FAILURE MAP
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FA-87356 / Collision detection broadphase / Open access

Ended boxes stay in the active list · case 01

Boxes far apart on x are reported as candidates.

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

ROOT CAUSE

The end event does not remove the id from the active set.

THE FAILURE

The end event does not remove the id from the active set.

Unsuccessful approach: Popping the oldest active entry removes the wrong box when intervals end out of order.

Case contract

solve(boxes): boxes [id,minx,miny,maxx,maxy] with closed intervals (touching overlaps). Sweep x endpoints sorted by (coord, begin-before-end); on each begin, test y against every active box. Return sorted [min id, max id] pairs overlapping on both axes.

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):
    ev = []
    for b in boxes:
        ev.append((b[1], 0, b[0]))
        ev.append((b[3], 1, b[0]))
    ev.sort()
    byid = {b[0]: b for b in boxes}
    active = []
    pairs = []
    for x, kind, i in ev:
        if kind == 0:
            bi = byid[i]
            for j in active:
                bj = byid[j]
                if bi[2] <= bj[4] and bj[2] <= bi[4]:
                    pairs.append([min(i, j), max(i, j)])
            active.append(i)
        else:
            pass
    pairs.sort()
    return pairs
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[[[[6, -1.0, -4.0, 2.0, -3.0], [25, -5.0, 0.0, -5.0, 0.0]]], []], [[[[14, 1.0, -4.0, 4.0, -1.0], [6, 0.0, -1.0, 4.0, 3.0], [32, -2.0, -3.0, 2.0, -1.0], [15, -4.0, 0.0, -4.0, 4.0], [7, -4.0, -2.0, -1.0, -2.0]]], [[6, 14], [6, 32], [7, 32], [14, 32]]], [[[[28, -3.0, 6.0, -1.0, 6.0], [15, 4.0, 5.0, 4.0, 5.0], [5, -5.0, 4.0, -3.0, 4.0], [23, -3.0, 0.0, 1.0, 2.0], [37, 2.0, -6.0, 6.0, -2.0]]], []], [[[[5, 0.0, 3.0, 2.0, 5.0], [15, -2.0, 3.0, -1.0, 6.0], [34, -3.0, 6.0, -2.0, 6.0], [20, -2.0, 1.0, 2.0, 4.0], [23, -2.0, -1.0, -2.0, -1.0], [1, 4.0, -5.0, 6.0, -2.0], [25, 0.0, 5.0, 1.0, 9.0]]], [[5, 20], [5, 25], [15, 20], [15, 34]]], [[[[3, 2.0, -5.0, 2.0, -2.0], [24, -2.0, -4.0, 2.0, -4.0], [26, 6.0, 4.0, 10.0, 