FA-87501 / Collision detection broadphase / Open access

Group index zero is treated as a shared group · case 01

All ungrouped fixtures stop colliding with each other.

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

ROOT CAUSE

The group override fires whenever ga == gb, including 0.

VERIFIED REPAIR

Zero means no group; fall through to the mask test.

Unsuccessful approach: Only honoring positive groups lets negative groups fall back to masks and collide.

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:
            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((min(a, b), max(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, 4, 15, -1, True, 'kinematic'], [2, 1, 4, 1, 0, False, 'dynamic'], [3, 2, 4, 1, -2, False, 'static']], [[2, 1], [2, 3], [2, 3], [2, 3]]], []], [[[[1, 2, 4, 3, -1, False, 'dynamic'], [2, 1, 1, 7, -1, False, 'kinematic']], [[2, 1], [2, 1], [1, 2], [2, 1], [2, 1], [2, 1], [1, 2]]], []], [[[[1, 1, 8, 6, 2, False, 'static'], [2, 1, 2, 6, 1, False, 'dynamic'], [3, 3, 8, 3, 2, False, 'dynamic']], [[1, 3], [3, 1], [3, 2], [1, 2], [1, 3]]], [[1, 3]]], [[[[1, 2, 8, 12, -1, True, 'dynamic'], [2, 4, 2, 6, 0, True, 'dynamic'], [3, 1, 4, 6, -1, True, 'dynamic'], [4, 2, 8, 15, 0, False, 'kinematic'], [5, 4, 2, 7, 1, True, 'kinematic'], [6, 3, 8, 15, 0, False, 'dynamic']], [[5, 1], [5, 3], [3, 1], [6, 1], [2, 3], [6, 4], [5, 1], [4, 3], [6, 3]]], [[1, 6], [4, 6]]], [[[[1, 3, 1, 15, -2, False, 'dynamic'], [2, 4, 4, 15, -2, False, 'kinematic'], [3, 4, 8, 6, -2, True, 'kinematic'], [4, 4, 1, 6, 2, False, 'kinematic'], [5, 4, 2, 6, 1, False, 'dynamic'], [6, 1, 1, 6, -1, False, 'kinematic']], [[6, 2], [5, 4], [2, 5], [4, 6], [5, 1], [2, 5], [6, 3], [6, 1], [2, 3]]], []], [[[[1, 4, 4, 12, 2, False, 'dynamic'], [2, 1, 1, 15, 0, False, 'static'], [3, 2, 1, 12, -1, False, 'static'], [4, 4, 8, 7, 0, False, 'static'], [5, 1, 4, 1, -2, False, 'dynamic'], [6, 1, 4, 15, -1, False, 'dynamic']], [[2, 3], [3, 6], [1, 3], [3, 1], [1, 4]]], []], [[[[1, 3, 1, 15, 0, False, 'dynamic'], [2, 1, 8, 1, 1, True, 'kinematic'], [3, 2, 1, 6, -1, False, 'dynamic'], [4, 1, 2, 15, 0, False, 'dynamic'], [5, 3, 4, 3, 0, False, 'dynamic']], [[3, 4], [4, 3], [3, 2], [4, 1]]], [[1, 4], [3, 4]]], [[[[1, 2, 4, 12, -1, False, 'static'], [2, 2, 1, 7, 0, False, 'static'], [3, 2, 1, 3, 0, True, 'kinematic'], [4, 3, 1, 3, 0, False, 'dynamic'], [5, 2, 2, 12, 0, False, 'static']], [[2, 4], [3, 4], [5, 1]]], [[2, 4], [3, 4]]]], [[[[[1, 1, 8, 12, 0, False, 'static'], [2, 4, 2, 7, 0, False, 'dynamic'], [3, 1, 1, 12, 0, False, 'static'], [4, 1, 1, 15, 0, False, 'kinematic'], [5, 3, 8, 3, -2, True, 'static'], [6, 1, 2, 15, 0, False, 'dynamic'], [7, 1, 1, 7, 0, True, 'dynamic']], [[2, 6], [2, 7], [4, 6], [4, 6], [6, 4], [4, 6]]], [[2, 6], [2, 7]]], [[[[1, 3, 1, 6, -2, False, 'dynamic'], [2, 4, 8, 12, -1, False, 'dynamic'], [3, 3, 2, 6, 1, False, 'kinematic'], [4, 3, 4, 3, 1, False, 'kinematic'], [5, 4, 8, 15, -1, True, 'static']], [[4, 2], [2, 1], [5, 1], [1, 4]]], []], [[[[1, 1, 2, 7, -1, False, 'dynamic'], [2, 3, 8, 15, -2, True, 'dynamic'], [3, 2, 4, 15, 0, False, 'dynamic']], [[1, 2], [3, 2], [3, 1], [2, 1], [1, 3], [3, 2]]], [[1, 3], [2, 3]]], [[[[1, 2, 1, 15, 2, False, 'kinematic'], [2, 4, 4, 3, -1, False, 'static'], [3, 3, 2, 7, 0, True, 'dynamic']], [[3, 2], [3, 2], [1, 3], [2, 3], [3, 1]]], [[1, 3], [2, 3]]], [[[[1, 3, 1, 3, -2, False, 'dynamic'], [2, 4, 1, 15, 2, True, 'static'], [3, 4, 8, 12, 0, False, 'dynamic'], [4, 2, 8, 15, 0, False, 'kinematic'], [5, 1, 2, 7, 1, False, 'dynamic']], [[2, 5], [2, 4], [4, 1], [2, 5], [2, 3], [2, 3], [3, 4], [5, 4]]], [[2, 5], [3, 4]]], [[[[1, 1, 2, 12, 0, True, 'dynamic'], [2, 3, 4, 7, 0, False, 'dynamic'], [3, 3, 1, 6, -1, False, 'static'], [4, 2, 1, 15, 0, False, 'dynamic']], [[4, 1], [3, 4], [2, 4], [4, 3], [4, 3], [1, 4]]], [[2, 4]]], [[[[1, 1, 2, 12, -2, False, 'static'], [2, 2, 4, 3, -2, False, 'dynamic']], [[2, 1], [2, 1], [1, 2], [1, 2]]], []], [[[[1, 1, 4, 12, -2, True, 