FAILURE MAP
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FA-87531 / Collision detection broadphase / Open access

Accepted pairs keep candidate orientation · case 01

The same pair appears twice when candidates list both orders.

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

ROOT CAUSE

out stores (a,b) as given.

THE FAILURE

out stores (a,b) as given.

Unsuccessful approach: Sorting the output without normalizing still keeps both orientations.

Case contract

solve(fixtures, candidates): fixture [id, body, category bits, mask bits, group, sensor, body type]. A candidate [a,b] is accepted unless: same body; neither body is dynamic; both are sensors. Group rule: equal nonzero groups override masks (positive always collide, negative never); otherwise require (catA & maskB) and (catB & maskA). Return sorted unique [min,max] accepted 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(fixtures, candidates):
    fx = {f[0]: f for f in fixtures}
    out = set()
    for a, b in candidates:
        fa, fb = fx[a], fx[b]
        if fa[1] == fb[1]:
            continue
        if fa[6] != 'dynamic' and fb[6] != 'dynamic':
            continue
        ga, gb = fa[4], fb[4]
        if ga == gb and ga != 0:
            ok = ga > 0
        else:
            ok = (fa[2] & fb[3]) != 0 and (fb[2] & fa[3]) != 0
        if not ok:
            continue
        if fa[5] and fb[5]:
            continue
        out.add((a, b))
    return [list(p) for p in sorted(out)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[[[[1, 4, 8, 3, 0, False, 'dynamic'], [2, 4, 8, 12, 1, True, 'static'], [3, 4, 4, 15, -2, True, 'kinematic'], [4, 3, 1, 7, 1, False, 'dynamic'], [5, 2, 1, 12, 2, False, 'kinematic']], [[5, 1], [2, 5], [5, 4], [4, 5]]], [[1, 5]]], [[[[1, 2, 4, 12, 0, True, 'static'], [2, 1, 2, 6, 1, True, 'dynamic'], [3, 4, 4, 15, 0, True, 'static'], [4, 2, 8, 15, 0, False, 'kinematic'], [5, 2, 2, 3, 0, False, 'kinematic'], [6, 1, 8, 15, -1, False, 'dynamic']], [[2, 1], [2, 3], [2, 4], [4, 1], [1, 4], [3, 1]]], []], [[[[1, 4, 4, 6, 0, False, 'static'], [2, 2, 1, 1, 0, False, 'dynamic'], [3, 1, 8, 12, 1, False, 'dynamic']], [[3, 2], [1, 3], [2, 3], [1, 3], [2, 3]]], []], [[[[1, 2, 2, 12, 1, False, 'dynamic'], [2, 1, 4, 3, 2, False, 'dynamic'], [3, 4, 8, 15, 0, False, 'dynamic']], [[1, 2], [1, 2], [3, 2], [2, 3], [3, 2], [3, 2]]], [[1, 2]]], [[[[1, 4, 2, 12, 0, False, 'dynamic'], [2, 3, 8, 15, 0, False, 'kinematic'], [3, 1, 2, 12, 2, True, 'dynamic'], [4, 2, 2, 15, -1, True, 'kinematic'], [5, 3, 1, 7, -1, False, 'static']], [[4, 1], [1, 2], [1, 2], [1, 2], [4, 3], [2, 1], [3, 4], [4, 5], [5, 3], [2, 3]]], [[1, 2], [2, 3]]], [[[[1, 4, 4, 7, 0, False, 'kinematic'], [2, 2, 4, 15, -2, False, 'kinematic'], [3, 3, 1, 6, 0, False, 'dynamic']], [[1, 2], [1, 3], [3, 1], [3, 1], [2, 1], [2, 1], [1, 3]]], [[1, 3]]], [[[[1, 3, 1, 12, -1, True, 'kinematic'], [2, 4, 4, 15, 1, False, 'dynamic'], [3, 1, 8, 6, 1, False, 'dynamic'], [4, 3, 1, 15, 0, False, 'kinematic'], [5, 3, 4, 15, 