FAILURE MAP
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FA-87766 / Collision detection broadphase / Open access

First pruning pass excludes boxes starting at the end of a · case 01

Static boxes that just touch a dynamic box are missed.

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

ROOT CAUSE

Pass 1 scans while minx < a.maxx.

THE FAILURE

Pass 1 scans while minx < a.maxx.

Unsuccessful approach: Making pass 2 strict instead misses touching pairs from the other side.

Case contract

solve(A, B): bipartite box pruning (dynamic set A vs static set B), boxes [id,minx,miny,maxx,maxy], closed intervals. Sort both by (minx,id). Pass 1: for each a, B boxes with minx in [a.minx, a.maxx]; pass 2: for each b, A boxes with minx in (b.minx, b.maxx]; y overlap required. Return sorted [a id, b id] pairs.

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(A, B):
    As = sorted(A, key=lambda r: (r[1], r[0]))
    Bs = sorted(B, key=lambda r: (r[1], r[0]))
    def yover(p, q):
        return p[2] <= q[4] and q[2] <= p[4]
    pairs = []
    j = 0
    for a in As:
        while j < len(Bs) and Bs[j][1] < a[1]:
            j += 1
        k = j
        while k < len(Bs) and Bs[k][1] < a[3]:
            if yover(a, Bs[k]):
                pairs.append([a[0], Bs[k][0]])
            k += 1
    j2 = 0
    for b in Bs:
        while j2 < len(As) and As[j2][1] <= b[1]:
            j2 += 1
        k = j2
        while k < len(As) and As[k][1] <= b[3]:
            if yover(As[k], b):
                pairs.append([As[k][0], b[0]])
            k += 1
    pairs.sort()
    return pairs
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[[[[8, 3.0, 4.0, 5.0, 7.0]], [[35, -2.0, -1.0, 1.0, 2.0], [25, -3.0, -1.0, -3.0, -1.0], [19, -3.0, -4.0, 0.0, -2.0], [26, 0.0, 0.0, 2.0, 1.0]]], []], [[[[10, 4.0, 0.0, 4.0, 1.0], [22, -4.0, 5.0, -2.0, 8.0], [8, -1.0, -2.0, 2.0, 0.0], [24, 0.0, 2.0, 1.0, 2.0]], [[35, 1.0, 1.0, 4.0, 4.0], [13, 2.0, 0.0, 4.0, 1.0], [18, -4.0, 1.0, -2.0, 2.0], [6, -3.0, -1.0, -3.0, 0.0]]], [[8, 13], [10, 13], [10, 35], [24, 35]]], [[[[8, 2.0, -1.0, 4.0, 1.0]], [[21, 2.0, 4.0, 5.0, 7.0]]], []], [[[[16, -3.0, 4.0, -3.0, 4.0], [21, 0.0, -2.0, 1.0, -2.0], [17, -3.0, -1.0, -2.0, 