8.0], [4, -2.0, 2.0, -1.0, 3.0], [29, -5.0, -2.0, -2.0, 2.0], [11, 4.0, 3.0, 4.0, 6.0]]], [[3, 24], [4, 29]]], [[[[26, 4.0, -5.0, 7.0, -5.0], [33, -1.0, 1.0, 3.0, 2.0], [37, 0.0, -3.0, 2.0, 0.0], [6, -3.0, -2.0, 1.0, -2.0], [24, -3.0, 3.0, -2.0, 7.0]]], [[6, 37]]], [[[[16, 1.0, -6.0, 1.0, -4.0], [2, 3.0, 3.0, 6.0, 4.0], [25, 5.0, 2.0, 8.0, 2.0], [39, 2.0, 6.0, 2.0, 6.0], [30, -1.0, 5.0, -1.0, 6.0], [15, 0.0, 4.0, 3.0, 8.0], [17, 4.0, -1.0, 4.0, -1.0]]], [[2, 15], [15, 39]]], [[[[23, 5.0, 6.0, 5.0, 7.0], [39, 0.0, 3.0, 4.0, 3.0], [27, -5.0, -4.0, -4.0, -4.0]]], []]], [[[[[14, 0.0, 3.0, 0.0, 5.0], [29, -6.0, -6.0, -6.0, -2.0], [27, 5.0, -5.0, 9.0, -1.0]]], []], [[[[13, 5.0, -3.0, 6.0, -2.0], [34, 3.0, 3.0, 5.0, 4.0], [8, -4.0, 5.0, -3.0, 6.0], [10, 0.0, 1.0, 3.0, 4.0], [27, 2.0, 3.0, 2.0, 5.0], [4, -5.0, -2.0, -5.0, 2.0], [22, -6.0, 0.0, -5.0, 1.0]]], [[4, 22], [10, 27], [10, 34]]], [[[[29, 3.0, -1.0, 7.0, 0.0], [20, -4.0, -6.0, -3.0, -4.0]]], []], [[[[16, 2.0, 6.0, 2.0, 10.0], [6, 2.0, -4.0, 4.0, -2.0], [22, 0.0, 2.0, 1.0, 4.0], [3, 2.0, -4.0, 2.0, -1.0], [17, -2.0, -4.0, -1.0, -3.0], [30, -6.0, -6.0, -2.0, -6.0], [34, 4.0, -5.0, 5.0, -1.0], [14, -1.0, 3.0, -1.0, 7.0]]], [[3, 6], [6, 34]]], [[[[5, 3.0, 4.0, 4.0, 8.0], [37, 2.0, 1.0, 6.0, 4.0]]], [[5, 37]]], [[[[11, -1.0, 2.0, 3.0, 2.0], [9, 3.0, -1.0, 4.0, 0.0], [20, 5.0, -4.0, 9.0, -2.0]]], []], [[[[37, 4.0, -5.0, 6.0, -1.0], [20, -4.0, -3.0, -2.0, 1.0], [3, 6.0, -1.0, 8.0, 3.0], [8, -5.0, 0.0, -5.0, 4.0], [25, 4.0, 6.0, 6.0, 9.0]]], [[3, 37]]], [[[[7, 0.0, -3.0, 2.0, 1.0], [37, -4.0, -6.0, -3.0, -5.0], [13, -6.0, -3.0, -6.0, -3.0], [6, -2.0, 0.0, -1.0, 2.0], [31, 5.0, -5.0, 6.0, -1.0], [14, -2.0, 6.0, -1.0, 10.0]]], []]], [[[[[2, 0.0, 6.0, 1.0, 7.0], [8, 2.0, 4.0, 4.0, 6.0], [10, 2.0, 2.0, 5.0, 5.0], [6, -5.0, -6.0, -1.0, -2.0], [24, -1.0, 3.0, 0.0, 3.0]]], [[8, 10]]], [[[[24, 3.0, -4.0, 3.0, -1.0], [20, 0.0, -6.0, 3.0, -4.0]]], [[20, 24]]], [[[[35, 5.0, 1.0, 9.0, 1.0], [28, 4.0, -1.0, 7.0, 0.0]]], []], [[[[18, 2.0, 2.0, 4.0, 2.0], [9, 4.0, 2.0, 4.0, 3.0]]], [[9, 18]]], [[[[12, -1.0, -5.0, 2.0, -2.0], [19, -2.0, -1.0, -1.0, 0.0]]], []], [[[[5, -6.0, 5.0, -6.0, 