FA-87516 / Collision detection broadphase / Open access

Only static-static pairs are culled by body type · case 01

Kinematic platforms generate pairs with static level geometry.

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

ROOT CAUSE

The body-type rule checks both static.

VERIFIED REPAIR

Cull any pair in which neither body is dynamic.

Unsuccessful approach: Culling equal non-dynamic types still keeps static-kinematic pairs.

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] == 'static' and fb[6] == 'static':
            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, 2, 15, 0, False, 'static'], [2, 3, 2, 1, 1, False, 'static'], [3, 1, 2, 15, -1, True, 'dynamic'], [4, 2, 1, 3, -1, True, 'kinematic']], [[4, 1], [4, 2], [2, 1], [4, 2], [4, 1], [1, 4], [1, 4], [4, 2]]], []], [[[[1, 1, 4, 6, -2, False, 'kinematic'], [2, 3, 1, 6, -1, True, 'kinematic'], [3, 2, 8, 7, 2, False, 'dynamic'], [4, 3, 1, 1, 2, False, 'dynamic'], [5, 1, 1, 6, 2, False, 'dynamic']], [[5, 2], [5, 4], [2, 3], [3, 4]]], [[3, 4], [4, 5]]], [[[[1, 2, 8, 15, 2, False, 'kinematic'], [2, 1, 1, 12, 0, False, 'dynamic'], [3, 4, 4, 15, 1, False, 'dynamic']], [[3, 1], [1, 2], [3, 1], [3, 1], [3, 1], [1, 2]]], [[1, 2], [1, 3]]], [[[[1, 3, 1, 1, -2, False, 'kinematic'], [2, 4, 2, 6, 2, True, 'dynamic'], [3, 1, 1, 7, -1, False, 'static']], [[3, 2], [2, 1], [3, 2], [1, 2], [1, 3], [3, 1], [3, 1], [1, 3], [1, 3]]], []], [[[[1, 2, 1, 1, 0, False, 'dynamic'], [2, 2, 2, 15, 2, False, 'kinematic'], [3, 2, 2, 6, 0, False, 'dynamic']], [[1, 3], [2, 1], [3, 2], [1, 3], [3, 2], [2, 1], [1, 2], [2, 3]]], []], [[[[1, 2, 1, 1, 0, False, 'dynamic'], [2, 2, 1, 6, 0, False, 'kinematic'], [3, 4, 2, 3, 2, True, 'kinematic'], [4, 2, 2, 15, 0, False, 'dynamic'], [5, 1, 8, 12, 1, False, 'dynamic']], [[2, 5], [1, 2], [2, 1], [3, 1], [3, 2], [1, 3], [4, 1], [5, 3], [2, 4], [2, 3]]], []], [[[[1, 4, 8, 15, -2, False, 'static'], [2, 3, 4, 15, 0, False, 'kinematic']], [[1, 2], [2, 1], [2, 1], [2, 1], [1, 2], [2, 1], [2, 1], [2, 1], [1, 2], [2, 1]]], []], [[[[1, 1, 8, 3, 0, False, 'static'], [2, 2, 2, 15, -1, False, 'kinematic'], [3, 1, 8, 12, -2, False, 'dynamic'], [4, 2, 4, 6, 0, False, 'kinematic']], [[2, 1], [4, 1], [4, 2], [1, 3], [3, 2], [1, 3], [3, 1], [4, 1], [1, 4], [2, 4]]], []]], [[[[[1, 4, 8, 12, 2, False, 'static'], [2, 2, 4, 1, 2, False, 'dynamic']], [[2, 1], [1, 2], [1, 2]]], [[1, 2]]], [[[[1, 1, 1, 7, 0, False, 'kinematic'], [2, 4, 8, 6, 0, False, 'dynamic'], [3, 4, 1, 15, 2, False, 'static'], [4, 2, 8, 7, 0, True, 'dynamic'], [5, 3, 8, 1, 0, True, 'dynamic']], [[4, 3], [3, 5], [4, 2], [5, 2], [1, 2], [4, 2], [1, 3], [3, 4], [3, 1], [2, 5]]], [[3, 4], [3, 5]]], [[[[1, 2, 8, 12, 0, False, 'kinematic'], [2, 4, 1, 3, 0, False, 'static'], [3, 3, 1, 15, 0, False, 'dynamic'], [4, 3, 4, 3, -2, False, 'kinematic'], [5, 3, 2, 12, -2, False, 'static']], [[1, 5], [1, 4], [3, 4], [4, 1], [2, 1]]], []], [[[[1, 3, 8, 15, 0, False, 'kinematic'], [2, 4, 4, 15, 0, False, 'static']], [[1, 2], [1, 2], [1, 2], [1, 2]]], []], [[[[1, 2, 2, 12, 0, False, 'static'], [2, 1, 8, 15, -1, False, 'kinematic'], [3, 3, 4, 7, -2, False, 'kinematic'], [4, 2, 2, 12, 0, True, 'dynamic'], [5, 4, 1, 6, -1, False, 'static']], [[2, 5], [4, 1], [5, 4], [2, 1]]], []], [[[[1, 4, 2, 12, 0, False, 'kinematic'], [2, 1, 4, 6, 1, True, 'dynamic']], [[1, 2], [2, 1], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [2, 1]]], [[1, 2]]], [[[[1, 4, 8, 15, 2, False, 'kinematic'], [2, 2, 2, 15, 1, False, 'kinematic'], [3, 2, 4, 7, 0, False, 'dynamic'], [4, 2, 4, 1, 1, False, 