0.0]], [[11, -3.0, -2.0, 2.0, -2.0], [24, -5.0, 4.0, -3.0, 7.0], [5, -5.0, 0.0, -4.0, 2.0]]], [[16, 24], [21, 11]]], [[[[4, -5.0, -2.0, -5.0, -1.0], [36, 5.0, -4.0, 6.0, -3.0], [16, -3.0, -2.0, 0.0, 0.0]], [[39, -5.0, -2.0, -1.0, -1.0], [20, 0.0, 0.0, 3.0, 2.0], [26, -1.0, -5.0, -1.0, -4.0], [5, 2.0, 5.0, 2.0, 7.0]]], [[4, 39], [16, 20], [16, 39]]], [[[[11, 4.0, 0.0, 6.0, 1.0]], [[5, 4.0, 2.0, 4.0, 5.0], [24, -4.0, 0.0, -3.0, 2.0], [1, 3.0, 1.0, 4.0, 3.0], [27, 3.0, 1.0, 4.0, 1.0]]], [[11, 1], [11, 27]]], [[[[17, -1.0, -3.0, -1.0, -2.0], [6, -3.0, 1.0, -1.0, 3.0], [34, 1.0, -2.0, 3.0, 1.0]], [[27, -1.0, -4.0, 1.0, -2.0], [12, -1.0, -5.0, 2.0, -5.0], [4, -2.0, 3.0, -1.0, 4.0]]], [[6, 4], [17, 27], [34, 27]]], [[[[1, 2.0, -1.0, 4.0, 1.0], [29, 0.0, -3.0, 1.0, -1.0], [7, 0.0, 4.0, 1.0, 4.0]], [[19, 2.0, 2.0, 2.0, 4.0], [28, -3.0, 4.0, -1.0, 4.0], [30, 4.0, 1.0, 5.0, 1.0]]], [[1, 30]]]], [[[[[31, -2.0, -1.0, -2.0, 1.0]], [[18, -2.0, -5.0, 1.0, -3.0]]], []], [[[[24, 1.0, -3.0, 4.0, -1.0], [9, -3.0, 1.0, -2.0, 3.0], [27, 2.0, 2.0, 3.0, 5.0]], [[32, 4.0, 5.0, 5.0, 8.0], [1, -2.0, -4.0, 0.0, -2.0], [6, 2.0, -2.0, 2.0, 0.0]]], [[24, 6]]], [[[[9, 1.0, 5.0, 2.0, 7.0], [2, 2.0, 3.0, 5.0, 5.0], [18, -1.0, 1.0, 1.0, 2.0]], [[10, 5.0, -4.0, 7.0, -2.0], [7, -4.0, 2.0, -1.0, 4.0], [37, 4.0, 3.0, 5.0, 3.0], [23, 1.0, -2.0, 1.0, -2.0]]], [[2, 37], [18, 7]]], [[[[8, -2.0, 3.0, -2.0, 6.0], [12, 2.0, 1.0, 2.0, 4.0], [37, -1.0, 4.0, 1.0, 7.0], [32, 0.0, -3.0, 2.0, -3.0]], [[26, 2.0, 4.0, 4.0, 6.0], [22, 0.0, -1.0, 2.0, 2.0], [38, 3.0, -1.0, 4.0, -1.0], [16, -3.0, 1.0, -3.0, 4.0]]], [[12, 22], [12, 26]]], [[[[6, -3.0, -3.0, -3.0, 0.0], [9, -3.0, 5.0, -2.0, 8.0]], [[28, -3.0, -3.0, 1.0, -2.0]]], [[6, 28]]], [[[[23, 1.0, 3.0, 1.0, 5.0], [15, 0.0, -5.0, 3.0, -4.0]], [[1, 1.0, 2.0, 1.0, 3.0], [35, 3.0, -3.0, 5.0, 0.0]]], [[23, 1]]], [[[[19, 2.0, 1.0, 2.0, 2.0], [32, -1.0, 2.0, -1.0, 3.0], [18, 5.0, -2.0, 5.0, 0.0]], [[25, 2.0, 1.0, 2.0, 2.0], [33, 5.0, -1.0, 5.0, 0.0], [30, 0.0, 5.0, 3.0, 7.0]]], [[18, 33], [19, 25]]], [[[[17, -2.0, -5.0, 1.0, -2.0], [23, 5.0, 3.0, 6.0, 5.0], [31, -3.0, -5.0, -1.0, -5.0]], [[7, -2.0, -1.0, 5.0, -1.0]]], []]], [[[[[12, -5.0, 1.0, -2.0, 3.0], [27, -5.0, 0.0, -2.0, 0.0], [31, 