0, False, 'dynamic'], [6, 1, 1, 3, -2, True, 'kinematic']], [[5, 6], [3, 1], [2, 4], [2, 4], [5, 1], [2, 5], [1, 4], [2, 1], [6, 3]]], [[1, 2], [2, 4], [2, 5]]], [[[[1, 3, 1, 15, -1, False, 'dynamic'], [2, 4, 4, 6, 2, False, 'static'], [3, 2, 8, 15, 0, False, 'dynamic'], [4, 4, 8, 7, 2, False, 'dynamic']], [[1, 3], [2, 3], [4, 3]]], [[1, 3]]]], [[[[[1, 2, 2, 7, 1, False, 'kinematic'], [2, 4, 2, 3, -2, False, 'dynamic'], [3, 3, 1, 6, 1, False, 'kinematic'], [4, 2, 8, 3, 2, False, 'static'], [5, 4, 4, 1, 0, False, 'dynamic'], [6, 1, 4, 7, 2, False, 'kinematic']], [[5, 4], [2, 6], [1, 4], [1, 3], [3, 6], [5, 3], [1, 3], [3, 4], [4, 1]]], [[3, 5]]], [[[[1, 3, 8, 6, 1, False, 'dynamic'], [2, 2, 8, 3, 1, False, 'dynamic'], [3, 1, 1, 3, 2, False, 'dynamic'], [4, 3, 2, 3, 1, False, 'static'], [5, 2, 8, 3, 2, False, 'dynamic']], [[5, 2], [4, 5], [1, 2], [2, 1], [1, 5], [3, 1], [4, 5], [4, 3], [3, 4]]], [[1, 2], [3, 4]]], [[[[1, 4, 1, 6, 0, False, 'dynamic'], [2, 2, 1, 15, 1, False, 'dynamic'], [3, 4, 1, 1, -1, False, 'dynamic'], [4, 3, 4, 15, 0, False, 'kinematic']], [[3, 1], [1, 4], [3, 1]]], [[1, 4]]], [[[[1, 4, 2, 1, 1, False, 'static'], [2, 4, 4, 12, 2, True, 'dynamic'], [3, 3, 1, 12, 0, False, 'kinematic'], [4, 3, 4, 3, -1, False, 'dynamic'], [5, 2, 2, 12, -2, False, 'kinematic'], [6, 2, 4, 15, 2, False, 'kinematic'], [7, 1, 4, 12, 0, False, 'dynamic']], [[6, 2], [5, 6], [7, 4], [7, 3], [3, 1]]], [[2, 6]]], [[[[1, 2, 2, 15, -2, False, 'dynamic'], [2, 2, 4, 1, -1, False, 'dynamic'], [3, 2, 2, 1, -2, True, 'dynamic'], [4, 3, 4, 15, -2, False, 'kinematic'], [5, 3, 8, 6, -1, False, 'dynamic']], [[1, 4], [3, 2], [2, 1], [2, 1], [2, 4], [1, 3], [3, 5], [1, 3], [4, 2], [2, 1]]], []], [[[[1, 4, 4, 15, -1, False, 'dynamic'], [2, 2, 8, 3, 1, False, 'kinematic'], [3, 1, 1, 6, 0, False, 'static'], [4, 2, 4, 15, 0, False, 'kinematic'], [5, 4, 8, 7, 2, False, 'static'], [6, 3, 8, 15, 0, True, 'kinematic'], [7, 4, 4, 1, 1, False, 'kinematic']], [[1, 4], [2, 7], [7, 1], [6, 7], [1, 2], [1, 6], [7, 3]]], [[1, 4], [1, 6]]], [[[[1, 3, 1, 15, 0, False, 'dynamic'], [2, 1, 1, 6, -2, True, 'kinematic']], [[1, 2], [2, 1], [1, 2], [2, 1], [1, 2], [2, 1], [2, 1]]], []], [[[[1, 2, 4, 15, 1, False, 'kinematic'], [2, 1, 4, 6, -1, False, 'kinematic'], [3, 3, 4, 3, 2, True, 'kinematic'], [4, 4, 1, 7, 1, False, 'static']], [[1, 3], [1, 2], [2, 4], [1, 2], [4, 1], [1, 3]]], []]], [[[[[1, 3, 2, 3, -2, False, 'static'], [2, 4, 1, 12, 0, True, 'dynamic'], [3, 4, 4, 12, 0, False, 'static'], [4, 1, 2, 3, -1, False, 'dynamic'], [5, 2, 4, 1, -2, False, 'dynamic'], [6, 2, 4, 12, 2, True, 'dynamic'], [7, 4, 4, 1, -2, False, 'kinematic']], [[3, 2], [2, 3], [3, 2], [4, 5], [2, 5]]], [[2, 5]]], [[[[1, 1, 4, 15, 1, True, 'dynamic'], [2, 3, 2, 7, -2, False, 'kinematic'], [3, 4, 8, 15, 0, False, 'static'], [4, 2, 2, 12, 1, False, 'dynamic']], [[2, 3], [3, 4], [2, 1], [4, 2], [4, 1], [1, 4], [3, 4], [3, 4], [2, 1]]], [[1, 2], [1, 4], [3, 4]]], [[[[1, 3, 8, 15, -2, False, 'kinematic'], [2, 3, 2, 7, -2, False, 