FAILURE MAP
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FA-87661 / Collision detection broadphase / Open access

Axis spread uses absolute deviation · case 01

Axis choice flips for distributions with outliers.

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

ROOT CAUSE

Deviations are abs(c-mean).

THE FAILURE

Deviations are abs(c-mean).

Unsuccessful approach: Summing signed deviations always yields zero.

Case contract

solve(boxes): 3D sweep-and-prune axis selection. Boxes [id,minx,miny,minz,maxx,maxy,maxz]. Pick the axis with the largest population variance of box centres (first axis on ties), then order ids by (min on that axis, id). Return [axis, variance rounded to 6, ordered ids].

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(boxes):
    n = len(boxes)
    best_axis, best_var = 0, -1.0
    for ax in (0, 1, 2):
        cs_ = [(b[1 + ax] + b[4 + ax]) / 2 for b in boxes]
        mean = sum(cs_) / n
        var = sum(abs(c - mean) for c in cs_) / n
        if var > best_var:
            best_axis, best_var = ax, var
    order = [b[0] for b in sorted(boxes, key=lambda b: (b[1 + best_axis], b[0]))]
    return [best_axis, round(best_var, 6), order]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[[[[3, 0, 20, 0, 4, 30, 3], [32, 3, 28, 14, 8, 34, 24], [6, 3, 8, 2, 14, 9, 12], [34, 10, 9, 20, 19, 20, 20]]], [1, 77.0625, [6, 34, 3, 32]]], [[[[3, 2, 1, 9, 4, 2, 16], [22, 0, 0, 10, 2, 2, 20], [31, 1, 0, 1, 12, 6, 8], [16, 1, 0, 9, 9, 10, 16]]], [2, 15.671875, [31, 3, 16, 22]]], [[[[8, 0, 22, 17, 8, 31, 23], [14, 1, 2, 25, 1, 9, 25], [38, 0, 25, 6, 7, 35, 17], [36, 1, 11, 9, 11, 19, 12]]], [1, 93.8125, [14, 36, 8, 38]]], [[[[28, 12, 13, 1, 14, 25, 5], [36, 10, 28, 0, 10, 32, 6], [17, 4, 16, 0, 7, 28, 9], [26, 2, 16, 0, 14, 27, 3], [20, 6, 12, 2, 14, 19, 13], [38, 17, 9, 0, 22, 18, 3]]], [1, 28.229167, [38, 20, 28, 17, 26, 36]]], [[[[5, 0, 17, 9, 2, 25, 9], [7, 2, 24, 1, 2, 35, 9], [17, 1, 19, 13, 4, 27, 25]]], [2, 34.666667, [7, 5, 17]]], [[[[25, 10, 4, 26, 11, 15, 37], [12, 10, 6, 1, 12, 15, 10], [39, 7, 10, 8, 14, 11, 16], [36, 7, 10, 29, 15, 14, 30], [14, 1, 8, 24, 7, 18, 28]]], [2, 105.74, [12, 