'dynamic'], [2, 4, 4, 6, 1, False, 'dynamic'], [3, 4, 8, 7, 1, False, 'kinematic'], [4, 2, 4, 15, -2, False, 'dynamic'], [5, 4, 1, 15, 2, False, 'kinematic'], [6, 3, 4, 15, 2, False, 'kinematic']], [[1, 3], [5, 1], [6, 1], [1, 4], [4, 6], [3, 5], [4, 2], [4, 1], [4, 1], [1, 2]]], [[1, 2], [1, 3], [1, 6], [2, 4], [4, 6]]]], [[[[[1, 3, 1, 7, -1, False, 'dynamic'], [2, 3, 1, 7, -1, False, 'dynamic'], [3, 3, 1, 6, -1, False, 'static'], [4, 1, 8, 6, 2, False, 'static'], [5, 3, 2, 12, -1, False, 'dynamic'], [6, 1, 8, 15, -1, False, 'static'], [7, 4, 2, 1, 1, True, 'dynamic']], [[4, 2], [6, 5], [3, 6], [5, 7], [2, 7], [5, 6], [1, 4], [6, 2], [6, 2], [6, 4]]], [[2, 7]]], [[[[1, 3, 8, 1, 2, False, 'dynamic'], [2, 4, 8, 3, -1, True, 'dynamic'], [3, 1, 4, 15, -2, True, 'static'], [4, 4, 8, 1, -1, False, 'dynamic'], [5, 3, 1, 15, 0, False, 'static']], [[5, 1], [5, 1], [4, 3], [4, 1], [2, 1], [5, 3], [3, 4], [1, 4], [2, 1]]], []], [[[[1, 4, 1, 1, 2, False, 'dynamic'], [2, 4, 4, 1, 0, False, 'dynamic'], [3, 2, 2, 7, 2, False, 'static'], [4, 3, 2, 7, 2, False, 'static']], [[3, 2], [3, 1], [4, 2], [2, 4], [1, 4], [2, 1], [4, 2], [4, 3], [2, 4], [4, 2]]], [[1, 3], [1, 4]]], [[[[1, 3, 2, 3, 0, False, 'dynamic'], [2, 1, 2, 7, -2, False, 'dynamic'], [3, 4, 2, 7, -2, False, 'static']], [[1, 3], [3, 1], [2, 3], [2, 3], [1, 3], [1, 3]]], [[1, 3]]], [[[[1, 1, 1, 3, 0, False, 'dynamic'], [2, 3, 4, 15, 2, False, 'dynamic'], [3, 4, 1, 3, 0, False, 'kinematic'], [4, 4, 8, 15, 0, False, 'kinematic'], [5, 3, 8, 6, -2, False, 'dynamic'], [6, 1, 2, 1, 0, True, 'kinematic'], [7, 1, 4, 6, -2, False, 'dynamic'], [8, 1, 8, 15, -1, True, 'dynamic']], [[5, 8], [2, 6], [3, 4], [1, 6], [3, 1], [4, 7], [2, 5], [3, 6], [3, 6], [3, 1]]], [[1, 3]]], [[[[1, 2, 1, 15, 0, False, 'dynamic'], [2, 3, 2, 3, 2, False, 'dynamic'], [3, 4, 4, 1, -1, True, 'kinematic'], [4, 1, 1, 6, -2, True, 'kinematic'], [5, 3, 4, 3, 0, False, 'dynamic'], [6, 2, 1, 15, 0, False, 'static']], [[5, 2], [5, 2], [5, 6], [5, 3], [5, 3], [6, 4], [1, 5], [1, 3]]], [[1, 3], [1, 5], [5, 6]]], [[[[1, 4, 4, 6, 0, True, 'dynamic'], [2, 4, 1, 1, 0, False, 'kinematic']], [[1, 2], [2, 1], [1, 2]]], []], [[[[1, 2, 2, 15, 0, False, 'dynamic'], [2, 3, 1, 6, 0, False, 'dynamic'], [3, 1, 8, 7, 2, False, 'static'], [4, 3, 8, 15, 1, False, 'dynamic'], [5, 2, 2, 6, 0, False, 'kinematic'], [6, 3, 4, 7, -2, False, 'static']], [[6, 4], [3, 6], [2, 1], [6, 2], [2, 3], [1, 5], [5, 6], [5, 2], [4, 1], [4, 1]]], [[1, 2], [1, 4]]]], [[[[[1, 2, 1, 15, 0, True, 'dynamic'], [2, 3, 8, 12, -1, False, 'kinematic'], [3, 3, 1, 15, -2, False, 'static'], [4, 3, 4, 15, 2, False, 'kinematic'], [5, 4, 2, 15, 0, False, 'kinematic'], [6, 1, 4, 12, 0, True, 'kinematic'], [7, 4, 8, 12, 2, False, 'static'], [8, 3, 2, 12, -2, False, 'static']], [[4, 7], [4, 3], [7, 6], [5, 8], [6, 7], [5, 6], [1, 5]]], [[1, 5]]], [[[[1, 4, 1, 12, 1, False, 'dynamic'], [2, 2, 2, 3, -2, False, 'kinematic']], [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]], []], [[[[1, 4, 1, 3, 0, True, 'dynamic'], [2, 4, 8, 15, -2, False, 'dynamic'], [3, 4, 8, 3, 2, True, 'kinematic'], [4, 3, 2, 15, 0, False, 'dynamic'], [5, 4, 8, 12, -2, True, 'kinematic'], [6, 1, 4, 15, 0, False, 'dynamic'], [7, 1, 2, 12, 2, False, 'dynamic'], [8, 2, 8, 1, 2, True, 'kinematic']], [[8, 5], [8, 5], [4, 6]]], [[4, 6]]], [[[[1, 4, 1, 15, 0, False, 'static'], [2, 3, 8, 15, 1, False, 'dynamic'], [3, 4, 1, 6, 0, False, 'static'], [4, 2, 1, 1, -2, True, 'kinematic'], [5, 2, 8, 15, 0, False, 'dynamic'], [6, 4, 8, 15, 0, False, 'static']], [[4, 1], [5, 1], [5, 6], [4, 6], [5, 6], [6, 4], [5, 4], [2, 3], [3, 2]]], [[1, 5], [5, 6]]], [[[[1, 2, 8, 6, -2, False, 'dynamic'], [2, 3, 8, 3, 0, False, 'static'], [3, 4, 4, 7, -1, False, 'dynamic'], [4, 2, 1, 7, -1, False, 'kinematic'], [5, 1, 1, 1, 0, False, 'dynamic'], [6, 4, 8, 7, 2, False, 'static'], [7, 3, 1, 1, -2, False, 'dynamic'], [8, 2, 4, 7, 2, False, 'static']], [[6, 1], [1, 5], [3, 6], [3, 4], [2, 3], [7, 8]]], []], [[[[1, 