4.0, 0.0, 4.0, 1.0], [25, 3.0, 5.0, 6.0, 6.0]], [[32, 1.0, 1.0, 3.0, 2.0], [9, -3.0, -3.0, 0.0, 0.0], [30, -4.0, 2.0, -4.0, 2.0], [8, -2.0, -4.0, 1.0, -1.0]]], [[12, 30], [27, 9]]], [[[[23, 4.0, -4.0, 4.0, -1.0], [10, 3.0, -5.0, 3.0, -5.0], [29, -5.0, -5.0, -4.0, -5.0]], [[39, 4.0, -4.0, 4.0, -2.0], [12, 0.0, -4.0, 0.0, -1.0], [25, 3.0, -5.0, 6.0, -2.0]]], [[10, 25], [23, 25], [23, 39]]], [[[[18, -5.0, 4.0, -5.0, 5.0], [6, -1.0, -2.0, 1.0, -1.0]], [[21, 1.0, -2.0, 1.0, 1.0], [9, 0.0, 0.0, 0.0, 1.0], [14, -2.0, -3.0, -1.0, -2.0], [30, 4.0, -5.0, 6.0, -2.0]]], [[6, 14], [6, 21]]], [[[[11, 1.0, 2.0, 1.0, 4.0], [5, 4.0, 2.0, 5.0, 2.0], [32, -2.0, -5.0, -1.0, -2.0]], [[30, 0.0, 4.0, 0.0, 7.0], [36, 1.0, 1.0, 4.0, 1.0], [19, -4.0, -4.0, -1.0, -3.0], [31, -2.0, 3.0, 1.0, 6.0]]], [[11, 31], [32, 19]]], [[[[31, -2.0, 2.0, -2.0, 3.0], [26, -5.0, -5.0, -3.0, -5.0], [12, -3.0, 4.0, -2.0, 4.0]], [[38, -3.0, -1.0, -2.0, -1.0], [7, -3.0, 5.0, -1.0, 8.0]]], []], [[[[32, 3.0, -5.0, 4.0, -3.0]], [[9, -3.0, 3.0, 0.0, 4.0], [19, -4.0, -2.0, -2.0, -1.0], [28, -3.0, -4.0, 0.0, -3.0], [18, 0.0, 3.0, 0.0, 6.0]]], []], [[[[31, 4.0, -2.0, 4.0, 0.0], [8, -5.0, -5.0, -3.0, -2.0]], [[18, 0.0, -5.0, 2.0, -3.0], [25, 0.0, 5.0, 0.0, 7.0], [6, -2.0, 4.0, -1.0, 7.0]]], []], [[[[35, 4.0, -2.0, 5.0, 0.0], [12, 0.0, 2.0, 3.0, 4.0]], [[39, 4.0, 0.0, 4.0, 3.0], [18, 2.0, 2.0, 3.0, 5.0], [34, 2.0, 0.0, 5.0, 3.0], [22, 3.0, 3.0, 3.0, 3.0]]], [[12, 18], [12, 22], [12, 34], [35, 34], [35, 39]]]], [[[[[16, -3.0, -1.0, -1.0, -1.0], [31, -2.0, -2.0, 1.0, 0.0]], [[23, -3.0, 4.0, 4.0, 6.0], [14, 1.0, -2.0, 3.0, -2.0]]], [[31, 14]]], [[[[25, 5.0, 5.0, 8.0, 6.0], [4, -1.0, -3.0, 1.0, 0.0]], [[33, 5.0, 5.0, 5.0, 8.0], [20, -4.0, -3.0, -1.0, -3.0], [37, 4.0, 5.0, 7.0, 6.0], [17, -4.0, 4.0, -3.0, 7.0]]], [[4, 20], [25, 33], [25, 37]]], [[[[28, -1.0, 5.0, -1.0, 6.0], [1, 4.0, 2.0, 5.0, 4.0]], [[13, -1.0, 3.0, 1.0, 3.0], [21, -1.0, 1.0, 2.0, 4.0], [17, 4.0, -1.0, 6.0, 0.0]]], []], [[[[32, 1.0, 3.0, 1.0, 4.0]], [[10, -1.0, 3.0, 1.0, 5.0], [8, 1.0, 1.0, 4.0, 2.0], [30, -5.0, 4.0, -3.0, 6.0], [24, 4.0, 5.0, 5.0, 7.0]]], [[32, 10]]], [[[[33, 5.0, -3.0, 6.0, -3.0], [29, -3.0, 2.0, 0.0, 3.0], [20, 4.0, -5.0, 4.0, -2.0], [30, 3.0, -1.0, 