39, 14, 25, 36]]], [[[[6, 4, 13, 9, 14, 22, 21], [7, 0, 28, 11, 5, 33, 18], [22, 7, 2, 27, 19, 9, 28], [12, 2, 9, 17, 13, 16, 25], [29, 3, 10, 19, 4, 19, 25]]], [1, 67.44, [22, 12, 29, 6, 7]]], [[[[38, 0, 1, 1, 2, 3, 6], [11, 0, 5, 2, 12, 14, 3]]], [1, 14.0625, [38, 11]]]], [[[[[3, 0, 1, 16, 2, 10, 22], [39, 9, 2, 0, 13, 8, 4], [6, 6, 1, 22, 15, 9, 29], [27, 2, 0, 3, 14, 7, 3]]], [2, 102.921875, [39, 27, 3, 6]]], [[[[12, 5, 8, 7, 9, 9, 12], [28, 27, 5, 5, 37, 17, 5], [27, 17, 9, 21, 25, 10, 22], [26, 17, 4, 26, 24, 10, 32], [15, 25, 3, 16, 25, 11, 23], [19, 18, 1, 8, 19, 7, 8], [7, 0, 2, 28, 8, 11, 40]]], [2, 104.673469, [28, 12, 19, 15, 27, 26, 7]]], [[[[22, 2, 5, 2, 5, 17, 10], [8, 0, 7, 2, 5, 8, 7], [36, 2, 3, 2, 9, 14, 13], [15, 1, 10, 0, 9, 10, 2], [29, 0, 10, 2, 7, 10, 9], [26, 0, 4, 2, 12, 10, 4], [10, 0, 10, 0, 2, 19, 0]]], [2, 6.387755, [10, 15, 8, 22, 26, 29, 36]]], [[[[9, 10, 2, 1, 18, 9, 3], [39, 1, 1, 2, 8, 9, 8]]], [0, 22.5625, [39, 9]]], [[[[3, 27, 2, 2, 37, 6, 5], [35, 0, 10, 1, 10, 13, 13]]], [0, 182.25, [35, 3]]], [[[[15, 1, 2, 1, 13, 9, 2], [20, 9, 0, 2, 19, 12, 7], [24, 5, 2, 0, 15, 8, 8], [9, 7, 2, 2, 9, 7, 8]]], [0, 7.1875, [15, 24, 9, 20]]], [[[[3, 1, 3, 1, 13, 6, 10], [24, 1, 5, 5, 9, 14, 14], [36, 2, 1, 2, 5, 5, 2], [33, 0, 8, 17, 9, 10, 17], [1, 0, 10, 7, 5, 12, 14]]], [2, 25.54, [3, 36, 24, 1, 33]]], [[[[30, 0, 0, 7, 1, 4, 12], [7, 1, 0, 8, 8, 0, 11], [2, 2, 2, 4, 8, 11, 7], [35, 0, 0, 9, 3, 7, 19], [22, 0, 1, 8, 2, 6, 8], [3, 1, 1, 2, 9, 13, 14], [29, 1, 2, 4, 5, 3, 14]]], [2, 5.673469, [3, 2, 29, 30, 7, 22, 35]]]], [[[[[10, 22, 0, 4, 31, 9, 7], [8, 15, 2, 2, 24, 4, 12], [22, 19, 1, 1, 20, 3, 6], [27, 22, 1, 0, 31, 2, 9], [14, 6, 2, 7, 8, 4, 15], [21, 10, 1, 2, 17, 13, 5], [2, 18, 0, 8, 28, 6, 19], [18, 4, 2, 0, 9, 8, 2]]], [0, 55.875, [18, 14, 21, 8, 2, 22, 10, 27]]], [[[[37, 8, 1, 6, 16, 5, 10], [10, 5, 3, 10, 17, 15, 12], [29, 5, 5, 8, 9, 17, 8], [23, 3, 10, 6, 15, 19, 11], [7, 9, 5, 10, 17, 10, 10], [18, 7, 6, 5, 12, 12, 7]]], [1, 12.083333, [37, 10, 7, 29, 18, 23]]], [[[[20, 10, 2, 25, 12, 7, 27], [1, 10, 26, 11, 12, 27, 18], [28, 2, 12, 8, 3, 19, 9], [3, 10, 29, 9, 15, 33, 14], [24, 4, 20, 