4, 4, 15, -2, False, 'dynamic'], [2, 1, 8, 3, -1, False, 'kinematic'], [3, 4, 2, 15, 2, False, 'dynamic']], [[2, 3], [2, 1], [2, 1], [3, 1], [3, 1], [3, 2]]], [[2, 3]]], [[[[1, 4, 4, 12, -2, True, 'dynamic'], [2, 1, 2, 15, 0, False, 'static'], [3, 1, 8, 1, 0, False, 'static'], [4, 2, 1, 3, 1, False, 'kinematic'], [5, 3, 8, 7, -2, False, 'dynamic'], [6, 1, 4, 15, -2, False, 'dynamic'], [7, 4, 4, 15, 2, False, 'kinematic']], [[6, 4], [4, 1], [1, 5], [5, 6], [3, 5], [2, 1], [7, 4], [7, 1], [3, 7]]], []], [[[[1, 3, 8, 1, 1, False, 'dynamic'], [2, 2, 4, 12, -1, False, 'kinematic'], [3, 2, 4, 3, -2, False, 'dynamic'], [4, 4, 2, 6, 0, False, 'dynamic'], [5, 2, 8, 7, 0, False, 'dynamic'], [6, 3, 8, 15, 2, False, 'dynamic'], [7, 4, 1, 12, -1, False, 'dynamic'], [8, 3, 8, 15, 2, False, 'kinematic'], [9, 1, 4, 1, -1, False, 'static']], [[6, 3], [3, 5], [7, 4], [9, 1]]], []]], [[[[[1, 2, 8, 3, 2, False, 'dynamic'], [2, 4, 8, 3, 1, False, 'dynamic'], [3, 3, 4, 3, 0, False, 'dynamic'], [4, 4, 1, 6, 1, False, 'kinematic'], [5, 2, 8, 3, -1, False, 'kinematic'], [6, 3, 8, 6, -1, False, 'static'], [7, 2, 1, 3, -2, False, 'kinematic'], [8, 2, 2, 3, 0, False, 'static'], [9, 3, 8, 15, 0, True, 'kinematic']], [[3, 5], [3, 1], [3, 8], [2, 9], [6, 2], [9, 4], [9, 2], [5, 6], [4, 7]]], []], [[[[1, 1, 1, 15, 0, False, 'dynamic'], [2, 2, 4, 15, 1, False, 'kinematic'], [3, 1, 4, 6, 0, False, 'kinematic'], [4, 2, 2, 15, -2, False, 'dynamic'], [5, 2, 1, 12, -2, False, 'kinematic'], [6, 2, 2, 12, 0, False, 'dynamic'], [7, 2, 2, 6, 1, True, 'dynamic']], [[3, 7], [1, 3], [7, 3], [5, 7], [4, 6], [5, 2], [3, 6], [2, 3], [7, 3]]], [[3, 6], [3, 7]]], [[[[1, 4, 4, 6, -2, True, 'kinematic'], [2, 2, 8, 3, 1, False, 'kinematic'], [3, 2, 2, 1, 0, False, 'dynamic'], [4, 2, 2, 3, -1, False, 'kinematic'], [5, 2, 8, 12, -1, True, 'kinematic'], [6, 1, 1, 15, 2, False, 'dynamic'], [7, 2, 8, 6, 2, False, 'static'], [8, 3, 8, 15, 0, False, 'kinematic'], [9, 3, 1, 3, 2, False, 'static']], [[6, 5], [4, 5], [8, 3]]], []], [[[[1, 1, 8, 12, 0, True, 'dynamic'], [2, 2, 4, 15, 0, False, 'dynamic'], [3, 4, 1, 15, 0, False, 'static'], [4, 2, 2, 15, -1, False, 'dynamic'], [5, 3, 4, 6, 1, False, 'static'], [6, 4, 8, 15, -1, False, 'static']], [[2, 1], [2, 1], [4, 6], [6, 1], [2, 6]]], [[1, 2], [1, 6], [2, 6]]], [[[[1, 3, 4, 12, 0, False, 'dynamic'], [2, 3, 1, 6, 2, False, 'static'], [3, 4, 1, 12, 2, False, 'kinematic'], [4, 2, 4, 15, 0, False, 'dynamic'], [5, 2, 1, 3, 0, False, 'kinematic'], [6, 1, 8, 15, 0, True, 'kinematic'], [7, 4, 2, 15, 0, False, 'kinematic'], [8, 3, 8, 12, 1, False, 'static'], [9, 1, 8, 1, 0, False, 'static'], [10, 3, 1, 7, 0, False, 'static']], [[4, 1], [3, 1], [10, 9], [4, 9], [5, 3], [8, 4], [9, 1], [3, 5], [8, 7], [1, 2]]], [[1, 4], [4, 8]]], [[[[1, 1, 1, 7, 0, False, 'dynamic'], [2, 3, 8, 12, -2, True, 'static'], [3, 2, 1, 6, -2, False, 'dynamic'], [4, 2, 2, 1, 0, False, 'static']], [[4, 3], [1, 3], [1, 2], [4, 1], [1, 3], [1, 4]]], [[1, 4]]], [[[[1, 1, 2, 1, 0, False, 'dynamic'], [2, 3, 8, 7, -2, False, 'dynamic'], [3, 2, 4, 15, 2, False, 'dynamic'], [4, 4, 2, 12, 0, False, 'kinematic']], [[2, 4], [3, 4], [3, 1], [4, 3], [2, 4], [1, 3], [4, 1], [3, 2], [3, 2], [1, 2]]], [[2, 3], [2, 4], [3, 4]]], [[[[1, 2, 1, 15, 0, False, 'kinematic'], [2, 4, 8, 7, 0, True, 'dynamic'], [3, 2, 8, 15, 2, False, 'dynamic'], [4, 1, 2, 6, -2, False, 'dynamic'], [5, 3, 8, 1, 0, False, 'dynamic'], [6, 3, 2, 15, 0, True, 'kinematic'], [7, 3, 2, 6, -2, False, 'kinematic'], [8, 3, 2, 7, -2, False, 'dynamic'], [9, 3, 1, 15, 1, False, 'dynamic']], [[2, 5], [6, 1], [9, 8], [3, 4], [8, 5], [2, 7], [8, 1], [4, 7]]], [[1, 8]]]]]
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 fixture	Actual	Expected	Outcome
case 0	`[]`	`[]`	Passed
case 1	`[]`	`[]`	Passed
case 2	`[[1, 3]]`	`[[1, 3]]`	Passed
case 3	`[[1, 6]]`	`[[1, 6], [4, 6]]`	Failed
case 4	`[]`	`[]`	Passed
case 5	`[]`	`[]`	Passed
case 6	`[[3, 4]]`	`[[1, 4], [3, 4]]`	Failed
case 7	`[]`	`[[2, 4], [3, 4]]`	Failed

