FAILURE MAP
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FA-87561 / Collision detection broadphase / Open access

Centroids on the upper scene bound wrap to cell zero · case 01

Objects on the far edge sort next to the origin and the LBVH gets huge nodes.

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

ROOT CAUSE

The quantized value is not clamped to 1023, so 1024 masks to 0.

THE FAILURE

The quantized value is not clamped to 1023, so 1024 masks to 0.

Unsuccessful approach: Scaling by 1023 instead avoids the wrap but shifts every other code.

Case contract

solve(pts, bounds): LBVH ordering. Each centroid [id,x,y] is quantized per axis to min(1023, max(0, floor((c-lo)/(hi-lo)*1024))) (0 for a flat axis), and the 10-bit values are interleaved with x in even bits and y in odd bits. Return [[id, code]] sorted by (code, numeric id).

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(pts, bounds):
    def part(v):
        v &= 0x3FF
        v = (v | (v << 8)) & 0x00FF00FF
        v = (v | (v << 4)) & 0x0F0F0F0F
        v = (v | (v << 2)) & 0x33333333
        v = (v | (v << 1)) & 0x55555555
        return v
    def quant(c, lo, hi):
        if hi <= lo:
            return 0
        return max(0, math.floor((c - lo) / (hi - lo) * 1024))
    out = []
    for i, x, y in pts:
        code = part(quant(x, bounds[0], bounds[2])) | (part(quant(y, bounds[1], bounds[3])) << 1)
        out.append([i, code])
    out.sort(key=lambda r: (r[1], r[0]))
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[[[[23, 11.15, 0.0], [29, 11.15, 0.0], [13, 45.93, 3.76], [24, 99.01, 0.0]], [0.0, 0.0, 100.0, 32.0]], [[23, 5380], [29, 5380], [13, 97172], [24, 349457]]], [[[[20, 3.4, -4.0], [23, 3.4, -4.0], [1, 0.66, -4.0], [26, 10.0, 4.55], [10, 7.68, -4.0], [14, 10.0, -4.0], [19, 0.12, -4.0]], [0.0, -4.0, 10.0, 4.0]], [[19, 80], [1, 4101], [20, 69968], [23, 69968], [10, 327940], [14, 349525], [26, 1048575]]], [[[[25, -10.0, -4.0], [21, -10.0, -4.0], [16, 82.55, 16.96], [18, -10.0, -4.0], [7, 75.11, 28.0], [1, 75.9, 27.07], [27, -10.0, -4.0]], [-10.0, -4.0, 90.0, 28.0]], [[18, 0], [21, 0], [25, 0], [27, 0], [16, 903085], [1, 1031261], [7, 1031871]]], [[[[7, 34.1, -4.0], [18, 0.0, -4.0]], [0.0, -4.0, 100.0, 4.0]], [[18, 0], [7, 69969]]], [[[[6, -10.0, 6.28], [27, -10.0, 8.0]], [-10.0, 0.0, 90.0, 8.0]], [[6, 657418], [27, 699050]]], [[[[15, -9.79, -4.0], [23, -8.97, 28.0], [4, 1.83, -4.0], [3, -10.0, 28.0]], [-10.0, -4.0, 6.0, 28.0]], [[15, 81], [4, 283921], [3, 699050], [23, 703147]]], [[[[20, 