'dynamic'], [5, 4, 8, 15, -1, False, 'dynamic'], [6, 2, 4, 15, 0, False, 'static'], [7, 1, 1, 6, -2, False, 'static']], [[5, 2], [3, 1], [6, 1], [6, 2], [2, 6], [5, 6], [1, 5], [3, 6]]], [[2, 5], [5, 6]]], [[[[1, 2, 2, 15, 2, False, 'dynamic'], [2, 2, 4, 12, -2, False, 'dynamic'], [3, 2, 2, 15, -2, False, 'static'], [4, 1, 1, 7, 0, False, 'kinematic'], [5, 1, 8, 1, 1, True, 'dynamic'], [6, 4, 8, 6, 0, False, 'kinematic']], [[1, 5], [2, 3], [6, 3]]], []]], [[[[[1, 4, 1, 15, 0, False, 'static'], [2, 3, 2, 15, 0, False, 'kinematic'], [3, 4, 8, 15, -1, False, 'dynamic'], [4, 2, 1, 15, 0, False, 'static'], [5, 4, 8, 15, -2, True, 'static'], [6, 2, 4, 7, 2, False, 'kinematic']], [[4, 2], [6, 2], [6, 5], [3, 6], [4, 1], [4, 3], [1, 6]]], [[3, 4]]], [[[[1, 4, 8, 6, 0, False, 'dynamic'], [2, 2, 1, 12, -2, True, 'dynamic'], [3, 1, 4, 3, -2, True, 'dynamic'], [4, 3, 4, 15, 0, True, 'dynamic'], [5, 2, 4, 12, 2, False, 'dynamic'], [6, 1, 8, 15, 0, True, 'kinematic']], [[3, 4], [5, 3], [2, 5], [1, 4], [1, 5], [4, 2], [6, 3], [4, 1], [6, 2]]], [[1, 4], [1, 5]]], [[[[1, 3, 2, 15, 0, True, 'kinematic'], [2, 1, 4, 15, 2, False, 'static'], [3, 3, 8, 12, -2, False, 'static'], [4, 2, 4, 15, -1, False, 'static'], [5, 2, 2, 1, -2, False, 'dynamic']], [[3, 2], [2, 4], [1, 2], [2, 1], [2, 1], [4, 2], [5, 4], [1, 2], [5, 1], [2, 3]]], []], [[[[1, 4, 4, 6, 0, True, 'dynamic'], [2, 4, 1, 1, 0, False, 'kinematic']], [[1, 2], [2, 1], [1, 2]]], []], [[[[1, 1, 2, 3, -2, True, 'kinematic'], [2, 3, 2, 6, 0, False, 'static'], [3, 1, 1, 12, 0, False, 'kinematic'], [4, 4, 2, 6, -1, False, 'kinematic'], [5, 4, 4, 15, -1, True, 'kinematic']], [[2, 3], [1, 3], [5, 2], [1, 3]]], []], [[[[1, 2, 8, 15, 0, True, 'kinematic'], [2, 1, 4, 15, -1, False, 'static']], [[2, 1], [1, 2], [2, 1], [1, 2]]], []], [[[[1, 1, 1, 7, 1, True, 'static'], [2, 4, 8, 12, 0, False, 'dynamic'], [3, 2, 8, 6, 1, False, 'dynamic'], [4, 3, 2, 3, -2, False, 'kinematic'], [5, 2, 4, 7, -1, False, 'dynamic'], [6, 3, 1, 6, 0, True, 'static'], [7, 3, 1, 15, 2, False, 'static'], [8, 1, 4, 1, -2, False, 'kinematic']], [[3, 7], [1, 6], [4, 1], [5, 2]]], []], [[[[1, 4, 4, 3, -2, False, 'static'], [2, 2, 8, 1, 2, False, 'dynamic']], [[1, 2], [1, 2], [2, 1], [1, 2], [2, 1], [2, 1], [1, 2]]], []]], [[[[[1, 1, 4, 1, 0, False, 'kinematic'], [2, 3, 4, 7, -2, False, 'dynamic'], [3, 1, 4, 12, 0, True, 'dynamic']], [[1, 3], [3, 2], [3, 1], [3, 1], [2, 1], [3, 2], [2, 3], [1, 2], [1, 3]]], [[2, 3]]], [[[[1, 1, 8, 15, 0, False, 'static'], [2, 4, 8, 12, -2, False, 'kinematic']], [[1, 2], [2, 1], [1, 2], [2, 1], [2, 1], [1, 2], [1, 2], [1, 2], [2, 1]]], []], [[[[1, 2, 1, 3, 0, False, 'kinematic'], [2, 3, 1, 7, 0, False, 'static'], [3, 1, 4, 7, -2, False, 'static']], [[3, 2], [1, 2], [2, 1]]], []], [[[[1, 4, 2, 6, 0, True, 'static'], [2, 4, 4, 15, -2, False, 'static'], [3, 3, 4, 1, -2, False, 'static'], [4, 3, 4, 7, 0, False, 'kinematic']], [[1, 3], [2, 3], [2, 4], [2, 3], [1, 2], [1, 3], [3, 4], [1, 4], [4, 3], [2, 1]]], []], [[[[1, 1, 4, 15, 2, False, 'static'], [2, 4, 1, 1, 0, False, 'static'], [3, 2, 8, 3, 0, False, 'dynamic'], [4, 3, 4, 7, 0, False, 'static'], [5, 1, 4, 15, 0, False, 'static'], [6, 1, 1, 15, -2, True, 'dynamic'], [7, 2, 8, 12, 0, True, 'static'], [8, 3, 4, 12, -2, False, 'dynamic']], [[1, 4], [1, 3], [8, 6], [5, 4]]], []], [[[[1, 3, 4, 15, 1, False, 'dynamic'], [2, 3, 4, 3, -1, False, 'dynamic'], [3, 2, 4, 6, 2, False, 'dynamic'], [4, 3, 2, 3, -2, True, 'kinematic']], [[2, 1], [3, 4], [3, 1], [2, 3], [3, 4], [2, 1], [3, 4]]], [[1, 3]]], [[[[1, 3, 2, 6, 0, False, 'dynamic'], [2, 