'kinematic'], [3, 3, 2, 15, 2, True, 'static'], [4, 2, 2, 3, -2, False, 'dynamic'], [5, 1, 1, 6, -1, False, 'dynamic'], [6, 4, 2, 3, 0, False, 'static']], [[2, 4], [6, 5], [5, 6]]], [[5, 6]]], [[[[1, 2, 1, 7, 0, False, 'kinematic'], [2, 2, 4, 7, 0, False, 'dynamic']], [[1, 2], [2, 1], [1, 2]]], []], [[[[1, 1, 2, 7, 0, False, 'dynamic'], [2, 4, 1, 1, 0, False, 'dynamic'], [3, 2, 4, 6, -2, False, 'static']], [[1, 2], [1, 3], [1, 2], [2, 3], [3, 1]]], [[1, 3]]], [[[[1, 2, 8, 1, 1, False, 'kinematic'], [2, 1, 1, 7, 2, False, 'static'], [3, 3, 2, 15, 2, True, 'kinematic'], [4, 3, 4, 7, -1, False, 'kinematic'], [5, 3, 4, 6, 1, False, 'dynamic'], [6, 1, 4, 15, 0, False, 'dynamic']], [[4, 5], [3, 6], [4, 6], [4, 1], [5, 3], [1, 3]]], [[3, 6], [4, 6]]], [[[[1, 2, 2, 1, 0, False, 'dynamic'], [2, 4, 2, 12, 0, False, 'dynamic'], [3, 4, 1, 15, 1, False, 'static'], [4, 2, 8, 12, 0, False, 'dynamic'], [5, 4, 2, 6, 2, False, 'dynamic']], [[5, 3], [3, 1], [3, 1], [2, 3], [3, 4], [1, 2], [1, 5], [5, 4]]], [[1, 3]]], [[[[1, 3, 1, 7, -1, False, 'dynamic'], [2, 1, 8, 12, 0, True, 'kinematic']], [[1, 2], [2, 1], [1, 2], [1, 2], [2, 1], [2, 1], [2, 1], [2, 1], [1, 2]]], []]], [[[[[1, 2, 1, 7, -1, False, 'dynamic'], [2, 2, 2, 6, 0, False, 'dynamic'], [3, 2, 1, 6, 2, False, 'kinematic'], [4, 2, 1, 6, 0, False, 'dynamic'], [5, 4, 4, 7, 1, True, 'static'], [6, 3, 2, 1, 2, False, 'static']], [[6, 4], [1, 4], [6, 5], [4, 5]]], [[4, 5], [4, 6]]], [[[[1, 1, 4, 12, 0, False, 'static'], [2, 3, 2, 12, 2, True, 'dynamic'], [3, 3, 1, 1, -1, True, 'dynamic'], [4, 4, 1, 15, 2, False, 'dynamic'], [5, 1, 4, 15, 0, False, 'static']], [[1, 3], [2, 4], [5, 3], [4, 1], [5, 2]]], [[2, 4], [2, 5]]], [[[[1, 3, 4, 15, 0, False, 'dynamic'], [2, 1, 2, 15, 0, False, 'dynamic'], [3, 3, 2, 3, -2, False, 'dynamic'], [4, 4, 4, 6, -1, False, 'kinematic'], [5, 3, 2, 15, 0, False, 'kinematic']], [[3, 2], [4, 3], [2, 4], [4, 2], [4, 1], [2, 4], [2, 5], [5, 3]]], [[1, 4], [2, 3], [2, 4], [2, 5]]], [[[[1, 1, 1, 15, -1, True, 'kinematic'], [2, 1, 8, 3, 1, False, 'kinematic']], [[1, 2], [2, 1], [2, 1]]], []], [[[[1, 1, 8, 6, -2, True, 'dynamic'], [2, 3, 2, 7, 0, False, 'kinematic'], [3, 1, 2, 15, -2, False, 'dynamic'], [4, 1, 1, 15, 0, False, 'kinematic']], [[2, 3], [4, 2], [4, 3], [1, 4], [2, 3], [2, 1], [1, 4], [4, 2], [2, 1]]], [[2, 3]]], [[[[1, 2, 8, 3, 2, False, 'kinematic'], [2, 2, 1, 1, -2, False, 'dynamic'], [3, 3, 2, 15, 0, True, 'dynamic'], [4, 1, 2, 3, 0, False, 'dynamic'], [5, 2, 2, 15, 1, False, 'kinematic'], [6, 4, 8, 3, 0, False, 'kinematic'], [7, 2, 1, 12, -1, False, 'dynamic'], [8, 4, 8, 1, 1, False, 'kinematic'], [9, 1, 2, 6, -1, False, 'dynamic']], [[3, 2], [6, 3], [5, 6], [1, 2], [6, 9], [6, 7]]], [[3, 6], [6, 7]]], [[[[1, 1, 8, 15, 1, False, 'dynamic'], [2, 1, 4, 6, -1, False, 'kinematic'], [3, 2, 2, 15, 2, False, 'static'], [4, 3, 1, 15, -1, False, 'dynamic'], [5, 3, 2, 7, 0, False, 'kinematic'], [6, 4, 4, 12, 1, False, 'kinematic']], [[2, 4], [1, 2], [3, 2], [5, 3], [6, 3], [4, 3], [5, 4], [4, 