [17, 4, 0, 0], [30, 4, -1, 0]]`	`[[4, 3, -1, 0], [14, 3, -1, -1], [17, 4, 0, 0], [30, 4, -1, 0]]`	Passed
case 1	`[[13, 2, 5, 0], [36, 2, -1, 0]]`	`[[13, 2, 2, -1], [36, 2, -1, 0]]`	Failed
case 2	`[[2, 0, 2, 4], [16, 3, 0, 1], [18, 3, 1, 0], [25, 2, -1, 2], [32, 3, 1, 0]]`	`[[2, 0, 2, 3], [16, 3, -2, 1], [18, 3, -1, 0], [25, 2, -1, 2], [32, 3, 0, 0]]`	Failed
case 3	`[[15, 3, 1, 0], [17, 3, 0, -2], [27, 0, 7, -6], [31, 1, 2, -4]]`	`[[15, 3, 1, 0], [17, 3, -2, -2], [27, 0, 6, -6], [31, 1, 2, -5]]`	Failed
case 4	`[[9, 2, -2, -1], [31, 1, 2, -5], [36, 2, 0, -3]]`	`[[9, 2, -2, -2], [31, 1, 1, -5], [36, 2, 0, -3]]`	Failed
case 5	`[[8, 4, 0, -1], [10, 3, -1, 0], [37, 3, 0, 0]]`	`[[8, 4, 0, -1], [10, 3, -1, 0], [37, 3, 0, 0]]`	Passed
case 6	`[[1, 2, 1, 0], [3, 0, -2, -1], [18, 1, 2, 1], [20, 3, 0, 0], [37, 3, 0, -1]]`	`[[1, 2, 0, 0], [3, 0, -2, -1], [18, 1, 2, 0], [20, 3, -1, 0], [37, 3, 0, -1]]`	Failed
case 7	`[[16, 0, -4, 0], [20, 2, -1, -2]]`	`[[16, 0, -4, 0], [20, 2, -1, -2]]`	Passed

SHA-256 / 2552ec3290997ce6d4b9620e1a4fb8dce7b3d25d09ff165c0b1b9de392fc9cfd

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(objs, base, levels):
    out = []
    for i, a, b, c, d in objs:
        ext = max(c - a, d - b)
        lvl = 0
        size = base
        while size < ext and lvl < levels - 1:
            size *= 2
            lvl += 1
        out.append([i, lvl, round(a / size), round(b / size)])
    out.sort()
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[[[[30, -8.0, 10.0, -1.0, 19.0], [14, -4.5, -6.5, -0.5, -1.5], [4, -7.5, 0.0, -0.5, 2.0], [17, 3.5, 9.5, 19.5, 10.5]], 1.0, 5], [[4, 3, -1, 0], [14, 3, -1, -1], [17, 4, 0, 0], [30, 4, -1, 0]]], [[[[13, 8.5, -0.5, 38.5, 4.5], [36, -4.0, 3.0, 3.0, 3.5]], 1.0, 3], [[13, 2, 2, -1], [36, 2, -1, 0]]], [[[[18, -3.0, 1.5, 27.0, 2.0], [25, -3.0, 8.5, 1.0, 10.5], [2, 2.0, 3.5, 2.5, 4.5], [32, 7.0, 2.5, 14.0, 11.5], [16, -8.5, 9.0, 21.5, 14.0]], 1.0, 4], [[2, 0, 2, 3], [16, 3, -2, 1], [18, 3, -1, 0], [25, 2, -1, 2], [32, 3, 0, 0]]], [[[[27, 6.5, -6.0, 7.5, -5.0], [17, -8.5, -9.5, 21.5, -7.5], [15, 10.0, 2.5, 11.0, 11.5], [31, 5.0, -9.0, 5.5, -7.0]], 1.0, 4], [[15, 3, 1, 0], [17, 3, -2, -2], [27, 0, 6, -6], [31, 1, 2, -5]]], [[[[36, 1.0, -10.0, 4.0, -9.5], [9, -7.0, -5.5, -4.0, 3.5], [31, 3.0, -10.0, 5.0, -8.0]], 1.0, 3], [[9, 2, -2, -2], [31, 1, 1, -5], [36, 2, 0, -3]]], [[[[37, 0.5, 7.5, 7.5, 8.0], [8, 0.5, -9.0, 30.5, -5.0], [10, -6.5, 1.5, -3.5, 6.5]], 1.0, 5], [[8, 4, 0, -1], [10, 3, -1, 0], [37, 3, 0, 0]]], [[[[37, 9.0, -9.5, 17.0, -0.5], [1, 7.5, 3.0, 14.5, 7.0], [18, 8.5, 3.0, 12.5, 7.0], [20, -1.0, 10.0, 15.0, 11.0], [3, -3.0, -1.0, -2.5, 0.0]], 2.0, 5], [[1, 2, 0, 0], [3, 0, -2, -1], [18, 1, 2, 0], [20, 3, -1, 0], [37, 3, 0, -1]]], [[[[20, -4.0, -9.0, 3.0, -8.5], [16, -7.0, 1.5, -6.0, 2.0]], 2.0, 5], [[16, 