1, 4, 15, -1, False, 'static'], [3, 4, 2, 15, 0, False, 'dynamic'], [4, 4, 2, 15, -2, False, 'static'], [5, 4, 8, 1, 2, False, 'kinematic'], [6, 3, 4, 1, 2, True, 'dynamic'], [7, 3, 8, 3, 0, False, 'kinematic']], [[2, 3], [4, 7], [2, 3], [2, 3], [3, 6], [5, 6], [1, 4], [4, 3], [5, 6], [7, 3]]], [[1, 4], [2, 3], [3, 7], [5, 6]]], [[[[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, 7, 1, False, 'kinematic'], [2, 2, 1, 3, -1, False, 'dynamic'], [3, 2, 1, 1, 0, False, 'kinematic'], [4, 4, 4, 12, 0, False, 'dynamic'], [5, 2, 1, 12, 2, False, 'dynamic'], [6, 4, 2, 15, 0, False, 'static'], [7, 1, 1, 3, -2, False, 'kinematic'], [8, 4, 2, 6, 2, True, 'dynamic'], [9, 3, 2, 15, 0, False, 'static'], [10, 3, 1, 1, -1, False, 'dynamic']], [[6, 7], [4, 8], [7, 4], [9, 3], [3, 6]]], []], [[[[1, 4, 4, 6, 0, False, 'kinematic'], [2, 3, 4, 3, -1, False, 'static'], [3, 4, 8, 3, 1, True, 'kinematic'], [4, 4, 8, 7, 2, False, 'kinematic'], [5, 1, 1, 15, 1, False, 'static'], [6, 1, 1, 3, 2, False, 'kinematic'], [7, 4, 4, 15, 2, False, 'dynamic']], [[4, 1], [6, 5], [1, 4], [2, 7], [4, 5], [6, 5], [6, 7], [5, 3], [2, 5], [6, 5]]], [[6, 7]]], [[[[1, 4, 4, 7, 0, False, 'dynamic'], [2, 2, 4, 15, -1, False, 'static'], [3, 3, 8, 1, 2, False, 'dynamic'], [4, 3, 2, 1, 2, False, 'kinematic'], [5, 4, 2, 15, 1, False, 'kinematic'], [6, 4, 4, 1, -2, True, 'dynamic'], [7, 4, 1, 15, 0, False, 'dynamic']], [[3, 2], [5, 2], [3, 7], [5, 7]]], [[3, 7]]], [[[[1, 4, 1, 15, 0, False, 'kinematic'], [2, 2, 4, 12, -1, True, 'dynamic'], [3, 1, 1, 1, 0, False, 'static'], [4, 1, 1, 6, 2, False, 'dynamic'], [5, 2, 4, 15, 2, False, 'dynamic'], [6, 2, 8, 1, 2, True, 'kinematic'], [7, 2, 2, 3, -2, False, 'static'], [8, 4, 2, 3, 2, False, 'kinematic'], [9, 4, 2, 6, -2, False, 'kinematic'], [10, 3, 4, 7, 0, False, 'dynamic']], [[1, 10], [4, 1], [8, 9]]], [[1, 10]]], [[[[1, 2, 1, 1, -2, False, 'kinematic'], [2, 1, 1, 12, -2, False, 'kinematic'], [3, 2, 2, 7, 2, False, 'dynamic'], [4, 4, 4, 1, -1, True, 'dynamic'], [5, 2, 4, 6, 0, False, 'dynamic'], [6, 2, 8, 6, 0, False, 'dynamic'], [7, 1, 1, 15, 0, True, 'kinematic'], [8, 1, 1, 1, 1, False, 'static'], [9, 2, 8, 3, -2, False, 'dynamic']], [[8, 3], [3, 5], [7, 1]]], []], [[[[1, 1, 8, 1, -1, False, 'dynamic'], [2, 4, 2, 15, 2, False, 'static'], [3, 2, 8, 7, 2, False, 'kinematic'], [4, 3, 8, 6, 0, False, 'dynamic'], [5, 2, 8, 3, -1, True, 'dynamic'], [6, 4, 4, 12, 1, False, 'kinematic'], [7, 1, 8, 1, 0, True, 'dynamic'], [8, 3, 1, 6, -2, False, 'dynamic'], [9, 2, 1, 15, 2, False, 'dynamic'], [10, 2, 1, 6, 0, True, 'dynamic']], [[5, 8], [2, 10], [1, 10]]], [[2, 10]]], [[[[1, 4, 2, 7, 2, True, 'dynamic'], [2, 2, 2, 12, -2, False, 'kinematic'], [3, 1, 4, 12, 1, False, 'dynamic'], [4, 4, 8, 3, -1, False, 'dynamic'], [5, 2, 4, 1, 2, False, 'dynamic'], [6, 1, 1, 15, -1, False, 'dynamic'], [7, 4, 4, 12, -1, False, 'kinematic'], [8, 2, 2, 15, 1, False, 'dynamic'], [9, 3, 1, 6, 1, False, 'static']], [[1, 4], [9, 7], [2, 9], [9, 6], [4, 7]]], []], [[[[1, 1, 2, 15, 0, True, 'dynamic'], [2, 2, 8, 15, 1, True, 'dynamic'], [3, 2, 2, 12, 1, False, 'kinematic'], [4, 1, 1, 15, 2, True, 'kinematic'], [5, 1, 8, 15, -1, False, 'kinematic']], [[5, 3], [1, 5], [4, 5], [3, 4], [4, 3]]], []]]]
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	`[[1, 4], [2, 4]]`	`[]`	Failed
case 1	`[[3, 4], [4, 5]]`	`[[3, 4], [4, 5]]`	Passed
case 2	`[[1, 2], [1, 3]]`	`[[1, 2], [1, 3]]`	Passed
case 3	`[[1, 3]]`	`[]`	Failed
case 4	`[]`	`[]`	Passed
case 5	`[[2, 3]]`	`[]`	Failed
case 6	`[[1, 2]]`	`[]`	Failed
case 7	`[[1, 2]]`	`[]`	Failed