5], [1, 4], [1, 4]]], [[1, 4], [3, 4]]], [[[[1, 2, 1, 6, 0, False, 'dynamic'], [2, 4, 2, 3, -1, True, 'dynamic'], [3, 3, 1, 3, 0, False, 'static'], [4, 4, 8, 6, 2, False, 'kinematic'], [5, 1, 2, 6, -1, False, 'kinematic'], [6, 1, 1, 12, -1, False, 'dynamic'], [7, 3, 8, 3, -1, True, 'dynamic']], [[5, 7], [5, 2], [5, 4], [7, 2]]], []]], [[[[[1, 3, 1, 7, 1, False, 'static'], [2, 4, 2, 1, -1, True, 'kinematic'], [3, 1, 1, 12, 0, False, 'kinematic'], [4, 4, 4, 15, -2, True, 'dynamic'], [5, 4, 2, 7, 0, False, 'kinematic']], [[3, 1], [3, 2], [5, 3], [2, 3], [2, 3], [1, 3], [1, 3], [1, 3], [4, 5], [4, 2]]], []], [[[[1, 2, 1, 12, 0, True, 'dynamic'], [2, 1, 8, 15, 0, False, 'dynamic'], [3, 1, 1, 7, -2, False, 'kinematic'], [4, 2, 4, 15, -1, True, 'dynamic']], [[4, 3], [3, 2], [2, 1], [4, 2], [3, 1]]], [[1, 2], [2, 4], [3, 4]]], [[[[1, 3, 2, 6, 0, False, 'static'], [2, 2, 1, 15, 0, True, 'kinematic']], [[2, 1], [2, 1], [2, 1], [2, 1], [1, 2], [2, 1], [2, 1]]], []], [[[[1, 1, 4, 15, 1, True, 'dynamic'], [2, 4, 8, 15, 1, False, 'static'], [3, 4, 2, 15, 0, False, 'dynamic'], [4, 2, 1, 7, 0, False, 'static']], [[1, 2], [2, 3], [2, 4], [2, 3], [2, 3], [3, 1], [2, 3], [1, 4], [3, 2], [2, 3]]], [[1, 2], [1, 3], [1, 4]]], [[[[1, 2, 8, 1, 0, False, 'dynamic'], [2, 1, 8, 3, 2, False, 'static'], [3, 3, 2, 3, 2, False, 'dynamic'], [4, 2, 4, 6, -2, False, 'kinematic'], [5, 2, 4, 7, 1, False, 'kinematic'], [6, 4, 8, 15, -1, False, 'dynamic']], [[3, 5], [1, 5], [6, 1], [4, 2], [3, 2], [4, 1], [3, 1]]], [[2, 3]]], [[[[1, 3, 2, 15, 1, False, 'static'], [2, 2, 1, 15, -1, False, 'static'], [3, 4, 8, 15, -2, False, 'dynamic'], [4, 4, 1, 3, 0, False, 'dynamic'], [5, 1, 4, 3, 0, False, 'kinematic'], [6, 4, 4, 7, 2, False, 'dynamic'], [7, 4, 8, 15, 1, True, 'kinematic'], [8, 2, 1, 3, -2, False, 'dynamic'], [9, 2, 4, 1, -1, False, 'static'], [10, 1, 8, 15, 1, False, 'static']], [[8, 2], [10, 9], [5, 3], [2, 4], [6, 5], [3, 7], [7, 9], [6, 5], [10, 5]]], [[2, 4]]], [[[[1, 3, 1, 15, 1, False, 'dynamic'], [2, 4, 8, 6, 0, False, 'static'], [3, 3, 2, 6, 2, True, 'kinematic'], [4, 4, 1, 1, 0, True, 'kinematic'], [5, 1, 2, 15, 0, False, 'dynamic'], [6, 1, 2, 15, 0, False, 'kinematic'], [7, 2, 4, 3, 0, False, 'static']], [[1, 7], [3, 1], [3, 1], [2, 4], [6, 5], [1, 5], [1, 3]]], [[1, 5], [1, 7]]], [[[[1, 1, 1, 12, 0, True, 'static'], [2, 3, 1, 6, 0, False, 'dynamic'], [3, 3, 2, 12, 0, False, 'static'], [4, 1, 8, 7, 0, False, 'dynamic'], [5, 1, 4, 12, -2, True, 'kinematic'], [6, 4, 8, 7, 1, False, 'kinematic'], [7, 2, 4, 6, 2, False, 'dynamic'], [8, 4, 4, 15, 2, False, 'dynamic'], [9, 2, 8, 6, -2, False, 'kinematic'], [10, 2, 8, 1, 0, True, 'static']], [[10, 8], [2, 3], [7, 3]]], [[3, 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[[5, 1]][[1, 5]]Failed
case 1[][]Passed
case 2[][]Passed
case 3[[1, 2]][[1, 2]]Passed
case 4[[1, 2], [2, 1], [2, 3]][[1, 2], [2, 3]]Failed
case 5[[1, 3], [3, 1]][[1, 3]]Failed
case 6[[2, 1], [2, 4], [2, 5]][[1, 2], [2, 4], [2, 5]]Failed
case 7[[1, 3]][[1, 3]]Passed