6.0, -1.0]], [[13, 5.0, -2.0, 5.0, -1.0], [24, -3.0, 3.0, -3.0, 5.0]]], [[29, 24], [30, 13]]], [[[[37, 4.0, 2.0, 4.0, 3.0], [11, 3.0, -3.0, 3.0, 0.0]], [[3, 4.0, 1.0, 6.0, 3.0], [24, 4.0, 3.0, 6.0, 3.0], [13, 4.0, 5.0, 4.0, 7.0], [39, 0.0, 4.0, 3.0, 6.0]]], [[37, 3], [37, 24]]], [[[[39, -4.0, 2.0, -2.0, 2.0], [36, -4.0, -3.0, -4.0, -1.0]], [[20, 5.0, -5.0, 7.0, -2.0], [22, -5.0, 4.0, -5.0, 4.0], [25, -3.0, 3.0, -2.0, 3.0]]], []], [[[[36, 4.0, -3.0, 4.0, 0.0], [6, -3.0, 1.0, -3.0, 1.0], [37, -3.0, -3.0, -1.0, -2.0]], [[33, 3.0, -2.0, 4.0, -2.0], [18, -1.0, 5.0, -1.0, 7.0], [25, -3.0, -1.0, -1.0, 1.0], [2, -3.0, 5.0, 0.0, 6.0]]], [[6, 25], [36, 33]]]], [[[[[26, -3.0, -3.0, -1.0, -1.0], [2, 1.0, 5.0, 3.0, 5.0], [7, 2.0, 5.0, 5.0, 5.0]], [[20, -1.0, -1.0, -1.0, 0.0], [14, 5.0, 2.0, 7.0, 2.0], [5, 0.0, 3.0, 3.0, 6.0]]], [[2, 5], [7, 5], [26, 20]]], [[[[14, -5.0, -5.0, -5.0, -5.0], [26, -3.0, -1.0, -1.0, 1.0], [20, 1.0, 3.0, 3.0, 4.0]], [[10, -5.0, -5.0, 2.0, -4.0]]], [[14, 10]]], [[[[7, 5.0, 3.0, 6.0, 4.0], [29, 0.0, -3.0, 2.0, -3.0]], [[14, 5.0, 0.0, 5.0, 0.0], [9, 3.0, 0.0, 4.0, 2.0], [19, -2.0, -3.0, 0.0, -2.0]]], [[29, 19]]], [[[[32, 0.0, 2.0, 3.0, 2.0]], [[37, 0.0, -5.0, 4.0, -3.0]]], []], [[[[21, -2.0, 4.0, -2.0, 6.0], [3, 3.0, -5.0, 4.0, -2.0], [36, -1.0, -3.0, 1.0, -2.0]], [[23, -1.0, 0.0, 2.0, 0.0], [12, 0.0, -1.0, 2.0, 0.0], [8, -2.0, 5.0, 1.0, 7.0], [1, -1.0, 0.0, 0.0, 1.0]]], [[21, 8]]], [[[[19, 2.0, 1.0, 5.0, 4.0]], [[39, 2.0, 4.0, 6.0, 7.0], [14, 5.0, -3.0, 8.0, 0.0]]], [[19, 39]]], [[[[15, 1.0, 1.0, 3.0, 2.0], [27, 2.0, 4.0, 4.0, 4.0], [6, -4.0, -4.0, -3.0, -4.0]], [[20, 2.0, -4.0, 3.0, -3.0], [2, 0.0, 0.0, 1.0, 2.0]]], [[15, 2]]], [[[[38, 5.0, 0.0, 5.0, 2.0], [37, -5.0, 5.0, -4.0, 5.0]], [[7, 3.0, 1.0, 5.0, 4.0], [33, -5.0, 3.0, -4.0, 5.0], [13, -4.0, -4.0, -4.0, -1.0]]], [[37, 33], [38, 7]]]]]
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[[10, 13], [10, 35]][[8, 13], [10, 13], [10, 35], [24, 35]]Failed
case 2[][]Passed
case 3[[16, 24], [21, 11]][[16, 24], [21, 11]]Passed
case 4[[16, 39]][[4, 39], [16, 20], [16, 39]]Failed
case 5[[11, 1], [11, 27]][[11, 1], [11, 27]]Passed
case 6[[6, 4], [34, 27]][[6, 4], [17, 27], [34, 27]]Failed
case 7[][[1, 30]]Failed

