FAILURE MAP
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FA-87626 / Collision detection broadphase / Open access

Objects exactly one cell wide are promoted a level · case 01

Grid level populations shift upward and coarse levels get crowded.

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

ROOT CAUSE

The loop continues while size <= ext.

THE FAILURE

The loop continues while size <= ext.

Unsuccessful approach: Comparing against half the extent treats size as a radius.

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 / 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 = [[[[[[29, -9.0, -5.0, -1.0, -4.5], [31, -2.0, 4.0, 0.0, 13.0], [8, -2.0, -10.0, 28.0, -6.0]], 1.0, 5], [[8, 4, -1, -1], [29, 3, -2, -1], [31, 4, -1, 0]]], [[[[26, 3.5, 5.0, 4.0, 10.0], [4, -8.5, 9.0, -4.5, 18.0], [5, -4.5, 2.0, -3.5, 6.0], [10, 6.5, 9.0, 14.5, 9.5], [1, 3.0, 5.5, 5.0, 14.5], [23, 8.0, -2.0, 10.0, 2.0]], 1.0, 2], [[1, 1, 1, 2], [4, 1, -5, 4], [5, 1, -3, 1], [10, 1, 3, 4], [23, 1, 4, -1], [26, 1, 1, 2]]], [[[[6, 8.5, 1.0, 11.5, 2.0], [10, -8.0, 1.5, -7.0, 3.5]], 1.0, 2], [[6, 1, 4, 0], [10, 1, -4, 0]]], [[[[37, -2.0, 2.5, 0.0, 7.5], [34, 6.0, -9.0, 10.0, -5.0], [2, 8.5, 2.0, 12.5, 11.0], [27, 9.5, 6.5, 16.5, 11.5]], 1.0, 2], [[2, 1, 4, 1], [27, 1, 4, 3], [34, 1, 3, -5], [37, 1, -1, 1]]], [[[[10, -1.5, 7.5, 0.5, 11.5], [11, -8.0, 3.5, -4.0, 8.5], [17, -5.5, 0.0, -4.5, 4.0], [3, 4.0, -8.5, 12.0, -4.5]], 1.0, 4], [[3, 3, 0, -2], [10, 2, -1, 1], [11, 3, -1, 0], [17, 2, -2, 0]]], [[[[5, -5.0, 3.0, 11.0, 8.0], [31, 7.0, -5.0, 23.0, -3.0], [37, -8.0, 10.0, 22.0, 15.0], [22, 1.0, -9.5, 17.0, -7.5], [14, 3.5, -4.0, 5.5, 0.0]], 1.0, 5], [[5, 4, -1, 0], [14, 2, 0, -1], [22, 4, 0, -1], [31, 4, 0, -1], [37, 4, -1, 0]]], [[[[34, 9.5, 5.0, 17.5, 14.0], [1, 8.0, 1.0, 11.0, 5.0]], 2.0, 3], [[1, 1, 2, 0], [34, 2, 1, 0]]], [[[[36, -1.5, 10.0, 1.5, 10.5], [28, -7.5, -2.0, 0.5, 3.0], [31, 7.0, 10.0, 11.0, 15.0]], 2.0, 3], [[28, 2, -1, -1], [31, 2, 0, 1], [36, 1, -1, 2]]]], [[[[[25, -6.0, 9.0, -4.0, 18.0], [12, 9.5, -7.0, 25.5, -3.0], [33, -2.0, -9.5, 1.0, -0.5], [15, 0.0, -4.0, 0.5, 1.0], [19, 0.0, 2.5, 1.0, 11.5]], 1.0, 2], [[12, 1, 4, -4], [15, 1, 0, -2], [19, 1, 0, 1], [25, 1, -3, 4], [33, 1, -1, -5]]], [[[[19, 10.0, -8.5, 13.0, -4.5], [4, 8.5, 10.0, 10.5, 14.0], [23, -9.0, 4.5, -7.0, 9.5], [14, -3.5, 5.5, 3.5, 6.5], [2, 3.0, -8.0, 11.0, -4.0], [11, -4.0, 3.5, 4.0, 4.5]], 2.0, 3], [[2, 2, 0, -1], [4, 1, 2, 2], [11, 2, -1, 0], [14, 2, -1, 0], [19, 1, 2, -3], [23, 2, -2, 0]]], [[[[28, 3.5, 2.5, 6.5, 4.5], [6, 8.5, 5.0, 15.5, 6.0], [11, 3.5, -3.0, 