SHA-256 / b4c1a92bca7b0ee815153489ffd5b4537081d4ba64104c28d2a750a107307ad9

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(fixtures, candidates):
    fx = {f[0]: f for f in fixtures}
    out = set()
    for a, b in candidates:
        fa, fb = fx[a], fx[b]
        if fa[1] == fb[1]:
            continue
        if fa[6] != 'dynamic' and fb[6] != 'dynamic':
            continue
        ga, gb = fa[4], fb[4]
        if ga == gb and ga != 0:
            ok = ga > 0
        else:
            ok = (fa[2] & fb[3]) != 0 and (fb[2] & fa[3]) != 0
        if not ok:
            continue
        if fa[5] and fb[5]:
            continue
        out.add((b, a))
    return [list(p) for p in sorted(out)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[[[[1, 4, 8, 3, 0, False, 'dynamic'], [2, 4, 8, 12, 1, True, 'static'], [3, 4, 4, 15, -2, True, 'kinematic'], [4, 3, 1, 7, 1, False, 'dynamic'], [5, 2, 1, 12, 2, False, 'kinematic']], [[5, 1], [2, 5], [5, 4], [4, 5]]], [[1, 5]]], [[[[1, 2, 4, 12, 0, True, 'static'], [2, 1, 2, 6, 1, True, 'dynamic'], [3, 4, 4, 15, 0, True, 'static'], [4, 2, 8, 15, 0, False, 'kinematic'], [5, 2, 2, 3, 0, False, 'kinematic'], [6, 1, 8, 15, -1, False, 'dynamic']], [[2, 1], [2, 3], [2, 4], [4, 1], [1, 4], [3, 1]]], []], [[[[1, 4, 4, 6, 0, False, 'static'], [2, 2, 1, 1, 0, False, 'dynamic'], [3, 1, 8, 12, 1, False, 'dynamic']], [[3, 2], [1, 3], [2, 3], [1, 3], [2, 3]]], []], [[[[1, 2, 2, 12, 1, False, 'dynamic'], [2, 1, 4, 3, 2, False, 'dynamic'], [3, 4, 8, 15, 0, False, 'dynamic']], [[1, 2], [1, 2], [3, 2], [2, 3], [3, 2], [3, 2]]], [[1, 2]]], [[[[1, 4, 2, 12, 0, False, 'dynamic'], [2, 3, 8, 15, 0, False, 'kinematic'], [3, 1, 2, 12, 2, True, 'dynamic'], [4, 2, 2, 15, -1, True, 'kinematic'], [5, 3, 1, 7, -1, False, 'static']], [[4, 1], [1, 2], [1, 2], [1, 2], [4, 3], [2, 1], [3, 4], [4, 5], [5, 3], [2, 3]]], [[1, 2], [2, 3]]], [[[[1, 4, 4, 7, 0, False, 'kinematic'], [2, 2, 4, 15, -2, False, 'kinematic'], [3, 3, 1, 6, 0, False, 'dynamic']], [[1, 2], [1, 3], [3, 1], [3, 1], [2, 1], [2, 1], [1, 3]]], [[1, 3]]], [[[[1, 3, 1, 12, -1, True, 'kinematic'], [2, 4, 4, 15, 1, False, 'dynamic'], [3, 1, 8, 6, 1, False, 'dynamic'], [4, 3, 1, 15, 0, False, 'kinematic'], [5, 3, 4, 15, 0, False, 'dynamic'], [6, 1, 1, 3, -2, True, 'kinematic']], [[5, 6], [3, 1], [2, 4], [2, 4], [5, 1], [2, 5], [1, 4], [2, 1], [6, 3]]], [[1, 2], [2, 4], [2, 5]]], [[[[1, 3, 1, 15, -1, False, 'dynamic'], [2, 4, 4, 6, 2, False, 'static'], [3, 2, 8, 15, 0, False, 'dynamic'], [4, 4, 8, 7, 2, False, 'dynamic']], [[1, 3], [2, 3], [4, 3]]], [[1, 3]]]], [[[[[1, 2, 2, 7, 1, False, 'kinematic'], [2, 4, 2, 3, -2, False, 'dynamic'], [3, 3, 1, 6, 1, False, 'kinematic'], [4, 2, 8, 3, 2, False, 'static'], [5, 4, 4, 1, 0, False, 'dynamic'], [6, 1, 4, 7, 2, False, 'kinematic']], [[5, 4], [2, 6], [1, 4], [1, 3], [3, 6], [5, 3], [1, 3], [3, 4], [4, 1]]], [[3, 