5.0, 9.07], [21, 5.0, 8.49], [28, 20.12, 26.83], [9, 59.81, 0.0]], [5.0, 0.0, 105.0, 32.0]], [[21, 131242], [20, 133128], [9, 263425], [28, 680908]]], [[[[15, -10.0, 30.56], [2, -10.0, 32.0], [1, -10.0, 32.0], [27, -10.51, 15.54]], [-10.0, 0.0, 0.0, 32.0]], [[27, 174594], [15, 696834], [1, 699050], [2, 699050]]]], [[[[[13, 4.71, 4.67], [19, 4.71, 4.67], [11, 5.0, 8.0], [21, 4.43, 0.91], [2, 4.2, 0.0], [9, 5.0, 3.28], [3, 5.0, 6.75]], [5.0, 0.0, 5.0, 8.0]], [[2, 0], [21, 10784], [9, 165898], [13, 533026], [19, 533026], [3, 665600], [11, 699050]]], [[[[29, -10.0, -0.25], [3, -10.57, 28.0], [19, -10.0, -4.0], [9, -10.0, -4.0], [20, -10.0, -4.0]], [-10.0, -4.0, -10.0, 28.0]], [[9, 0], [19, 0], [20, 0], [29, 10880], [3, 699050]]], [[[[26, 0.85, 18.54], [29, 0.85, 18.54], [17, -10.0, 32.0]], [-10.0, 0.0, 0.0, 32.0]], [[17, 699050], [26, 882519], [29, 882519]]], [[[[7, 2.09, 26.27], [12, 0.0, 29.03], [3, 13.02, 11.98], [10, 0.0, 21.46]], [0.0, 0.0, 16.0, 32.0]], [[3, 473771], [10, 559272], [7, 680081], [12, 690176]]], [[[[12, 5.05, 22.98], [5, 15.0, 32.0], [21, 7.47, 17.17], [26, 7.31, 3.09], [15, 13.84, 10.33], [2, 5.0, 32.0], [24, 15.0, 32.0]], [5.0, 0.0, 15.0, 32.0]], [[26, 31832], [15, 483529], [21, 548210], [12, 565947], [2, 699050], [5, 1048575], [24, 1048575]]], [[[[13, 4.02, 10.58], [22, 4.02, 10.58], [23, 5.0, 0.0]], [5.0, 0.0, 5.0, 32.0]], [[23, 0], [13, 139784], [22, 139784]]], [[[[27, 5.0, 4.0], [21, 5.0, 4.0], [22, 105.0, -3.16], [3, 42.29, 4.0], [17, 5.0, 2.25], [12, 25.35, -0.08], [8, 70.41, 2.16]], [5.0, -4.0, 105.0, 4.0]], [[12, 195362], [22, 359903], [17, 657408], [21, 699050], [27, 699050], [3, 770043], [8, 934769]]], [[[[14, 0.0, -4.0], [22, 0.0, 13.71], [15, 0.13, 7.52], [1, 0.0, -4.0], [29, 0.0, 27.3], [3, 0.0, -1.25]], [0.0, -4.0, 0.0, 28.0]], [[1, 0], [14, 0], [3, 8832], [15, 141824], [22, 526888], [29, 698498]]]], [[[[[18, 10.38, 4.0], [21, 10.38, 4.0], [9, 10.0, 4.0], [7, 6.82, 4.0], [11, 2.93, -4.0], [27, 1.97, 4.7], [3, 0.0, 1.79]], [0.0, -4.0, 10.0, 4.0]], [[11, 66640], [3, 567330], [27, 719595], [7, 978926], [9, 1048575], [18, 1048575], [21, 1048575]]], [[[[28, 8.07, -4.0], [18, 8.07, -4.0], [6, 8.12, -0.78], [23, 5.0, 4.0], [1, 5.0, -4.0], [3, 11.1, 3.03], [5, 13.26, 4.0], [12, 6.24, 4.0], [25, 5.0, -2.08]], [5.0, -4.0, 15.0, 4.0]], [[1, 0], [25, 43554], [18, 66884], [28, 66884], [6, 231413], [23, 699050], [12, 704510], [3, 955658], [5, 1030907]]], [[[[27, -10.0, 7.72], [4, -10.0, 1.55]], [-10.0, 0.0, -10.0, 8.0]], [[4, 41000], [27, 696992]]], [[[[9, 5.0, 