SHA-256 / c9a13eac85e40d97f4d9e856e24a23a0e21018e9198bde49d3acf6636f1e6760

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(A, B):
    As = sorted(A, key=lambda r: (r[1], r[0]))
    Bs = sorted(B, key=lambda r: (r[1], r[0]))
    def yover(p, q):
        return p[2] <= q[4] and q[2] <= p[4]
    pairs = []
    j = 0
    for a in As:
        while j < len(Bs) and Bs[j][1] < a[1]:
            j += 1
        k = j
        while k < len(Bs) and Bs[k][1] <= a[3]:
            if yover(a, Bs[k]):
                pairs.append([a[0], Bs[k][0]])
            k += 1
    j2 = 0
    for b in Bs:
        while j2 < len(As) and As[j2][1] <= b[1]:
            j2 += 1
        k = j2
        while k < len(As) and As[k][1] < b[3]:
            if yover(As[k], b):
                pairs.append([As[k][0], b[0]])
            k += 1
    pairs.sort()
    return pairs
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[[[[8, 3.0, 4.0, 5.0, 7.0]], [[35, -2.0, -1.0, 1.0, 2.0], [25, -3.0, -1.0, -3.0, -1.0], [19, -3.0, -4.0, 0.0, -2.0], [26, 0.0, 0.0, 2.0, 1.0]]], []], [[[[10, 4.0, 0.0, 4.0, 1.0], [22, -4.0, 5.0, -2.0, 8.0], [8, -1.0, -2.0, 2.0, 0.0], [24, 0.0, 2.0, 1.0, 2.0]], [[35, 1.0, 1.0, 4.0, 4.0], [13, 2.0, 0.0, 4.0, 1.0], [18, -4.0, 1.0, -2.0, 2.0], [6, -3.0, -1.0, -3.0, 0.0]]], [[8, 13], [10, 13], [10, 35], [24, 35]]], [[[[8, 2.0, -1.0, 4.0, 1.0]], [[21, 2.0, 4.0, 5.0, 7.0]]], []], [[[[16, -3.0, 4.0, -3.0, 4.0], [21, 0.0, -2.0, 1.0, -2.0], [17, -3.0, -1.0, -2.0, 0.0]], [[11, -3.0, -2.0, 2.0, -2.0], [24, -5.0, 4.0, -3.0, 7.0], [5, -5.0, 0.0, -4.0, 2.0]]], [[16, 24], [21, 11]]], [[[[4, -5.0, -2.0, -5.0, -1.0], [36, 5.0, -4.0, 6.0, -3.0], [16, -3.0, -2.0, 0.0, 0.0]], [[39, -5.0, -2.0, -1.0, -1.0], [20, 0.0, 0.0, 3.0, 2.0], [26, -1.0, -5.0, -1.0, -4.0], [5, 2.0, 5.0, 2.0, 7.0]]], [[4, 39], [16, 20], [16, 39]]], [[[[11, 4.0, 0.0, 6.0, 1.0]], [[5, 4.0, 2.0, 4.0, 5.0], [24, -4.0, 0.0, -3.0, 2.0], [1, 3.0, 1.0, 4.0, 3.0], [27, 3.0, 1.0, 4.0, 1.0]]], [[11, 1], [11, 27]]], [[[[17, -1.0, -3.0, -1.0, -2.0], [6, -3.0, 1.0, -1.0, 3.0], [34, 1.0, -2.0, 3.0, 1.0]], [[27, -1.0, -4.0, 