5]]], [[[[1, 3, 8, 6, 1, False, 'dynamic'], [2, 2, 8, 3, 1, False, 'dynamic'], [3, 1, 1, 3, 2, False, 'dynamic'], [4, 3, 2, 3, 1, False, 'static'], [5, 2, 8, 3, 2, False, 'dynamic']], [[5, 2], [4, 5], [1, 2], [2, 1], [1, 5], [3, 1], [4, 5], [4, 3], [3, 4]]], [[1, 2], [3, 4]]], [[[[1, 4, 1, 6, 0, False, 'dynamic'], [2, 2, 1, 15, 1, False, 'dynamic'], [3, 4, 1, 1, -1, False, 'dynamic'], [4, 3, 4, 15, 0, False, 'kinematic']], [[3, 1], [1, 4], [3, 1]]], [[1, 4]]], [[[[1, 4, 2, 1, 1, False, 'static'], [2, 4, 4, 12, 2, True, 'dynamic'], [3, 3, 1, 12, 0, False, 'kinematic'], [4, 3, 4, 3, -1, False, 'dynamic'], [5, 2, 2, 12, -2, False, 'kinematic'], [6, 2, 4, 15, 2, False, 'kinematic'], [7, 1, 4, 12, 0, False, 'dynamic']], [[6, 2], [5, 6], [7, 4], [7, 3], [3, 1]]], [[2, 6]]], [[[[1, 2, 2, 15, -2, False, 'dynamic'], [2, 2, 4, 1, -1, False, 'dynamic'], [3, 2, 2, 1, -2, True, 'dynamic'], [4, 3, 4, 15, -2, False, 'kinematic'], [5, 3, 8, 6, -1, False, 'dynamic']], [[1, 4], [3, 2], [2, 1], [2, 1], [2, 4], [1, 3], [3, 5], [1, 3], [4, 2], [2, 1]]], []], [[[[1, 4, 4, 15, -1, False, 'dynamic'], [2, 2, 8, 3, 1, False, 'kinematic'], [3, 1, 1, 6, 0, False, 'static'], [4, 2, 4, 15, 0, False, 'kinematic'], [5, 4, 8, 7, 2, False, 'static'], [6, 3, 8, 15, 0, True, 'kinematic'], [7, 4, 4, 1, 1, False, 'kinematic']], [[1, 4], [2, 7], [7, 1], [6, 7], [1, 2], [1, 6], [7, 3]]], [[1, 4], [1, 6]]], [[[[1, 3, 1, 15, 0, False, 'dynamic'], [2, 1, 1, 6, -2, True, 'kinematic']], [[1, 2], [2, 1], [1, 2], [2, 1], [1, 2], [2, 1], [2, 1]]], []], [[[[1, 2, 4, 15, 1, False, 'kinematic'], [2, 1, 4, 6, -1, False, 'kinematic'], [3, 3, 4, 3, 2, True, 'kinematic'], [4, 4, 1, 7, 1, False, 'static']], [[1, 3], [1, 2], [2, 4], [1, 2], [4, 1], [1, 3]]], []]], [[[[[1, 3, 2, 3, -2, False, 'static'], [2, 4, 1, 12, 0, True, 'dynamic'], [3, 4, 4, 12, 0, False, 'static'], [4, 1, 2, 3, -1, False, 'dynamic'], [5, 2, 4, 1, -2, False, 'dynamic'], [6, 2, 4, 12, 2, True, 'dynamic'], [7, 4, 4, 1, -2, False, 'kinematic']], [[3, 2], [2, 3], [3, 2], [4, 5], [2, 5]]], [[2, 5]]], [[[[1, 1, 4, 15, 1, True, 'dynamic'], [2, 3, 2, 7, -2, False, 'kinematic'], [3, 4, 8, 15, 0, False, 'static'], [4, 2, 2, 12, 1, False, 'dynamic']], [[2, 3], [3, 4], [2, 1], [4, 2], [4, 1], [1, 4], [3, 4], [3, 4], [2, 1]]], [[1, 2], [1, 4], [3, 4]]], [[[[1, 3, 8, 15, -2, False, 'kinematic'], [2, 3, 2, 7, -2, False, 'kinematic'], [3, 3, 2, 15, 2, True, 'static'], [4, 2, 2, 3, -2, False, 'dynamic'], [5, 1, 1, 6, -1, False, 'dynamic'], [6, 4, 2, 3, 0, False, 'static']], [[2, 4], [6, 5], [5, 6]]], [[5, 6]]], [[[[1, 2, 1, 7, 0, False, 'kinematic'], [2, 2, 4, 7, 0, False, 'dynamic']], [[1, 2], [2, 1], [1, 2]]], []], [[[[1, 1, 2, 7, 0, False, 'dynamic'], [2, 4, 1, 1, 0, False, 'dynamic'], [3, 2, 4, 6, -2, False, 'static']], [[1, 2], [1, 3], [1, 2], [2, 3], [3, 1]]], [[1, 3]]], [[[[1, 2, 8, 1, 1, False, 'kinematic'], [2, 1, 