3.16], [20, 5.0, 3.16], [4, 5.0, 0.0], [17, 5.0, 0.0], [18, 5.0, 0.0]], [5.0, 0.0, 5.0, 8.0]], [[4, 0], [17, 0], [18, 0], [9, 164384], [20, 164384]]], [[[[6, 1.61, 0.0], [20, -10.0, 8.0], [7, 6.0, 0.0], [16, 5.81, 2.39], [21, -9.33, 0.0]], [-10.0, 0.0, 6.0, 8.0]], [[21, 1092], [6, 283669], [7, 349525], [16, 483079], [20, 699050]]], [[[[28, -7.77, 4.0], [19, -9.68, 1.96], [21, 5.53, 1.02], [14, -10.0, 2.58]], [-10.0, -4.0, 6.0, 4.0]], [[19, 568216], [14, 663688], [28, 715518], [21, 906249]]], [[[[18, -5.18, 28.0], [22, -4.56, 8.95], [15, -2.07, 10.7], [2, -10.0, -4.13], [11, 0.0, -4.0]], [-10.0, -4.0, 0.0, 28.0]], [[2, 0], [11, 349525], [22, 427769], [15, 501368], [18, 786171]]], [[[[29, 5.19, -4.0], [12, 5.19, -4.0]], [5.0, -4.0, 15.0, 4.0]], [[12, 261], [29, 261]]]], [[[[[5, 3.93, -4.0], [23, 3.93, -4.0], [25, 0.0, -4.0]], [0.0, -4.0, 16.0, 4.0]], [[25, 0], [5, 21829], [23, 21829]]], [[[[20, 5.0, 15.36], [9, 5.0, 15.36], [6, 5.0, -4.0], [8, 5.0, 7.29], [2, 5.0, -4.0], [14, 5.0, 24.78], [17, 5.0, 2.43], [7, 5.69, -4.0]], [5.0, -4.0, 5.0, 28.0]], [[2, 0], [6, 0], [7, 0], [17, 41122], [8, 141442], [9, 534666], [20, 534666], [14, 688768]]], [[[[28, 5.0, -3.83], [6, 5.0, -3.83], [1, 17.93, -4.0], [21, 5.0, 26.93]], [5.0, -4.0, 105.0, 28.0]], [[6, 34], [28, 34], [1, 16400], [21, 696994]]], [[[[10, 3.1, 28.0], [9, 3.1, 28.0], [12, 6.8, -4.0], [27, 10.0, -4.0]], [0.0, -4.0, 10.0, 28.0]], [[12, 279872], [27, 349525], [9, 765947], [10, 765947]]], [[[[29, -10.0, -1.72], [19, -10.0, -1.72], [27, 4.61, 4.0], [24, 43.35, 4.0], [11, 90.0, -0.83], [21, -10.0, -4.0], [3, 90.0, -4.0], [4, 10.23, 2.21], [9, -10.0, -4.0], [7, 40.89, -4.0]], [-10.0, -4.0, 90.0, 4.0]], [[9, 0], [21, 0], [19, 133130], [29, 133130], [7, 262209], [3, 349525], [11, 513911], [4, 676573], [27, 715707], [24, 962222]]], [[[[12, 5.0, -1.65], [13, 5.0, -4.0], [10, 85.95, 0.41], [24, 5.0, -4.0]], [5.0, -4.0, 105.0, 4.0]], [[13, 0], [24, 0], [12, 133280], [10, 855920]]], [[[[12, 5.76, 2.78], [24, 4.73, 0.0], [27, 10.0, 0.78]], [0.0, 0.0, 10.0, 8.0]], [[24, 87056], [27, 359775], [12, 407643]]], [[[[7, 10.0, 3.93], [25, 0.0, 5.78], [23, 3.34, 8.0]], [0.0, 0.0, 10.0, 8.0]], [[7, 524159], [25, 567306], [23, 768958]]]], [[[[[15, 94.67, 0.0], [16, 100.0, 0.0], [12, 0.0, 10.42], [20, 59.05, 23.9], [7, 100.0, 32.0], [2, 0.91, 12.9]], [0.0, 0.0, 100.0, 32.0]], [[12, 139426], [2, 164577], [15, 348225], [16, 349525], [20, 834544], [7, 1048575]]], [[[[21, 0.12, 0.0], [19, 7.02, 32.0], [28, 8.31, 21.26], [26, 16.0, 12.31], [8, 0.0, 32.0], [3, 15.19, 