0, -4, 0], [20, 2, -1, -2]]]], [[[[[7, 8.0, 2.5, 16.0, 4.5], [20, 7.5, 5.5, 11.5, 14.5], [25, -4.0, -10.0, 3.0, -9.0], [1, 0.5, -0.5, 4.5, 0.0]], 2.0, 5], [[1, 1, 0, -1], [7, 2, 1, 0], [20, 3, 0, 0], [25, 2, -1, -2]]], [[[[28, -6.5, 5.0, 23.5, 7.0], [2, -1.0, 3.5, 7.0, 4.5], [33, 5.5, 5.5, 9.5, 9.5], [39, 10.0, -8.0, 11.0, -7.0], [36, 8.5, -9.0, 16.5, -8.5], [10, -2.0, -6.5, 28.0, -6.0], [37, 6.5, -7.5, 22.5, -5.5]], 1.0, 2], [[2, 1, -1, 1], [10, 1, -1, -4], [28, 1, -4, 2], [33, 1, 2, 2], [36, 1, 4, -5], [37, 1, 3, -4], [39, 0, 10, -8]]], [[[[4, -4.5, 1.5, -2.5, 6.5], [12, 4.5, 0.0, 8.5, 1.0]], 2.0, 4], [[4, 2, -1, 0], [12, 1, 1, 0]]], [[[[27, -5.0, 1.0, 11.0, 1.5], [25, -9.5, -2.0, -1.5, 2.0], [2, -4.0, -5.0, -2.0, -1.0], [4, -7.5, 5.0, 8.5, 14.0], [28, -2.0, 7.0, 1.0, 11.0], [1, 10.0, 7.0, 17.0, 11.0]], 2.0, 3], [[1, 2, 1, 0], [2, 1, -1, -2], [4, 2, -1, 0], [25, 2, -2, -1], [27, 2, -1, 0], [28, 1, -1, 1]]], [[[[20, 2.5, -4.0, 3.0, 0.0], [1, -3.0, 2.5, 4.0, 6.5], [13, -4.0, -3.5, 4.0, -3.0], [35, -4.0, -1.0, 3.0, 8.0]], 1.0, 3], [[1, 2, -1, 0], [13, 2, -1, -1], [20, 2, 0, -1], [35, 2, -1, -1]]], [[[[16, -10.0, -5.5, -8.0, -5.0], [6, -7.5, -3.5, -7.0, -1.5]], 1.0, 5], [[6, 1, -4, -2], [16, 1, -5, -3]]], [[[[10, -2.5, 7.5, -2.0, 8.5], [25, 10.0, 2.0, 40.0, 6.0], [11, -5.5, 7.5, -1.5, 8.0]], 2.0, 2], [[10, 0, -2, 3], [11, 1, -2, 1], [25, 1, 2, 0]]], [[[[21, -9.0, -1.0, -2.0, 8.0], [20, -7.5, 2.0, -6.5, 2.5], [36, 6.5, -7.5, 14.5, -7.0], [17, 5.0, 2.0, 6.0, 4.0]], 1.0, 3], [[17, 1, 2, 1], [20, 0, -8, 2], [21, 2, -3, -1], [36, 2, 1, -2]]]], [[[[[15, 7.5, -4.5, 11.5, 0.5], [3, -4.5, 6.5, 11.5, 10.5], [8, 8.0, -2.0, 10.0, -1.0], [10, -6.5, -3.0, -2.5, 6.0], [17, -8.5, 9.0, -1.5, 14.0], [34, -6.0, 9.0, -3.0, 18.0], [39, 5.0, -8.5, 9.0, -7.5], [28, 0.5, 0.0, 7.5, 0.5]], 2.0, 3], [[3, 2, -1, 0], [8, 0, 4, -1], [10, 2, -1, -1], [15, 2, 0, -1], [17, 2, -2, 1], [28, 2, 0, 0], [34, 2, -1, 1], [39, 1, 1, -3]]], [[[[34, -9.5, -9.0, -5.5, 0.0], [16, -7.0, -1.5, -6.0, -1.0]], 2.0, 3], [[16, 0, -4, -1], [34, 2, -2, -2]]], [[[[7, -8.0, -9.0, -1.0, -8.5], [10, 3.0, -9.0, 6.0, -5.0], [3, -5.5, -8.0, -2.5, -3.0]], 1.0, 4], [[3, 3, -1, -1], [7, 3, -1, -2], [10, 2, 0, -3]]], [[[[14, -8.5, 1.0, -7.5, 5.0], [8, -2.5, 5.0, -1.5, 9.0], [10, -7.5, 6.0, -6.5, 10.0], [25, -7.5, 0.5, 0.5, 2.5], [38, -8.5, -7.5, -0.5, -5.5], [5, 0.5, -9.0, 30.5, -4.0], [12, -6.5, -8.0, 9.5, -7.0], [4, -6.0, -3.0, -5.0, -1.0]], 1.0, 5], [[4, 1, -3, -2], [5, 4, 0, -1], [8, 2, -1, 1], [10, 2, -2, 1], [12, 4, -1, -1], [14, 2, -3, 0], [25, 3, -1, 0], [38, 3, -2, -1]]], [[[[27, 6.0, 3.0, 8.0, 4.0], [2, -1.0, 3.0, 6.0, 3.5], [19, -0.5, -5.0, 1.5, 0.0], [23, -7.5, -9.0, 0.5, -5.0], [3, 7.0, -6.0, 11.0, -1.0]], 2.0, 3], [[2, 2, -1, 0], [3, 2, 0, -1], [19, 2, -1, -1], [23, 2, -1, -2], [27, 0, 3, 