1, 7, 2, False, 'static'], [3, 3, 2, 15, 2, True, 'kinematic'], [4, 3, 4, 7, -1, False, 'kinematic'], [5, 3, 4, 6, 1, False, 'dynamic'], [6, 1, 4, 15, 0, False, 'dynamic']], [[4, 5], [3, 6], [4, 6], [4, 1], [5, 3], [1, 3]]], [[3, 6], [4, 6]]], [[[[1, 2, 2, 1, 0, False, 'dynamic'], [2, 4, 2, 12, 0, False, 'dynamic'], [3, 4, 1, 15, 1, False, 'static'], [4, 2, 8, 12, 0, False, 'dynamic'], [5, 4, 2, 6, 2, False, 'dynamic']], [[5, 3], [3, 1], [3, 1], [2, 3], [3, 4], [1, 2], [1, 5], [5, 4]]], [[1, 3]]], [[[[1, 3, 1, 7, -1, False, 'dynamic'], [2, 1, 8, 12, 0, True, 'kinematic']], [[1, 2], [2, 1], [1, 2], [1, 2], [2, 1], [2, 1], [2, 1], [2, 1], [1, 2]]], []]], [[[[[1, 2, 1, 7, -1, False, 'dynamic'], [2, 2, 2, 6, 0, False, 'dynamic'], [3, 2, 1, 6, 2, False, 'kinematic'], [4, 2, 1, 6, 0, False, 'dynamic'], [5, 4, 4, 7, 1, True, 'static'], [6, 3, 2, 1, 2, False, 'static']], [[6, 4], [1, 4], [6, 5], [4, 5]]], [[4, 5], [4, 6]]], [[[[1, 1, 4, 12, 0, False, 'static'], [2, 3, 2, 12, 2, True, 'dynamic'], [3, 3, 1, 1, -1, True, 'dynamic'], [4, 4, 1, 15, 2, False, 'dynamic'], [5, 1, 4, 15, 0, False, 'static']], [[1, 3], [2, 4], [5, 3], [4, 1], [5, 2]]], [[2, 4], [2, 5]]], [[[[1, 3, 4, 15, 0, False, 'dynamic'], [2, 1, 2, 15, 0, False, 'dynamic'], [3, 3, 2, 3, -2, False, 'dynamic'], [4, 4, 4, 6, -1, False, 'kinematic'], [5, 3, 2, 15, 0, False, 'kinematic']], [[3, 2], [4, 3], [2, 4], [4, 2], [4, 1], [2, 4], [2, 5], [5, 3]]], [[1, 4], [2, 3], [2, 4], [2, 5]]], [[[[1, 1, 1, 15, -1, True, 'kinematic'], [2, 1, 8, 3, 1, False, 'kinematic']], [[1, 2], [2, 1], [2, 1]]], []], [[[[1, 1, 8, 6, -2, True, 'dynamic'], [2, 3, 2, 7, 0, False, 'kinematic'], [3, 1, 2, 15, -2, False, 'dynamic'], [4, 1, 1, 15, 0, False, 'kinematic']], [[2, 3], [4, 2], [4, 3], [1, 4], [2, 3], [2, 1], [1, 4], [4, 2], [2, 1]]], [[2, 3]]], [[[[1, 2, 8, 3, 2, False, 'kinematic'], [2, 2, 1, 1, -2, False, 'dynamic'], [3, 3, 2, 15, 0, True, 'dynamic'], [4, 1, 2, 3, 0, False, 'dynamic'], [5, 2, 2, 15, 1, False, 'kinematic'], [6, 4, 8, 3, 0, False, 'kinematic'], [7, 2, 1, 12, -1, False, 'dynamic'], [8, 4, 8, 1, 1, False, 'kinematic'], [9, 1, 2, 6, -1, False, 'dynamic']], [[3, 2], [6, 3], [5, 6], [1, 2], [6, 9], [6, 7]]], [[3, 6], [6, 7]]], [[[[1, 1, 8, 15, 1, False, 'dynamic'], [2, 1, 4, 6, -1, False, 'kinematic'], [3, 2, 2, 15, 2, False, 'static'], [4, 3, 1, 15, -1, False, 'dynamic'], [5, 3, 2, 7, 0, False, 'kinematic'], [6, 4, 4, 12, 1, False, 'kinematic']], [[2, 4], [1, 2], [3, 2], [5, 3], [6, 3], [4, 3], [5, 4], [4, 5], [1, 4], [1, 4]]], [[1, 4], [3, 4]]], [[[[1, 2, 1, 6, 0, False, 'dynamic'], [2, 4, 2, 3, -1, True, 'dynamic'], [3, 3, 1, 3, 0, False, 'static'], [4, 4, 8, 6, 2, False, 'kinematic'], [5, 1, 2, 6, -1, False, 'kinematic'], [6, 1, 1, 12, -1, False, 'dynamic'], [7, 3, 8, 3, -1, True, 'dynamic']], [[5, 7], [5, 2], [5, 4], [7, 2]]], []]], [[[[[1, 3, 1, 7, 1, False, 'static'], [2, 