SHA-256 / 6f8c72d537bb7c946f7ddb7a59695c8294b202f0cef0e032be30e02b7f5e070b

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] == fb[6] and fa[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, 2, 15, 0, False, 'static'], [2, 3, 2, 1, 1, False, 'static'], [3, 1, 2, 15, -1, True, 'dynamic'], [4, 2, 1, 3, -1, True, 'kinematic']], [[4, 1], [4, 2], [2, 1], [4, 2], [4, 1], [1, 4], [1, 4], [4, 2]]], []], [[[[1, 1, 4, 6, -2, False, 'kinematic'], [2, 3, 1, 6, -1, True, 'kinematic'], [3, 2, 8, 7, 2, False, 'dynamic'], [4, 3, 1, 1, 2, False, 'dynamic'], [5, 1, 1, 6, 2, False, 'dynamic']], [[5, 2], [5, 4], [2, 3], [3, 4]]], [[3, 4], [4, 5]]], [[[[1, 2, 8, 15, 2, False, 'kinematic'], [2, 1, 1, 12, 0, False, 'dynamic'], [3, 4, 4, 15, 1, False, 'dynamic']], [[3, 1], [1, 2], [3, 1], [3, 1], [3, 1], [1, 2]]], [[1, 2], [1, 3]]], [[[[1, 3, 1, 1, -2, False, 'kinematic'], [2, 4, 2, 6, 2, True, 'dynamic'], [3, 1, 1, 7, -1, False, 'static']], [[3, 2], [2, 1], [3, 2], [1, 2], [1, 3], [3, 1], [3, 1], [1, 3], [1, 3]]], []], [[[[1, 2, 1, 1, 0, False, 'dynamic'], [2, 2, 2, 15, 2, False, 'kinematic'], [3, 2, 2, 6, 0, False, 'dynamic']], [[1, 3], [2, 1], [3, 2], [1, 3], [3, 2], [2, 1], [1, 2], [2, 3]]], []], [[[[1, 2, 1, 1, 0, False, 'dynamic'], [2, 2, 1, 6, 0, False, 'kinematic'], [3, 4, 2, 3, 2, True, 'kinematic'], [4, 2, 2, 15, 0, False, 'dynamic'], [5, 1, 8, 12, 1, False, 'dynamic']], [[2, 5], [1, 2], [2, 1], [3, 1], [3, 2], [1, 3], [4, 1], [5, 3], [2, 4], [2, 3]]], []], [[[[1, 4, 8, 15, -2, False, 'static'], [2, 3, 4, 15, 0, False, 'kinematic']], [[1, 2], [2, 1], [2, 1], [2, 1], [1, 2], [2, 1], [2, 1], [2, 1], [1, 2], [2, 1]]], []], [[[[1, 1, 8, 3, 0, False, 'static'], [2, 2, 2, 15, -1, False, 'kinematic'], [3, 1, 8, 12, -2, False, 'dynamic'], [4, 2, 4, 6, 0, False, 'kinematic']], [[2, 1], [4, 1], [4, 2], [1, 3], [3, 2], [1, 3], [3, 1], [4, 1], [1, 4], [2, 4]]], []]], [[[[[1, 4, 8, 12, 2, False, 'static'], [2, 2, 4, 1, 2, False, 'dynamic']], [[2, 1], [1, 2], [1, 2]]], [[1, 2]]], [[[[1, 1, 1, 7, 0, False, 'kinematic'], [2, 4, 8, 6, 0, False, 'dynamic'], [3, 4, 1, 15, 2, False, 'static'], [4, 2, 8, 7, 0, True, 'dynamic'], [5, 3, 8, 1, 0, True, 'dynamic']], [[4, 3], [3, 5], [4, 2], [5, 2], [1, 2], [4, 2], [1, 3], [3, 4], [3, 1], [2, 5]]], [[3, 4], [3, 5]]], [[[[1, 2, 8, 12, 0, False, 'kinematic'], [2, 4, 1, 3, 0, False, 'static'], [3, 3, 1, 15, 0, False, 'dynamic'], [4, 3, 4, 3, -2, False, 'kinematic'], [5, 3, 2, 12, -2, False, 'static']], [[1, 5], [1, 4], [3, 4], [4, 1], [2, 1]]], []], [[[[1, 3, 8, 15, 0, False, 'kinematic'], [2, 4, 4, 15, 0, False, 'static']], [[1, 2], [1, 2], [1, 2], [1, 2]]], []], [[[[1, 2, 2, 12, 0, False, 'static'], [2, 1, 8, 15, -1, False, 'kinematic'], [3, 3, 4, 7, -2, False, 'kinematic'], [4, 2, 2, 12, 0, True, 'dynamic'], [5, 4, 1, 6, -1, False, 'static']], [[2, 5], [4, 1], [5, 4], [2, 1]]], []], [[[[1, 4, 2, 12, 0, False, 'kinematic'], [2, 1, 4, 6, 1, True, 'dynamic']], [[1, 2], [2, 1], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [2, 1]]], [[1, 2]]], [[[[1, 4, 8, 15, 2, False, 'kinematic'], [2, 2, 2, 15, 1, False, 'kinematic'], [3, 2, 4, 7, 0, False, 'dynamic'], [4, 2, 4, 1, 1, False, 'dynamic'], [5, 4, 8, 15, -1, False, 'dynamic'], [6, 2, 4, 15, 0, False, 'static'], [7, 1, 1, 6, -2, False, 'static']], [[5, 2], [3, 1], [6, 1], [6, 2], [2, 6], [5, 6], [1, 5], [3, 6]]], [[2, 5], [5, 6]]], [[[[1, 2, 2, 15, 2, False, 'dynamic'], [2, 2, 4, 12, -2, False, 'dynamic'], [3, 2, 2, 15, -2, False, 'static'], [4, 1, 1, 7, 0, False, 'kinematic'], [5, 1, 8, 1, 1, True, 'dynamic'], [6, 4, 8, 6, 0, False, 'kinematic']], [[1, 5], [2, 3], [6, 3]]], []]], [[[[[1, 4, 1, 15, 0, False, 'static'], [2, 3, 2, 15, 0, False, 'kinematic'], [3, 4, 8, 15, -1, False, 'dynamic'], [4, 2, 1, 15, 0, False, 'static'], [5, 4, 8, 15, -2, True, 'static'], [6, 2, 4, 7, 2, False, 'kinematic']], [[4, 2], [6, 2], [6, 5], [3, 6], [4, 1], [4, 3], [1, 6]]], [[3, 4]]], [[[[1, 4, 8, 6, 0, False, 'dynamic'], [2, 2, 1, 12, -2, True, 'dynamic'], [3, 1, 4, 3, -2, True, 'dynamic'], [4, 3, 4, 15, 0, True, 'dynamic'], [5, 2, 4, 12, 2, False, 'dynamic'], [6, 1, 8, 15, 0, True, 'kinematic']], [[3, 4], [5, 3], [2, 5], [1, 4], [1, 5], [4, 2], [6, 3], [4, 1], [6, 2]]], [[1, 4], [1, 5]]], [[[[1, 3, 2, 15, 0, True, 'kinematic'], [2, 1, 4, 15, 2, False, 'static'], [3, 3, 8, 12, -2, False, 'static'], [4, 2, 4, 15, -1, False, 'static'], [5, 2, 2, 1, -2, False, 'dynamic']], [[3, 2], [2, 4], [1, 2], [2, 1], [2, 1], [4, 2], [5, 4], [1, 2], [5, 1], [2, 3]]], []], [[[[1, 4, 4, 6, 0, True, 'dynamic'], [2, 4, 1, 1, 0, False, 'kinematic']], [[1, 2], [2, 1], [1, 2]]], []], [[[[1, 1, 2, 3, -2, True, 'kinematic'], [2, 3, 2, 6, 0, False, 'static'], [3, 1, 1, 12, 0, False, 'kinematic'], [4, 4, 2, 6, -1, False, 'kinematic'], [5, 4, 4, 15, -1, True, 'kinematic']], [[2, 3], [1, 3], [5, 2], [1, 3]]], []], [[[[1, 2, 8, 15, 0, True, 'kinematic'], [2, 1, 4, 15, -1, False, 'static']], [[2, 1], [1, 2], [2, 1], [1, 2]]], []], [[[[1, 1, 1, 7, 1, True, 'static'], [2, 4, 8, 12, 0, False, 'dynamic'], [3, 2, 8, 6, 1, False, 'dynamic'], [4, 3, 2, 3, -2, False, 'kinematic'], [5, 2, 4, 7, -1, False, 'dynamic'], [6, 3, 1, 6, 