6.0], [36, -2.0, -3.0, -2.0, -2.0], [27, 2.0, 5.0, 5.0, 6.0], [13, 6.0, 1.0, 7.0, 5.0], [14, 6.0, 5.0, 8.0, 9.0], [16, -6.0, -4.0, -5.0, 0.0], [12, 5.0, 6.0, 7.0, 8.0]]], [[12, 14], [12, 27], [13, 14]]], [[[[14, 6.0, 3.0, 7.0, 5.0], [11, -2.0, -6.0, 0.0, -6.0], [30, -6.0, 2.0, -2.0, 3.0], [34, 1.0, 1.0, 5.0, 5.0], [25, 5.0, -4.0, 6.0, -1.0], [24, -3.0, -6.0, -3.0, -5.0]]], []], [[[[39, 0.0, -6.0, 1.0, -6.0], [24, -6.0, -2.0, -2.0, 1.0], [27, 2.0, -5.0, 6.0, -1.0], [7, 3.0, -5.0, 4.0, -2.0], [28, -5.0, 0.0, -1.0, 1.0], [13, -4.0, -3.0, -1.0, 0.0], [9, 6.0, -2.0, 10.0, -1.0], [37, 3.0, 6.0, 6.0, 7.0]]], [[7, 27], [9, 27], [13, 24], [13, 28], [24, 28]]]], [[[[[25, -6.0, -6.0, -3.0, -5.0], [23, 5.0, -2.0, 7.0, -1.0], [3, 1.0, -3.0, 5.0, 1.0]]], [[3, 23]]], [[[[34, -2.0, -6.0, -1.0, -6.0], [39, 5.0, -4.0, 7.0, -3.0], [9, 1.0, -3.0, 2.0, -2.0], [38, 2.0, 5.0, 4.0, 6.0], [8, -5.0, 1.0, -3.0, 4.0], [26, -2.0, -2.0, 2.0, 0.0], [4, 5.0, -5.0, 6.0, -3.0], [35, 3.0, 1.0, 6.0, 2.0], [10, -4.0, 6.0, -2.0, 6.0], [31, 2.0, 1.0, 5.0, 3.0]]], [[4, 39], [9, 26], [31, 35]]], [[[[39, 4.0, -4.0, 8.0, -2.0], [4, -2.0, -1.0, 1.0, 0.0], [20, 0.0, -4.0, 2.0, -1.0], [17, 3.0, -5.0, 4.0, -4.0]]], [[4, 20], [17, 39]]], [[[[5, 0.0, -2.0, 3.0, -2.0], [7, 5.0, 2.0, 5.0, 5.0], [21, 4.0, 3.0, 4.0, 4.0], [27, 6.0, 3.0, 9.0, 6.0], [1, 2.0, 5.0, 5.0, 7.0]]], [[1, 7]]], [[[[27, 1.0, -4.0, 2.0, -3.0], [22, -3.0, 5.0, 0.0, 7.0], [36, 0.0, -2.0, 4.0, -1.0]]], []], [[[[10, 1.0, 3.0, 5.0, 4.0], [21, 5.0, 0.0, 7.0, 2.0], [27, 5.0, 1.0, 6.0, 5.0], [34, -1.0, -4.0, 2.0, -3.0]]], [[10, 27], [21, 27]]], [[[[23, -4.0, -3.0, -1.0, -3.0], [30, -6.0, -4.0, -4.0, -4.0], [13, 5.0, 0.0, 9.0, 3.0], [1, -5.0, 6.0, -4.0, 6.0], [37, -1.0, 2.0, 0.0, 2.0], [11, 5.0, 0.0, 9.0, 0.0], [21, 0.0, 4.0, 1.0, 8.0], [35, -5.0, -4.0, -5.0, -1.0], [4, 0.0, -4.0, 0.0, -2.0], [32, -4.0, 0.0, 0.0, 4.0]]], [[11, 13], [21, 32], [30, 35], [32, 37]]], [[[[39, -6.0, 1.0, -6.0, 5.0], [6, -5.0, -4.0, -2.0, 0.0], [17, 0.0, 4.0, 2.0, 7.0], [35, -6.0, 5.0, -6.0, 7.0]]], [[35, 39]]]], [[[[[24, 5.0, -5.0, 8.0, -3.0], [23, -4.0, 1.0, 0.0, 4.0], [4, -6.0, -6.0, -2.0, -6.0], [2, -4.0, 