SHA-256 / 2bb48423f871fa25e2c2144eda9ebec33695d4c7b0970d7a1b5c40982efa8598

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((min(a, b), max(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, 4, 15, -1, True, 'kinematic'], [2, 1, 4, 1, 0, False, 'dynamic'], [3, 2, 4, 1, -2, False, 'static']], [[2, 1], [2, 3], [2, 3], [2, 3]]], []], [[[[1, 2, 4, 3, -1, False, 'dynamic'], [2, 1, 1, 7, -1, False, 'kinematic']], [[2, 1], [2, 1], [1, 2], [2, 1], [2, 1], [2, 1], [1, 2]]], []], [[[[1, 1, 8, 6, 2, False, 'static'], [2, 1, 2, 6, 1, False, 'dynamic'], [3, 3, 8, 3, 2, False, 'dynamic']], [[1, 3], [3, 1], [3, 2], [1, 2], [1, 3]]], [[1, 3]]], [[[[1, 2, 8, 12, -1, True, 'dynamic'], [2, 4, 2, 6, 0, True, 'dynamic'], [3, 1, 4, 6, -1, True, 'dynamic'], [4, 2, 8, 15, 0, False, 'kinematic'], [5, 4, 2, 7, 1, True, 'kinematic'], [6, 3, 8, 15, 0, False, 'dynamic']], [[5, 1], [5, 3], [3, 1], [6, 1], [2, 3], [6, 4], [5, 1], [4, 3], [6, 3]]], [[1, 6], [4, 6]]], [[[[1, 3, 1, 15, -2, False, 'dynamic'], [2, 4, 4, 15, -2, False, 'kinematic'], [3, 4, 8, 6, -2, True, 'kinematic'], [4, 4, 1, 6, 2, False, 'kinematic'], [5, 4, 2, 6, 1, False, 'dynamic'], [6, 1, 1, 6, -1, False, 'kinematic']], [[6, 2], [5, 4], [2, 5], [4, 6], [5, 1], [2, 5], [6, 3], [6, 1], [2, 3]]], []], [[[[1, 4, 4, 12, 2, False, 'dynamic'], [2, 1, 1, 15, 0, False, 'static'], [3, 2, 1, 12, -1, False, 'static'], [4, 4, 8, 7, 0, False, 'static'], [5, 1, 4, 1, -2, False, 'dynamic'], [6, 1, 4, 15, -1, False, 'dynamic']], [[2, 3], [3, 6], [1, 3], [3, 1], [1, 4]]], []], [[[[1, 3, 1, 15, 0, False, 'dynamic'], [2, 1, 8, 1, 1, True, 'kinematic'], [3, 2, 1, 6, -1, False, 'dynamic'], [4, 1, 2, 15, 0, False, 'dynamic'], [5, 3, 4, 3, 0, False, 'dynamic']], [[3, 4], [4, 3], [3, 2], [4, 1]]], [[1, 4], [3, 4]]], [[[[1, 2, 4, 12, -1, False, 'static'], [2, 2, 1, 7, 0, False, 'static'], [3, 2, 1, 3, 0, True, 'kinematic'], [4, 3, 1, 3, 0, False, 'dynamic'], [5, 2, 2, 12, 0, False, 'static']], [[2, 4], [3, 4], [5, 1]]], [[2, 4], [3, 4]]]], [[[[[1, 1, 8, 12, 0, False, 'static'], [2, 4, 2, 7, 0, False, 'dynamic'], [3, 1, 1, 12, 0, False, 'static'], [4, 1, 1, 15, 0, False, 'kinematic'], [5, 3, 8, 3, -2, True, 'static'], [6, 1, 2, 15, 0, False, 'dynamic'], [7, 1, 1, 7, 0, True, 'dynamic']], [[2, 6], [2, 7], [4, 6], [4, 6], [6, 4], [4, 6]]], [[2, 6], [2, 7]]], [[[[1, 3, 1, 6, -2, False, 'dynamic'], [2, 4, 8, 12, -1, False, 'dynamic'], [3, 3, 2, 6, 1, False, 'kinematic'], [4, 3, 4, 3, 1, False, 'kinematic'], [5, 4, 8, 15, -1, True, 'static']], [[4, 2], [2, 1], [5, 1], [1, 4]]], []], [[[[1, 1, 2, 7, -1, False, 'dynamic'], [2, 3, 8, 15, -2, True, 'dynamic'], [3, 2, 4, 15, 0, False, 'dynamic']], [[1, 2], [3, 2], [3, 1], [2, 1], [1, 3], [3, 2]]], [[1, 3], [2, 3]]], [[[[1, 2, 1, 15, 2, False, 'kinematic'], [2, 4, 4, 3, -1, False, 'static'], [3, 3, 2, 7, 0, True, 'dynamic']], [[3, 2], [3, 2], [1, 3], [2, 3], [3, 1]]], [[1, 3], [2, 3]]], [[[[1, 3, 1, 3, -2, False, 'dynamic'], [2, 4, 1, 15, 2, True, 'static'], [3, 4, 8, 12, 0, False, 'dynamic'], [4, 2, 8, 15, 0, False, 'kinematic'], [5, 1, 2, 7, 1, False, 'dynamic']], [[2, 5], [2, 4], [4, 1], [2, 5], [2, 3], [2, 3], [3, 4], [5, 4]]], [[2, 5], [3, 4]]], [[[[1, 1, 2, 12, 0, True, 'dynamic'], [2, 3, 4, 7, 0, False, 'dynamic'], [3, 3, 1, 6, -1, False, 'static'], [4, 2, 1, 15, 0, False, 'dynamic']], [[4, 1], [3, 4], [2, 4], [4, 3], [4, 3], [1, 4]]], [[2, 4]]], [[[[1, 1, 2, 12, -2, False, 'static'], [2, 2, 4, 3, -2, False, 'dynamic']], [[2, 1], [2, 1], [1, 2], [1, 2]]], []], [[[[1, 1, 4, 12, -2, True, 'dynamic'], [2, 4, 4, 6, 1, False, 'dynamic'], [3, 4, 8, 7, 1, False, 'kinematic'], [4, 2, 4, 15, -2, False, 'dynamic'], [5, 4, 1, 15, 2, False, 'kinematic'], [6, 3, 4, 15, 2, False, 'kinematic']], [[1, 3], [5, 1], [6, 1], [1, 4], [4, 6], [3, 5], [4, 2], [4, 1], [4, 1], [1, 2]]], [[1, 2], [1, 3], [1, 6], [2, 4], [4, 6]]]], [[[[[1, 3, 1, 7, -1, False, 'dynamic'], [2, 3, 1, 7, -1, False, 'dynamic'], [3, 3, 1, 6, -1, False, 'static'], [4, 1, 8, 6, 2, False, 'static'], [5, 3, 2, 12, -1, False, 'dynamic'], [6, 1, 8, 15, -1, False, 'static'], [7, 4, 2, 1, 1, True, 'dynamic']], [[4, 2], [6, 5], [3, 6], [5, 7], [2, 7], [5, 6], [1, 4], [6, 2], [6, 2], [6, 4]]], [[2, 7]]], [[[[1, 3, 8, 1, 2, False, 'dynamic'], [2, 4, 8, 3, -1, True, 'dynamic'], [3, 1, 4, 15, -2, True, 'static'], [4, 4, 8, 1, -1, False, 'dynamic'], [5, 3, 1, 15, 0, False, 'static']], [[5, 1], [5, 1], [4, 3], [4, 1], [2, 1], [5, 3], [3, 4], [1, 4], [2, 1]]], []], [[[[1, 4, 1, 1, 2, False, 'dynamic'], [2, 4, 4, 1, 0, False, 'dynamic'], [3, 2, 2, 7, 2, False, 'static'], [4, 3, 2, 7, 2, False, 'static']], [[3, 2], [3, 1], [4, 2], [2, 4], [1, 4], [2, 1], [4, 2], [4, 3], [2, 4], [4, 2]]], [[1, 3], [1, 4]]], [[[[1, 3, 2, 3, 0, False, 'dynamic'], [2, 1, 2, 7, -2, False, 'dynamic'], [3, 4, 2, 7, -2, False, 'static']], [[1, 3], [3, 1], [2, 3], [2, 3], [1, 3], [1, 3]]], [[1, 3]]], [[[[1, 1, 1, 3, 0, False, 'dynamic'], [2, 3, 4, 15, 2, False, 'dynamic'], [3, 4, 1, 3, 0, False, 'kinematic'], [4, 4, 8, 15, 0, False, 'kinematic'], [5, 3, 8, 6, -2, False, 'dynamic'], [6, 1, 2, 1, 0, True, 'kinematic'], [7, 1, 4, 6, -2, False, 'dynamic'], [8, 1, 8, 15, -1, True, 'dynamic']], [[5, 8], [2, 6], [3, 4], [1, 6], [3, 1], [4, 7], [2, 5], [3, 6], [3, 6], [3, 1]]], [[1, 3]]], [[[[1, 2, 1, 15, 0, False, 'dynamic'], [2, 3, 2, 3, 2, False, 'dynamic'], [3, 4, 4, 1, -1, True, 'kinematic'], [4, 1, 1, 6, -2, True, 'kinematic'], [5, 3, 4, 3, 0, False, 'dynamic'], [6, 2, 1, 15, 0, False, 'static']], [[5, 2], [5, 2], [5, 6], [5, 3], [5, 3], [6, 4], [1, 5], [1, 3]]], [[1, 3], [1, 5], [5, 6]]], [[[[1, 4, 4, 6, 0, True, 'dynamic'], [2, 4, 1, 1, 0, False, 'kinematic']], [[1, 2], [2, 1], [1, 2]]], []], [[[[1, 2, 2, 15, 0, False, 'dynamic'], [2, 3, 1, 6, 0, False, 'dynamic'], [3, 1, 8, 