32.0], [20, 16.0, 0.0], [4, 0.0, 18.69], [29, 0.0, 24.15], [24, 16.0, 28.82], [11, 2.01, 6.28]], [0.0, 0.0, 16.0, 32.0]], [[21, 21], [11, 57472], [20, 349525], [26, 513495], [4, 533032], [29, 655392], [8, 699050], [19, 785067], [28, 821637], [24, 1038301], [3, 1047290]]], [[[[19, 5.0, -3.05], [25, 5.0, -3.05], [2, 5.0, -4.0], [7, 5.0, -0.21], [4, 5.0, -0.44]], [5.0, -4.0, 5.0, 28.0]], [[2, 0], [19, 680], [25, 680], [4, 10754], [7, 10882]]], [[[[5, 8.05, -0.06], [8, 19.59, -4.0], [16, 13.1, 14.81]], [5.0, -4.0, 21.0, 28.0]], [[5, 31405], [8, 345105], [16, 795286]]], [[[[14, 0.0, 6.96], [19, 0.0, 7.92], [23, 0.0, 3.51], [27, 100.0, 0.82], [20, 100.0, 0.0], [2, 63.48, 8.0]], [0.0, 0.0, 100.0, 8.0]], [[23, 172034], [20, 349525], [27, 359893], [14, 666248], [19, 698914], [2, 977646]]], [[[[6, -10.0, 1.87], [22, -10.0, 1.87], [18, -10.0, 19.83], [27, -7.05, 6.24], [13, -7.53, 27.93], [8, -8.41, -0.77], [23, -10.0, 0.56]], [-10.0, 0.0, 6.0, 32.0]], [[23, 514], [6, 2698], [22, 2698], [8, 5137], [27, 58746], [18, 535176], [13, 682998]]], [[[[23, 0.0, 0.0], [10, 0.0, 0.0], [2, 0.0, 23.84], [29, -0.27, 20.79], [15, 0.0, 0.0], [27, 0.0, 30.52], [21, -0.47, 17.6], [4, 0.0, 32.0], [18, 0.0, 0.0]], [0.0, 0.0, 0.0, 32.0]], [[10, 0], [15, 0], [18, 0], [23, 0], [21, 526858], [29, 557698], [2, 567944], [27, 696832], [4, 699050]]], [[[[2, 50.41, -4.0], [8, 61.32, -4.0], [11, 0.0, 1.98], [24, 11.47, -4.0], [22, 24.0, -4.71], [19, 100.0, -4.0]], [0.0, -4.0, 100.0, 4.0]], [[24, 5393], [22, 21777], [2, 262160], [8, 267525], [19, 349525], [11, 567970]]]]]
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[[23, 5380], [29, 5380], [13, 97172], [24, 349457]][[23, 5380], [29, 5380], [13, 97172], [24, 349457]]Passed
case 1[[14, 0], [19, 80], [1, 4101], [26, 8232], [20, 69968], [23, 69968], [10, 327940]][[19, 80], [1, 4101], [20, 69968], [23, 69968], [10, 327940], [14, 349525], [26, 1048575]]Failed
case 2[[18, 0], [21, 0], [25, 0], [27, 0], [7, 332821], [16, 903085], [1, 1031261]][[18, 0], [21, 0], [25, 0], [27, 0], [16, 903085], [1, 1031261], [7, 1031871]]Failed
case 3[[18, 0], [7, 69969]][[18, 0], [7, 69969]]Passed
case 4[[27, 0], [6, 657418]][[6, 657418], [27, 699050]]Failed
case 5[[3, 0], [15, 81], [23, 4097], [4, 283921]][[15, 81], [4, 283921], [3, 699050], [23, 703147]]Failed
case 6[[21, 131242], [20, 133128], [9, 263425], [28, 680908]][[21, 131242], [20, 133128], [9, 263425], [28, 680908]]Passed
case 7[[1, 0], [2, 0], [27, 174594], [15, 696834]][[27, 174594], [15, 696834], [1, 699050], [2, 699050]]Failed

