FA-70531 / GIS polygon topology / Open access

Simple ring validity diagnosis: cyclic repeated vertex · case 01

A ring whose closing position is doubled is diagnosed as a spike instead of a repeated point.

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

ROOT CAUSE

Consecutive-duplicate detection does not wrap from the last vertex to the first.

VERIFIED REPAIR

At the cyclic repeated vertex step restore `for i in range(n): if pts[i] == pts[(i + 1) % n]:`, leaving the rest of the model unchanged.

Unsuccessful approach: Searching for any later duplicate also flags non-consecutive self-touching vertices as repeated points.

Case contract

Input: one ring as a list of integer [x, y]. Report the first failing check in this order: fewer than 4 positions "too_few_points"; first != last "not_closed"; two cyclically consecutive equal vertices "repeated_point"; a vertex where the boundary reverses direction along a line (collinear with a negative dot product of the incoming and outgoing edge, checked cyclically) "spike"; any two non-adjacent edges sharing a point (crossing, touching or collinear overlap) "self_intersection"; otherwise "valid".

Why this case matters

Topology validators run before editing, overlay and publishing; a wrong diagnosis sends users to fix the wrong vertex or lets broken rings through.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    ring = x
    if len(ring) < 4:
        return 'too_few_points'
    if ring[0] != ring[-1]:
        return 'not_closed'
    pts = ring[:-1]
    n = len(pts)
    for i in range(n - 1):
        if pts[i] == pts[i + 1]:
            return 'repeated_point'
    for i in range(n):
        a, b, c = pts[i - 1], pts[i], pts[(i + 1) % n]
        cross = (b[0] - a[0]) * (c[1] - b[1]) - (b[1] - a[1]) * (c[0] - b[0])
        dot = (b[0] - a[0]) * (c[0] - b[0]) + (b[1] - a[1]) * (c[1] - b[1])
        if cross == 0 and dot < 0:
            return 'spike'
    def orient(p, q, r):
        v = (q[0] - p[0]) * (r[1] - p[1]) - (q[1] - p[1]) * (r[0] - p[0])
        return (v > 0) - (v < 0)
    def within(p, q, r):
        return min(p[0], r[0]) <= q[0] <= max(p[0], r[0]) and min(p[1], r[1]) <= q[1] <= max(p[1], r[1])
    def hit(p1, p2, p3, p4):
        o1, o2, o3, o4 = orient(p1, p2, p3), orient(p1, p2, p4), orient(p3, p4, p1), orient(p3, p4, p2)
        if o1 * o2 < 0 and o3 * o4 < 0:
            return True
        return (o1 == 0 and within(p1, p3, p2)) or (o2 == 0 and within(p1, p4, p2)) or (o3 == 0 and within(p3, p1, p4)) or (o4 == 0 and within(p3, p2, p4))
    for i in range(n):
        for j in range(i + 1, n):
            if j == i + 1 or (i == 0 and j == n - 1):
                continue
            if hit(pts[i], pts[(i + 1) % n], pts[j], pts[(j + 1) % n]):
                return 'self_intersection'
    return 'valid'
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('control #0', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 0]], 'valid'), ('control #1', [[0, 0], [10, 0], [5, 8], [0, 0]], 'valid'), ('control #2', [[0, 0], [5, 0], [10, 0], [10, 10], [0, 10], [0, 0]], 'valid'), ('regression #3', [[0, 0], [10, 10], [10, 0], [0, 10], [0, 0]], 'self_intersection'), ('regression #4', [[0, 0], [10, 0], [10, 10], [10, 5], [0, 5], [0, 0]], 'spike'), ('regression #5', [[5, 0], [10, 0], [10, 10], [0, 10], [0, 0], [5, 0], [0, 0]], 'not_closed'), ('regression #10', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 0], [0, 0]], 'repeated_point'), ('regression #13', [[0, 