4, 2, 1, -1, True, 'kinematic'], [3, 1, 1, 12, 0, False, 'kinematic'], [4, 4, 4, 15, -2, True, 'dynamic'], [5, 4, 2, 7, 0, False, 'kinematic']], [[3, 1], [3, 2], [5, 3], [2, 3], [2, 3], [1, 3], [1, 3], [1, 3], [4, 5], [4, 2]]], []], [[[[1, 2, 1, 12, 0, True, 'dynamic'], [2, 1, 8, 15, 0, False, 'dynamic'], [3, 1, 1, 7, -2, False, 'kinematic'], [4, 2, 4, 15, -1, True, 'dynamic']], [[4, 3], [3, 2], [2, 1], [4, 2], [3, 1]]], [[1, 2], [2, 4], [3, 4]]], [[[[1, 3, 2, 6, 0, False, 'static'], [2, 2, 1, 15, 0, True, 'kinematic']], [[2, 1], [2, 1], [2, 1], [2, 1], [1, 2], [2, 1], [2, 1]]], []], [[[[1, 1, 4, 15, 1, True, 'dynamic'], [2, 4, 8, 15, 1, False, 'static'], [3, 4, 2, 15, 0, False, 'dynamic'], [4, 2, 1, 7, 0, False, 'static']], [[1, 2], [2, 3], [2, 4], [2, 3], [2, 3], [3, 1], [2, 3], [1, 4], [3, 2], [2, 3]]], [[1, 2], [1, 3], [1, 4]]], [[[[1, 2, 8, 1, 0, False, 'dynamic'], [2, 1, 8, 3, 2, False, 'static'], [3, 3, 2, 3, 2, False, 'dynamic'], [4, 2, 4, 6, -2, False, 'kinematic'], [5, 2, 4, 7, 1, False, 'kinematic'], [6, 4, 8, 15, -1, False, 'dynamic']], [[3, 5], [1, 5], [6, 1], [4, 2], [3, 2], [4, 1], [3, 1]]], [[2, 3]]], [[[[1, 3, 2, 15, 1, False, 'static'], [2, 2, 1, 15, -1, False, 'static'], [3, 4, 8, 15, -2, False, 'dynamic'], [4, 4, 1, 3, 0, False, 'dynamic'], [5, 1, 4, 3, 0, False, 'kinematic'], [6, 4, 4, 7, 2, False, 'dynamic'], [7, 4, 8, 15, 1, True, 'kinematic'], [8, 2, 1, 3, -2, False, 'dynamic'], [9, 2, 4, 1, -1, False, 'static'], [10, 1, 8, 15, 1, False, 'static']], [[8, 2], [10, 9], [5, 3], [2, 4], [6, 5], [3, 7], [7, 9], [6, 5], [10, 5]]], [[2, 4]]], [[[[1, 3, 1, 15, 1, False, 'dynamic'], [2, 4, 8, 6, 0, False, 'static'], [3, 3, 2, 6, 2, True, 'kinematic'], [4, 4, 1, 1, 0, True, 'kinematic'], [5, 1, 2, 15, 0, False, 'dynamic'], [6, 1, 2, 15, 0, False, 'kinematic'], [7, 2, 4, 3, 0, False, 'static']], [[1, 7], [3, 1], [3, 1], [2, 4], [6, 5], [1, 5], [1, 3]]], [[1, 5], [1, 7]]], [[[[1, 1, 1, 12, 0, True, 'static'], [2, 3, 1, 6, 0, False, 'dynamic'], [3, 3, 2, 12, 0, False, 'static'], [4, 1, 8, 7, 0, False, 'dynamic'], [5, 1, 4, 12, -2, True, 'kinematic'], [6, 4, 8, 7, 1, False, 'kinematic'], [7, 2, 4, 6, 2, False, 'dynamic'], [8, 4, 4, 15, 2, False, 'dynamic'], [9, 2, 8, 6, -2, False, 'kinematic'], [10, 2, 8, 1, 0, True, 'static']], [[10, 8], [2, 3], [7, 3]]], [[3, 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[[1, 5]][[1, 5]]Passed
case 1[][]Passed
case 2[][]Passed
case 3[[2, 1]][[1, 2]]Failed
case 4[[1, 2], [2, 1], [3, 2]][[1, 2], [2, 3]]Failed
case 5[[1, 3], [3, 1]][[1, 3]]Failed
case 6[[1, 2], [4, 2], [5, 2]][[1, 2], [2, 4], [2, 5]]Failed
case 7[[3, 1]][[1, 3]]Failed

SHA-256 / b3483894414e0a8a828f9a04645d1558fdcc19af089ac9942254c863abbd9d42

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 2026-09-29T14:50:59.677485+00:00.

Case digest / e5891d0521e852470a381258bbe182c9f793673df74d4e01720cf62174b12d55