SHA-256 / 8dc0bbf9bffc96082589a8f455bec53a8f632e339b27169e1b7da6a072d922a2

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(pts, bounds):
    def part(v):
        v &= 0x3FF
        v = (v | (v << 8)) & 0x00FF00FF
        v = (v | (v << 4)) & 0x0F0F0F0F
        v = (v | (v << 2)) & 0x33333333
        v = (v | (v << 1)) & 0x55555555
        return v
    def quant(c, lo, hi):
        if hi <= lo:
            return 0
        return min(1023, max(0, math.floor((c - lo) / (hi - lo) * 1023)))
    out = []
    for i, x, y in pts:
        code = part(quant(x, bounds[0], bounds[2])) | (part(quant(y, bounds[1], bounds[3])) << 1)
        out.append([i, code])
    out.sort(key=lambda r: (r[1], r[0]))
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[[[[23, 11.15, 0.0], [29, 11.15, 0.0], [13, 45.93, 3.76], [24, 99.01, 0.0]], [0.0, 0.0, 100.0, 32.0]], [[23, 5380], [29, 5380], [13, 97172], [24, 349457]]], [[[[20, 3.4, -4.0], [23, 3.4, -4.0], [1, 0.66, -4.0], [26, 10.0, 4.55], [10, 7.68, -4.0], [14, 10.0, -4.0], [19, 0.12, -4.0]], [0.0, -4.0, 10.0, 4.0]], [[19, 80], [1, 4101], [20, 69968], [23, 69968], [10, 327940], [14, 349525], [26, 1048575]]], [[[[25, -10.0, -4.0], [21, -10.0, -4.0], [16, 82.55, 16.96], [18, -10.0, -4.0], [7, 75.11, 28.0], [1, 75.9, 27.07], [27, -10.0, -4.0]], [-10.0, -4.0, 90.0, 28.0]], [[18, 0], [21, 0], [25, 0], [27, 0], [16, 903085], [1, 1031261], [7, 1031871]]], [[[[7, 34.1, -4.0], [18, 0.0, -4.0]], [0.0, -4.0, 100.0, 4.0]], [[18, 0], [7, 69969]]], [[[[6, -10.0, 6.28], [27, -10.0, 8.0]], [-10.0, 0.0, 90.0, 8.0]], [[6, 657418], [27, 699050]]], [[[[15, -9.79, -4.0], [23, -8.97, 28.0], [4, 1.83, -4.0], [3, -10.0, 28.0]], [-10.0, -4.0, 6.0, 28.0]], [[15, 81], [4, 283921], [3, 699050], [23, 703147]]], [[[[20, 5.0, 9.07], [21, 5.0, 8.49], [28, 20.12, 26.83], [9, 59.81, 0.0]], [5.0, 0.0, 105.0, 32.0]], [[21, 131242], [20, 133128], [9, 263425], [28, 680908]]], [[[[15, -10.0, 30.56], [2, -10.0, 32.0], [1, -10.0, 32.0], [27, -10.51, 15.54]], [-10.0, 0.0, 0.0, 32.0]], [[27, 174594], [15, 696834], [1, 699050], [2, 699050]]]], [[[[[13, 4.71, 4.67], [19, 4.71, 4.67], [11, 5.0, 8.0], [21, 4.43, 0.91], [2, 4.2, 0.0], [9, 5.0, 3.28], [3, 5.0, 6.75]], [5.0, 0.0, 5.0, 8.0]], [[2, 0], [21, 10784], [9, 165898], [13, 533026], [19, 533026], [3, 665600], [11, 699050]]], [[[[29, -10.0, -0.25], [3, -10.57, 28.0], [19, -10.0, -4.0], [9, -10.0, -4.0], [20, -10.0, -4.0]], [-10.0, -4.0, -10.0, 