1.0, -2.0], [12, -1.0, -5.0, 2.0, -5.0], [4, -2.0, 3.0, -1.0, 4.0]]], [[6, 4], [17, 27], [34, 27]]], [[[[1, 2.0, -1.0, 4.0, 1.0], [29, 0.0, -3.0, 1.0, -1.0], [7, 0.0, 4.0, 1.0, 4.0]], [[19, 2.0, 2.0, 2.0, 4.0], [28, -3.0, 4.0, -1.0, 4.0], [30, 4.0, 1.0, 5.0, 1.0]]], [[1, 30]]]], [[[[[31, -2.0, -1.0, -2.0, 1.0]], [[18, -2.0, -5.0, 1.0, -3.0]]], []], [[[[24, 1.0, -3.0, 4.0, -1.0], [9, -3.0, 1.0, -2.0, 3.0], [27, 2.0, 2.0, 3.0, 5.0]], [[32, 4.0, 5.0, 5.0, 8.0], [1, -2.0, -4.0, 0.0, -2.0], [6, 2.0, -2.0, 2.0, 0.0]]], [[24, 6]]], [[[[9, 1.0, 5.0, 2.0, 7.0], [2, 2.0, 3.0, 5.0, 5.0], [18, -1.0, 1.0, 1.0, 2.0]], [[10, 5.0, -4.0, 7.0, -2.0], [7, -4.0, 2.0, -1.0, 4.0], [37, 4.0, 3.0, 5.0, 3.0], [23, 1.0, -2.0, 1.0, -2.0]]], [[2, 37], [18, 7]]], [[[[8, -2.0, 3.0, -2.0, 6.0], [12, 2.0, 1.0, 2.0, 4.0], [37, -1.0, 4.0, 1.0, 7.0], [32, 0.0, -3.0, 2.0, -3.0]], [[26, 2.0, 4.0, 4.0, 6.0], [22, 0.0, -1.0, 2.0, 2.0], [38, 3.0, -1.0, 4.0, -1.0], [16, -3.0, 1.0, -3.0, 4.0]]], [[12, 22], [12, 26]]], [[[[6, -3.0, -3.0, -3.0, 0.0], [9, -3.0, 5.0, -2.0, 8.0]], [[28, -3.0, -3.0, 1.0, -2.0]]], [[6, 28]]], [[[[23, 1.0, 3.0, 1.0, 5.0], [15, 0.0, -5.0, 3.0, -4.0]], [[1, 1.0, 2.0, 1.0, 3.0], [35, 3.0, -3.0, 5.0, 0.0]]], [[23, 1]]], [[[[19, 2.0, 1.0, 2.0, 2.0], [32, -1.0, 2.0, -1.0, 3.0], [18, 5.0, -2.0, 5.0, 0.0]], [[25, 2.0, 1.0, 2.0, 2.0], [33, 5.0, -1.0, 5.0, 0.0], [30, 0.0, 5.0, 3.0, 7.0]]], [[18, 33], [19, 25]]], [[[[17, -2.0, -5.0, 1.0, -2.0], [23, 5.0, 3.0, 6.0, 5.0], [31, -3.0, -5.0, -1.0, -5.0]], [[7, -2.0, -1.0, 5.0, -1.0]]], []]], [[[[[12, -5.0, 1.0, -2.0, 3.0], [27, -5.0, 0.0, -2.0, 0.0], [31, 4.0, 0.0, 4.0, 1.0], [25, 3.0, 5.0, 6.0, 6.0]], [[32, 1.0, 1.0, 3.0, 2.0], [9, -3.0, -3.0, 0.0, 0.0], [30, -4.0, 2.0, -4.0, 2.0], [8, -2.0, -4.0, 1.0, -1.0]]], [[12, 30], [27, 9]]], [[[[23, 4.0, -4.0, 4.0, -1.0], [10, 3.0, -5.0, 3.0, -5.0], [29, -5.0, -5.0, -4.0, -5.0]], [[39, 4.0, -4.0, 4.0, -2.0], [12, 0.0, -4.0, 0.0, -1.0], [25, 3.0, -5.0, 6.0, -2.0]]], [[10, 25], [23, 25], [23, 39]]], [[[[18, -5.0, 4.0, -5.0, 5.0], [6, -1.0, -2.0, 1.0, -1.0]], [[21, 1.0, -2.0, 1.0, 1.0], [9, 0.0, 