2.0, -3.0, 2.0], [7, 0.0, 3.0, 2.0, 4.0], [19, 0.0, -5.0, 4.0, -1.0]]], [[2, 23], [7, 23]]], [[[[35, 1.0, 0.0, 1.0, 0.0], [39, 0.0, -3.0, 4.0, 0.0], [7, 2.0, -3.0, 2.0, -2.0], [2, 5.0, 5.0, 5.0, 6.0]]], [[7, 39], [35, 39]]], [[[[4, 1.0, -1.0, 5.0, -1.0], [36, -4.0, -5.0, -1.0, -5.0], [10, 3.0, 6.0, 5.0, 6.0], [11, 0.0, -1.0, 4.0, 0.0], [22, -1.0, 0.0, 1.0, 4.0], [14, 1.0, -4.0, 4.0, -2.0], [3, -1.0, 0.0, 1.0, 0.0]]], [[3, 11], [3, 22], [4, 11], [11, 22]]], [[[[22, 6.0, 3.0, 7.0, 5.0], [2, -3.0, 2.0, -3.0, 2.0], [1, -5.0, 4.0, -3.0, 8.0], [18, 2.0, 4.0, 4.0, 6.0], [29, 0.0, -5.0, 0.0, -2.0], [21, 6.0, 4.0, 6.0, 4.0], [10, 2.0, 1.0, 6.0, 5.0], [4, -6.0, 5.0, -6.0, 9.0], [20, -1.0, 4.0, 0.0, 7.0], [12, 3.0, 6.0, 6.0, 10.0], [5, -4.0, 4.0, -1.0, 5.0]]], [[1, 5], [5, 20], [10, 18], [10, 21], [10, 22], [12, 18], [21, 22]]], [[[[21, 5.0, 1.0, 6.0, 2.0], [6, 0.0, 6.0, 2.0, 8.0], [3, 5.0, 4.0, 5.0, 5.0]]], []], [[[[34, 5.0, 0.0, 6.0, 2.0], [15, 0.0, 3.0, 3.0, 5.0], [29, -3.0, -4.0, -1.0, -2.0]]], []], [[[[5, 2.0, 6.0, 5.0, 6.0], [12, -3.0, 3.0, -2.0, 4.0], [35, -2.0, -4.0, -1.0, -4.0], [22, 6.0, 6.0, 9.0, 6.0], [28, 1.0, -6.0, 1.0, -2.0], [3, -2.0, -2.0, -2.0, 2.0], [16, 6.0, 5.0, 6.0, 5.0], [11, -3.0, 4.0, -3.0, 6.0], [37, -4.0, 3.0, -1.0, 7.0], [32, -5.0, -2.0, -1.0, -2.0], [18, 0.0, -5.0, 0.0, -2.0]]], [[3, 32], [11, 12], [11, 37], [12, 37]]], [[[[11, 6.0, -3.0, 7.0, 1.0], [26, -3.0, -5.0, 0.0, -4.0], [32, 1.0, 5.0, 1.0, 5.0], [1, -3.0, -2.0, 1.0, 2.0], [39, 5.0, -3.0, 5.0, -2.0], [12, 5.0, 4.0, 8.0, 7.0], [21, 0.0, -6.0, 3.0, -3.0], [17, 5.0, -3.0, 7.0, -1.0], [9, -6.0, -2.0, -4.0, 0.0]]], [[11, 17], [17, 39], [21, 26]]]]]
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[][]Passed
case 1[[6, 14], [6, 15], [6, 32], [7, 14], [7, 32], [14, 32]][[6, 14], [6, 32], [7, 32], [14, 32]]Failed
case 2[][]Passed
case 3[[5, 15], [5, 20], [5, 25], [15, 20], [15, 25], [15, 34], [25, 34]][[5, 20], [5, 25], [15, 20], [15, 34]]Failed
case 4[[3, 24], [3, 29], [4, 11], [4, 29], [11, 26]][[3, 24], [4, 29]]Failed
case 5[[6, 37]][[6, 37]]Passed
case 6[[2, 15], [15, 30], [15, 39], [30, 39]][[2, 15], [15, 39]]Failed
case 7[][]Passed