0, True, 'static'], [7, 3, 1, 15, 2, False, 'static'], [8, 1, 4, 1, -2, False, 'kinematic']], [[3, 7], [1, 6], [4, 1], [5, 2]]], []], [[[[1, 4, 4, 3, -2, False, 'static'], [2, 2, 8, 1, 2, False, 'dynamic']], [[1, 2], [1, 2], [2, 1], [1, 2], [2, 1], [2, 1], [1, 2]]], []]], [[[[[1, 1, 4, 1, 0, False, 'kinematic'], [2, 3, 4, 7, -2, False, 'dynamic'], [3, 1, 4, 12, 0, True, 'dynamic']], [[1, 3], [3, 2], [3, 1], [3, 1], [2, 1], [3, 2], [2, 3], [1, 2], [1, 3]]], [[2, 3]]], [[[[1, 1, 8, 15, 0, False, 'static'], [2, 4, 8, 12, -2, False, 'kinematic']], [[1, 2], [2, 1], [1, 2], [2, 1], [2, 1], [1, 2], [1, 2], [1, 2], [2, 1]]], []], [[[[1, 2, 1, 3, 0, False, 'kinematic'], [2, 3, 1, 7, 0, False, 'static'], [3, 1, 4, 7, -2, False, 'static']], [[3, 2], [1, 2], [2, 1]]], []], [[[[1, 4, 2, 6, 0, True, 'static'], [2, 4, 4, 15, -2, False, 'static'], [3, 3, 4, 1, -2, False, 'static'], [4, 3, 4, 7, 0, False, 'kinematic']], [[1, 3], [2, 3], [2, 4], [2, 3], [1, 2], [1, 3], [3, 4], [1, 4], [4, 3], [2, 1]]], []], [[[[1, 1, 4, 15, 2, False, 'static'], [2, 4, 1, 1, 0, False, 'static'], [3, 2, 8, 3, 0, False, 'dynamic'], [4, 3, 4, 7, 0, False, 'static'], [5, 1, 4, 15, 0, False, 'static'], [6, 1, 1, 15, -2, True, 'dynamic'], [7, 2, 8, 12, 0, True, 'static'], [8, 3, 4, 12, -2, False, 'dynamic']], [[1, 4], [1, 3], [8, 6], [5, 4]]], []], [[[[1, 3, 4, 15, 1, False, 'dynamic'], [2, 3, 4, 3, -1, False, 'dynamic'], [3, 2, 4, 6, 2, False, 'dynamic'], [4, 3, 2, 3, -2, True, 'kinematic']], [[2, 1], [3, 4], [3, 1], [2, 3], [3, 4], [2, 1], [3, 4]]], [[1, 3]]], [[[[1, 3, 2, 6, 0, False, 'dynamic'], [2, 1, 4, 15, -1, False, 'static'], [3, 4, 2, 15, 0, False, 'dynamic'], [4, 4, 2, 15, -2, False, 'static'], [5, 4, 8, 1, 2, False, 'kinematic'], [6, 3, 4, 1, 2, True, 'dynamic'], [7, 3, 8, 3, 0, False, 'kinematic']], [[2, 3], [4, 7], [2, 3], [2, 3], [3, 6], [5, 6], [1, 4], [4, 3], [5, 6], [7, 3]]], [[1, 4], [2, 3], [3, 7], [5, 6]]], [[[[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, 7, 1, False, 'kinematic'], [2, 2, 1, 3, -1, False, 'dynamic'], [3, 2, 1, 1, 0, False, 'kinematic'], [4, 4, 4, 12, 0, False, 'dynamic'], [5, 2, 1, 12, 2, False, 'dynamic'], [6, 4, 2, 15, 0, False, 'static'], [7, 1, 1, 3, -2, False, 'kinematic'], [8, 4, 2, 6, 2, True, 'dynamic'], [9, 3, 2, 15, 0, False, 'static'], [10, 3, 1, 1, -1, False, 'dynamic']], [[6, 7], [4, 8], [7, 4], [9, 3], [3, 6]]], []], [[[[1, 4, 4, 6, 0, False, 'kinematic'], [2, 3, 4, 3, -1, False, 'static'], [3, 4, 8, 3, 1, True, 'kinematic'], [4, 4, 8, 7, 2, False, 'kinematic'], [5, 1, 1, 15, 1, False, 'static'], [6, 1, 1, 3, 2, False, 'kinematic'], [7, 4, 4, 15, 2, False, 'dynamic']], [[4, 1], [6, 5], [1, 4], [2, 7], [4, 5], [6, 5], [6, 7], [5, 3], [2, 5], [6, 5]]], [[6, 7]]], [[[[1, 4, 4, 7, 0, False, 'dynamic'], [2, 2, 4, 15, -1, False, 'static'], [3, 3, 8, 1, 2, False, 'dynamic'], [4, 3, 2, 1, 2, False, 'kinematic'], [5, 4, 2, 15, 1, False, 'kinematic'], [6, 4, 4, 1, -2, True, 'dynamic'], [7, 4, 1, 15, 0, False, 'dynamic']], [[3, 2], [5, 2], [3, 7], [5, 7]]], [[3, 7]]], [[[[1, 4, 1, 15, 0, False, 'kinematic'], [2, 2, 4, 12, -1, True, 'dynamic'], [3, 1, 1, 1, 0, False, 'static'], [4, 1, 1, 6, 2, False, 'dynamic'], [5, 2, 4, 15, 2, False, 'dynamic'], [6, 2, 8, 1, 2, True, 'kinematic'], [7, 2, 2, 3, -2, False, 'static'], [8, 4, 2, 3, 2, False, 'kinematic'], [9, 4, 2, 6, -2, False, 'kinematic'], [10, 3, 4, 7, 0, False, 'dynamic']], [[1, 10], [4, 1], [8, 9]]], [[1, 10]]], [[[[1, 2, 1, 1, -2, False, 'kinematic'], [2, 1, 1, 12, -2, False, 'kinematic'], [3, 2, 2, 7, 2, False, 'dynamic'], [4, 4, 4, 1, -1, True, 'dynamic'], [5, 2, 4, 6, 0, False, 'dynamic'], [6, 2, 8, 6, 0, False, 'dynamic'], [7, 1, 1, 15, 0, True, 'kinematic'], [8, 1, 1, 1, 1, False, 'static'], [9, 2, 8, 3, -2, False, 'dynamic']], [[8, 3], [3, 5], [7, 1]]], []], [[[[1, 1, 8, 1, -1, False, 'dynamic'], [2, 4, 2, 15, 2, False, 'static'], [3, 2, 8, 7, 2, False, 'kinematic'], [4, 3, 8, 6, 0, False, 'dynamic'], [5, 2, 8, 3, -1, True, 'dynamic'], [6, 4, 4, 12, 1, False, 'kinematic'], [7, 1, 8, 1, 0, True, 'dynamic'], [8, 3, 1, 6, -2, False, 'dynamic'], [9, 2, 1, 15, 2, False, 'dynamic'], [10, 2, 1, 6, 0, True, 'dynamic']], [[5, 8], [2, 10], [1, 10]]], [[2, 10]]], [[[[1, 4, 2, 7, 2, True, 'dynamic'], [2, 2, 2, 12, -2, False, 'kinematic'], [3, 1, 4, 12, 1, False, 'dynamic'], [4, 4, 8, 3, -1, False, 'dynamic'], [5, 2, 4, 1, 2, False, 'dynamic'], [6, 1, 1, 15, -1, False, 'dynamic'], [7, 4, 4, 12, -1, False, 'kinematic'], [8, 2, 2, 15, 1, False, 'dynamic'], [9, 3, 1, 6, 1, False, 'static']], [[1, 4], [9, 7], [2, 9], [9, 6], [4, 7]]], []], [[[[1, 1, 2, 15, 0, True, 'dynamic'], [2, 2, 8, 15, 1, True, 'dynamic'], [3, 2, 2, 12, 1, False, 'kinematic'], [4, 1, 1, 15, 2, True, 'kinematic'], [5, 1, 8, 15, -1, False, 'kinematic']], [[5, 3], [1, 5], [4, 5], [3, 4], [4, 3]]], []]]]
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	`[[1, 4], [2, 4]]`	`[]`	Failed
case 1	`[[3, 4], [4, 5]]`	`[[3, 4], [4, 5]]`	Passed
case 2	`[[1, 2], [1, 3]]`	`[[1, 2], [1, 3]]`	Passed
case 3	`[[1, 3]]`	`[]`	Failed
case 4	`[]`	`[]`	Passed
case 5	`[]`	`[]`	Passed
case 6	`[[1, 2]]`	`[]`	Failed
case 7	`[[1, 2]]`	`[]`	Failed