0.0, 0.0, 1.0], [14, -2.0, -3.0, -1.0, -2.0], [30, 4.0, -5.0, 6.0, -2.0]]], [[6, 14], [6, 21]]], [[[[11, 1.0, 2.0, 1.0, 4.0], [5, 4.0, 2.0, 5.0, 2.0], [32, -2.0, -5.0, -1.0, -2.0]], [[30, 0.0, 4.0, 0.0, 7.0], [36, 1.0, 1.0, 4.0, 1.0], [19, -4.0, -4.0, -1.0, -3.0], [31, -2.0, 3.0, 1.0, 6.0]]], [[11, 31], [32, 19]]], [[[[31, -2.0, 2.0, -2.0, 3.0], [26, -5.0, -5.0, -3.0, -5.0], [12, -3.0, 4.0, -2.0, 4.0]], [[38, -3.0, -1.0, -2.0, -1.0], [7, -3.0, 5.0, -1.0, 8.0]]], []], [[[[32, 3.0, -5.0, 4.0, -3.0]], [[9, -3.0, 3.0, 0.0, 4.0], [19, -4.0, -2.0, -2.0, -1.0], [28, -3.0, -4.0, 0.0, -3.0], [18, 0.0, 3.0, 0.0, 6.0]]], []], [[[[31, 4.0, -2.0, 4.0, 0.0], [8, -5.0, -5.0, -3.0, -2.0]], [[18, 0.0, -5.0, 2.0, -3.0], [25, 0.0, 5.0, 0.0, 7.0], [6, -2.0, 4.0, -1.0, 7.0]]], []], [[[[35, 4.0, -2.0, 5.0, 0.0], [12, 0.0, 2.0, 3.0, 4.0]], [[39, 4.0, 0.0, 4.0, 3.0], [18, 2.0, 2.0, 3.0, 5.0], [34, 2.0, 0.0, 5.0, 3.0], [22, 3.0, 3.0, 3.0, 3.0]]], [[12, 18], [12, 22], [12, 34], [35, 34], [35, 39]]]], [[[[[16, -3.0, -1.0, -1.0, -1.0], [31, -2.0, -2.0, 1.0, 0.0]], [[23, -3.0, 4.0, 4.0, 6.0], [14, 1.0, -2.0, 3.0, -2.0]]], [[31, 14]]], [[[[25, 5.0, 5.0, 8.0, 6.0], [4, -1.0, -3.0, 1.0, 0.0]], [[33, 5.0, 5.0, 5.0, 8.0], [20, -4.0, -3.0, -1.0, -3.0], [37, 4.0, 5.0, 7.0, 6.0], [17, -4.0, 4.0, -3.0, 7.0]]], [[4, 20], [25, 33], [25, 37]]], [[[[28, -1.0, 5.0, -1.0, 6.0], [1, 4.0, 2.0, 5.0, 4.0]], [[13, -1.0, 3.0, 1.0, 3.0], [21, -1.0, 1.0, 2.0, 4.0], [17, 4.0, -1.0, 6.0, 0.0]]], []], [[[[32, 1.0, 3.0, 1.0, 4.0]], [[10, -1.0, 3.0, 1.0, 5.0], [8, 1.0, 1.0, 4.0, 2.0], [30, -5.0, 4.0, -3.0, 6.0], [24, 4.0, 5.0, 5.0, 7.0]]], [[32, 10]]], [[[[33, 5.0, -3.0, 6.0, -3.0], [29, -3.0, 2.0, 0.0, 3.0], [20, 4.0, -5.0, 4.0, -2.0], [30, 3.0, -1.0, 6.0, -1.0]], [[13, 5.0, -2.0, 5.0, -1.0], [24, -3.0, 3.0, -3.0, 5.0]]], [[29, 24], [30, 13]]], [[[[37, 4.0, 2.0, 4.0, 3.0], [11, 3.0, -3.0, 3.0, 0.0]], [[3, 4.0, 1.0, 6.0, 3.0], [24, 4.0, 3.0, 6.0, 3.0], [13, 4.0, 5.0, 4.0, 7.0], [39, 0.0, 4.0, 3.0, 6.0]]], [[37, 3], [37, 24]]], [[[[39, -4.0, 2.0, -2.0, 2.0], [36, -4.0, -3.0, -4.0, -1.0]], [[20, 5.0, -5.0, 