28.0]], [[9, 0], [19, 0], [20, 0], [29, 10880], [3, 699050]]], [[[[26, 0.85, 18.54], [29, 0.85, 18.54], [17, -10.0, 32.0]], [-10.0, 0.0, 0.0, 32.0]], [[17, 699050], [26, 882519], [29, 882519]]], [[[[7, 2.09, 26.27], [12, 0.0, 29.03], [3, 13.02, 11.98], [10, 0.0, 21.46]], [0.0, 0.0, 16.0, 32.0]], [[3, 473771], [10, 559272], [7, 680081], [12, 690176]]], [[[[12, 5.05, 22.98], [5, 15.0, 32.0], [21, 7.47, 17.17], [26, 7.31, 3.09], [15, 13.84, 10.33], [2, 5.0, 32.0], [24, 15.0, 32.0]], [5.0, 0.0, 15.0, 32.0]], [[26, 31832], [15, 483529], [21, 548210], [12, 565947], [2, 699050], [5, 1048575], [24, 1048575]]], [[[[13, 4.02, 10.58], [22, 4.02, 10.58], [23, 5.0, 0.0]], [5.0, 0.0, 5.0, 32.0]], [[23, 0], [13, 139784], [22, 139784]]], [[[[27, 5.0, 4.0], [21, 5.0, 4.0], [22, 105.0, -3.16], [3, 42.29, 4.0], [17, 5.0, 2.25], [12, 25.35, -0.08], [8, 70.41, 2.16]], [5.0, -4.0, 105.0, 4.0]], [[12, 195362], [22, 359903], [17, 657408], [21, 699050], [27, 699050], [3, 770043], [8, 934769]]], [[[[14, 0.0, -4.0], [22, 0.0, 13.71], [15, 0.13, 7.52], [1, 0.0, -4.0], [29, 0.0, 27.3], [3, 0.0, -1.25]], [0.0, -4.0, 0.0, 28.0]], [[1, 0], [14, 0], [3, 8832], [15, 141824], [22, 526888], [29, 698498]]]], [[[[[18, 10.38, 4.0], [21, 10.38, 4.0], [9, 10.0, 4.0], [7, 6.82, 4.0], [11, 2.93, -4.0], [27, 1.97, 4.7], [3, 0.0, 1.79]], [0.0, -4.0, 10.0, 4.0]], [[11, 66640], [3, 567330], [27, 719595], [7, 978926], [9, 1048575], [18, 1048575], [21, 1048575]]], [[[[28, 8.07, -4.0], [18, 8.07, -4.0], [6, 8.12, -0.78], [23, 5.0, 4.0], [1, 5.0, -4.0], [3, 11.1, 3.03], [5, 13.26, 4.0], [12, 6.24, 4.0], [25, 5.0, -2.08]], [5.0, -4.0, 15.0, 4.0]], [[1, 0], [25, 43554], [18, 66884], [28, 66884], [6, 231413], [23, 699050], [12, 704510], [3, 955658], [5, 1030907]]], [[[[27, -10.0, 7.72], [4, -10.0, 1.55]], [-10.0, 0.0, -10.0, 8.0]], [[4, 41000], [27, 696992]]], [[[[9, 5.0, 3.16], [20, 5.0, 3.16], [4, 5.0, 0.0], [17, 5.0, 0.0], [18, 5.0, 0.0]], [5.0, 0.0, 5.0, 8.0]], [[4, 0], [17, 0], [18, 0], [9, 164384], [20, 164384]]], [[[[6, 1.61, 0.0], [20, -10.0, 8.0], [7, 6.0, 0.0], [16, 5.81, 2.39], [21, -9.33, 0.0]], [-10.0, 0.0, 6.0, 8.0]], [[21, 1092], [6, 283669], [7, 349525], [16, 483079], [20, 699050]]], [[[[28, -7.77, 4.0], [19, -9.68, 1.96], [21, 5.53, 1.02], [14, -10.0, 2.58]], [-10.0, -4.0, 6.0, 4.0]], [[19, 568216], [14, 663688], [28, 715518], [21, 906249]]], [[[[18, -5.18, 28.0], [22, -4.56, 