8, 12, 23, 20], [15, 1, 27, 22, 6, 32, 22]]], [1, 84.034722, [20, 28, 24, 1, 15, 3]]], [[[[32, 27, 8, 0, 27, 18, 0], [4, 26, 1, 0, 38, 13, 3]]], [1, 9.0, [4, 32]]], [[[[37, 8, 1, 0, 14, 5, 1], [38, 0, 2, 22, 7, 5, 25], [10, 3, 5, 29, 7, 12, 38], [35, 6, 7, 7, 6, 19, 16]]], [2, 154.1875, [37, 35, 38, 10]]], [[[[1, 27, 25, 1, 39, 34, 10], [35, 21, 20, 2, 32, 29, 5], [22, 6, 14, 1, 10, 16, 12], [13, 3, 27, 2, 4, 34, 7], [8, 19, 15, 1, 26, 25, 12], [39, 0, 16, 0, 6, 22, 12]]], [0, 138.451389, [39, 13, 22, 8, 35, 1]]], [[[[21, 2, 22, 9, 4, 29, 14], [16, 0, 26, 9, 4, 29, 13]]], [1, 1.0, [21, 16]]], [[[[39, 25, 25, 27, 33, 27, 38], [11, 22, 16, 6, 30, 19, 18]]], [2, 105.0625, [11, 39]]]], [[[[[29, 0, 18, 0, 1, 26, 10], [2, 1, 16, 2, 8, 21, 13], [21, 2, 25, 0, 5, 30, 12], [35, 1, 4, 1, 9, 10, 4], [19, 2, 1, 1, 8, 13, 3], [15, 0, 6, 0, 9, 18, 0]]], [1, 58.638889, [19, 35, 15, 2, 29, 21]]], [[[[10, 5, 2, 1, 7, 6, 10], [32, 9, 1, 11, 17, 12, 13], [13, 4, 0, 29, 11, 4, 32], [28, 3, 1, 18, 6, 9, 21], [3, 8, 2, 1, 9, 11, 1], [6, 2, 0, 16, 10, 3, 24]]], [2, 96.729167, [3, 10, 32, 6, 28, 13]]], [[[[3, 4, 1, 1, 9, 9, 12], [13, 10, 1, 0, 22, 10, 1], [25, 2, 7, 1, 11, 17, 6], [23, 2, 8, 0, 10, 17, 5], [24, 2, 6, 2, 5, 10, 11]]], [0, 18.46, [23, 24, 25, 3, 13]]], [[[[33, 3, 26, 4, 5, 37, 7], [18, 9, 13, 12, 13, 13, 13], [24, 9, 17, 24, 21, 25, 31], [20, 8, 27, 23, 15, 27, 34], [35, 4, 9, 9, 5, 16, 20], [31, 5, 4, 6, 13, 7, 18]]], [1, 80.451389, [31, 35, 18, 24, 33, 20]]], [[[[36, 2, 10, 0, 12, 13, 9], [34, 1, 0, 0, 4, 11, 9], [37, 2, 4, 1, 9, 16, 5], [14, 0, 3, 2, 12, 8, 10], [22, 1, 4, 2, 6, 13, 9]]], [1, 5.76, [34, 14, 22, 37, 36]]], [[[[22, 2, 2, 2, 7, 13, 8], [23, 0, 1, 0, 4, 8, 12], [1, 0, 1, 2, 3, 13, 4], [34, 2, 1, 2, 14, 6, 5]]], [0, 6.625, [1, 23, 22, 34]]], [[[[15, 2, 6, 0, 6, 13, 7], [32, 0, 10, 10, 12, 10, 14], [16, 1, 9, 10, 1, 9, 19], [31, 2, 24, 7, 13, 31, 10], [20, 1, 5, 9, 5, 6, 9], [8, 0, 10, 8, 0, 17, 15]]], [1, 50.416667, [20, 15, 16, 8, 32, 31]]], [[[[39, 9, 10, 0, 20, 17, 8], [9, 5, 9, 16, 10, 20, 24], [4, 3, 10, 6, 12, 18, 14]]], [2, 43.555556, [39, 4, 9]]]], [[[[[22, 0, 0, 3, 4, 0, 11], [17, 2, 9, 5, 9, 19, 6], [3, 0, 6, 