7, 2, False, 'static'], [4, 3, 8, 15, 1, False, 'dynamic'], [5, 2, 2, 6, 0, False, 'kinematic'], [6, 3, 4, 7, -2, False, 'static']], [[6, 4], [3, 6], [2, 1], [6, 2], [2, 3], [1, 5], [5, 6], [5, 2], [4, 1], [4, 1]]], [[1, 2], [1, 4]]]], [[[[[1, 2, 1, 15, 0, True, 'dynamic'], [2, 3, 8, 12, -1, False, 'kinematic'], [3, 3, 1, 15, -2, False, 'static'], [4, 3, 4, 15, 2, False, 'kinematic'], [5, 4, 2, 15, 0, False, 'kinematic'], [6, 1, 4, 12, 0, True, 'kinematic'], [7, 4, 8, 12, 2, False, 'static'], [8, 3, 2, 12, -2, False, 'static']], [[4, 7], [4, 3], [7, 6], [5, 8], [6, 7], [5, 6], [1, 5]]], [[1, 5]]], [[[[1, 4, 1, 12, 1, False, 'dynamic'], [2, 2, 2, 3, -2, False, 'kinematic']], [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]], []], [[[[1, 4, 1, 3, 0, True, 'dynamic'], [2, 4, 8, 15, -2, False, 'dynamic'], [3, 4, 8, 3, 2, True, 'kinematic'], [4, 3, 2, 15, 0, False, 'dynamic'], [5, 4, 8, 12, -2, True, 'kinematic'], [6, 1, 4, 15, 0, False, 'dynamic'], [7, 1, 2, 12, 2, False, 'dynamic'], [8, 2, 8, 1, 2, True, 'kinematic']], [[8, 5], [8, 5], [4, 6]]], [[4, 6]]], [[[[1, 4, 1, 15, 0, False, 'static'], [2, 3, 8, 15, 1, False, 'dynamic'], [3, 4, 1, 6, 0, False, 'static'], [4, 2, 1, 1, -2, True, 'kinematic'], [5, 2, 8, 15, 0, False, 'dynamic'], [6, 4, 8, 15, 0, False, 'static']], [[4, 1], [5, 1], [5, 6], [4, 6], [5, 6], [6, 4], [5, 4], [2, 3], [3, 2]]], [[1, 5], [5, 6]]], [[[[1, 2, 8, 6, -2, False, 'dynamic'], [2, 3, 8, 3, 0, False, 'static'], [3, 4, 4, 7, -1, False, 'dynamic'], [4, 2, 1, 7, -1, False, 'kinematic'], [5, 1, 1, 1, 0, False, 'dynamic'], [6, 4, 8, 7, 2, False, 'static'], [7, 3, 1, 1, -2, False, 'dynamic'], [8, 2, 4, 7, 2, False, 'static']], [[6, 1], [1, 5], [3, 6], [3, 4], [2, 3], [7, 8]]], []], [[[[1, 4, 4, 15, -2, False, 'dynamic'], [2, 1, 8, 3, -1, False, 'kinematic'], [3, 4, 2, 15, 2, False, 'dynamic']], [[2, 3], [2, 1], [2, 1], [3, 1], [3, 1], [3, 2]]], [[2, 3]]], [[[[1, 4, 4, 12, -2, True, 'dynamic'], [2, 1, 2, 15, 0, False, 'static'], [3, 1, 8, 1, 0, False, 'static'], [4, 2, 1, 3, 1, False, 'kinematic'], [5, 3, 8, 7, -2, False, 'dynamic'], [6, 1, 4, 15, -2, False, 'dynamic'], [7, 4, 4, 15, 2, False, 'kinematic']], [[6, 4], [4, 1], [1, 5], [5, 6], [3, 5], [2, 1], [7, 4], [7, 1], [3, 7]]], []], [[[[1, 3, 8, 1, 1, False, 'dynamic'], [2, 2, 4, 12, -1, False, 'kinematic'], [3, 2, 4, 3, -2, False, 'dynamic'], [4, 4, 2, 6, 0, False, 'dynamic'], [5, 2, 8, 7, 0, False, 'dynamic'], [6, 3, 8, 15, 2, False, 'dynamic'], [7, 4, 1, 12, -1, False, 'dynamic'], [8, 3, 8, 15, 2, False, 'kinematic'], [9, 1, 4, 1, -1, False, 'static']], [[6, 3], [3, 5], [7, 4], [9, 1]]], []]], [[[[[1, 2, 8, 3, 2, False, 'dynamic'], [2, 4, 8, 3, 1, False, 'dynamic'], [3, 3, 4, 3, 0, False, 'dynamic'], [4, 4, 1, 6, 1, False, 'kinematic'], [5, 2, 8, 3, -1, False, 'kinematic'], [6, 3, 8, 6, -1, False, 'static'], [7, 2, 1, 3, -2, False, 'kinematic'], [8, 2, 2, 3, 0, False, 'static'], [9, 3, 8, 15, 0, True, 'kinematic']], [[3, 5], [3, 1], [3, 8], [2, 9], [6, 2], [9, 4], [9, 2], [5, 6], [4, 7]]], []], [[[[1, 1, 1, 15, 0, False, 'dynamic'], [2, 2, 4, 15, 1, False, 'kinematic'], [3, 1, 4, 6, 0, False, 'kinematic'], [4, 2, 2, 15, -2, False, 'dynamic'], [5, 2, 1, 12, -2, False, 'kinematic'], [6, 2, 2, 12, 0, False, 'dynamic'], [7, 2, 2, 6, 1, True, 'dynamic']], [[3, 7], [1, 3], [7, 3], [5, 7], [4, 6], [5, 2], [3, 6], [2, 3], [7, 3]]], [[3, 6], [3, 7]]], [[[[1, 4, 4, 6, -2, True, 'kinematic'], [2, 2, 8, 3, 1, False, 'kinematic'], [3, 2, 2, 1, 0, False, 'dynamic'], [4, 2, 2, 3, -1, False, 'kinematic'], [5, 2, 8, 12, -1, True, 'kinematic'], [6, 1, 1, 15, 2, False, 'dynamic'], [7, 2, 8, 6, 2, False, 'static'], [8, 3, 8, 15, 0, False, 'kinematic'], [9, 3, 1, 3, 2, False, 'static']], [[6, 5], [4, 5], [8, 3]]], []], [[[[1, 1, 8, 12, 0, True, 'dynamic'], [2, 2, 4, 15, 0, False, 'dynamic'], [3, 4, 1, 15, 0, False, 'static'], [4, 2, 2, 15, -1, False, 'dynamic'], [5, 3, 4, 6, 1, False, 'static'], [6, 4, 8, 15, -1, False, 'static']], [[2, 1], [2, 1], [4, 6], [6, 1], [2, 6]]], [[1, 2], [1, 6], [2, 6]]], [[[[1, 3, 4, 12, 0, False, 'dynamic'], [2, 3, 1, 6, 2, False, 'static'], [3, 4, 1, 12, 2, False, 'kinematic'], [4, 2, 4, 15, 0, False, 'dynamic'], [5, 2, 1, 3, 0, False, 'kinematic'], [6, 1, 8, 15, 0, True, 'kinematic'], [7, 4, 2, 15, 0, False, 'kinematic'], [8, 3, 8, 12, 1, False, 'static'], [9, 1, 8, 1, 0, False, 'static'], [10, 3, 1, 7, 0, False, 'static']], [[4, 1], [3, 1], [10, 9], [4, 9], [5, 3], [8, 4], [9, 1], [3, 5], [8, 7], [1, 2]]], [[1, 4], [4, 8]]], [[[[1, 1, 1, 7, 0, False, 'dynamic'], [2, 3, 8, 12, -2, True, 'static'], [3, 2, 1, 6, -2, False, 'dynamic'], [4, 2, 2, 1, 0, False, 'static']], [[4, 3], [1, 3], [1, 2], [4, 1], [1, 3], [1, 4]]], [[1, 4]]], [[[[1, 1, 2, 1, 0, False, 'dynamic'], [2, 3, 8, 7, -2, False, 'dynamic'], [3, 2, 4, 15, 2, False, 'dynamic'], [4, 4, 2, 12, 0, False, 'kinematic']], [[2, 4], [3, 4], [3, 1], [4, 3], [2, 4], [1, 3], [4, 1], [3, 2], [3, 2], [1, 2]]], [[2, 3], [2, 4], [3, 4]]], [[[[1, 2, 1, 15, 0, False, 'kinematic'], [2, 4, 8, 7, 0, True, 'dynamic'], [3, 2, 8, 15, 2, False, 'dynamic'], [4, 1, 2, 6, -2, False, 'dynamic'], [5, 3, 8, 1, 0, False, 'dynamic'], [6, 3, 2, 15, 0, True, 'kinematic'], [7, 3, 2, 6, -2, False, 'kinematic'], [8, 3, 2, 7, -2, False, 'dynamic'], [9, 3, 1, 15, 1, False, 'dynamic']], [[2, 5], [6, 1], [9, 8], [3, 4], [8, 5], [2, 7], [8, 1], [4, 7]]], [[1, 8]]]]]
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 fixture	Actual	Expected	Outcome
case 0	`[]`	`[]`	Passed
case 1	`[[1, 2]]`	`[]`	Failed
case 2	`[[1, 3]]`	`[[1, 3]]`	Passed
case 3	`[[1, 6], [4, 6]]`	`[[1, 6], [4, 6]]`	Passed
case 4	`[]`	`[]`	Passed
case 5	`[[3, 6]]`	`[]`	Failed
case 6	`[[1, 4], [3, 4]]`	`[[1, 4], [3, 4]]`	Passed
case 7	`[[2, 4], [3, 4]]`	`[[2, 4], [3, 4]]`	Passed