4.0, -2.0], [4, 0.5, 1.5, 3.5, 5.5], [19, 9.0, 3.5, 17.0, 12.5], [35, 1.0, -2.5, 31.0, -1.5], [12, 2.0, 9.0, 5.0, 13.0]], 1.0, 5], [[4, 2, 0, 0], [6, 3, 1, 0], [11, 0, 3, -3], [12, 2, 0, 2], [19, 4, 0, 0], [28, 2, 0, 0], [35, 4, 0, -1]]], [[[[19, -1.0, -8.5, 29.0, -3.5], [24, -7.0, 1.5, -3.0, 10.5], [39, -3.0, 0.5, -2.5, 1.5]], 2.0, 3], [[19, 2, -1, -2], [24, 2, -1, 0], [39, 0, -2, 0]]], [[[[20, -9.0, -2.0, 21.0, -1.0], [6, -5.5, 2.5, -5.0, 7.5], [12, 0.0, 9.0, 2.0, 14.0], [16, 10.0, 7.0, 13.0, 11.0], [17, 8.5, 6.5, 24.5, 10.5], [31, -7.5, 3.0, -5.5, 12.0]], 1.0, 2], [[6, 1, -3, 1], [12, 1, 0, 4], [16, 1, 5, 3], [17, 1, 4, 3], [20, 1, -5, -1], [31, 1, -4, 1]]], [[[[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]]], [[[[13, 4.5, 1.0, 12.5, 6.0], [11, -1.0, 5.0, 3.0, 6.0], [21, -6.0, -3.5, -4.0, -2.5], [5, 0.5, -6.5, 7.5, -1.5], [32, 6.0, 4.5, 36.0, 9.5], [10, -1.0, 8.0, 29.0, 8.5]], 2.0, 3], [[5, 2, 0, -1], [10, 2, -1, 1], [11, 1, -1, 1], [13, 2, 0, 0], [21, 0, -3, -2], [32, 2, 0, 0]]], [[[[8, 9.0, 3.0, 17.0, 3.5], [17, 7.0, 3.5, 8.0, 4.0], [25, 2.5, -6.5, 4.5, 2.5], [37, -9.0, -4.5, -7.0, -2.5], [19, 6.5, 4.5, 14.5, 13.5], [36, 3.5, -7.0, 4.5, -6.0]], 1.0, 3], [[8, 2, 2, 0], [17, 0, 7, 3], [19, 2, 1, 1], [25, 2, 0, -2], [36, 0, 3, -7], [37, 1, -5, -3]]]], [[[[[22, -9.0, 8.0, 7.0, 8.5], [39, 3.5, 10.0, 10.5, 11.0], [12, -9.5, -5.0, 6.5, 4.0], [8, -0.5, -1.0, 0.5, 8.0], [16, 4.0, 5.0, 20.0, 14.0]], 1.0, 5], [[8, 4, -1, -1], [12, 4, -1, -1], [16, 4, 0, 0], [22, 4, -1, 0], [39, 3, 0, 1]]], [[[[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]]], [[[[29, 0.0, -2.5, 3.0, -0.5], [18, 9.0, -5.0, 12.0, 0.0], [1, 5.0, -4.0, 6.0, 5.0], [11, -4.5, -4.0, -3.5, -3.5], [3, 2.0, -2.0, 5.0, -1.5], [28, 9.0, 10.0, 25.0, 19.0], [9, -5.0, -4.0, 11.0, -3.0]], 1.0, 2], [[1, 1, 2, -2], [3, 1, 1, -1], [9, 1, -3, -2], [11, 0, -5, -4], [18, 1, 4, -3], [28, 1, 4, 5], [29, 1, 0, -2]]], [[[[22, 7.5, 9.0, 23.5, 11.0], [16, 7.5, 6.0, 8.5, 15.0], [35, 3.0, -3.0, 4.0, 1.0], [39, -8.5, 9.0, -5.5, 11.0], [20, -9.5, 3.0, 6.5, 12.0], [15, -4.0, -10.0, 26.0, -8.0], [17, -8.0, 5.5, -4.0, 9.5], [14, 2.5, 1.5, 4.5, 6.5]], 2.0, 2], [[14, 1, 0, 0], [15, 1, -1, -3], [16, 1, 1, 1], [17, 1, -2, 1], [20, 1, -3, 0], [22, 1, 1, 2], [35, 1, 0, -1], [39, 1, -3, 2]]], [[[[27, -2.5, -2.5, -0.5, -0.5], [16, -9.5, 10.0, -9.0, 12.0], [36, -4.0, 2.5, 3.0, 6.5], [4, -0.5, 2.0, 15.5, 6.0], [26, -0.5, 10.0, 3.5, 12.0], [3, -6.5, 1.5, -4.5, 3.5]], 1.0, 4], [[3, 1, -4, 0], [4, 3, -1, 0], [16, 1, -5, 5], [26, 2, -1, 2], [27, 1, -2, -2], [36, 3, -1, 0]]], [[[[37, 1.5, -1.5, 8.5, 