7, 5, 14, 17], [24, 1, 3, 0, 12, 3, 10]]], [1, 30.6875, [22, 24, 3, 17]]], [[[[7, 6, 2, 1, 7, 7, 11], [25, 21, 2, 1, 23, 6, 8], [15, 9, 0, 1, 16, 5, 5], [37, 8, 0, 2, 20, 6, 10], [16, 25, 0, 2, 28, 6, 10]]], [0, 50.46, [7, 37, 15, 25, 16]]], [[[[13, 5, 25, 23, 5, 26, 29], [19, 24, 6, 27, 32, 14, 33], [17, 1, 2, 17, 11, 9, 22], [4, 21, 25, 22, 27, 30, 24], [27, 29, 26, 1, 38, 30, 9], [30, 11, 22, 2, 13, 32, 7]]], [0, 120.868056, [17, 13, 30, 4, 19, 27]]], [[[[10, 3, 0, 22, 3, 6, 32], [2, 4, 1, 28, 10, 9, 40], [17, 8, 0, 1, 13, 12, 12], [32, 9, 2, 4, 19, 3, 5], [29, 6, 2, 13, 8, 8, 16], [9, 4, 1, 2, 13, 3, 2], [27, 9, 0, 26, 13, 7, 36], [1, 1, 1, 21, 7, 9, 30], [16, 8, 2, 23, 8, 12, 28], [6, 6, 1, 9, 7, 4, 15]]], [2, 123.6625, [17, 9, 32, 6, 29, 1, 10, 16, 27, 2]]], [[[[23, 23, 14, 0, 35, 18, 11], [31, 23, 5, 16, 26, 8, 19], [2, 0, 10, 28, 10, 21, 29], [18, 7, 19, 0, 17, 20, 5], [12, 7, 19, 14, 7, 25, 26], [36, 17, 1, 23, 18, 13, 29]]], [2, 94.055556, [18, 23, 12, 31, 36, 2]]], [[[[12, 1, 8, 2, 5, 16, 14], [10, 2, 2, 2, 7, 8, 3], [31, 1, 7, 2, 3, 7, 10], [36, 0, 3, 0, 10, 15, 0], [39, 1, 4, 0, 12, 15, 4], [25, 2, 0, 2, 2, 4, 5]]], [1, 10.534722, [25, 10, 36, 39, 31, 12]]], [[[[18, 0, 3, 1, 7, 4, 6], [3, 0, 7, 1, 11, 11, 5], [17, 0, 9, 0, 6, 18, 9], [4, 0, 7, 0, 0, 10, 10], [11, 2, 5, 0, 9, 11, 1], [31, 2, 3, 0, 8, 5, 11], [16, 1, 6, 2, 1, 17, 9], [26, 0, 3, 0, 0, 9, 10]]], [1, 10.5, [18, 26, 31, 11, 16, 3, 4, 17]]], [[[[18, 10, 21, 1, 14, 27, 2], [16, 20, 5, 1, 26, 8, 11], [1, 6, 4, 2, 9, 7, 11]]], [1, 72.166667, [1, 16, 18]]]]]
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[1, 8.25, [6, 34, 3, 32]][1, 77.0625, [6, 34, 3, 32]]Failed
case 1[2, 3.3125, [31, 3, 16, 22]][2, 15.671875, [31, 3, 16, 22]]Failed
case 2[1, 9.0, [14, 36, 8, 38]][1, 93.8125, [14, 36, 8, 38]]Failed
case 3[1, 4.25, [38, 20, 28, 17, 26, 36]][1, 28.229167, [38, 20, 28, 17, 26, 36]]Failed
case 4[2, 5.333333, [7, 5, 17]][2, 34.666667, [7, 5, 17]]Failed
case 5[2, 9.72, [12, 39, 14, 25, 36]][2, 105.74, [12, 39, 14, 25, 36]]Failed
case 6[1, 6.32, [22, 12, 29, 6, 7]][1, 67.44, [22, 12, 29, 6, 7]]Failed
case 7[1, 3.75, [38, 11]][1, 14.0625, [38, 11]]Failed