SHA-256 / 65d4c23a0b52b9085e9f56734dede47cdbca7e84d07600cb43d08c6fa8805ccd

3 / The verified repair

Exit 0

"""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((min(a, b), max(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, 4, 15, -1, True, 'kinematic'], [2, 1, 4, 1, 0, False, 'dynamic'], [3, 2, 4, 1, -2, False, 'static']], [[2, 1], [2, 3], [2, 3], [2, 3]]], []], [[[[1, 2, 4, 3, -1, False, 'dynamic'], [2, 1, 1, 7, -1, False, 'kinematic']], [[2, 1], [2, 1], [1, 2], [2, 1], [2, 1], [2, 1], [1, 2]]], []], [[[[1, 1, 8, 6, 2, False, 'static'], [2, 1, 2, 6, 1, False, 'dynamic'], [3, 3, 8, 3, 2, False, 'dynamic']], [[1, 3], [3, 1], [3, 2], [1, 2], [1, 3]]], [[1, 3]]], [[[[1, 2, 8, 12, -1, True, 'dynamic'], [2, 4, 2, 6, 0, True, 'dynamic'], [3, 1, 4, 6, -1, True, 'dynamic'], [4, 2, 8, 15, 0, False, 'kinematic'], [5, 4, 2, 7, 1, True, 'kinematic'], [6, 3, 8, 15, 0, False, 'dynamic']], [[5, 1], [5, 3], [3, 1], [6, 1], [2, 3], [6, 4], [5, 1], [4, 3], [6, 3]]], [[1, 6], [4, 6]]], [[[[1, 3, 1, 15, -2, False, 'dynamic'], [2, 4, 4, 15, -2, False, 'kinematic'], [3, 4, 8, 6, -2, True, 'kinematic'], [4, 4, 1, 6, 2, False, 'kinematic'], [5, 4, 2, 6, 1, False, 'dynamic'], [6, 1, 1, 6, -1, False, 'kinematic']], [[6, 2], [5, 4], [2, 5], [4, 6], [5, 1], [2, 5], [6, 3], [6, 1], [2, 3]]], []], [[[[1, 4, 4, 12, 2, False, 'dynamic'], [2, 1, 1, 15, 0, False, 'static'], [3, 2, 1, 12, -1, False, 'static'], [4, 4, 8, 7, 0, False, 'static'], [5, 1, 4, 1, -2, False, 'dynamic'], [6, 1, 4, 15, -1, False, 'dynamic']], [[2, 3], [3, 6], [1, 3], [3, 1], [1, 4]]], []], [[[[1, 3, 1, 15, 0, False, 'dynamic'], [2, 1, 8, 1, 1, True, 'kinematic'], [3, 2, 1, 6, -1, False, 'dynamic'], [4, 1, 2, 15, 0, False, 'dynamic'], [5, 3, 4, 3, 0, False, 'dynamic']], [[3, 4], [4, 3], [3, 2], [4, 1]]], [[1, 4], [3, 4]]], [[[[1, 2, 4, 12, -1, False, 'static'], [2, 2, 1, 7, 0, False, 'static'], [3, 2, 1, 3, 0, True, 'kinematic'], [4, 3, 1, 3, 0, False, 'dynamic'], [5, 2, 2, 12, 0, False, 'static']], [[2, 4], [3, 4], [5, 1]]], [[2, 4], [3, 4]]]], [[[[[1, 1, 8, 12, 0, False, 'static'], [2, 4, 2, 7, 0, False, 'dynamic'], [3, 1, 1, 12, 0, False, 'static'], [4, 1, 1, 15, 0, False, 'kinematic'], [5, 3, 8, 3, -2, True, 'static'], [6, 1, 2, 15, 0, False, 'dynamic'], [7, 1, 1, 7, 0, True, 'dynamic']], [[2, 6], [2, 7], [4, 6], [4, 6], [6, 4], [4, 6]]], [[2, 6], [2, 7]]], [[[[1, 3, 1, 6, -2, False, 'dynamic'], [2, 4, 8, 12, -1, False, 'dynamic'], [3, 3, 2, 6, 1, False, 'kinematic'], [4, 3, 4, 3, 1, False, 'kinematic'], [5, 4, 8, 15, -1, True, 'static']], [[4, 2], [2, 1], [5, 1], [1, 4]]], []], [[[[1, 1, 2, 7, -1, False, 'dynamic'], [2, 3, 8, 15, -2, True, 'dynamic'], [3, 2, 4, 15, 0, False, 'dynamic']], [[1, 2], [3, 2], [3, 1], [2, 1], [1, 3], [3, 2]]], [[1, 3], [2, 3]]], [[[[1, 2, 1, 15, 2, False, 'kinematic'], [2, 4, 4, 3, -1, False, 'static'], [3, 3, 2, 7, 0, True, 'dynamic']], [[3, 2], [3, 2], [1, 3], [2, 3], [3, 1]]], [[1, 3], [2, 3]]], [[[[1, 3, 1, 3, -2, False, 'dynamic'], [2, 4, 1, 15, 2, True, 'static'], [3, 4, 8, 12, 0, False, 'dynamic'], [4, 2, 8, 15, 0, False, 'kinematic'], [5, 1, 2, 7, 1, False, 'dynamic']], [[2, 5], [2, 4], [4, 1], [2, 5], [2, 3], [2, 3], [3, 4], [5, 4]]], [[2, 5], [3, 4]]], [[[[1, 1, 2, 12, 0, True, 'dynamic'], [2, 3, 4, 7, 0, False, 'dynamic'], [3, 3, 1, 6, -1, False, 'static'], [4, 2, 1, 15, 0, False, 'dynamic']], [[4, 1], [3, 4], [2, 4], [4, 3], [4, 3], [1, 4]]], [[2, 4]]], [[[[1, 1, 2, 12, -2, False, 'static'], [2, 2, 4, 3, -2, False, 'dynamic']], [[2, 1], [2, 1], [1, 2], [1, 2]]], []], [[[[1, 1, 4, 12, -2, True, 'dynamic'], [2, 4, 4, 6, 1, False, 'dynamic'], [3, 4, 8, 7, 1, False, 'kinematic'], [4, 2, 4, 15, -2, False, 'dynamic'], [5, 4, 1, 15, 2, False, 'kinematic'], [6, 3, 4, 15, 2, False, 'kinematic']], [[1, 3], [5, 1], [6, 1], [1, 4], [4, 6], [3, 5], [4, 2], [4, 1], [4, 1], [1, 2]]], [[1, 2], [1, 3], [1, 6], [2, 4], [4, 6]]]], [[[[[1, 3, 1, 7, -1, False, 'dynamic'], [2, 3, 