SHA-256 / dab6d59b09943c6fcf3f42be9f094b963199c4d3ce5e40b829c659c93cc51dbc

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, 2, 15, 0, False, 'static'], [2, 3, 2, 1, 1, False, 'static'], [3, 1, 2, 15, -1, True, 'dynamic'], [4, 2, 1, 3, -1, True, 'kinematic']], [[4, 1], [4, 2], [2, 1], [4, 2], [4, 1], [1, 4], [1, 4], [4, 2]]], []], [[[[1, 1, 4, 6, -2, False, 'kinematic'], [2, 3, 1, 6, -1, True, 'kinematic'], [3, 2, 8, 7, 2, False, 'dynamic'], [4, 3, 1, 1, 2, False, 'dynamic'], [5, 1, 1, 6, 2, False, 'dynamic']], [[5, 2], [5, 4], [2, 3], [3, 4]]], [[3, 4], [4, 5]]], [[[[1, 2, 8, 15, 2, False, 'kinematic'], [2, 1, 1, 12, 0, False, 'dynamic'], [3, 4, 4, 15, 1, False, 'dynamic']], [[3, 1], [1, 2], [3, 1], [3, 1], [3, 1], [1, 2]]], [[1, 2], [1, 3]]], [[[[1, 3, 1, 1, -2, False, 'kinematic'], [2, 4, 2, 6, 2, True, 'dynamic'], [3, 1, 1, 7, -1, False, 'static']], [[3, 2], [2, 1], [3, 2], [1, 2], [1, 3], [3, 1], [3, 1], [1, 3], [1, 3]]], []], [[[[1, 2, 1, 1, 0, False, 'dynamic'], [2, 2, 2, 15, 2, False, 'kinematic'], [3, 2, 2, 6, 0, False, 'dynamic']], [[1, 3], [2, 1], [3, 2], [1, 3], [3, 2], [2, 1], [1, 2], [2, 3]]], []], [[[[1, 2, 1, 1, 0, False, 'dynamic'], [2, 2, 1, 6, 0, False, 'kinematic'], [3, 4, 2, 3, 2, True, 'kinematic'], [4, 2, 2, 15, 0, False, 'dynamic'], [5, 1, 8, 12, 1, False, 'dynamic']], [[2, 5], [1, 2], [2, 1], [3, 1], [3, 2], [1, 3], [4, 1], [5, 3], [2, 4], [2, 3]]], []], [[[[1, 4, 8, 15, -2, False, 'static'], [2, 3, 4, 15, 0, False, 'kinematic']], [[1, 2], [2, 1], [2, 1], [2, 1], [1, 2], [2, 1], [2, 1], [2, 1], [1, 2], [2, 1]]], []], [[[[1, 1, 8, 3, 0, False, 'static'], [2, 2, 2, 15, -1, False, 'kinematic'], [3, 1, 8, 12, -2, False, 'dynamic'], [4, 2, 4, 6, 0, False, 'kinematic']], [[2, 1], [4, 1], [4, 2], [1, 3], [3, 2], [1, 3], [3, 1], [4, 1], [1, 4], [2, 4]]], []]], [[[[[1, 4, 8, 12, 2, False, 'static'], [2, 2, 4, 1, 2, False, 'dynamic']], [[2, 1], [1, 2], [1, 2]]], [[1, 2]]], [[[[1, 1, 1, 7, 0, False, 'kinematic'], [2, 4, 8, 6, 0, False, 'dynamic'], [3, 4, 1, 15, 2, False, 'static'], [4, 2, 8, 7, 0, True, 'dynamic'], [5, 3, 8, 1, 0, True, 'dynamic']], [[4, 3], [3, 5], [4, 2], [5, 2], [1, 2], [4, 2], [1, 3], [3, 4], [3, 1], [2, 5]]], [[3, 4], [3, 5]]], [[[[1, 2, 8, 12, 0, False, 'kinematic'], [2, 4, 1, 3, 0, False, 'static'], [3, 3, 1, 15, 0, False, 'dynamic'], [4, 3, 4, 3, -2, False, 'kinematic'], [5, 3, 2, 12, -2, False, 'static']], [[1, 5], [1, 4], [3, 4], [4, 1], [2, 1]]], []], [[[[1, 3, 8, 15, 0, False, 'kinematic'], [2, 4, 4, 15, 0, False, 'static']], [[1, 2], [1, 2], [1, 2], [1, 2]]], []], [[[[1, 2, 2, 12, 0, False, 'static'], [2, 1, 8, 15, -1, False, 'kinematic'], [3, 3, 4, 7, -2, False, 'kinematic'], [4, 2, 2, 12, 0, True, 'dynamic'], [5, 4, 1, 6, -1, False, 'static']], [[2, 5], [4, 1], [5, 4], [2, 1]]], []], [[[[1, 4, 2, 12, 0, False, 'kinematic'], [2, 1, 4, 6, 1, True, 'dynamic']], [[1, 2], [2, 1], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [2, 1]]], [[1, 2]]], [[[[1, 4, 8, 15, 2, False, 'kinematic'], [2, 2, 2, 15, 1, False, 'kinematic'], [3, 2, 4, 7, 0, False, 'dynamic'], [4, 2, 4, 1, 1, False, 'dynamic'], [5, 4, 8, 15, -1, False, 'dynamic'], [6, 2, 4, 15, 0, False, 'static'], [7, 1, 1, 6, -2, False, 'static']], [[5, 2], [3, 1], [6, 1], [6, 2], [2, 6], [5, 6], [1, 5], [3, 6]]], [[2, 5], [5, 6]]], [[[[1, 2, 2, 15, 2, False, 'dynamic'], [2, 2, 4, 12, -2, False, 'dynamic'], [3, 2, 2, 15, -2, False, 'static'], [4, 1, 1, 7, 0, False, 'kinematic'], [5, 1, 8, 1, 1, True, 