SHA-256 / 6f1274c34edfe3909b86e17cd3c9e914d0dc05f87f530b1203d2782866d52ed0

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(boxes):
    n = len(boxes)
    best_axis, best_var = 0, -1.0
    for ax in (0, 1, 2):
        cs_ = [(b[1 + ax] + b[4 + ax]) / 2 for b in boxes]
        mean = sum(cs_) / n
        var = sum((c - mean) for c in cs_) / n
        if var > best_var:
            best_axis, best_var = ax, var
    order = [b[0] for b in sorted(boxes, key=lambda b: (b[1 + best_axis], b[0]))]
    return [best_axis, round(best_var, 6), order]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[[[[3, 0, 20, 0, 4, 30, 3], [32, 3, 28, 14, 8, 34, 24], [6, 3, 8, 2, 14, 9, 12], [34, 10, 9, 20, 19, 20, 20]]], [1, 77.0625, [6, 34, 3, 32]]], [[[[3, 2, 1, 9, 4, 2, 16], [22, 0, 0, 10, 2, 2, 20], [31, 1, 0, 1, 12, 6, 8], [16, 1, 0, 9, 9, 10, 16]]], [2, 15.671875, [31, 3, 16, 22]]], [[[[8, 0, 22, 17, 8, 31, 23], [14, 1, 2, 25, 1, 9, 25], [38, 0, 25, 6, 7, 35, 17], [36, 1, 11, 9, 11, 19, 12]]], [1, 93.8125, [14, 36, 8, 38]]], [[[[28, 12, 13, 1, 14, 25, 5], [36, 10, 28, 0, 10, 32, 6], [17, 4, 16, 0, 7, 28, 9], [26, 2, 16, 0, 14, 27, 3], [20, 6, 12, 2, 14, 19, 13], [38, 17, 9, 0, 22, 18, 3]]], [1, 28.229167, [38, 20, 28, 17, 26, 36]]], [[[[5, 0, 17, 9, 2, 25, 9], [7, 2, 24, 1, 2, 35, 9], [17, 1, 19, 13, 4, 27, 25]]], [2, 34.666667, [7, 5, 17]]], [[[[25, 10, 4, 26, 11, 15, 37], [12, 10, 6, 1, 12, 15, 10], [39, 7, 10, 8, 14, 11, 16], [36, 7, 10, 29, 15, 14, 30], [14, 1, 8, 24, 7, 18, 28]]], [2, 105.74, [12, 39, 14, 25, 36]]], [[[[6, 4, 13, 9, 14, 22, 21], [7, 0, 28, 11, 5, 33, 18], [22, 7, 2, 27, 19, 9, 28], [12, 2, 9, 17, 13, 16, 25], [29, 3, 10, 19, 4, 19, 25]]], [1, 67.44, [22, 12, 29, 6, 7]]], [[[[38, 0, 1, 1, 2, 3, 6], [11, 0, 5, 2, 12, 14, 3]]], [1, 14.0625, [38, 11]]]], [[[[[3, 0, 1, 16, 2, 10, 22], [39, 9, 2, 0, 13, 8, 4], [6, 6, 1, 22, 15, 9, 29], [27, 2, 0, 3, 14, 7, 3]]], [2, 102.921875, [39, 27, 3, 6]]], [[[[12, 5, 8, 7, 9, 9, 12], [28, 27, 5, 5, 37, 17, 5], [27, 17, 9, 21, 25, 10, 22], [26, 17, 4, 26, 24, 10, 32], [15, 25, 3, 16, 25, 11, 23], [19, 18, 