1]]], [[[[5, -3.0, 1.5, 1.0, 5.5], [24, -1.5, -10.0, 6.5, -1.0], [19, 1.0, 7.5, 2.0, 11.5], [17, -4.5, 3.5, -4.0, 5.5], [7, 5.5, 10.0, 21.5, 19.0]], 1.0, 2], [[5, 1, -2, 0], [7, 1, 2, 5], [17, 1, -3, 1], [19, 1, 0, 3], [24, 1, -1, -5]]], [[[[20, -3.5, 1.0, -3.0, 10.0], [11, 0.0, 2.5, 4.0, 4.5]], 1.0, 4], [[11, 2, 0, 0], [20, 3, -1, 0]]], [[[[17, -1.0, -3.5, 3.0, 0.5], [31, -3.0, 2.0, -2.0, 11.0], [27, 8.5, 1.5, 12.5, 10.5], [20, 9.0, 6.0, 25.0, 7.0], [13, -2.0, -6.5, 6.0, -1.5], [19, -1.5, 6.0, 28.5, 6.5], [9, 9.0, 10.0, 39.0, 10.5]], 2.0, 2], [[9, 1, 2, 2], [13, 1, -1, -2], [17, 1, -1, -1], [19, 1, -1, 1], [20, 1, 2, 1], [27, 1, 2, 0], [31, 1, -1, 0]]]], [[[[[16, -9.5, -7.5, -7.5, -7.0], [29, -0.5, -10.0, 0.0, -8.0]], 2.0, 4], [[16, 0, -5, -4], [29, 0, -1, -5]]], [[[[19, -9.5, -0.5, -8.5, 0.0], [25, 6.0, -9.0, 7.0, -8.5]], 2.0, 2], [[19, 0, -5, -1], [25, 0, 3, -5]]], [[[[13, 1.5, 1.5, 17.5, 5.5], [2, 5.0, 10.0, 8.0, 19.0], [33, -3.5, -2.0, 12.5, 7.0], [12, 8.5, -5.0, 10.5, -3.0]], 1.0, 4], [[2, 3, 0, 1], [12, 1, 4, -3], [13, 3, 0, 0], [33, 3, -1, -1]]], [[[[3, 6.0, -5.0, 6.5, 0.0], [22, 6.0, 10.0, 8.0, 15.0], [30, -1.5, 1.0, 6.5, 5.0], [39, -3.5, -1.0, 0.5, -0.5], [1, -10.0, -1.0, -6.0, 8.0], [12, -5.5, -2.0, -2.5, 0.0]], 2.0, 4], [[1, 3, -1, -1], [3, 2, 0, -1], [12, 1, -2, -1], [22, 2, 0, 1], [30, 2, -1, 0], [39, 1, -1, -1]]], [[[[25, 8.0, 8.0, 24.0, 12.0], [29, -1.0, 7.0, 3.0, 7.5], [24, 2.0, 2.0, 4.0, 3.0]], 2.0, 4], [[24, 0, 1, 1], [25, 3, 0, 0], [29, 1, -1, 1]]], [[[[16, -5.0, 1.5, -1.0, 10.5], [34, 6.5, 3.0, 22.5, 3.5], [17, -10.0, -6.5, -6.0, 2.5], [4, -1.0, 6.0, 0.0, 7.0], [24, -7.5, 9.0, -3.5, 10.0], [1, -5.5, -4.5, -3.5, 0.5], [2, 2.5, 5.5, 18.5, 7.5]], 2.0, 4], [[1, 2, -1, -1], [2, 3, 0, 0], [4, 0, -1, 3], [16, 3, -1, 0], [17, 3, -1, -1], [24, 1, -2, 2], [34, 3, 0, 0]]], [[[[23, -6.5, 4.5, -4.5, 9.5], [4, 4.0, 8.5, 12.0, 12.5], [5, -6.0, -3.5, 1.0, 1.5], [7, -4.5, -2.0, 11.5, -1.5], [11, -1.0, 0.5, 1.0, 9.5], [15, -1.5, 3.5, 14.5, 5.5], [17, 8.5, -1.0, 11.5, 4.0]], 1.0, 5], [[4, 3, 0, 1], [5, 3, -1, -1], [7, 4, -1, -1], [11, 4, -1, 0], [15, 4, -1, 0], [17, 3, 1, -1], [23, 3, -1, 0]]], [[[[6, 5.5, -4.5, 7.5, -0.5], [14, -6.0, 6.5, -5.0, 11.5], [34, -0.5, -5.5, 29.5, -0.5], [23, 1.0, 9.0, 8.0, 10.0], [32, 1.0, -6.5, 4.0, -2.5]], 2.0, 2], [[6, 1, 1, -2], [14, 1, -2, 1], [23, 1, 0, 2], [32, 1, 0, -2], [34, 1, -1, -2]]]], [[[[[25, 8.5, 6.0, 10.5, 15.0], [27, -0.5, 1.5, 2.5, 5.5], [12, -7.0, 8.0, -4.0, 12.0], [23, 9.0, -5.0, 13.0, -1.0], [7, 7.0, 2.5, 14.0, 6.5], [8, -5.5, 5.5, 24.5, 6.0], [32, -8.5, -9.5, 21.5, -4.5], [31, -5.0, -8.5, -4.0, -3.5], [10, 8.0, 2.5, 24.0, 3.5]], 2.0, 3], [[7, 2, 0, 0], [8, 2, -1, 0], [10, 2, 1, 0], [12, 1, -2, 2], [23, 1, 2, -2], [25, 2, 1, 0], [27, 1, -1, 0], [31, 2, -1, -2], [32, 2, -2, -2]]], [[[[39, 1.0, -1.5, 9.0, -0.5], [35, 