1, 7, -1, False, 'dynamic'], [3, 3, 1, 6, -1, False, 'static'], [4, 1, 8, 6, 2, False, 'static'], [5, 3, 2, 12, -1, False, 'dynamic'], [6, 1, 8, 15, -1, False, 'static'], [7, 4, 2, 1, 1, True, 'dynamic']], [[4, 2], [6, 5], [3, 6], [5, 7], [2, 7], [5, 6], [1, 4], [6, 2], [6, 2], [6, 4]]], [[2, 7]]], [[[[1, 3, 8, 1, 2, False, 'dynamic'], [2, 4, 8, 3, -1, True, 'dynamic'], [3, 1, 4, 15, -2, True, 'static'], [4, 4, 8, 1, -1, False, 'dynamic'], [5, 3, 1, 15, 0, False, 'static']], [[5, 1], [5, 1], [4, 3], [4, 1], [2, 1], [5, 3], [3, 4], [1, 4], [2, 1]]], []], [[[[1, 4, 1, 1, 2, False, 'dynamic'], [2, 4, 4, 1, 0, False, 'dynamic'], [3, 2, 2, 7, 2, False, 'static'], [4, 3, 2, 7, 2, False, 'static']], [[3, 2], [3, 1], [4, 2], [2, 4], [1, 4], [2, 1], [4, 2], [4, 3], [2, 4], [4, 2]]], [[1, 3], [1, 4]]], [[[[1, 3, 2, 3, 0, False, 'dynamic'], [2, 1, 2, 7, -2, False, 'dynamic'], [3, 4, 2, 7, -2, False, 'static']], [[1, 3], [3, 1], [2, 3], [2, 3], [1, 3], [1, 3]]], [[1, 3]]], [[[[1, 1, 1, 3, 0, False, 'dynamic'], [2, 3, 4, 15, 2, False, 'dynamic'], [3, 4, 1, 3, 0, False, 'kinematic'], [4, 4, 8, 15, 0, False, 'kinematic'], [5, 3, 8, 6, -2, False, 'dynamic'], [6, 1, 2, 1, 0, True, 'kinematic'], [7, 1, 4, 6, -2, False, 'dynamic'], [8, 1, 8, 15, -1, True, 'dynamic']], [[5, 8], [2, 6], [3, 4], [1, 6], [3, 1], [4, 7], [2, 5], [3, 6], [3, 6], [3, 1]]], [[1, 3]]], [[[[1, 2, 1, 15, 0, False, 'dynamic'], [2, 3, 2, 3, 2, False, 'dynamic'], [3, 4, 4, 1, -1, True, 'kinematic'], [4, 1, 1, 6, -2, True, 'kinematic'], [5, 3, 4, 3, 0, False, 'dynamic'], [6, 2, 1, 15, 0, False, 'static']], [[5, 2], [5, 2], [5, 6], [5, 3], [5, 3], [6, 4], [1, 5], [1, 3]]], [[1, 3], [1, 5], [5, 6]]], [[[[1, 4, 4, 6, 0, True, 'dynamic'], [2, 4, 1, 1, 0, False, 'kinematic']], [[1, 2], [2, 1], [1, 2]]], []], [[[[1, 2, 2, 15, 0, False, 'dynamic'], [2, 3, 1, 6, 0, False, 'dynamic'], [3, 1, 8, 7, 2, False, 'static'], [4, 3, 8, 15, 1, False, 'dynamic'], [5, 2, 2, 6, 0, False, 'kinematic'], [6, 3, 4, 7, -2, False, 'static']], [[6, 4], [3, 6], [2, 1], [6, 2], [2, 3], [1, 5], [5, 6], [5, 2], [4, 1], [4, 1]]], [[1, 2], [1, 4]]]], [[[[[1, 2, 1, 15, 0, True, 'dynamic'], [2, 3, 8, 12, -1, False, 'kinematic'], [3, 3, 1, 15, -2, False, 'static'], [4, 3, 4, 15, 2, False, 'kinematic'], [5, 4, 2, 15, 0, False, 'kinematic'], [6, 1, 4, 12, 0, True, 'kinematic'], [7, 4, 8, 12, 2, False, 'static'], [8, 3, 2, 12, -2, False, 'static']], [[4, 7], [4, 3], [7, 6], [5, 8], [6, 7], [5, 6], [1, 5]]], [[1, 5]]], [[[[1, 4, 1, 12, 1, False, 'dynamic'], [2, 2, 2, 3, -2, False, 'kinematic']], [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]], []], [[[[1, 4, 1, 3, 0, True, 'dynamic'], [2, 4, 8, 15, -2, False, 'dynamic'], [3, 4, 8, 3, 2, True, 'kinematic'], [4, 3, 2, 15, 0, False, 'dynamic'], [5, 4, 8, 12, -2, True, 'kinematic'], [6, 1, 4, 15, 0, False, 'dynamic'], [7, 1, 2, 12, 2, False, 'dynamic'], [8, 2, 8, 1, 2, True, 'kinematic']], [[8, 5], [8, 5], [4, 6]]], [[4, 6]]], [[[[1, 4, 1, 15, 0, False, 'static'], [2, 3, 8, 15, 1, False, 'dynamic'], [3, 4, 1, 6, 0, False, 'static'], [4, 2, 1, 1, -2, True, 'kinematic'], [5, 2, 8, 15, 0, False, 'dynamic'], [6, 4, 8, 15, 0, False, 'static']], [[4, 1], [5, 1], [5, 6], [4, 6], [5, 6], [6, 4], [5, 4], [2, 3], [3, 2]]], [[1, 5], [5, 6]]], [[[[1, 2, 8, 6, -2, False, 'dynamic'], [2, 3, 8, 3, 0, False, 'static'], [3, 4, 4, 7, -1, False, 'dynamic'], [4, 2, 1, 7, -1, False, 'kinematic'], [5, 1, 1, 1, 0, False, 'dynamic'], [6, 4, 8, 7, 2, False, 'static'], [7, 3, 1, 1, -2, False, 'dynamic'], [8, 2, 4, 7, 2, False, 'static']], [[6, 1], [1, 5], [3, 6], [3, 4], [2, 3], [7, 8]]], []], [[[[1, 4, 4, 15, -2, False, 'dynamic'], [2, 1, 8, 3, -1, False, 'kinematic'], [3, 4, 2, 15, 2, False, 'dynamic']], [[2, 3], [2, 1], [2, 1], [3, 1], [3, 1], [3, 2]]], [[2, 3]]], [[[[1, 4, 4, 12, -2, True, 'dynamic'], [2, 1, 2, 15, 0, False, 'static'], [3, 1, 8, 1, 0, False, 'static'], [4, 2, 1, 3, 1, False, 'kinematic'], [5, 3, 