SHA-256 / 1bf21dd4ffc5dab08bd2dd821f1a2e7f9b38115fdb1b1dc06aaafecf5feb46e1

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(boxes):
    ev = []
    for b in boxes:
        ev.append((b[1], 0, b[0]))
        ev.append((b[3], 1, b[0]))
    ev.sort()
    byid = {b[0]: b for b in boxes}
    active = []
    pairs = []
    for x, kind, i in ev:
        if kind == 0:
            bi = byid[i]
            for j in active:
                bj = byid[j]
                if bi[2] <= bj[4] and bj[2] <= bi[4]:
                    pairs.append([min(i, j), max(i, j)])
            active.append(i)
        else:
            active.pop(0)
    pairs.sort()
    return pairs
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[[[[6, -1.0, -4.0, 2.0, -3.0], [25, -5.0, 0.0, -5.0, 0.0]]], []], [[[[14, 1.0, -4.0, 4.0, -1.0], [6, 0.0, -1.0, 4.0, 3.0], [32, -2.0, -3.0, 2.0, -1.0], [15, -4.0, 0.0, -4.0, 4.0], [7, -4.0, -2.0, -1.0, -2.0]]], [[6, 14], [6, 32], [7, 32], [14, 32]]], [[[[28, -3.0, 6.0, -1.0, 6.0], [15, 4.0, 5.0, 4.0, 5.0], [5, -5.0, 4.0, -3.0, 4.0], [23, -3.0, 0.0, 1.0, 2.0], [37, 2.0, -6.0, 6.0, -2.0]]], []], [[[[5, 0.0, 3.0, 2.0, 5.0], [15, -2.0, 3.0, -1.0, 6.0], [34, -3.0, 6.0, -2.0, 6.0], [20, -2.0, 1.0, 2.0, 4.0], [23, -2.0, -1.0, -2.0, -1.0], [1, 4.0, -5.0, 6.0, -2.0], [25, 0.0, 5.0, 1.0, 9.0]]], [[5, 20], [5, 25], [15, 20], [15, 34]]], [[[[3, 2.0, -5.0, 2.0, -2.0], [24, -2.0, -4.0, 2.0, -4.0], [26, 6.0, 4.0, 10.0, 8.0], [4, -2.0, 2.0, -1.0, 3.0], [29, -5.0, -2.0, -2.0, 2.0], [11, 4.0, 3.0, 4.0, 6.0]]], [[3, 24], [4, 29]]], [[[[26, 4.0, -5.0, 7.0, -5.0], [33, -1.0, 1.0, 3.0, 2.0], [37, 0.0, -3.0, 2.0, 0.0], [6, -3.0, -2.0, 1.0, -2.0], [24, -3.0, 3.0, -2.0, 7.0]]], [[6, 37]]], [[[[16, 1.0, -6.0, 1.0, -4.0], [2, 3.0, 3.0, 6.0, 4.0], [25, 5.0, 2.0, 8.0, 2.0], [39, 2.0, 6.0, 2.0, 6.0], [30, -1.0, 5.0, -1.0, 6.0], [15, 0.0, 4.0, 3.0, 8.0], [17, 4.0, -1.0, 4.0, -1.0]]], [[2, 15], [15, 39]]], [[[[23, 5.0, 6.0, 5.0, 7.0], [39, 0.0, 3.0, 4.0, 3.0], [27, -5.0, -4.0, -4.0, -4.0]]], []]], [[[[[14, 