7.5], [6, 0.0, -3.5, 3.0, -1.5], [10, 7.0, -2.5, 15.0, -2.0], [27, -0.5, 2.0, 0.5, 11.0], [9, 1.5, -6.5, 5.5, -6.0], [34, -7.5, 0.5, 0.5, 1.5], [17, 5.0, 6.5, 9.0, 15.5], [33, 10.0, -6.5, 12.0, 2.5]], 2.0, 5], [[6, 1, 0, -1], [9, 1, 0, -2], [10, 2, 0, -1], [17, 3, 0, 0], [27, 3, -1, 0], [33, 3, 0, -1], [34, 2, -1, 0], [37, 3, 0, -1]]], [[[[17, -8.0, 2.5, 8.0, 6.5], [31, 1.5, 5.5, 9.5, 7.5], [8, 5.0, -2.5, 13.0, -1.5]], 2.0, 3], [[8, 2, 0, -1], [17, 2, -1, 0], [31, 2, 0, 0]]], [[[[4, 0.0, -4.0, 16.0, 1.0], [2, -1.5, -9.5, 5.5, -7.5], [33, -6.5, 3.0, -2.5, 7.0], [39, -5.0, 5.5, 11.0, 6.0], [13, -9.0, -4.0, 7.0, 5.0]], 2.0, 2], [[2, 1, -1, -3], [4, 1, 0, -1], [13, 1, -3, -1], [33, 1, -2, 0], [39, 1, -2, 1]]]], [[[[[15, 7.5, -3.5, 11.5, -3.0], [9, 8.0, 0.0, 9.0, 2.0], [3, -5.0, -7.5, 11.0, 1.5]], 1.0, 2], [[3, 1, -3, -4], [9, 1, 4, 0], [15, 1, 3, -2]]], [[[[32, 7.5, -0.5, 8.5, 4.5], [11, 8.0, -2.0, 11.0, 0.0], [29, 9.0, 1.5, 16.0, 10.5], [1, -9.0, -3.5, -2.0, 0.5], [10, -10.0, -6.5, -8.0, -4.5], [24, 0.0, 9.0, 8.0, 13.0], [23, 1.5, -0.5, 2.5, 4.5], [38, 6.5, -7.5, 36.5, 1.5]], 1.0, 5], [[1, 3, -2, -1], [10, 1, -5, -4], [11, 2, 2, -1], [23, 3, 0, -1], [24, 3, 0, 1], [29, 4, 0, 0], [32, 3, 0, -1], [38, 4, 0, -1]]], [[[[20, -9.5, 10.0, -7.5, 19.0], [2, -2.5, -0.5, 5.5, 3.5], [13, -10.0, -2.5, -3.0, -0.5], [24, 2.0, -0.5, 9.0, 1.5], [23, 1.5, 1.0, 5.5, 2.0], [17, -10.0, -8.5, 6.0, -3.5], [1, 2.5, -0.5, 10.5, 0.5], [8, 9.5, 4.0, 13.5, 6.0]], 2.0, 2], [[1, 1, 0, -1], [2, 1, -1, -1], [8, 1, 2, 1], [13, 1, -3, -1], [17, 1, -3, -3], [20, 1, -3, 2], [23, 1, 0, 0], [24, 1, 0, -1]]], [[[[10, -8.0, 1.5, 8.0, 2.5], [20, 3.5, -0.5, 10.5, 0.5], [27, -7.5, -4.5, -4.5, 0.5]], 2.0, 5], [[10, 3, -1, 0], [20, 2, 0, -1], [27, 2, -1, -1]]], [[[[7, 0.5, -3.0, 1.5, 6.0], [6, -10.0, 1.5, -2.0, 10.5], [32, 9.0, -7.0, 11.0, -3.0], [3, 8.5, -2.5, 16.5, -2.0]], 1.0, 5], [[3, 3, 1, -1], [6, 4, -1, 0], [7, 4, 0, -1], [32, 2, 2, -2]]], [[[[32, -8.0, -8.0, -7.0, -4.0], [26, -6.0, -4.5, -5.0, 0.5]], 1.0, 2], [[26, 1, -3, -3], [32, 1, -4, -4]]], [[[[36, 1.0, 10.0, 31.0, 14.0], [27, 9.5, 9.0, 16.5, 13.0], [3, -5.5, 3.0, -2.5, 8.0]], 2.0, 2], [[3, 1, -2, 0], [27, 1, 2, 2], [36, 1, 0, 2]]], [[[[25, 8.5, 0.5, 9.5, 4.5], [16, 6.5, -10.0, 7.5, -8.0], [9, -0.5, 1.5, 3.5, 6.5], [21, -6.5, -1.5, -3.5, 2.5], [29, -5.0, -9.5, -4.5, -0.5], [37, 4.5, 6.0, 20.5, 10.0], [33, 0.5, -0.5, 30.5, 3.5], [35, 8.5, 0.5, 9.0, 1.5]], 2.0, 4], [[9, 2, -1, 0], [16, 0, 3, -5], [21, 1, -2, -1], [25, 1, 2, 0], [29, 3, -1, -1], [33, 3, 0, -1], [35, 0, 4, 0], [37, 3, 0, 0]]]], [[[[[7, 7.0, 0.5, 10.0, 