0], [4, 0], [4, 4], [8, 4], [8, 8], [4, 8], [4, 4], [0, 4], [0, 0]], 'self_intersection')], [('regression #3', [[0, 0], [10, 10], [10, 0], [0, 10], [0, 0]], 'self_intersection'), ('regression #4', [[0, 0], [10, 0], [10, 10], [10, 5], [0, 5], [0, 0]], 'spike'), ('regression #5', [[5, 0], [10, 0], [10, 10], [0, 10], [0, 0], [5, 0], [0, 0]], 'not_closed'), ('boundary #6', [[0, 0], [10, 0], [10, 10], [0, 0]], 'valid'), ('boundary #7', [[0, 0], [10, 0], [10, 10]], 'too_few_points'), ('boundary #8', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 1]], 'not_closed'), ('regression #10', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 0], [0, 0]], 'repeated_point'), ('regression #13', [[0, 0], [4, 0], [4, 4], [8, 4], [8, 8], [4, 8], [4, 4], [0, 4], [0, 0]], 'self_intersection')], [('boundary #6', [[0, 0], [10, 0], [10, 10], [0, 0]], 'valid'), ('boundary #7', [[0, 0], [10, 0], [10, 10]], 'too_few_points'), ('boundary #8', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 1]], 'not_closed'), ('boundary #9', [[0, 0], [10, 0], [10, 0], [10, 10], [0, 0]], 'repeated_point'), ('regression #10', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 0], [0, 0]], 'repeated_point'), ('regression #11', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 5], [0, 12], [0, 0]], 'spike'), ('regression #12', [[0, 5], [0, 0], [10, 0], [10, 10], [0, 10], [0, 12], [0, 5]], 'spike'), ('regression #13', [[0, 0], [4, 0], [4, 4], [8, 4], [8, 8], [4, 8], [4, 4], [0, 4], [0, 0]], 'self_intersection')], [('boundary #9', [[0, 0], [10, 0], [10, 0], [10, 10], [0, 0]], 'repeated_point'), ('regression #10', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 0], [0, 0]], 'repeated_point'), ('regression #11', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 5], [0, 12], [0, 0]], 'spike'), ('regression #12', [[0, 5], [0, 0], [10, 0], [10, 10], [0, 10], [0, 12], [0, 5]], 'spike'), ('regression #13', [[0, 0], [4, 0], [4, 4], [8, 4], [8, 8], [4, 8], [4, 4], [0, 4], [0, 0]], 'self_intersection'), ('regression #14', [[0, 0], [10, 0], [10, 10], [5, 0], [0, 10], [0, 0]], 'self_intersection'), ('regression #15', [[0, 0], [10, 0], [10, 5], [2, 5], [6, 5], [6, 8], [0, 8], [0, 0]], 'spike'), ('control #16', [[0, 0], [6, 0], [6, 6], [3, 3], [0, 6], [0, 0]], 'valid')], [('regression #10', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 0], [0, 0]], 'repeated_point'), ('regression #13', [[0, 0], [4, 0], [4, 4], [8, 4], [8, 8], [4, 8], [4, 4], [0, 4], [0, 0]], 'self_intersection'), ('regression #14', [[0, 0], [10, 0], [10, 10], [5, 0], [0, 10], [0, 0]], 'self_intersection'), ('regression #15', [[0, 0], [10, 0], [10, 5], [2, 5], [6, 5], [6, 8], [0, 8], [0, 0]], 'spike'), ('control #16', [[0, 0], [6, 0], [6, 6], [3, 3], [0, 6], [0, 0]], 'valid'), ('regression #17', [[0, 0], [10, 0], [10, 10], [0, 10], [4, 10], [0, 0]], 'spike'), ('control #18', [[1, 1], [9, 2], [8, 9], [2, 7], [1, 1]], 'valid'), ('regression #19', [[0, 0], [8, 0], [8, 8], [0, 8], [0, 4], [8, 4], [0, 0]], 'self_intersection')]]
for label, args, expected in fixtures[N-1]:
    check(label, 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
control #0	`valid`	`valid`	Passed
control #1	`valid`	`valid`	Passed
control #2	`valid`	`valid`	Passed
regression #3	`self_intersection`	`self_intersection`	Passed
regression #4	`spike`	`spike`	Passed
regression #5	`not_closed`	`not_closed`	Passed
regression #10	`self_intersection`	`repeated_point`	Failed
regression #13	`self_intersection`	`self_intersection`	Passed