8.95], [15, -2.07, 10.7], [2, -10.0, -4.13], [11, 0.0, -4.0]], [-10.0, -4.0, 0.0, 28.0]], [[2, 0], [11, 349525], [22, 427769], [15, 501368], [18, 786171]]], [[[[29, 5.19, -4.0], [12, 5.19, -4.0]], [5.0, -4.0, 15.0, 4.0]], [[12, 261], [29, 261]]]], [[[[[5, 3.93, -4.0], [23, 3.93, -4.0], [25, 0.0, -4.0]], [0.0, -4.0, 16.0, 4.0]], [[25, 0], [5, 21829], [23, 21829]]], [[[[20, 5.0, 15.36], [9, 5.0, 15.36], [6, 5.0, -4.0], [8, 5.0, 7.29], [2, 5.0, -4.0], [14, 5.0, 24.78], [17, 5.0, 2.43], [7, 5.69, -4.0]], [5.0, -4.0, 5.0, 28.0]], [[2, 0], [6, 0], [7, 0], [17, 41122], [8, 141442], [9, 534666], [20, 534666], [14, 688768]]], [[[[28, 5.0, -3.83], [6, 5.0, -3.83], [1, 17.93, -4.0], [21, 5.0, 26.93]], [5.0, -4.0, 105.0, 28.0]], [[6, 34], [28, 34], [1, 16400], [21, 696994]]], [[[[10, 3.1, 28.0], [9, 3.1, 28.0], [12, 6.8, -4.0], [27, 10.0, -4.0]], [0.0, -4.0, 10.0, 28.0]], [[12, 279872], [27, 349525], [9, 765947], [10, 765947]]], [[[[29, -10.0, -1.72], [19, -10.0, -1.72], [27, 4.61, 4.0], [24, 43.35, 4.0], [11, 90.0, -0.83], [21, -10.0, -4.0], [3, 90.0, -4.0], [4, 10.23, 2.21], [9, -10.0, -4.0], [7, 40.89, -4.0]], [-10.0, -4.0, 90.0, 4.0]], [[9, 0], [21, 0], [19, 133130], [29, 133130], [7, 262209], [3, 349525], [11, 513911], [4, 676573], [27, 715707], [24, 962222]]], [[[[12, 5.0, -1.65], [13, 5.0, -4.0], [10, 85.95, 0.41], [24, 5.0, -4.0]], [5.0, -4.0, 105.0, 4.0]], [[13, 0], [24, 0], [12, 133280], [10, 855920]]], [[[[12, 5.76, 2.78], [24, 4.73, 0.0], [27, 10.0, 0.78]], [0.0, 0.0, 10.0, 8.0]], [[24, 87056], [27, 359775], [12, 407643]]], [[[[7, 10.0, 3.93], [25, 0.0, 5.78], [23, 3.34, 8.0]], [0.0, 0.0, 10.0, 8.0]], [[7, 524159], [25, 567306], [23, 768958]]]], [[[[[15, 94.67, 0.0], [16, 100.0, 0.0], [12, 0.0, 10.42], [20, 59.05, 23.9], [7, 100.0, 32.0], [2, 0.91, 12.9]], [0.0, 0.0, 100.0, 32.0]], [[12, 139426], [2, 164577], [15, 348225], [16, 349525], [20, 834544], [7, 1048575]]], [[[[21, 0.12, 0.0], [19, 7.02, 32.0], [28, 8.31, 21.26], [26, 16.0, 12.31], [8, 0.0, 32.0], [3, 15.19, 32.0], [20, 16.0, 0.0], [4, 0.0, 18.69], [29, 0.0, 24.15], [24, 16.0, 28.82], [11, 2.01, 6.28]], [0.0, 0.0, 16.0, 32.0]], [[21, 21], [11, 57472], [20, 349525], [26, 513495], [4, 533032], [29, 655392], [8, 699050], [19, 785067], [28, 821637], [24, 1038301], [3, 1047290]]], [[[[19, 5.0, -3.05], [25, 5.0, -3.05], [2, 5.0, -4.0], [7, 5.0, -0.21], [4, 5.0, -0.44]], [5.0, -4.0, 5.0, 28.0]], [[2, 0], [19, 