9.5, 8.5, 10.0, 9.0], [37, -6.5, -6.0, -2.5, -5.5], [32, -10.0, -3.5, -9.0, 0.5], [34, 1.5, 1.5, 8.5, 5.5], [21, -4.5, 4.5, -4.0, 5.5], [36, -4.5, -5.0, 25.5, 0.0]], 1.0, 2], [[21, 0, -5, 4], [32, 1, -5, -2], [34, 1, 0, 0], [35, 0, 9, 8], [36, 1, -3, -3], [37, 1, -4, -3], [39, 1, 0, -1]]], [[[[11, 6.0, -6.0, 10.0, -2.0], [24, -1.5, -5.0, -1.0, -4.5], [13, 2.0, 1.5, 10.0, 6.5], [35, -3.0, -10.0, 27.0, -9.5], [25, 8.5, -1.0, 12.5, 3.0]], 1.0, 3], [[11, 2, 1, -2], [13, 2, 0, 0], [24, 0, -2, -5], [25, 2, 2, -1], [35, 2, -1, -3]]], [[[[7, 4.5, 1.5, 11.5, 2.5], [37, 2.0, 3.5, 10.0, 4.5], [2, 4.0, -5.5, 5.0, 3.5], [5, -7.0, 10.0, 0.0, 14.0], [33, 6.0, -6.5, 14.0, 2.5], [30, 0.0, 0.0, 2.0, 9.0], [38, -1.0, -5.5, 1.0, -3.5], [10, -7.5, -9.0, 0.5, -5.0], [28, -0.5, 2.5, 15.5, 4.5]], 1.0, 5], [[2, 4, 0, -1], [5, 3, -1, 1], [7, 3, 0, 0], [10, 3, -1, -2], [28, 4, -1, 0], [30, 4, 0, 0], [33, 4, 0, -1], [37, 3, 0, 0], [38, 1, -1, -3]]], [[[[24, -8.5, 1.5, 21.5, 2.5], [29, 5.0, -8.5, 12.0, -6.5], [39, -6.0, 7.5, -2.0, 12.5]], 1.0, 5], [[24, 4, -1, 0], [29, 3, 0, -2], [39, 3, -1, 0]]], [[[[31, -10.0, 1.5, 6.0, 10.5], [28, 3.5, 3.5, 7.5, 8.5], [13, 6.0, 6.0, 8.0, 10.0], [20, 7.0, 3.5, 8.0, 8.5], [19, 7.5, -3.0, 14.5, 6.0], [8, 9.5, 9.0, 12.5, 11.0], [32, 7.0, 9.5, 9.0, 10.0], [9, -4.5, 3.0, -4.0, 8.0], [14, 9.5, -2.0, 10.0, -1.5], [4, 8.0, -2.5, 11.0, -2.0]], 1.0, 5], [[4, 2, 2, -1], [8, 2, 2, 2], [9, 3, -1, 0], [13, 2, 1, 1], [14, 0, 9, -2], [19, 4, 0, -1], [20, 3, 0, 0], [28, 3, 0, 0], [31, 4, -1, 0], [32, 1, 3, 4]]], [[[[28, -2.0, 0.0, 14.0, 9.0], [34, 4.5, 0.5, 5.5, 4.5], [14, 6.5, -10.0, 9.5, -9.5], [20, -0.5, -6.0, 15.5, 3.0], [31, -9.5, 5.5, -1.5, 6.0], [4, -1.5, 9.0, 5.5, 9.5], [23, -4.5, -5.5, 25.5, -3.5]], 1.0, 4], [[4, 3, -1, 1], [14, 2, 1, -3], [20, 3, -1, -1], [23, 3, -1, -1], [28, 3, -1, 0], [31, 3, -2, 0], [34, 2, 1, 0]]], [[[[24, 10.0, 2.5, 26.0, 11.5], [1, -7.5, -10.0, 0.5, -9.0], [4, 0.0, 6.0, 4.0, 8.0], [17, -0.5, 5.0, 7.5, 14.0], [32, 3.5, -1.5, 19.5, -0.5]], 2.0, 4], [[1, 2, -1, -2], [4, 1, 0, 1], [17, 3, -1, 0], [24, 3, 0, 0], [32, 3, 0, -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	`[[4, 3, -1, 0], [14, 3, -1, -1], [17, 4, 0, 1], [30, 4, 0, 1]]`	`[[4, 3, -1, 0], [14, 3, -1, -1], [17, 4, 0, 0], [30, 4, -1, 0]]`	Failed
case 1	`[[13, 2, 2, 0], [36, 2, -1, 1]]`	`[[13, 2, 2, -1], [36, 2, -1, 0]]`	Failed
case 2	`[[2, 0, 2, 4], [16, 3, -1, 1], [18, 3, 0, 0], [25, 2, -1, 2], [32, 3, 1, 0]]`	`[[2, 0, 2, 3], [16, 3, -2, 1], [18, 3, -1, 0], [25, 2, -1, 2], [32, 3, 0, 0]]`	Failed
case 3	`[[15, 3, 1, 0], [17, 3, -1, -1], [27, 0, 6, -6], [31, 1, 2, -4]]`	`[[15, 3, 1, 0], [17, 3, -2, -2], [27, 0, 6, -6], [31, 1, 2, -5]]`	Failed
case 4	`[[9, 2, -2, -1], [31, 1, 2, -5], [36, 2, 0, -2]]`	`[[9, 2, -2, -2], [31, 1, 1, -5], [36, 2, 0, -3]]`	Failed