SHA-256 / 59b8b7832e5f314d779af15914ba4018b30b11c96e77cc2277506ce3211d1fe8

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    ring = x
    if len(ring) < 4:
        return 'too_few_points'
    if ring[0] != ring[-1]:
        return 'not_closed'
    pts = ring[:-1]
    n = len(pts)
    for i in range(n):
        if pts[i] in pts[i + 1:]:
            return 'repeated_point'
    for i in range(n):
        a, b, c = pts[i - 1], pts[i], pts[(i + 1) % n]
        cross = (b[0] - a[0]) * (c[1] - b[1]) - (b[1] - a[1]) * (c[0] - b[0])
        dot = (b[0] - a[0]) * (c[0] - b[0]) + (b[1] - a[1]) * (c[1] - b[1])
        if cross == 0 and dot < 0:
            return 'spike'
    def orient(p, q, r):
        v = (q[0] - p[0]) * (r[1] - p[1]) - (q[1] - p[1]) * (r[0] - p[0])
        return (v > 0) - (v < 0)
    def within(p, q, r):
        return min(p[0], r[0]) <= q[0] <= max(p[0], r[0]) and min(p[1], r[1]) <= q[1] <= max(p[1], r[1])
    def hit(p1, p2, p3, p4):
        o1, o2, o3, o4 = orient(p1, p2, p3), orient(p1, p2, p4), orient(p3, p4, p1), orient(p3, p4, p2)
        if o1 * o2 < 0 and o3 * o4 < 0:
            return True
        return (o1 == 0 and within(p1, p3, p2)) or (o2 == 0 and within(p1, p4, p2)) or (o3 == 0 and within(p3, p1, p4)) or (o4 == 0 and within(p3, p2, p4))
    for i in range(n):
        for j in range(i + 1, n):
            if j == i + 1 or (i == 0 and j == n - 1):
                continue
            if hit(pts[i], pts[(i + 1) % n], pts[j], pts[(j + 1) % n]):
                return 'self_intersection'
    return 'valid'
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('control #0', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 0]], 'valid'), ('control #1', [[0, 0], [10, 0], [5, 8], [0, 0]], 'valid'), ('control #2', [[0, 0], [5, 0], [10, 0], [10, 10], [0, 10], [0, 0]], 'valid'), ('regression #3', [[0, 0], [10, 10], [10, 0], [0, 10], [0, 0]], 'self_intersection'), ('regression #4', [[0, 0], [10, 0], [10, 10], [10, 5], [0, 5], [0, 0]], 'spike'), ('regression #5', [[5, 0], [10, 0], [10, 10], [0, 10], [0, 0], [5, 0], [0, 0]], 'not_closed'), ('regression #10', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 0], [0, 0]], 'repeated_point'), ('regression #13', [[0, 0], [4, 0], [4, 4], [8, 4], [8, 8], [4, 8], [4, 4], [0, 4], [0, 0]], 'self_intersection')], [('regression #3', [[0, 0], [10, 10], [10, 0], [0, 10], [0, 0]], 'self_intersection'), ('regression #4', [[0, 0], [10, 0], [10, 10], [10, 5], [0, 5], [0, 0]], 'spike'), ('regression #5', [[5, 0], [10, 0], [10, 10], [0, 10], [0, 0], [5, 0], [0, 0]], 'not_closed'), ('boundary #6', [[0, 0], [10, 0], [10, 10], [0, 0]], 'valid'), ('boundary #7', [[0, 0], [10, 0], [10, 10]], 'too_few_points'), ('boundary #8', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 1]], 'not_closed'), ('regression #10', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 