1, 8, 19, 7, 8], [7, 0, 2, 28, 8, 11, 40]]], [2, 104.673469, [28, 12, 19, 15, 27, 26, 7]]], [[[[22, 2, 5, 2, 5, 17, 10], [8, 0, 7, 2, 5, 8, 7], [36, 2, 3, 2, 9, 14, 13], [15, 1, 10, 0, 9, 10, 2], [29, 0, 10, 2, 7, 10, 9], [26, 0, 4, 2, 12, 10, 4], [10, 0, 10, 0, 2, 19, 0]]], [2, 6.387755, [10, 15, 8, 22, 26, 29, 36]]], [[[[9, 10, 2, 1, 18, 9, 3], [39, 1, 1, 2, 8, 9, 8]]], [0, 22.5625, [39, 9]]], [[[[3, 27, 2, 2, 37, 6, 5], [35, 0, 10, 1, 10, 13, 13]]], [0, 182.25, [35, 3]]], [[[[15, 1, 2, 1, 13, 9, 2], [20, 9, 0, 2, 19, 12, 7], [24, 5, 2, 0, 15, 8, 8], [9, 7, 2, 2, 9, 7, 8]]], [0, 7.1875, [15, 24, 9, 20]]], [[[[3, 1, 3, 1, 13, 6, 10], [24, 1, 5, 5, 9, 14, 14], [36, 2, 1, 2, 5, 5, 2], [33, 0, 8, 17, 9, 10, 17], [1, 0, 10, 7, 5, 12, 14]]], [2, 25.54, [3, 36, 24, 1, 33]]], [[[[30, 0, 0, 7, 1, 4, 12], [7, 1, 0, 8, 8, 0, 11], [2, 2, 2, 4, 8, 11, 7], [35, 0, 0, 9, 3, 7, 19], [22, 0, 1, 8, 2, 6, 8], [3, 1, 1, 2, 9, 13, 14], [29, 1, 2, 4, 5, 3, 14]]], [2, 5.673469, [3, 2, 29, 30, 7, 22, 35]]]], [[[[[10, 22, 0, 4, 31, 9, 7], [8, 15, 2, 2, 24, 4, 12], [22, 19, 1, 1, 20, 3, 6], [27, 22, 1, 0, 31, 2, 9], [14, 6, 2, 7, 8, 4, 15], [21, 10, 1, 2, 17, 13, 5], [2, 18, 0, 8, 28, 6, 19], [18, 4, 2, 0, 9, 8, 2]]], [0, 55.875, [18, 14, 21, 8, 2, 22, 10, 27]]], [[[[37, 8, 1, 6, 16, 5, 10], [10, 5, 3, 10, 17, 15, 12], [29, 5, 5, 8, 9, 17, 8], [23, 3, 10, 6, 15, 19, 11], [7, 9, 5, 10, 17, 10, 10], [18, 7, 6, 5, 12, 12, 7]]], [1, 12.083333, [37, 10, 7, 29, 18, 23]]], [[[[20, 10, 2, 25, 12, 7, 27], [1, 10, 26, 11, 12, 27, 18], [28, 2, 12, 8, 3, 19, 9], [3, 10, 29, 9, 15, 33, 14], [24, 4, 20, 8, 12, 23, 20], [15, 1, 27, 22, 6, 32, 22]]], [1, 84.034722, [20, 28, 24, 1, 15, 3]]], [[[[32, 27, 8, 0, 27, 18, 0], [4, 26, 1, 0, 38, 13, 3]]], [1, 9.0, [4, 32]]], [[[[37, 8, 1, 0, 14, 5, 1], [38, 0, 2, 22, 7, 5, 25], [10, 3, 5, 29, 7, 12, 38], [35, 6, 7, 7, 6, 19, 16]]], [2, 154.1875, [37, 35, 38, 10]]], [[[[1, 27, 25, 1, 39, 34, 10], [35, 21, 20, 2, 32, 29, 5], [22, 6, 14, 1, 10, 16, 12], [13, 3, 27, 2, 4, 34, 7], [8, 19, 15, 1, 26, 25, 12], [39, 0, 16, 0, 6, 22, 12]]], [0, 138.451389, [39, 