case 5	`[[8, 4, 0, -1], [10, 3, -1, 0], [37, 3, 0, 1]]`	`[[8, 4, 0, -1], [10, 3, -1, 0], [37, 3, 0, 0]]`	Failed
case 6	`[[1, 2, 1, 0], [3, 0, -2, 0], [18, 1, 2, 1], [20, 3, 0, 1], [37, 3, 1, -1]]`	`[[1, 2, 0, 0], [3, 0, -2, -1], [18, 1, 2, 0], [20, 3, -1, 0], [37, 3, 0, -1]]`	Failed
case 7	`[[16, 0, -4, 1], [20, 2, 0, -1]]`	`[[16, 0, -4, 0], [20, 2, -1, -2]]`	Failed

SHA-256 / 58d6b27dfcf0ee4d4cd86fee797d186de267cf4c065bcd21fb6d76ef096b2f85

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(objs, base, levels):
    out = []
    for i, a, b, c, d in objs:
        ext = max(c - a, d - b)
        lvl = 0
        size = base
        while size < ext and lvl < levels - 1:
            size *= 2
            lvl += 1
        out.append([i, lvl, math.floor(a / size), math.floor(b / size)])
    out.sort()
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[[[[30, -8.0, 10.0, -1.0, 19.0], [14, -4.5, -6.5, -0.5, -1.5], [4, -7.5, 0.0, -0.5, 2.0], [17, 3.5, 9.5, 19.5, 10.5]], 1.0, 5], [[4, 3, -1, 0], [14, 3, -1, -1], [17, 4, 0, 0], [30, 4, -1, 0]]], [[[[13, 8.5, -0.5, 38.5, 4.5], [36, -4.0, 3.0, 3.0, 3.5]], 1.0, 3], [[13, 2, 2, -1], [36, 2, -1, 0]]], [[[[18, -3.0, 1.5, 27.0, 2.0], [25, -3.0, 8.5, 1.0, 10.5], [2, 2.0, 3.5, 2.5, 4.5], [32, 7.0, 2.5, 14.0, 11.5], [16, -8.5, 9.0, 21.5, 14.0]], 1.0, 4], [[2, 0, 2, 3], [16, 3, -2, 1], [18, 3, -1, 0], [25, 2, -1, 2], [32, 3, 0, 0]]], [[[[27, 6.5, -6.0, 7.5, -5.0], [17, -8.5, -9.5, 21.5, -7.5], [15, 10.0, 2.5, 11.0, 11.5], [31, 5.0, -9.0, 5.5, -7.0]], 1.0, 4], [[15, 3, 1, 0], [17, 3, -2, -2], [27, 0, 6, -6], [31, 1, 2, -5]]], [[[[36, 1.0, -10.0, 4.0, -9.5], [9, -7.0, -5.5, -4.0, 3.5], [31, 3.0, -10.0, 5.0, -8.0]], 1.0, 3], [[9, 2, -2, -2], [31, 1, 1, -5], [36, 2, 0, -3]]], [[[[37, 0.5, 7.5, 7.5, 8.0], [8, 0.5, -9.0, 30.5, -5.0], [10, -6.5, 1.5, -3.5, 6.5]], 1.0, 5], [[8, 4, 0, -1], [10, 3, -1, 0], [37, 3, 0, 0]]], [[[[37, 9.0, -9.5, 17.0, -0.5], [1, 7.5, 3.0, 14.5, 7.0], [18, 8.5, 3.0, 12.5, 7.0], [20, -1.0, 10.0, 15.0, 11.0], [3, -3.0, -1.0, -2.5, 0.0]], 2.0, 5], [[1, 2, 0, 0], [3, 0, -2, -1], [18, 1, 2, 0], [20, 3, -1, 0], [37, 3, 0, -1]]], [[[[20, -4.0, -9.0, 3.0, -8.5], [16, -7.0, 1.5, -6.0, 2.0]], 2.0, 5], [[16, 0, -4, 0], [20, 2, -1, -2]]]], [[[[[7, 8.0, 2.5, 16.0, 4.5], [20, 7.5, 5.5, 11.5, 14.5], [25, -4.0, -10.0, 3.0, -9.0], [1, 0.5, -0.5, 4.5, 0.0]], 2.0, 5], [[1, 1, 0, -1], [7, 2, 1, 0], [20, 3, 0, 0], [25, 2, -1, -2]]], [[[[28, -6.5, 5.0, 23.5, 7.0], [2, -1.0, 3.5, 7.0, 4.5], [33, 5.5, 5.5, 9.5, 9.5], [39, 10.0, -8.0, 11.0, -7.0], [36, 8.5, -9.0, 16.5, -8.5], [10, -2.0, -6.5, 28.0, -6.0], [37, 6.5, -7.5, 22.5, -5.5]], 1.0, 2], [[2, 1, -1, 1], [10, 1, -1, -4], [28, 1, -4, 2], [33, 1, 2, 2], [36, 1, 4, -5], [37, 1, 3, -4], [39, 0, 10, -8]]], [[[[4, -4.5, 1.5, -2.5, 6.5], [12, 4.5, 0.0, 8.5, 1.0]], 2.0, 4], [[4, 