0], [0, 0]], 'repeated_point'), ('regression #13', [[0, 0], [4, 0], [4, 4], [8, 4], [8, 8], [4, 8], [4, 4], [0, 4], [0, 0]], 'self_intersection')], [('boundary #6', [[0, 0], [10, 0], [10, 10], [0, 0]], 'valid'), ('boundary #7', [[0, 0], [10, 0], [10, 10]], 'too_few_points'), ('boundary #8', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 1]], 'not_closed'), ('boundary #9', [[0, 0], [10, 0], [10, 0], [10, 10], [0, 0]], 'repeated_point'), ('regression #10', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 0], [0, 0]], 'repeated_point'), ('regression #11', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 5], [0, 12], [0, 0]], 'spike'), ('regression #12', [[0, 5], [0, 0], [10, 0], [10, 10], [0, 10], [0, 12], [0, 5]], 'spike'), ('regression #13', [[0, 0], [4, 0], [4, 4], [8, 4], [8, 8], [4, 8], [4, 4], [0, 4], [0, 0]], 'self_intersection')], [('boundary #9', [[0, 0], [10, 0], [10, 0], [10, 10], [0, 0]], 'repeated_point'), ('regression #10', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 0], [0, 0]], 'repeated_point'), ('regression #11', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 5], [0, 12], [0, 0]], 'spike'), ('regression #12', [[0, 5], [0, 0], [10, 0], [10, 10], [0, 10], [0, 12], [0, 5]], 'spike'), ('regression #13', [[0, 0], [4, 0], [4, 4], [8, 4], [8, 8], [4, 8], [4, 4], [0, 4], [0, 0]], 'self_intersection'), ('regression #14', [[0, 0], [10, 0], [10, 10], [5, 0], [0, 10], [0, 0]], 'self_intersection'), ('regression #15', [[0, 0], [10, 0], [10, 5], [2, 5], [6, 5], [6, 8], [0, 8], [0, 0]], 'spike'), ('control #16', [[0, 0], [6, 0], [6, 6], [3, 3], [0, 6], [0, 0]], 'valid')], [('regression #10', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 0], [0, 0]], 'repeated_point'), ('regression #13', [[0, 0], [4, 0], [4, 4], [8, 4], [8, 8], [4, 8], [4, 4], [0, 4], [0, 0]], 'self_intersection'), ('regression #14', [[0, 0], [10, 0], [10, 10], [5, 0], [0, 10], [0, 0]], 'self_intersection'), ('regression #15', [[0, 0], [10, 0], [10, 5], [2, 5], [6, 5], [6, 8], [0, 8], [0, 0]], 'spike'), ('control #16', [[0, 0], [6, 0], [6, 6], [3, 3], [0, 6], [0, 0]], 'valid'), ('regression #17', [[0, 0], [10, 0], [10, 10], [0, 10], [4, 10], [0, 0]], 'spike'), ('control #18', [[1, 1], [9, 2], [8, 9], [2, 7], [1, 1]], 'valid'), ('regression #19', [[0, 0], [8, 0], [8, 8], [0, 8], [0, 4], [8, 4], [0, 0]], 'self_intersection')]]
for label, args, expected in fixtures[N-1]:
    check(label, 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
control #0	`valid`	`valid`	Passed
control #1	`valid`	`valid`	Passed
control #2	`valid`	`valid`	Passed
regression #3	`self_intersection`	`self_intersection`	Passed
regression #4	`spike`	`spike`	Passed
regression #5	`not_closed`	`not_closed`	Passed
regression #10	`repeated_point`	`repeated_point`	Passed
regression #13	`repeated_point`	`self_intersection`	Failed