1.0], [31, 7.5, 10.0, 23.5, 14.0], [11, -6.5, 9.0, -5.5, 14.0], [17, 8.0, -7.0, 8.5, -2.0], [22, 1.0, 3.0, 2.0, 5.0], [30, -2.0, -7.0, 1.0, -3.0]], 2.0, 5], [[7, 1, 1, 0], [11, 2, -1, 1], [17, 2, 1, -1], [22, 0, 0, 1], [30, 1, -1, -2], [31, 3, 0, 0]]], [[[[24, -0.5, -4.5, 0.5, -2.5], [8, -7.0, -8.0, 23.0, -7.0], [6, 1.0, 6.5, 4.0, 7.0], [2, 6.5, -9.0, 22.5, -7.0], [21, 0.5, -2.5, 4.5, 6.5], [19, -6.0, 9.0, -3.0, 13.0], [22, -3.5, 4.5, -2.5, 6.5], [26, -2.0, -5.0, -1.0, 0.0]], 1.0, 5], [[2, 4, 0, -1], [6, 2, 0, 1], [8, 4, -1, -1], [19, 2, -2, 2], [21, 4, 0, -1], [22, 1, -2, 2], [24, 1, -1, -3], [26, 3, -1, -1]]], [[[[39, 6.5, 1.0, 13.5, 3.0], [34, 8.0, -9.0, 15.0, 0.0], [38, 0.5, -10.0, 16.5, -8.0], [37, -1.0, -4.5, 7.0, -2.5], [22, 0.0, -3.5, 16.0, -1.5], [10, 7.5, -5.5, 8.5, -0.5], [7, 10.0, 4.5, 40.0, 9.5], [25, 2.0, 9.5, 10.0, 10.0]], 1.0, 4], [[7, 3, 1, 0], [10, 3, 0, -1], [22, 3, 0, -1], [25, 3, 0, 1], [34, 3, 1, -2], [37, 3, -1, -1], [38, 3, 0, -2], [39, 3, 0, 0]]], [[[[21, 2.5, -8.5, 3.5, -4.5], [32, -8.0, 9.0, -4.0, 10.0]], 2.0, 2], [[21, 1, 0, -3], [32, 1, -2, 2]]], [[[[13, -1.0, -5.5, 6.0, -3.5], [39, 8.0, -8.0, 8.5, -3.0], [4, -1.0, 2.0, 2.0, 7.0], [38, -6.0, 4.0, 2.0, 8.0], [21, -7.5, 8.5, -0.5, 17.5]], 1.0, 4], [[4, 3, -1, 0], [13, 3, -1, -1], [21, 3, -1, 1], [38, 3, -1, 0], [39, 3, 1, -1]]], [[[[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]]], [[[[26, -3.0, -3.0, 4.0, -1.0], [27, 4.0, 6.5, 34.0, 11.5]], 2.0, 2], [[26, 1, -1, -1], [27, 1, 1, 1]]], [[[[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 fixtureActualExpectedOutcome
case 0[[8, 4, -1, -1], [29, 4, -1, -1], [31, 4, -1, 0]][[8, 4, -1, -1], [29, 3, -2, -1], [31, 4, -1, 0]]Failed
case 1[[1, 1, 1, 2], [4, 1, -5, 4], [5, 1, -3, 1], [10, 1, 3, 4], [23, 1, 4, -1], [26, 1, 1, 2]][[1, 1, 1, 2], [4, 1, -5, 4], [5, 1, -3, 1], [10, 1, 3, 4], [23, 1, 4, -1], [26, 1, 1, 2]]Passed
case 2[[6, 1, 4, 0], [10, 1, -4, 0]][[6, 1, 4, 0], [10, 1, -4, 0]]Passed
case 3[[2, 1, 4, 1], [27, 1, 4, 3], [34, 1, 3, -5], [37, 1, -1, 1]][[2, 1, 4, 1], [27, 1, 4, 3], [34, 1, 3, -5], [37, 1, -1, 1]]Passed
case 4[[3, 3, 0, -2], [10, 3, -1, 0], [11, 3, -1, 0], [17, 3, -1, 0]][[3, 3, 0, -2], [10, 2, -1, 1], [11, 3, -1, 0], [17, 2, -2, 0]]Failed
case 5[[5, 4, -1, 0], [14, 3, 0, -1], [22, 4, 0, -1], [31, 4, 0, -1], [37, 4, -1, 0]][[5, 4, -1, 0], [14, 2, 0, -1], [22, 4, 0, -1], [31, 4, 0, -1], [37, 4, -1, 0]]Failed
case 6[[1, 2, 1, 0], [34, 2, 1, 0]][[1, 1, 2, 0], [34, 2, 1, 0]]Failed
case 7[[28, 2, -1, -1], [31, 2, 0, 1], [36, 1, -1, 2]][[28, 2, -1, -1], [31, 2, 0, 1], [36, 1, -1, 2]]Passed