2, -1, 0], [12, 1, 1, 0]]], [[[[27, -5.0, 1.0, 11.0, 1.5], [25, -9.5, -2.0, -1.5, 2.0], [2, -4.0, -5.0, -2.0, -1.0], [4, -7.5, 5.0, 8.5, 14.0], [28, -2.0, 7.0, 1.0, 11.0], [1, 10.0, 7.0, 17.0, 11.0]], 2.0, 3], [[1, 2, 1, 0], [2, 1, -1, -2], [4, 2, -1, 0], [25, 2, -2, -1], [27, 2, -1, 0], [28, 1, -1, 1]]], [[[[20, 2.5, -4.0, 3.0, 0.0], [1, -3.0, 2.5, 4.0, 6.5], [13, -4.0, -3.5, 4.0, -3.0], [35, -4.0, -1.0, 3.0, 8.0]], 1.0, 3], [[1, 2, -1, 0], [13, 2, -1, -1], [20, 2, 0, -1], [35, 2, -1, -1]]], [[[[16, -10.0, -5.5, -8.0, -5.0], [6, -7.5, -3.5, -7.0, -1.5]], 1.0, 5], [[6, 1, -4, -2], [16, 1, -5, -3]]], [[[[10, -2.5, 7.5, -2.0, 8.5], [25, 10.0, 2.0, 40.0, 6.0], [11, -5.5, 7.5, -1.5, 8.0]], 2.0, 2], [[10, 0, -2, 3], [11, 1, -2, 1], [25, 1, 2, 0]]], [[[[21, -9.0, -1.0, -2.0, 8.0], [20, -7.5, 2.0, -6.5, 2.5], [36, 6.5, -7.5, 14.5, -7.0], [17, 5.0, 2.0, 6.0, 4.0]], 1.0, 3], [[17, 1, 2, 1], [20, 0, -8, 2], [21, 2, -3, -1], [36, 2, 1, -2]]]], [[[[[15, 7.5, -4.5, 11.5, 0.5], [3, -4.5, 6.5, 11.5, 10.5], [8, 8.0, -2.0, 10.0, -1.0], [10, -6.5, -3.0, -2.5, 6.0], [17, -8.5, 9.0, -1.5, 14.0], [34, -6.0, 9.0, -3.0, 18.0], [39, 5.0, -8.5, 9.0, -7.5], [28, 0.5, 0.0, 7.5, 0.5]], 2.0, 3], [[3, 2, -1, 0], [8, 0, 4, -1], [10, 2, -1, -1], [15, 2, 0, -1], [17, 2, -2, 1], [28, 2, 0, 0], [34, 2, -1, 1], [39, 1, 1, -3]]], [[[[34, -9.5, -9.0, -5.5, 0.0], [16, -7.0, -1.5, -6.0, -1.0]], 2.0, 3], [[16, 0, -4, -1], [34, 2, -2, -2]]], [[[[7, -8.0, -9.0, -1.0, -8.5], [10, 3.0, -9.0, 6.0, -5.0], [3, -5.5, -8.0, -2.5, -3.0]], 1.0, 4], [[3, 3, -1, -1], [7, 3, -1, -2], [10, 2, 0, -3]]], [[[[14, -8.5, 1.0, -7.5, 5.0], [8, -2.5, 5.0, -1.5, 9.0], [10, -7.5, 6.0, -6.5, 10.0], [25, -7.5, 0.5, 0.5, 2.5], [38, -8.5, -7.5, -0.5, -5.5], [5, 0.5, -9.0, 30.5, -4.0], [12, -6.5, -8.0, 9.5, -7.0], [4, -6.0, -3.0, -5.0, -1.0]], 1.0, 5], [[4, 1, -3, -2], [5, 4, 0, -1], [8, 2, -1, 1], [10, 2, -2, 1], [12, 4, -1, -1], [14, 2, -3, 0], [25, 3, -1, 0], [38, 3, -2, -1]]], [[[[27, 6.0, 3.0, 8.0, 4.0], [2, -1.0, 3.0, 6.0, 3.5], [19, -0.5, -5.0, 1.5, 0.0], [23, -7.5, -9.0, 0.5, -5.0], [3, 7.0, -6.0, 11.0, -1.0]], 2.0, 3], [[2, 2, -1, 0], [3, 2, 0, -1], [19, 2, -1, -1], [23, 2, -1, -2], [27, 0, 3, 1]]], [[[[5, -3.0, 1.5, 1.0, 5.5], [24, -1.5, -10.0, 6.5, -1.0], [19, 1.0, 7.5, 2.0, 11.5], [17, -4.5, 3.5, -4.0, 5.5], [7, 5.5, 10.0, 21.5, 19.0]], 1.0, 2], [[5, 1, -2, 0], [7, 1, 2, 5], [17, 1, -3, 1], [19, 1, 0, 3], [24, 1, -1, -5]]], [[[[20, -3.5, 1.0, -3.0, 10.0], [11, 0.0, 2.5, 4.0, 4.5]], 1.0, 4], [[11, 2, 0, 0], [20, 3, -1, 0]]], [[[[17, -1.0, -3.5, 3.0, 0.5], [31, -3.0, 2.0, -2.0, 11.0], [27, 8.5, 1.5, 12.5, 10.5], [20, 9.0, 6.0, 25.0, 7.0], [13, -2.0, -6.5, 6.0, -1.5], [19, -1.5, 6.0, 28.5, 6.5], [9, 9.0, 10.0, 39.0, 10.5]], 2.0, 2], [[9, 1, 2, 2], [13, 1, -1, -2], [17, 1, -1, -1], [19, 1, -1, 1], [20, 1, 2, 