8, 7, -2, False, 'dynamic'], [6, 1, 4, 15, -2, False, 'dynamic'], [7, 4, 4, 15, 2, False, 'kinematic']], [[6, 4], [4, 1], [1, 5], [5, 6], [3, 5], [2, 1], [7, 4], [7, 1], [3, 7]]], []], [[[[1, 3, 8, 1, 1, False, 'dynamic'], [2, 2, 4, 12, -1, False, 'kinematic'], [3, 2, 4, 3, -2, False, 'dynamic'], [4, 4, 2, 6, 0, False, 'dynamic'], [5, 2, 8, 7, 0, False, 'dynamic'], [6, 3, 8, 15, 2, False, 'dynamic'], [7, 4, 1, 12, -1, False, 'dynamic'], [8, 3, 8, 15, 2, False, 'kinematic'], [9, 1, 4, 1, -1, False, 'static']], [[6, 3], [3, 5], [7, 4], [9, 1]]], []]], [[[[[1, 2, 8, 3, 2, False, 'dynamic'], [2, 4, 8, 3, 1, False, 'dynamic'], [3, 3, 4, 3, 0, False, 'dynamic'], [4, 4, 1, 6, 1, False, 'kinematic'], [5, 2, 8, 3, -1, False, 'kinematic'], [6, 3, 8, 6, -1, False, 'static'], [7, 2, 1, 3, -2, False, 'kinematic'], [8, 2, 2, 3, 0, False, 'static'], [9, 3, 8, 15, 0, True, 'kinematic']], [[3, 5], [3, 1], [3, 8], [2, 9], [6, 2], [9, 4], [9, 2], [5, 6], [4, 7]]], []], [[[[1, 1, 1, 15, 0, False, 'dynamic'], [2, 2, 4, 15, 1, False, 'kinematic'], [3, 1, 4, 6, 0, False, 'kinematic'], [4, 2, 2, 15, -2, False, 'dynamic'], [5, 2, 1, 12, -2, False, 'kinematic'], [6, 2, 2, 12, 0, False, 'dynamic'], [7, 2, 2, 6, 1, True, 'dynamic']], [[3, 7], [1, 3], [7, 3], [5, 7], [4, 6], [5, 2], [3, 6], [2, 3], [7, 3]]], [[3, 6], [3, 7]]], [[[[1, 4, 4, 6, -2, True, 'kinematic'], [2, 2, 8, 3, 1, False, 'kinematic'], [3, 2, 2, 1, 0, False, 'dynamic'], [4, 2, 2, 3, -1, False, 'kinematic'], [5, 2, 8, 12, -1, True, 'kinematic'], [6, 1, 1, 15, 2, False, 'dynamic'], [7, 2, 8, 6, 2, False, 'static'], [8, 3, 8, 15, 0, False, 'kinematic'], [9, 3, 1, 3, 2, False, 'static']], [[6, 5], [4, 5], [8, 3]]], []], [[[[1, 1, 8, 12, 0, True, 'dynamic'], [2, 2, 4, 15, 0, False, 'dynamic'], [3, 4, 1, 15, 0, False, 'static'], [4, 2, 2, 15, -1, False, 'dynamic'], [5, 3, 4, 6, 1, False, 'static'], [6, 4, 8, 15, -1, False, 'static']], [[2, 1], [2, 1], [4, 6], [6, 1], [2, 6]]], [[1, 2], [1, 6], [2, 6]]], [[[[1, 3, 4, 12, 0, False, 'dynamic'], [2, 3, 1, 6, 2, False, 'static'], [3, 4, 1, 12, 2, False, 'kinematic'], [4, 2, 4, 15, 0, False, 'dynamic'], [5, 2, 1, 3, 0, False, 'kinematic'], [6, 1, 8, 15, 0, True, 'kinematic'], [7, 4, 2, 15, 0, False, 'kinematic'], [8, 3, 8, 12, 1, False, 'static'], [9, 1, 8, 1, 0, False, 'static'], [10, 3, 1, 7, 0, False, 'static']], [[4, 1], [3, 1], [10, 9], [4, 9], [5, 3], [8, 4], [9, 1], [3, 5], [8, 7], [1, 2]]], [[1, 4], [4, 8]]], [[[[1, 1, 1, 7, 0, False, 'dynamic'], [2, 3, 8, 12, -2, True, 'static'], [3, 2, 1, 6, -2, False, 'dynamic'], [4, 2, 2, 1, 0, False, 'static']], [[4, 3], [1, 3], [1, 2], [4, 1], [1, 3], [1, 4]]], [[1, 4]]], [[[[1, 1, 2, 1, 0, False, 'dynamic'], [2, 3, 8, 7, -2, False, 'dynamic'], [3, 2, 4, 15, 2, False, 'dynamic'], [4, 4, 2, 12, 0, False, 'kinematic']], [[2, 4], [3, 4], [3, 1], [4, 3], [2, 4], [1, 3], [4, 1], [3, 2], [3, 2], [1, 2]]], [[2, 3], [2, 4], [3, 4]]], [[[[1, 2, 1, 15, 0, False, 'kinematic'], [2, 4, 8, 7, 0, True, 'dynamic'], [3, 2, 8, 15, 2, False, 'dynamic'], [4, 1, 2, 6, -2, False, 'dynamic'], [5, 3, 8, 1, 0, False, 'dynamic'], [6, 3, 2, 15, 0, True, 'kinematic'], [7, 3, 2, 6, -2, False, 'kinematic'], [8, 3, 2, 7, -2, False, 'dynamic'], [9, 3, 1, 15, 1, False, 'dynamic']], [[2, 5], [6, 1], [9, 8], [3, 4], [8, 5], [2, 7], [8, 1], [4, 7]]], [[1, 8]]]]]
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 fixture	Actual	Expected	Outcome
case 0	`[]`	`[]`	Passed
case 1	`[]`	`[]`	Passed
case 2	`[[1, 3]]`	`[[1, 3]]`	Passed
case 3	`[[1, 6], [4, 6]]`	`[[1, 6], [4, 6]]`	Passed
case 4	`[]`	`[]`	Passed
case 5	`[]`	`[]`	Passed
case 6	`[[1, 4], [3, 4]]`	`[[1, 4], [3, 4]]`	Passed
case 7	`[[2, 4], [3, 4]]`	`[[2, 4], [3, 4]]`	Passed

SHA-256 / 2653ebbf388b9ab6e349a752d2ab6283c880fb56fd7bea036837c105ac489bb9

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 2026-09-29T14:50:59.270748+00:00.

Case digest / f5536071d6da6f289567ba2e0876c31c0dade149687d88dda1beded3f1f9bc0c