SHA-256 / 94a4add375ba6930f1c69453d6e2f26cba78e5e88c7a2e5b8d01ca79000c82fc

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 / 2 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 = [[[[[[29, -9.0, -5.0, -1.0, -4.5], [31, -2.0, 4.0, 0.0, 13.0], [8, -2.0, -10.0, 28.0, -6.0]], 1.0, 5], [[8, 4, -1, -1], [29, 3, -2, -1], [31, 4, -1, 0]]], [[[[26, 3.5, 5.0, 4.0, 10.0], [4, -8.5, 9.0, -4.5, 18.0], [5, -4.5, 2.0, -3.5, 6.0], [10, 6.5, 9.0, 14.5, 9.5], [1, 3.0, 5.5, 5.0, 14.5], [23, 8.0, -2.0, 10.0, 2.0]], 1.0, 2], [[1, 1, 1, 2], [4, 1, -5, 4], [5, 1, -3, 1], [10, 1, 3, 4], [23, 1, 4, -1], [26, 1, 1, 2]]], [[[[6, 8.5, 1.0, 11.5, 2.0], [10, -8.0, 1.5, -7.0, 3.5]], 1.0, 2], [[6, 1, 4, 0], [10, 1, -4, 0]]], [[[[37, -2.0, 2.5, 0.0, 7.5], [34, 6.0, -9.0, 10.0, -5.0], [2, 8.5, 2.0, 12.5, 11.0], [27, 9.5, 6.5, 16.5, 11.5]], 1.0, 2], [[2, 1, 4, 1], [27, 1, 4, 3], [34, 1, 3, -5], [37, 1, -1, 1]]], [[[[10, -1.5, 7.5, 0.5, 11.5], [11, -8.0, 3.5, -4.0, 8.5], [17, -5.5, 0.0, -4.5, 4.0], [3, 4.0, -8.5, 12.0, -4.5]], 1.0, 4], [[3, 3, 0, -2], [10, 2, -1, 1], [11, 3, -1, 0], [17, 2, -2, 0]]], [[[[5, -5.0, 3.0, 11.0, 8.0], [31, 7.0, -5.0, 23.0, -3.0], [37, -8.0, 10.0, 22.0, 15.0], [22, 1.0, -9.5, 17.0, -7.5], [14, 3.5, -4.0, 5.5, 0.0]], 1.0, 5], [[5, 4, -1, 0], [14, 2, 0, -1], [22, 4, 0, -1], [31, 4, 0, -1], [37, 4, -1, 0]]], [[[[34, 9.5, 5.0, 17.5, 14.0], [1, 8.0, 1.0, 11.0, 5.0]], 2.0, 3], [[1, 1, 2, 0], [34, 2, 1, 0]]], [[[[36, -1.5, 10.0, 1.5, 10.5], [28, -7.5, -2.0, 0.5, 3.0], [31, 7.0, 10.0, 11.0, 15.0]], 2.0, 3], [[28, 2, -1, -1], [31, 2, 0, 1], [36, 1, -1, 2]]]], [[[[[25, -6.0, 9.0, -4.0, 18.0], [12, 9.5, -7.0, 25.5, -3.0], [33, -2.0, -9.5, 1.0, -0.5], [15, 0.0, -4.0, 0.5, 1.0], [19, 0.0, 2.5, 1.0, 11.5]], 1.0, 2], [[12, 1, 4, -4], [15, 1, 0, -2], [19, 1, 0, 1], [25, 1, -3, 4], [33, 1, -1, -5]]], [[[[19, 10.0, -8.5, 13.0, -4.5], [4, 8.5, 10.0, 10.5, 14.0], [23, -9.0, 4.5, -7.0, 9.5], [14, -3.5, 5.5, 3.5, 6.5], [2, 3.0, -8.0, 11.0, -4.0], [11, -4.0, 3.5, 4.0, 4.5]], 2.0, 3], [[2, 2, 0, -1], [4, 1, 2, 2], [11, 2, -1, 0], [14, 2, -1, 0], [19, 1, 2, -3], [23, 2, -2, 0]]], [[[[28, 3.5, 2.5, 6.5, 4.5], [6, 8.5, 5.0, 15.5, 6.0], [11, 3.5, -3.0, 4.0, -2.0], [4, 0.5, 1.5, 3.5, 5.5], [19, 9.0, 3.5, 17.0, 12.5], [35, 1.0, -2.5, 31.0, -1.5], [12, 2.0, 9.0, 5.0, 13.0]], 1.0, 5], [[4, 2, 0, 0], [6, 3, 1, 0], [11, 0, 3, -3], [12, 2, 0, 2], [19, 4, 0, 0], [28, 2, 0, 0], [35, 4, 0, -1]]], [[[[19, -1.0, -8.5, 29.0, -3.5], [24, -7.0, 1.5, -3.0, 10.5], [39, -3.0, 0.5, -2.5, 1.5]], 2.0, 3], [[19, 2, -1, -2], [24, 2, -1, 0], [39, 0, -2, 0]]], [[[[20, -9.0, -2.0, 21.0, -1.0], [6, -5.5, 