'dynamic'], [6, 4, 8, 6, 0, False, 'kinematic']], [[1, 5], [2, 3], [6, 3]]], []]], [[[[[1, 4, 1, 15, 0, False, 'static'], [2, 3, 2, 15, 0, False, 'kinematic'], [3, 4, 8, 15, -1, False, 'dynamic'], [4, 2, 1, 15, 0, False, 'static'], [5, 4, 8, 15, -2, True, 'static'], [6, 2, 4, 7, 2, False, 'kinematic']], [[4, 2], [6, 2], [6, 5], [3, 6], [4, 1], [4, 3], [1, 6]]], [[3, 4]]], [[[[1, 4, 8, 6, 0, False, 'dynamic'], [2, 2, 1, 12, -2, True, 'dynamic'], [3, 1, 4, 3, -2, True, 'dynamic'], [4, 3, 4, 15, 0, True, 'dynamic'], [5, 2, 4, 12, 2, False, 'dynamic'], [6, 1, 8, 15, 0, True, 'kinematic']], [[3, 4], [5, 3], [2, 5], [1, 4], [1, 5], [4, 2], [6, 3], [4, 1], [6, 2]]], [[1, 4], [1, 5]]], [[[[1, 3, 2, 15, 0, True, 'kinematic'], [2, 1, 4, 15, 2, False, 'static'], [3, 3, 8, 12, -2, False, 'static'], [4, 2, 4, 15, -1, False, 'static'], [5, 2, 2, 1, -2, False, 'dynamic']], [[3, 2], [2, 4], [1, 2], [2, 1], [2, 1], [4, 2], [5, 4], [1, 2], [5, 1], [2, 3]]], []], [[[[1, 4, 4, 6, 0, True, 'dynamic'], [2, 4, 1, 1, 0, False, 'kinematic']], [[1, 2], [2, 1], [1, 2]]], []], [[[[1, 1, 2, 3, -2, True, 'kinematic'], [2, 3, 2, 6, 0, False, 'static'], [3, 1, 1, 12, 0, False, 'kinematic'], [4, 4, 2, 6, -1, False, 'kinematic'], [5, 4, 4, 15, -1, True, 'kinematic']], [[2, 3], [1, 3], [5, 2], [1, 3]]], []], [[[[1, 2, 8, 15, 0, True, 'kinematic'], [2, 1, 4, 15, -1, False, 'static']], [[2, 1], [1, 2], [2, 1], [1, 2]]], []], [[[[1, 1, 1, 7, 1, True, 'static'], [2, 4, 8, 12, 0, False, 'dynamic'], [3, 2, 8, 6, 1, False, 'dynamic'], [4, 3, 2, 3, -2, False, 'kinematic'], [5, 2, 4, 7, -1, False, 'dynamic'], [6, 3, 1, 6, 0, True, 'static'], [7, 3, 1, 15, 2, False, 'static'], [8, 1, 4, 1, -2, False, 'kinematic']], [[3, 7], [1, 6], [4, 1], [5, 2]]], []], [[[[1, 4, 4, 3, -2, False, 'static'], [2, 2, 8, 1, 2, False, 'dynamic']], [[1, 2], [1, 2], [2, 1], [1, 2], [2, 1], [2, 1], [1, 2]]], []]], [[[[[1, 1, 4, 1, 0, False, 'kinematic'], [2, 3, 4, 7, -2, False, 'dynamic'], [3, 1, 4, 12, 0, True, 'dynamic']], [[1, 3], [3, 2], [3, 1], [3, 1], [2, 1], [3, 2], [2, 3], [1, 2], [1, 3]]], [[2, 3]]], [[[[1, 1, 8, 15, 0, False, 'static'], [2, 4, 8, 12, -2, False, 'kinematic']], [[1, 2], [2, 1], [1, 2], [2, 1], [2, 1], [1, 2], [1, 2], [1, 2], [2, 1]]], []], [[[[1, 2, 1, 3, 0, False, 'kinematic'], [2, 3, 1, 7, 0, False, 'static'], [3, 1, 4, 7, -2, False, 'static']], [[3, 2], [1, 2], [2, 1]]], []], [[[[1, 4, 2, 6, 0, True, 'static'], [2, 4, 4, 15, -2, False, 'static'], [3, 3, 4, 1, -2, False, 'static'], [4, 3, 4, 7, 0, False, 'kinematic']], [[1, 3], [2, 3], [2, 4], [2, 3], [1, 2], [1, 3], [3, 4], [1, 4], [4, 3], [2, 1]]], []], [[[[1, 1, 4, 15, 2, False, 'static'], [2, 4, 1, 1, 0, False, 'static'], [3, 2, 8, 3, 0, False, 'dynamic'], [4, 3, 4, 7, 0, False, 'static'], [5, 1, 4, 15, 0, False, 'static'], [6, 1, 1, 15, -2, True, 'dynamic'], [7, 2, 8, 12, 0, True, 'static'], [8, 3, 4, 12, -2, False, 'dynamic']], [[1, 4], [1, 3], [8, 6], [5, 4]]], []], [[[[1, 3, 4, 15, 1, False, 'dynamic'], [2, 3, 4, 3, -1, False, 'dynamic'], [3, 2, 4, 6, 2, False, 'dynamic'], [4, 3, 2, 3, -2, True, 'kinematic']], [[2, 1], [3, 4], [3, 1], [2, 3], [3, 4], [2, 1], [3, 4]]], [[1, 3]]], [[[[1, 3, 2, 6, 0, False, 'dynamic'], [2, 1, 4, 15, -1, False, 'static'], [3, 4, 2, 15, 0, False, 'dynamic'], [4, 4, 2, 15, -2, False, 'static'], [5, 4, 8, 1, 2, False, 'kinematic'], [6, 3, 4, 1, 2, True, 'dynamic'], [7, 3, 8, 3, 0, False, 'kinematic']], [[2, 3], [4, 7], [2, 3], [2, 3], [3, 6], [5, 6], [1, 4], [4, 