7.0, -2.0], [22, -5.0, 4.0, -5.0, 4.0], [25, -3.0, 3.0, -2.0, 3.0]]], []], [[[[36, 4.0, -3.0, 4.0, 0.0], [6, -3.0, 1.0, -3.0, 1.0], [37, -3.0, -3.0, -1.0, -2.0]], [[33, 3.0, -2.0, 4.0, -2.0], [18, -1.0, 5.0, -1.0, 7.0], [25, -3.0, -1.0, -1.0, 1.0], [2, -3.0, 5.0, 0.0, 6.0]]], [[6, 25], [36, 33]]]], [[[[[26, -3.0, -3.0, -1.0, -1.0], [2, 1.0, 5.0, 3.0, 5.0], [7, 2.0, 5.0, 5.0, 5.0]], [[20, -1.0, -1.0, -1.0, 0.0], [14, 5.0, 2.0, 7.0, 2.0], [5, 0.0, 3.0, 3.0, 6.0]]], [[2, 5], [7, 5], [26, 20]]], [[[[14, -5.0, -5.0, -5.0, -5.0], [26, -3.0, -1.0, -1.0, 1.0], [20, 1.0, 3.0, 3.0, 4.0]], [[10, -5.0, -5.0, 2.0, -4.0]]], [[14, 10]]], [[[[7, 5.0, 3.0, 6.0, 4.0], [29, 0.0, -3.0, 2.0, -3.0]], [[14, 5.0, 0.0, 5.0, 0.0], [9, 3.0, 0.0, 4.0, 2.0], [19, -2.0, -3.0, 0.0, -2.0]]], [[29, 19]]], [[[[32, 0.0, 2.0, 3.0, 2.0]], [[37, 0.0, -5.0, 4.0, -3.0]]], []], [[[[21, -2.0, 4.0, -2.0, 6.0], [3, 3.0, -5.0, 4.0, -2.0], [36, -1.0, -3.0, 1.0, -2.0]], [[23, -1.0, 0.0, 2.0, 0.0], [12, 0.0, -1.0, 2.0, 0.0], [8, -2.0, 5.0, 1.0, 7.0], [1, -1.0, 0.0, 0.0, 1.0]]], [[21, 8]]], [[[[19, 2.0, 1.0, 5.0, 4.0]], [[39, 2.0, 4.0, 6.0, 7.0], [14, 5.0, -3.0, 8.0, 0.0]]], [[19, 39]]], [[[[15, 1.0, 1.0, 3.0, 2.0], [27, 2.0, 4.0, 4.0, 4.0], [6, -4.0, -4.0, -3.0, -4.0]], [[20, 2.0, -4.0, 3.0, -3.0], [2, 0.0, 0.0, 1.0, 2.0]]], [[15, 2]]], [[[[38, 5.0, 0.0, 5.0, 2.0], [37, -5.0, 5.0, -4.0, 5.0]], [[7, 3.0, 1.0, 5.0, 4.0], [33, -5.0, 3.0, -4.0, 5.0], [13, -4.0, -4.0, -4.0, -1.0]]], [[37, 33], [38, 7]]]]]
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[[8, 13], [24, 35]][[8, 13], [10, 13], [10, 35], [24, 35]]Failed
case 2[][]Passed
case 3[[21, 11]][[16, 24], [21, 11]]Failed
case 4[[4, 39], [16, 20], [16, 39]][[4, 39], [16, 20], [16, 39]]Passed
case 5[][[11, 1], [11, 27]]Failed
case 6[[6, 4], [17, 27]][[6, 4], [17, 27], [34, 27]]Failed
case 7[[1, 30]][[1, 30]]Passed

SHA-256 / 54ecff396fee211fcc7fb9294832898c2f91c1dd563e539754428ad366a02bd5

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 2026-09-29T14:51:01.900989+00:00.

Case digest / 5aa8139c3e00d555b4a634974df8ebfd88633da0e939c265fb1def8a547bd0d5