2.5, -5.0, 7.5], [12, 0.0, 9.0, 2.0, 14.0], [16, 10.0, 7.0, 13.0, 11.0], [17, 8.5, 6.5, 24.5, 10.5], [31, -7.5, 3.0, -5.5, 12.0]], 1.0, 2], [[6, 1, -3, 1], [12, 1, 0, 4], [16, 1, 5, 3], [17, 1, 4, 3], [20, 1, -5, -1], [31, 1, -4, 1]]], [[[[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]]], [[[[13, 4.5, 1.0, 12.5, 6.0], [11, -1.0, 5.0, 3.0, 6.0], [21, -6.0, -3.5, -4.0, -2.5], [5, 0.5, -6.5, 7.5, -1.5], [32, 6.0, 4.5, 36.0, 9.5], [10, -1.0, 8.0, 29.0, 8.5]], 2.0, 3], [[5, 2, 0, -1], [10, 2, -1, 1], [11, 1, -1, 1], [13, 2, 0, 0], [21, 0, -3, -2], [32, 2, 0, 0]]], [[[[8, 9.0, 3.0, 17.0, 3.5], [17, 7.0, 3.5, 8.0, 4.0], [25, 2.5, -6.5, 4.5, 2.5], [37, -9.0, -4.5, -7.0, -2.5], [19, 6.5, 4.5, 14.5, 13.5], [36, 3.5, -7.0, 4.5, -6.0]], 1.0, 3], [[8, 2, 2, 0], [17, 0, 7, 3], [19, 2, 1, 1], [25, 2, 0, -2], [36, 0, 3, -7], [37, 1, -5, -3]]]], [[[[[22, -9.0, 8.0, 7.0, 8.5], [39, 3.5, 10.0, 10.5, 11.0], [12, -9.5, -5.0, 6.5, 4.0], [8, -0.5, -1.0, 0.5, 8.0], [16, 4.0, 5.0, 20.0, 14.0]], 1.0, 5], [[8, 4, -1, -1], [12, 4, -1, -1], [16, 4, 0, 0], [22, 4, -1, 0], [39, 3, 0, 1]]], [[[[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]]], [[[[29, 0.0, -2.5, 3.0, -0.5], [18, 9.0, -5.0, 12.0, 0.0], [1, 5.0, -4.0, 6.0, 5.0], [11, -4.5, -4.0, -3.5, -3.5], [3, 2.0, -2.0, 5.0, -1.5], [28, 9.0, 10.0, 25.0, 19.0], [9, -5.0, -4.0, 11.0, -3.0]], 1.0, 2], [[1, 1, 2, -2], [3, 1, 1, -1], [9, 1, -3, -2], [11, 0, -5, -4], [18, 1, 4, -3], [28, 1, 4, 5], [29, 1, 0, -2]]], [[[[22, 7.5, 9.0, 23.5, 11.0], [16, 7.5, 6.0, 8.5, 15.0], [35, 3.0, -3.0, 4.0, 1.0], [39, -8.5, 9.0, -5.5, 11.0], [20, -9.5, 3.0, 6.5, 12.0], [15, -4.0, -10.0, 26.0, -8.0], [17, -8.0, 5.5, -4.0, 9.5], [14, 2.5, 1.5, 4.5, 6.5]], 2.0, 2], [[14, 1, 0, 0], [15, 1, -1, -3], [16, 1, 1, 1], [17, 1, -2, 1], [20, 1, -3, 0], [22, 1, 1, 2], [35, 1, 0, -1], [39, 1, -3, 2]]], [[[[27, -2.5, -2.5, -0.5, -0.5], [16, -9.5, 10.0, -9.0, 12.0], [36, -4.0, 2.5, 3.0, 6.5], [4, -0.5, 2.0, 15.5, 6.0], [26, -0.5, 10.0, 3.5, 12.0], [3, -6.5, 1.5, -4.5, 3.5]], 1.0, 4], [[3, 1, -4, 0], [4, 3, -1, 0], [16, 1, -5, 5], [26, 2, -1, 2], [27, 1, -2, -2], [36, 3, -1, 0]]], [[[[37, 1.5, -1.5, 8.5, 7.5], [6, 0.0, -3.5, 3.0, -1.5], [10, 7.0, -2.5, 15.0, -2.0], [27, -0.5, 2.0, 0.5, 11.0], [9, 1.5, -6.5, 5.5, -6.0], [34, -7.5, 0.5, 0.5, 1.5], [17, 5.0, 6.5, 9.0, 15.5], [33, 10.0, -6.5, 12.0, 2.5]], 2.0, 5], [[6, 1, 0, -1], [9, 1, 0, -2], [10, 2, 0, -1], [17, 3, 0, 0], [27, 3, -1, 0], [33, 3, 0, -1], [34, 2, -1, 0], [37, 3, 0, -1]]], [[[[17, -8.0, 2.5, 8.0, 6.5], [31, 1.5, 5.5, 9.5, 7.5], [8, 5.0, -2.5, 13.0, -1.5]], 2.0, 3], [[8, 2, 0, -1], [17, 2, -1, 