1], [27, 1, 2, 0], [31, 1, -1, 0]]]], [[[[[16, -9.5, -7.5, -7.5, -7.0], [29, -0.5, -10.0, 0.0, -8.0]], 2.0, 4], [[16, 0, -5, -4], [29, 0, -1, -5]]], [[[[19, -9.5, -0.5, -8.5, 0.0], [25, 6.0, -9.0, 7.0, -8.5]], 2.0, 2], [[19, 0, -5, -1], [25, 0, 3, -5]]], [[[[13, 1.5, 1.5, 17.5, 5.5], [2, 5.0, 10.0, 8.0, 19.0], [33, -3.5, -2.0, 12.5, 7.0], [12, 8.5, -5.0, 10.5, -3.0]], 1.0, 4], [[2, 3, 0, 1], [12, 1, 4, -3], [13, 3, 0, 0], [33, 3, -1, -1]]], [[[[3, 6.0, -5.0, 6.5, 0.0], [22, 6.0, 10.0, 8.0, 15.0], [30, -1.5, 1.0, 6.5, 5.0], [39, -3.5, -1.0, 0.5, -0.5], [1, -10.0, -1.0, -6.0, 8.0], [12, -5.5, -2.0, -2.5, 0.0]], 2.0, 4], [[1, 3, -1, -1], [3, 2, 0, -1], [12, 1, -2, -1], [22, 2, 0, 1], [30, 2, -1, 0], [39, 1, -1, -1]]], [[[[25, 8.0, 8.0, 24.0, 12.0], [29, -1.0, 7.0, 3.0, 7.5], [24, 2.0, 2.0, 4.0, 3.0]], 2.0, 4], [[24, 0, 1, 1], [25, 3, 0, 0], [29, 1, -1, 1]]], [[[[16, -5.0, 1.5, -1.0, 10.5], [34, 6.5, 3.0, 22.5, 3.5], [17, -10.0, -6.5, -6.0, 2.5], [4, -1.0, 6.0, 0.0, 7.0], [24, -7.5, 9.0, -3.5, 10.0], [1, -5.5, -4.5, -3.5, 0.5], [2, 2.5, 5.5, 18.5, 7.5]], 2.0, 4], [[1, 2, -1, -1], [2, 3, 0, 0], [4, 0, -1, 3], [16, 3, -1, 0], [17, 3, -1, -1], [24, 1, -2, 2], [34, 3, 0, 0]]], [[[[23, -6.5, 4.5, -4.5, 9.5], [4, 4.0, 8.5, 12.0, 12.5], [5, -6.0, -3.5, 1.0, 1.5], [7, -4.5, -2.0, 11.5, -1.5], [11, -1.0, 0.5, 1.0, 9.5], [15, -1.5, 3.5, 14.5, 5.5], [17, 8.5, -1.0, 11.5, 4.0]], 1.0, 5], [[4, 3, 0, 1], [5, 3, -1, -1], [7, 4, -1, -1], [11, 4, -1, 0], [15, 4, -1, 0], [17, 3, 1, -1], [23, 3, -1, 0]]], [[[[6, 5.5, -4.5, 7.5, -0.5], [14, -6.0, 6.5, -5.0, 11.5], [34, -0.5, -5.5, 29.5, -0.5], [23, 1.0, 9.0, 8.0, 10.0], [32, 1.0, -6.5, 4.0, -2.5]], 2.0, 2], [[6, 1, 1, -2], [14, 1, -2, 1], [23, 1, 0, 2], [32, 1, 0, -2], [34, 1, -1, -2]]]], [[[[[25, 8.5, 6.0, 10.5, 15.0], [27, -0.5, 1.5, 2.5, 5.5], [12, -7.0, 8.0, -4.0, 12.0], [23, 9.0, -5.0, 13.0, -1.0], [7, 7.0, 2.5, 14.0, 6.5], [8, -5.5, 5.5, 24.5, 6.0], [32, -8.5, -9.5, 21.5, -4.5], [31, -5.0, -8.5, -4.0, -3.5], [10, 8.0, 2.5, 24.0, 3.5]], 2.0, 3], [[7, 2, 0, 0], [8, 2, -1, 0], [10, 2, 1, 0], [12, 1, -2, 2], [23, 1, 2, -2], [25, 2, 1, 0], [27, 1, -1, 0], [31, 2, -1, -2], [32, 2, -2, -2]]], [[[[39, 1.0, -1.5, 9.0, -0.5], [35, 9.5, 8.5, 10.0, 9.0], [37, -6.5, -6.0, -2.5, -5.5], [32, -10.0, -3.5, -9.0, 0.5], [34, 1.5, 1.5, 8.5, 5.5], [21, -4.5, 4.5, -4.0, 5.5], [36, -4.5, -5.0, 25.5, 0.0]], 1.0, 2], [[21, 0, -5, 4], [32, 1, -5, -2], [34, 1, 0, 0], [35, 0, 9, 8], [36, 1, -3, -3], [37, 1, -4, -3], [39, 1, 0, -1]]], [[[[11, 6.0, -6.0, 10.0, -2.0], [24, -1.5, -5.0, -1.0, -4.5], [13, 2.0, 1.5, 10.0, 6.5], [35, -3.0, -10.0, 27.0, -9.5], [25, 8.5, -1.0, 12.5, 3.0]], 1.0, 3], [[11, 2, 1, -2], [13, 2, 0, 0], [24, 0, -2, -5], [25, 2, 2, -1], [35, 2, -1, -3]]], [[[[7, 4.5, 1.5, 11.5, 2.5], [37, 2.0, 3.5, 10.0, 4.5], [2, 4.0, -5.5, 5.0, 