0.0, 3.0, 0.0, 5.0], [29, -6.0, -6.0, -6.0, -2.0], [27, 5.0, -5.0, 9.0, -1.0]]], []], [[[[13, 5.0, -3.0, 6.0, -2.0], [34, 3.0, 3.0, 5.0, 4.0], [8, -4.0, 5.0, -3.0, 6.0], [10, 0.0, 1.0, 3.0, 4.0], [27, 2.0, 3.0, 2.0, 5.0], [4, -5.0, -2.0, -5.0, 2.0], [22, -6.0, 0.0, -5.0, 1.0]]], [[4, 22], [10, 27], [10, 34]]], [[[[29, 3.0, -1.0, 7.0, 0.0], [20, -4.0, -6.0, -3.0, -4.0]]], []], [[[[16, 2.0, 6.0, 2.0, 10.0], [6, 2.0, -4.0, 4.0, -2.0], [22, 0.0, 2.0, 1.0, 4.0], [3, 2.0, -4.0, 2.0, -1.0], [17, -2.0, -4.0, -1.0, -3.0], [30, -6.0, -6.0, -2.0, -6.0], [34, 4.0, -5.0, 5.0, -1.0], [14, -1.0, 3.0, -1.0, 7.0]]], [[3, 6], [6, 34]]], [[[[5, 3.0, 4.0, 4.0, 8.0], [37, 2.0, 1.0, 6.0, 4.0]]], [[5, 37]]], [[[[11, -1.0, 2.0, 3.0, 2.0], [9, 3.0, -1.0, 4.0, 0.0], [20, 5.0, -4.0, 9.0, -2.0]]], []], [[[[37, 4.0, -5.0, 6.0, -1.0], [20, -4.0, -3.0, -2.0, 1.0], [3, 6.0, -1.0, 8.0, 3.0], [8, -5.0, 0.0, -5.0, 4.0], [25, 4.0, 6.0, 6.0, 9.0]]], [[3, 37]]], [[[[7, 0.0, -3.0, 2.0, 1.0], [37, -4.0, -6.0, -3.0, -5.0], [13, -6.0, -3.0, -6.0, -3.0], [6, -2.0, 0.0, -1.0, 2.0], [31, 5.0, -5.0, 6.0, -1.0], [14, -2.0, 6.0, -1.0, 10.0]]], []]], [[[[[2, 0.0, 6.0, 1.0, 7.0], [8, 2.0, 4.0, 4.0, 6.0], [10, 2.0, 2.0, 5.0, 5.0], [6, -5.0, -6.0, -1.0, -2.0], [24, -1.0, 3.0, 0.0, 3.0]]], [[8, 10]]], [[[[24, 3.0, -4.0, 3.0, -1.0], [20, 0.0, -6.0, 3.0, -4.0]]], [[20, 24]]], [[[[35, 5.0, 1.0, 9.0, 1.0], [28, 4.0, -1.0, 7.0, 0.0]]], []], [[[[18, 2.0, 2.0, 4.0, 2.0], [9, 4.0, 2.0, 4.0, 3.0]]], [[9, 18]]], [[[[12, -1.0, -5.0, 2.0, -2.0], [19, -2.0, -1.0, -1.0, 0.0]]], []], [[[[5, -6.0, 5.0, -6.0, 6.0], [36, -2.0, -3.0, -2.0, -2.0], [27, 2.0, 5.0, 5.0, 6.0], [13, 6.0, 1.0, 7.0, 5.0], [14, 6.0, 5.0, 8.0, 9.0], [16, -6.0, -4.0, -5.0, 0.0], [12, 5.0, 6.0, 7.0, 8.0]]], [[12, 14], [12, 27], [13, 14]]], [[[[14, 6.0, 3.0, 7.0, 5.0], [11, -2.0, -6.0, 0.0, -6.0], [30, -6.0, 2.0, -2.0, 3.0], [34, 1.0, 1.0, 5.0, 5.0], [25, 5.0, -4.0, 6.0, -1.0], [24, -3.0, -6.0, -3.0, -5.0]]], []], [[[[39, 0.0, -6.0, 