0], [31, 2, 0, 0]]], [[[[4, 0.0, -4.0, 16.0, 1.0], [2, -1.5, -9.5, 5.5, -7.5], [33, -6.5, 3.0, -2.5, 7.0], [39, -5.0, 5.5, 11.0, 6.0], [13, -9.0, -4.0, 7.0, 5.0]], 2.0, 2], [[2, 1, -1, -3], [4, 1, 0, -1], [13, 1, -3, -1], [33, 1, -2, 0], [39, 1, -2, 1]]]], [[[[[15, 7.5, -3.5, 11.5, -3.0], [9, 8.0, 0.0, 9.0, 2.0], [3, -5.0, -7.5, 11.0, 1.5]], 1.0, 2], [[3, 1, -3, -4], [9, 1, 4, 0], [15, 1, 3, -2]]], [[[[32, 7.5, -0.5, 8.5, 4.5], [11, 8.0, -2.0, 11.0, 0.0], [29, 9.0, 1.5, 16.0, 10.5], [1, -9.0, -3.5, -2.0, 0.5], [10, -10.0, -6.5, -8.0, -4.5], [24, 0.0, 9.0, 8.0, 13.0], [23, 1.5, -0.5, 2.5, 4.5], [38, 6.5, -7.5, 36.5, 1.5]], 1.0, 5], [[1, 3, -2, -1], [10, 1, -5, -4], [11, 2, 2, -1], [23, 3, 0, -1], [24, 3, 0, 1], [29, 4, 0, 0], [32, 3, 0, -1], [38, 4, 0, -1]]], [[[[20, -9.5, 10.0, -7.5, 19.0], [2, -2.5, -0.5, 5.5, 3.5], [13, -10.0, -2.5, -3.0, -0.5], [24, 2.0, -0.5, 9.0, 1.5], [23, 1.5, 1.0, 5.5, 2.0], [17, -10.0, -8.5, 6.0, -3.5], [1, 2.5, -0.5, 10.5, 0.5], [8, 9.5, 4.0, 13.5, 6.0]], 2.0, 2], [[1, 1, 0, -1], [2, 1, -1, -1], [8, 1, 2, 1], [13, 1, -3, -1], [17, 1, -3, -3], [20, 1, -3, 2], [23, 1, 0, 0], [24, 1, 0, -1]]], [[[[10, -8.0, 1.5, 8.0, 2.5], [20, 3.5, -0.5, 10.5, 0.5], [27, -7.5, -4.5, -4.5, 0.5]], 2.0, 5], [[10, 3, -1, 0], [20, 2, 0, -1], [27, 2, -1, -1]]], [[[[7, 0.5, -3.0, 1.5, 6.0], [6, -10.0, 1.5, -2.0, 10.5], [32, 9.0, -7.0, 11.0, -3.0], [3, 8.5, -2.5, 16.5, -2.0]], 1.0, 5], [[3, 3, 1, -1], [6, 4, -1, 0], [7, 4, 0, -1], [32, 2, 2, -2]]], [[[[32, -8.0, -8.0, -7.0, -4.0], [26, -6.0, -4.5, -5.0, 0.5]], 1.0, 2], [[26, 1, -3, -3], [32, 1, -4, -4]]], [[[[36, 1.0, 10.0, 31.0, 14.0], [27, 9.5, 9.0, 16.5, 13.0], [3, -5.5, 3.0, -2.5, 8.0]], 2.0, 2], [[3, 1, -2, 0], [27, 1, 2, 2], [36, 1, 0, 2]]], [[[[25, 8.5, 0.5, 9.5, 4.5], [16, 6.5, -10.0, 7.5, -8.0], [9, -0.5, 1.5, 3.5, 6.5], [21, -6.5, -1.5, -3.5, 2.5], [29, -5.0, -9.5, -4.5, -0.5], [37, 4.5, 6.0, 20.5, 10.0], [33, 0.5, -0.5, 30.5, 3.5], [35, 8.5, 0.5, 9.0, 1.5]], 2.0, 4], [[9, 2, -1, 0], [16, 0, 3, -5], [21, 1, -2, -1], [25, 1, 2, 0], [29, 3, -1, -1], [33, 3, 0, -1], [35, 0, 4, 0], [37, 3, 0, 0]]]], [[[[[7, 7.0, 0.5, 10.0, 1.0], [31, 7.5, 10.0, 23.5, 14.0], [11, -6.5, 9.0, -5.5, 14.0], [17, 8.0, -7.0, 8.5, -2.0], [22, 1.0, 3.0, 2.0, 5.0], [30, -2.0, -7.0, 1.0, -3.0]], 2.0, 5], [[7, 1, 1, 0], [11, 2, -1, 1], [17, 2, 1, -1], [22, 0, 0, 1], [30, 1, -1, -2], [31, 3, 0, 0]]], [[[[24, -0.5, -4.5, 0.5, -2.5], [8, -7.0, -8.0, 23.0, -7.0], [6, 1.0, 6.5, 4.0, 7.0], [2, 6.5, -9.0, 22.5, -7.0], [21, 0.5, -2.5, 4.5, 6.5], [19, -6.0, 9.0, -3.0, 13.0], [22, -3.5, 4.5, -2.5, 6.5], [26, -2.0, -5.0, -1.0, 0.0]], 1.0, 