13, 22, 8, 35, 1]]], [[[[21, 2, 22, 9, 4, 29, 14], [16, 0, 26, 9, 4, 29, 13]]], [1, 1.0, [21, 16]]], [[[[39, 25, 25, 27, 33, 27, 38], [11, 22, 16, 6, 30, 19, 18]]], [2, 105.0625, [11, 39]]]], [[[[[29, 0, 18, 0, 1, 26, 10], [2, 1, 16, 2, 8, 21, 13], [21, 2, 25, 0, 5, 30, 12], [35, 1, 4, 1, 9, 10, 4], [19, 2, 1, 1, 8, 13, 3], [15, 0, 6, 0, 9, 18, 0]]], [1, 58.638889, [19, 35, 15, 2, 29, 21]]], [[[[10, 5, 2, 1, 7, 6, 10], [32, 9, 1, 11, 17, 12, 13], [13, 4, 0, 29, 11, 4, 32], [28, 3, 1, 18, 6, 9, 21], [3, 8, 2, 1, 9, 11, 1], [6, 2, 0, 16, 10, 3, 24]]], [2, 96.729167, [3, 10, 32, 6, 28, 13]]], [[[[3, 4, 1, 1, 9, 9, 12], [13, 10, 1, 0, 22, 10, 1], [25, 2, 7, 1, 11, 17, 6], [23, 2, 8, 0, 10, 17, 5], [24, 2, 6, 2, 5, 10, 11]]], [0, 18.46, [23, 24, 25, 3, 13]]], [[[[33, 3, 26, 4, 5, 37, 7], [18, 9, 13, 12, 13, 13, 13], [24, 9, 17, 24, 21, 25, 31], [20, 8, 27, 23, 15, 27, 34], [35, 4, 9, 9, 5, 16, 20], [31, 5, 4, 6, 13, 7, 18]]], [1, 80.451389, [31, 35, 18, 24, 33, 20]]], [[[[36, 2, 10, 0, 12, 13, 9], [34, 1, 0, 0, 4, 11, 9], [37, 2, 4, 1, 9, 16, 5], [14, 0, 3, 2, 12, 8, 10], [22, 1, 4, 2, 6, 13, 9]]], [1, 5.76, [34, 14, 22, 37, 36]]], [[[[22, 2, 2, 2, 7, 13, 8], [23, 0, 1, 0, 4, 8, 12], [1, 0, 1, 2, 3, 13, 4], [34, 2, 1, 2, 14, 6, 5]]], [0, 6.625, [1, 23, 22, 34]]], [[[[15, 2, 6, 0, 6, 13, 7], [32, 0, 10, 10, 12, 10, 14], [16, 1, 9, 10, 1, 9, 19], [31, 2, 24, 7, 13, 31, 10], [20, 1, 5, 9, 5, 6, 9], [8, 0, 10, 8, 0, 17, 15]]], [1, 50.416667, [20, 15, 16, 8, 32, 31]]], [[[[39, 9, 10, 0, 20, 17, 8], [9, 5, 9, 16, 10, 20, 24], [4, 3, 10, 6, 12, 18, 14]]], [2, 43.555556, [39, 4, 9]]]], [[[[[22, 0, 0, 3, 4, 0, 11], [17, 2, 9, 5, 9, 19, 6], [3, 0, 6, 7, 5, 14, 17], [24, 1, 3, 0, 12, 3, 10]]], [1, 30.6875, [22, 24, 3, 17]]], [[[[7, 6, 2, 1, 7, 7, 11], [25, 21, 2, 1, 23, 6, 8], [15, 9, 0, 1, 16, 5, 5], [37, 8, 0, 2, 20, 6, 10], [16, 25, 0, 2, 28, 6, 10]]], [0, 50.46, [7, 37, 15, 25, 16]]], [[[[13, 5, 25, 23, 5, 26, 29], [19, 24, 6, 27, 32, 14, 33], [17, 1, 2, 17, 11, 9, 22], [4, 21, 25, 22, 27, 30, 24], [27, 29, 26, 1, 38, 30, 9], [30, 11, 22, 2, 13, 32, 