3.5], [5, -7.0, 10.0, 0.0, 14.0], [33, 6.0, -6.5, 14.0, 2.5], [30, 0.0, 0.0, 2.0, 9.0], [38, -1.0, -5.5, 1.0, -3.5], [10, -7.5, -9.0, 0.5, -5.0], [28, -0.5, 2.5, 15.5, 4.5]], 1.0, 5], [[2, 4, 0, -1], [5, 3, -1, 1], [7, 3, 0, 0], [10, 3, -1, -2], [28, 4, -1, 0], [30, 4, 0, 0], [33, 4, 0, -1], [37, 3, 0, 0], [38, 1, -1, -3]]], [[[[24, -8.5, 1.5, 21.5, 2.5], [29, 5.0, -8.5, 12.0, -6.5], [39, -6.0, 7.5, -2.0, 12.5]], 1.0, 5], [[24, 4, -1, 0], [29, 3, 0, -2], [39, 3, -1, 0]]], [[[[31, -10.0, 1.5, 6.0, 10.5], [28, 3.5, 3.5, 7.5, 8.5], [13, 6.0, 6.0, 8.0, 10.0], [20, 7.0, 3.5, 8.0, 8.5], [19, 7.5, -3.0, 14.5, 6.0], [8, 9.5, 9.0, 12.5, 11.0], [32, 7.0, 9.5, 9.0, 10.0], [9, -4.5, 3.0, -4.0, 8.0], [14, 9.5, -2.0, 10.0, -1.5], [4, 8.0, -2.5, 11.0, -2.0]], 1.0, 5], [[4, 2, 2, -1], [8, 2, 2, 2], [9, 3, -1, 0], [13, 2, 1, 1], [14, 0, 9, -2], [19, 4, 0, -1], [20, 3, 0, 0], [28, 3, 0, 0], [31, 4, -1, 0], [32, 1, 3, 4]]], [[[[28, -2.0, 0.0, 14.0, 9.0], [34, 4.5, 0.5, 5.5, 4.5], [14, 6.5, -10.0, 9.5, -9.5], [20, -0.5, -6.0, 15.5, 3.0], [31, -9.5, 5.5, -1.5, 6.0], [4, -1.5, 9.0, 5.5, 9.5], [23, -4.5, -5.5, 25.5, -3.5]], 1.0, 4], [[4, 3, -1, 1], [14, 2, 1, -3], [20, 3, -1, -1], [23, 3, -1, -1], [28, 3, -1, 0], [31, 3, -2, 0], [34, 2, 1, 0]]], [[[[24, 10.0, 2.5, 26.0, 11.5], [1, -7.5, -10.0, 0.5, -9.0], [4, 0.0, 6.0, 4.0, 8.0], [17, -0.5, 5.0, 7.5, 14.0], [32, 3.5, -1.5, 19.5, -0.5]], 2.0, 4], [[1, 2, -1, -2], [4, 1, 0, 1], [17, 3, -1, 0], [24, 3, 0, 0], [32, 3, 0, -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	`[[4, 3, -1, 0], [14, 3, -1, -1], [17, 4, 0, 0], [30, 4, -1, 0]]`	`[[4, 3, -1, 0], [14, 3, -1, -1], [17, 4, 0, 0], [30, 4, -1, 0]]`	Passed
case 1	`[[13, 2, 2, -1], [36, 2, -1, 0]]`	`[[13, 2, 2, -1], [36, 2, -1, 0]]`	Passed
case 2	`[[2, 0, 2, 3], [16, 3, -2, 1], [18, 3, -1, 0], [25, 2, -1, 2], [32, 3, 0, 0]]`	`[[2, 0, 2, 3], [16, 3, -2, 1], [18, 3, -1, 0], [25, 2, -1, 2], [32, 3, 0, 0]]`	Passed
case 3	`[[15, 3, 1, 0], [17, 3, -2, -2], [27, 0, 6, -6], [31, 1, 2, -5]]`	`[[15, 3, 1, 0], [17, 3, -2, -2], [27, 0, 6, -6], [31, 1, 2, -5]]`	Passed
case 4	`[[9, 2, -2, -2], [31, 1, 1, -5], [36, 2, 0, -3]]`	`[[9, 2, -2, -2], [31, 1, 1, -5], [36, 2, 0, -3]]`	Passed
case 5	`[[8, 4, 0, -1], [10, 3, -1, 0], [37, 3, 0, 0]]`	`[[8, 4, 0, -1], [10, 3, -1, 0], [37, 3, 0, 0]]`	Passed
case 6	`[[1, 2, 0, 0], [3, 0, -2, -1], [18, 1, 2, 0], [20, 3, -1, 0], [37, 3, 0, -1]]`	`[[1, 2, 0, 0], [3, 0, -2, -1], [18, 1, 2, 0], [20, 3, -1, 0], [37, 3, 0, -1]]`	Passed
case 7	`[[16, 0, -4, 0], [20, 2, -1, -2]]`	`[[16, 0, -4, 0], [20, 2, -1, -2]]`	Passed

SHA-256 / b54a1b81e95ce6b1a6bb37c08a16368ca6033e7e310fd89d8f397138351ed66d

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 2026-09-29T14:51:00.599504+00:00.

Case digest / 0106106b1829086684606d037377499f3bb076ceb209671acdbab0d1962650a4