5], [[2, 4, 0, -1], [6, 2, 0, 1], [8, 4, -1, -1], [19, 2, -2, 2], [21, 4, 0, -1], [22, 1, -2, 2], [24, 1, -1, -3], [26, 3, -1, -1]]], [[[[39, 6.5, 1.0, 13.5, 3.0], [34, 8.0, -9.0, 15.0, 0.0], [38, 0.5, -10.0, 16.5, -8.0], [37, -1.0, -4.5, 7.0, -2.5], [22, 0.0, -3.5, 16.0, -1.5], [10, 7.5, -5.5, 8.5, -0.5], [7, 10.0, 4.5, 40.0, 9.5], [25, 2.0, 9.5, 10.0, 10.0]], 1.0, 4], [[7, 3, 1, 0], [10, 3, 0, -1], [22, 3, 0, -1], [25, 3, 0, 1], [34, 3, 1, -2], [37, 3, -1, -1], [38, 3, 0, -2], [39, 3, 0, 0]]], [[[[21, 2.5, -8.5, 3.5, -4.5], [32, -8.0, 9.0, -4.0, 10.0]], 2.0, 2], [[21, 1, 0, -3], [32, 1, -2, 2]]], [[[[13, -1.0, -5.5, 6.0, -3.5], [39, 8.0, -8.0, 8.5, -3.0], [4, -1.0, 2.0, 2.0, 7.0], [38, -6.0, 4.0, 2.0, 8.0], [21, -7.5, 8.5, -0.5, 17.5]], 1.0, 4], [[4, 3, -1, 0], [13, 3, -1, -1], [21, 3, -1, 1], [38, 3, -1, 0], [39, 3, 1, -1]]], [[[[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]]], [[[[26, -3.0, -3.0, 4.0, -1.0], [27, 4.0, 6.5, 34.0, 11.5]], 2.0, 2], [[26, 1, -1, -1], [27, 1, 1, 1]]], [[[[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 fixtureActualExpectedOutcome
case 0[[8, 4, -1, -1], [29, 2, -3, -2], [31, 3, -1, 0]][[8, 4, -1, -1], [29, 3, -2, -1], [31, 4, -1, 0]]Failed
case 1[[1, 1, 1, 2], [4, 1, -5, 4], [5, 1, -3, 1], [10, 1, 3, 4], [23, 1, 4, -1], [26, 1, 1, 2]][[1, 1, 1, 2], [4, 1, -5, 4], [5, 1, -3, 1], [10, 1, 3, 4], [23, 1, 4, -1], [26, 1, 1, 2]]Passed
case 2[[6, 1, 4, 0], [10, 0, -8, 1]][[6, 1, 4, 0], [10, 1, -4, 0]]Failed
case 3[[2, 1, 4, 1], [27, 1, 4, 3], [34, 1, 3, -5], [37, 1, -1, 1]][[2, 1, 4, 1], [27, 1, 4, 3], [34, 1, 3, -5], [37, 1, -1, 1]]Passed
case 4[[3, 2, 1, -3], [10, 1, -1, 3], [11, 2, -2, 0], [17, 1, -3, 0]][[3, 3, 0, -2], [10, 2, -1, 1], [11, 3, -1, 0], [17, 2, -2, 0]]Failed
case 5[[5, 3, -1, 0], [14, 1, 1, -2], [22, 3, 0, -2], [31, 3, 0, -1], [37, 4, -1, 0]][[5, 4, -1, 0], [14, 2, 0, -1], [22, 4, 0, -1], [31, 4, 0, -1], [37, 4, -1, 0]]Failed
case 6[[1, 0, 4, 0], [34, 2, 1, 0]][[1, 1, 2, 0], [34, 2, 1, 0]]Failed
case 7[[28, 1, -2, -1], [31, 1, 1, 2], [36, 0, -1, 5]][[28, 2, -1, -1], [31, 2, 0, 1], [36, 1, -1, 2]]Failed

SHA-256 / 390f21353f76d0d7553ba259b058af86385362da49198556a0c560edb690dc27

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 8 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

Member access is invitation-based. Sign in with your invited account to inspect the repair.

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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 2026-09-29T14:51:00.590784+00:00.

Case digest / e87d527c2c9c8525c473ce7e1292e5c31b854d5ce1d9466f71c6bc7311482bc8