7]]], [0, 120.868056, [17, 13, 30, 4, 19, 27]]], [[[[10, 3, 0, 22, 3, 6, 32], [2, 4, 1, 28, 10, 9, 40], [17, 8, 0, 1, 13, 12, 12], [32, 9, 2, 4, 19, 3, 5], [29, 6, 2, 13, 8, 8, 16], [9, 4, 1, 2, 13, 3, 2], [27, 9, 0, 26, 13, 7, 36], [1, 1, 1, 21, 7, 9, 30], [16, 8, 2, 23, 8, 12, 28], [6, 6, 1, 9, 7, 4, 15]]], [2, 123.6625, [17, 9, 32, 6, 29, 1, 10, 16, 27, 2]]], [[[[23, 23, 14, 0, 35, 18, 11], [31, 23, 5, 16, 26, 8, 19], [2, 0, 10, 28, 10, 21, 29], [18, 7, 19, 0, 17, 20, 5], [12, 7, 19, 14, 7, 25, 26], [36, 17, 1, 23, 18, 13, 29]]], [2, 94.055556, [18, 23, 12, 31, 36, 2]]], [[[[12, 1, 8, 2, 5, 16, 14], [10, 2, 2, 2, 7, 8, 3], [31, 1, 7, 2, 3, 7, 10], [36, 0, 3, 0, 10, 15, 0], [39, 1, 4, 0, 12, 15, 4], [25, 2, 0, 2, 2, 4, 5]]], [1, 10.534722, [25, 10, 36, 39, 31, 12]]], [[[[18, 0, 3, 1, 7, 4, 6], [3, 0, 7, 1, 11, 11, 5], [17, 0, 9, 0, 6, 18, 9], [4, 0, 7, 0, 0, 10, 10], [11, 2, 5, 0, 9, 11, 1], [31, 2, 3, 0, 8, 5, 11], [16, 1, 6, 2, 1, 17, 9], [26, 0, 3, 0, 0, 9, 10]]], [1, 10.5, [18, 26, 31, 11, 16, 3, 4, 17]]], [[[[18, 10, 21, 1, 14, 27, 2], [16, 20, 5, 1, 26, 8, 11], [1, 6, 4, 2, 9, 7, 11]]], [1, 72.166667, [1, 16, 18]]]]]
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[0, 0.0, [3, 6, 32, 34]][1, 77.0625, [6, 34, 3, 32]]Failed
case 1[0, 0.0, [22, 16, 31, 3]][2, 15.671875, [31, 3, 16, 22]]Failed
case 2[0, 0.0, [8, 38, 14, 36]][1, 93.8125, [14, 36, 8, 38]]Failed
case 3[0, 0.0, [26, 17, 20, 36, 28, 38]][1, 28.229167, [38, 20, 28, 17, 26, 36]]Failed
case 4[0, 0.0, [5, 17, 7]][2, 34.666667, [7, 5, 17]]Failed
case 5[2, 0.0, [12, 39, 14, 25, 36]][2, 105.74, [12, 39, 14, 25, 36]]Failed
case 6[0, 0.0, [7, 12, 29, 6, 22]][1, 67.44, [22, 12, 29, 6, 7]]Failed
case 7[0, 0.0, [11, 38]][1, 14.0625, [38, 11]]Failed

SHA-256 / 1e95164442d705cc21e43387ca4bb2b844e3fd1d0dc12e8c476ff4089fa231e8

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.

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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 2026-09-29T14:51:00.964310+00:00.

Case digest / 1a50fe2bebf6ac5ffacdb50ab360ff637b3ef6d5451a74e530803b5c6758dd08