3], [5, 6], [7, 3]]], [[1, 4], [2, 3], [3, 7], [5, 6]]], [[[[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, 7, 1, False, 'kinematic'], [2, 2, 1, 3, -1, False, 'dynamic'], [3, 2, 1, 1, 0, False, 'kinematic'], [4, 4, 4, 12, 0, False, 'dynamic'], [5, 2, 1, 12, 2, False, 'dynamic'], [6, 4, 2, 15, 0, False, 'static'], [7, 1, 1, 3, -2, False, 'kinematic'], [8, 4, 2, 6, 2, True, 'dynamic'], [9, 3, 2, 15, 0, False, 'static'], [10, 3, 1, 1, -1, False, 'dynamic']], [[6, 7], [4, 8], [7, 4], [9, 3], [3, 6]]], []], [[[[1, 4, 4, 6, 0, False, 'kinematic'], [2, 3, 4, 3, -1, False, 'static'], [3, 4, 8, 3, 1, True, 'kinematic'], [4, 4, 8, 7, 2, False, 'kinematic'], [5, 1, 1, 15, 1, False, 'static'], [6, 1, 1, 3, 2, False, 'kinematic'], [7, 4, 4, 15, 2, False, 'dynamic']], [[4, 1], [6, 5], [1, 4], [2, 7], [4, 5], [6, 5], [6, 7], [5, 3], [2, 5], [6, 5]]], [[6, 7]]], [[[[1, 4, 4, 7, 0, False, 'dynamic'], [2, 2, 4, 15, -1, False, 'static'], [3, 3, 8, 1, 2, False, 'dynamic'], [4, 3, 2, 1, 2, False, 'kinematic'], [5, 4, 2, 15, 1, False, 'kinematic'], [6, 4, 4, 1, -2, True, 'dynamic'], [7, 4, 1, 15, 0, False, 'dynamic']], [[3, 2], [5, 2], [3, 7], [5, 7]]], [[3, 7]]], [[[[1, 4, 1, 15, 0, False, 'kinematic'], [2, 2, 4, 12, -1, True, 'dynamic'], [3, 1, 1, 1, 0, False, 'static'], [4, 1, 1, 6, 2, False, 'dynamic'], [5, 2, 4, 15, 2, False, 'dynamic'], [6, 2, 8, 1, 2, True, 'kinematic'], [7, 2, 2, 3, -2, False, 'static'], [8, 4, 2, 3, 2, False, 'kinematic'], [9, 4, 2, 6, -2, False, 'kinematic'], [10, 3, 4, 7, 0, False, 'dynamic']], [[1, 10], [4, 1], [8, 9]]], [[1, 10]]], [[[[1, 2, 1, 1, -2, False, 'kinematic'], [2, 1, 1, 12, -2, False, 'kinematic'], [3, 2, 2, 7, 2, False, 'dynamic'], [4, 4, 4, 1, -1, True, 'dynamic'], [5, 2, 4, 6, 0, False, 'dynamic'], [6, 2, 8, 6, 0, False, 'dynamic'], [7, 1, 1, 15, 0, True, 'kinematic'], [8, 1, 1, 1, 1, False, 'static'], [9, 2, 8, 3, -2, False, 'dynamic']], [[8, 3], [3, 5], [7, 1]]], []], [[[[1, 1, 8, 1, -1, False, 'dynamic'], [2, 4, 2, 15, 2, False, 'static'], [3, 2, 8, 7, 2, False, 'kinematic'], [4, 3, 8, 6, 0, False, 'dynamic'], [5, 2, 8, 3, -1, True, 'dynamic'], [6, 4, 4, 12, 1, False, 'kinematic'], [7, 1, 8, 1, 0, True, 'dynamic'], [8, 3, 1, 6, -2, False, 'dynamic'], [9, 2, 1, 15, 2, False, 'dynamic'], [10, 2, 1, 6, 0, True, 'dynamic']], [[5, 8], [2, 10], [1, 10]]], [[2, 10]]], [[[[1, 4, 2, 7, 2, True, 'dynamic'], [2, 2, 2, 12, -2, False, 'kinematic'], [3, 1, 4, 12, 1, False, 'dynamic'], [4, 4, 8, 3, -1, False, 'dynamic'], [5, 2, 4, 1, 2, False, 'dynamic'], [6, 1, 1, 15, -1, False, 'dynamic'], [7, 4, 4, 12, -1, False, 'kinematic'], [8, 2, 2, 15, 1, False, 'dynamic'], [9, 3, 1, 6, 1, False, 'static']], [[1, 4], [9, 7], [2, 9], [9, 6], [4, 7]]], []], [[[[1, 1, 2, 15, 0, True, 'dynamic'], [2, 2, 8, 15, 1, True, 'dynamic'], [3, 2, 2, 12, 1, False, 'kinematic'], [4, 1, 1, 15, 2, True, 'kinematic'], [5, 1, 8, 15, -1, False, 'kinematic']], [[5, 3], [1, 5], [4, 5], [3, 4], [4, 3]]], []]]]
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	`[[3, 4], [4, 5]]`	`[[3, 4], [4, 5]]`	Passed
case 2	`[[1, 2], [1, 3]]`	`[[1, 2], [1, 3]]`	Passed
case 3	`[]`	`[]`	Passed
case 4	`[]`	`[]`	Passed
case 5	`[]`	`[]`	Passed
case 6	`[]`	`[]`	Passed
case 7	`[]`	`[]`	Passed

SHA-256 / f6711f6290a45a3982b45fdb0262098f24d81c0570f7ca58eb0479af5b1dd5f3

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 2026-09-29T14:50:59.606286+00:00.

Case digest / 03ea6e4f1007c43ed6b2b0e5d411f419edca2d8ce19fc635224f93ba9ca40eff