680], [25, 680], [4, 10754], [7, 10882]]], [[[[5, 8.05, -0.06], [8, 19.59, -4.0], [16, 13.1, 14.81]], [5.0, -4.0, 21.0, 28.0]], [[5, 31405], [8, 345105], [16, 795286]]], [[[[14, 0.0, 6.96], [19, 0.0, 7.92], [23, 0.0, 3.51], [27, 100.0, 0.82], [20, 100.0, 0.0], [2, 63.48, 8.0]], [0.0, 0.0, 100.0, 8.0]], [[23, 172034], [20, 349525], [27, 359893], [14, 666248], [19, 698914], [2, 977646]]], [[[[6, -10.0, 1.87], [22, -10.0, 1.87], [18, -10.0, 19.83], [27, -7.05, 6.24], [13, -7.53, 27.93], [8, -8.41, -0.77], [23, -10.0, 0.56]], [-10.0, 0.0, 6.0, 32.0]], [[23, 514], [6, 2698], [22, 2698], [8, 5137], [27, 58746], [18, 535176], [13, 682998]]], [[[[23, 0.0, 0.0], [10, 0.0, 0.0], [2, 0.0, 23.84], [29, -0.27, 20.79], [15, 0.0, 0.0], [27, 0.0, 30.52], [21, -0.47, 17.6], [4, 0.0, 32.0], [18, 0.0, 0.0]], [0.0, 0.0, 0.0, 32.0]], [[10, 0], [15, 0], [18, 0], [23, 0], [21, 526858], [29, 557698], [2, 567944], [27, 696832], [4, 699050]]], [[[[2, 50.41, -4.0], [8, 61.32, -4.0], [11, 0.0, 1.98], [24, 11.47, -4.0], [22, 24.0, -4.71], [19, 100.0, -4.0]], [0.0, -4.0, 100.0, 4.0]], [[24, 5393], [22, 21777], [2, 262160], [8, 267525], [19, 349525], [11, 567970]]]]]
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[[23, 5380], [29, 5380], [13, 97169], [24, 349456]][[23, 5380], [29, 5380], [13, 97172], [24, 349457]]Failed
case 1[[19, 80], [1, 4101], [20, 69957], [23, 69957], [10, 327937], [14, 349525], [26, 1048575]][[19, 80], [1, 4101], [20, 69968], [23, 69968], [10, 327940], [14, 349525], [26, 1048575]]Failed
case 2[[18, 0], [21, 0], [25, 0], [27, 0], [16, 903084], [1, 1031254], [7, 1031870]][[18, 0], [21, 0], [25, 0], [27, 0], [16, 903085], [1, 1031261], [7, 1031871]]Failed
case 3[[18, 0], [7, 69968]][[18, 0], [7, 69969]]Failed
case 4[[6, 657418], [27, 699050]][[6, 657418], [27, 699050]]Passed
case 5[[15, 81], [4, 283920], [3, 699050], [23, 703147]][[15, 81], [4, 283921], [3, 699050], [23, 703147]]Failed
case 6[[21, 131242], [20, 133122], [9, 263424], [28, 680902]][[21, 131242], [20, 133128], [9, 263425], [28, 680908]]Failed
case 7[[27, 174592], [15, 696832], [1, 699050], [2, 699050]][[27, 174594], [15, 696834], [1, 699050], [2, 699050]]Failed

SHA-256 / 72f109791cda20f13ae34bf7c1d8a5a41a613b3235673ce491a3083ba80d68c3

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 2026-09-29T14:50:59.923836+00:00.

Case digest / 6cc898d1edc00c08b8c9d629acdcc054dffaf7ddb4cc4d82523edcb6e550cad8