1.0, -6.0], [24, -6.0, -2.0, -2.0, 1.0], [27, 2.0, -5.0, 6.0, -1.0], [7, 3.0, -5.0, 4.0, -2.0], [28, -5.0, 0.0, -1.0, 1.0], [13, -4.0, -3.0, -1.0, 0.0], [9, 6.0, -2.0, 10.0, -1.0], [37, 3.0, 6.0, 6.0, 7.0]]], [[7, 27], [9, 27], [13, 24], [13, 28], [24, 28]]]], [[[[[25, -6.0, -6.0, -3.0, -5.0], [23, 5.0, -2.0, 7.0, -1.0], [3, 1.0, -3.0, 5.0, 1.0]]], [[3, 23]]], [[[[34, -2.0, -6.0, -1.0, -6.0], [39, 5.0, -4.0, 7.0, -3.0], [9, 1.0, -3.0, 2.0, -2.0], [38, 2.0, 5.0, 4.0, 6.0], [8, -5.0, 1.0, -3.0, 4.0], [26, -2.0, -2.0, 2.0, 0.0], [4, 5.0, -5.0, 6.0, -3.0], [35, 3.0, 1.0, 6.0, 2.0], [10, -4.0, 6.0, -2.0, 6.0], [31, 2.0, 1.0, 5.0, 3.0]]], [[4, 39], [9, 26], [31, 35]]], [[[[39, 4.0, -4.0, 8.0, -2.0], [4, -2.0, -1.0, 1.0, 0.0], [20, 0.0, -4.0, 2.0, -1.0], [17, 3.0, -5.0, 4.0, -4.0]]], [[4, 20], [17, 39]]], [[[[5, 0.0, -2.0, 3.0, -2.0], [7, 5.0, 2.0, 5.0, 5.0], [21, 4.0, 3.0, 4.0, 4.0], [27, 6.0, 3.0, 9.0, 6.0], [1, 2.0, 5.0, 5.0, 7.0]]], [[1, 7]]], [[[[27, 1.0, -4.0, 2.0, -3.0], [22, -3.0, 5.0, 0.0, 7.0], [36, 0.0, -2.0, 4.0, -1.0]]], []], [[[[10, 1.0, 3.0, 5.0, 4.0], [21, 5.0, 0.0, 7.0, 2.0], [27, 5.0, 1.0, 6.0, 5.0], [34, -1.0, -4.0, 2.0, -3.0]]], [[10, 27], [21, 27]]], [[[[23, -4.0, -3.0, -1.0, -3.0], [30, -6.0, -4.0, -4.0, -4.0], [13, 5.0, 0.0, 9.0, 3.0], [1, -5.0, 6.0, -4.0, 6.0], [37, -1.0, 2.0, 0.0, 2.0], [11, 5.0, 0.0, 9.0, 0.0], [21, 0.0, 4.0, 1.0, 8.0], [35, -5.0, -4.0, -5.0, -1.0], [4, 0.0, -4.0, 0.0, -2.0], [32, -4.0, 0.0, 0.0, 4.0]]], [[11, 13], [21, 32], [30, 35], [32, 37]]], [[[[39, -6.0, 1.0, -6.0, 5.0], [6, -5.0, -4.0, -2.0, 0.0], [17, 0.0, 4.0, 2.0, 7.0], [35, -6.0, 5.0, -6.0, 7.0]]], [[35, 39]]]], [[[[[24, 5.0, -5.0, 8.0, -3.0], [23, -4.0, 1.0, 0.0, 4.0], [4, -6.0, -6.0, -2.0, -6.0], [2, -4.0, 2.0, -3.0, 2.0], [7, 0.0, 3.0, 2.0, 4.0], [19, 0.0, -5.0, 4.0, -1.0]]], [[2, 23], [7, 23]]], [[[[35, 1.0, 0.0, 1.0, 0.0], [39, 0.0, -3.0, 4.0, 0.0], [7, 2.0, -3.0, 2.0, -2.0], [2, 5.0, 5.0, 5.0, 6.0]]], [[7, 39], [35, 39]]], [[[[4, 1.0, -1.0, 5.0, -1.0], [36, -4.0, -5.0, -1.0, -5.0], [10, 3.0, 6.0, 5.0, 6.0], [11, 0.0, -1.0, 4.0, 0.0], [22, -1.0, 0.0, 1.0, 4.0], [14, 1.0, -4.0, 4.0, -2.0], [3, -1.0, 0.0, 1.0, 0.0]]], [[3, 11], [3, 22], [4, 11], [11, 22]]], [[[[22, 6.0, 3.0, 7.0, 5.0], [2, -3.0, 2.0, -3.0, 2.0], [1, -5.0, 4.0, -3.0, 8.0], [18, 2.0, 4.0, 4.0, 6.0], [29, 0.0, -5.0, 0.0, -2.0], [21, 6.0, 4.0, 6.0, 4.0], [10, 2.0, 1.0, 6.0, 5.0], [4, -6.0, 5.0, -6.0, 9.0], [20, -1.0, 4.0, 0.0, 7.0], [12, 3.0, 6.0, 6.0, 10.0], [5, -4.0, 4.0, -1.0, 5.0]]], [[1, 5], [5, 20], [10, 18], [10, 21], [10, 22], [12, 18], [21, 22]]], [[[[21, 5.0, 1.0, 6.0, 2.0], [6, 0.0, 6.0, 2.0, 8.0], [3, 5.0, 4.0, 5.0, 5.0]]], []], [[[[34, 5.0, 0.0, 6.0, 2.0], [15, 0.0, 3.0, 3.0, 5.0], [29, -3.0, -4.0, -1.0, -2.0]]], []], [[[[5, 2.0, 6.0, 5.0, 6.0], [12, -3.0, 3.0, -2.0, 4.0], [35, -2.0, -4.0, -1.0, -4.0], [22, 6.0, 6.0, 9.0, 6.0], [28, 1.0, -6.0, 1.0, -2.0], [3, -2.0, -2.0, -2.0, 2.0], [16, 6.0, 5.0, 6.0, 5.0], [11, -3.0, 4.0, -3.0, 6.0], [37, -4.0, 3.0, -1.0, 7.0], [32, -5.0, -2.0, -1.0, -2.0], [18, 0.0, -5.0, 0.0, -2.0]]], [[3, 32], [11, 12], [11, 37], [12, 37]]], [[[[11, 6.0, -3.0, 7.0, 1.0], [26, -3.0, -5.0, 0.0, -4.0], [32, 1.0, 5.0, 1.0, 5.0], [1, -3.0, -2.0, 1.0, 2.0], [39, 5.0, -3.0, 5.0, -2.0], [12, 5.0, 4.0, 8.0, 7.0], [21, 0.0, -6.0, 3.0, -3.0], [17, 5.0, -3.0, 7.0, -1.0], [9, -6.0, -2.0, -4.0, 0.0]]], [[11, 17], [17, 39], [21, 26]]]]]
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[][]Passed
case 1[[6, 14], [6, 32], [14, 32]][[6, 14], [6, 32], [7, 32], [14, 32]]Failed
case 2[][]Passed
case 3[[5, 25], [15, 20], [15, 34]][[5, 20], [5, 25], [15, 20], [15, 34]]Failed
case 4[[3, 24], [4, 29]][[3, 24], [4, 29]]Passed
case 5[][[6, 37]]Failed
case 6[][[2, 15], [15, 39]]Failed
case 7[][]Passed

SHA-256 / 95a1af6aada7d79fb76652e5d8f979b16a3e7b0f6db00d45f950ebd3e9a2c86a

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 2026-09-29T14:50:57.963646+00:00.

Case digest / a7fd2d07357ed589299a1b0d989e7fff7b1aa78f69c5c193d10355abcb4613c9