SHA-256 / 4159329ac64e4f624773df15885988e0a00e14010fd77c6f5852bca268a60d39

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    ring = x
    if len(ring) < 4:
        return 'too_few_points'
    if ring[0] != ring[-1]:
        return 'not_closed'
    pts = ring[:-1]
    n = len(pts)
    for i in range(n):
        if pts[i] == pts[(i + 1) % n]:
            return 'repeated_point'
    for i in range(n):
        a, b, c = pts[i - 1], pts[i], pts[(i + 1) % n]
        cross = (b[0] - a[0]) * (c[1] - b[1]) - (b[1] - a[1]) * (c[0] - b[0])
        dot = (b[0] - a[0]) * (c[0] - b[0]) + (b[1] - a[1]) * (c[1] - b[1])
        if cross == 0 and dot < 0:
            return 'spike'
    def orient(p, q, r):
        v = (q[0] - p[0]) * (r[1] - p[1]) - (q[1] - p[1]) * (r[0] - p[0])
        return (v > 0) - (v < 0)
    def within(p, q, r):
        return min(p[0], r[0]) <= q[0] <= max(p[0], r[0]) and min(p[1], r[1]) <= q[1] <= max(p[1], r[1])
    def hit(p1, p2, p3, p4):
        o1, o2, o3, o4 = orient(p1, p2, p3), orient(p1, p2, p4), orient(p3, p4, p1), orient(p3, p4, p2)
        if o1 * o2 < 0 and o3 * o4 < 0:
            return True
        return (o1 == 0 and within(p1, p3, p2)) or (o2 == 0 and within(p1, p4, p2)) or (o3 == 0 and within(p3, p1, p4)) or (o4 == 0 and within(p3, p2, p4))
    for i in range(n):
        for j in range(i + 1, n):
            if j == i + 1 or (i == 0 and j == n - 1):
                continue
            if hit(pts[i], pts[(i + 1) % n], pts[j], pts[(j + 1) % n]):
                return 'self_intersection'
    return 'valid'
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('control #0', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 0]], 'valid'), ('control #1', [[0, 0], [10, 0], [5, 8], [0, 0]], 'valid'), ('control #2', [[0, 0], [5, 0], [10, 0], [10, 10], [0, 10], [0, 0]], 'valid'), ('regression #3', [[0, 0], [10, 10], [10, 0], [0, 10], [0, 0]], 'self_intersection'), ('regression #4', [[0, 0], [10, 0], [10, 10], [10, 5], [0, 5], [0, 0]], 'spike'), ('regression #5', [[5, 0], [10, 0], [10, 10], [0, 10], [0, 0], [5, 0], [0, 0]], 'not_closed'), ('regression #10', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 0], [0, 0]], 'repeated_point'), ('regression #13', [[0, 0], [4, 0], [4, 4], [8, 4], [8, 8], [4, 8], [4, 4], [0, 4], [0, 0]], 'self_intersection')], [('regression #3', [[0, 0], [10, 10], [10, 0], [0, 10], [0, 0]], 'self_intersection'), ('regression #4', [[0, 0], [10, 0], [10, 10], [10, 5], [0, 5], [0, 0]], 'spike'), ('regression #5', [[5, 0], [10, 0], [10, 10], [0, 10], [0, 0], [5, 0], [0, 0]], 'not_closed'), ('boundary #6', [[0, 0], [10, 0], [10, 10], [0, 0]], 'valid'), ('boundary #7', [[0, 0], [10, 0], [10, 10]], 'too_few_points'), ('boundary #8', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 1]], 'not_closed'), ('regression #10', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 0], [0, 0]], 'repeated_point'), ('regression #13', [[0, 0], [4, 0], [4, 4], [8, 4], [8, 8], [4, 8], [4, 4], [0, 4], [0, 0]], 'self_intersection')], [('boundary #6', [[0, 0], [10, 0], [10, 10], [0, 0]], 'valid'), ('boundary #7', [[0, 0], [10, 0], [10, 10]], 'too_few_points'), ('boundary #8', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 1]], 'not_closed'), ('boundary #9', [[0, 0], [10, 0], [10, 0], [10, 10], [0, 0]], 'repeated_point'), ('regression #10', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 0], [0, 0]], 'repeated_point'), ('regression #11', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 5], [0, 12], [0, 0]], 'spike'), ('regression #12', [[0, 5], [0, 0], [10, 0], [10, 10], [0, 10], [0, 12], [0, 5]], 'spike'), ('regression #13', [[0, 0], [4, 0], [4, 4], [8, 4], [8, 8], [4, 8], [4, 4], [0, 4], [0, 0]], 'self_intersection')], [('boundary #9', [[0, 0], [10, 0], [10, 0], [10, 10], [0, 0]], 'repeated_point'), ('regression #10', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 0], [0, 0]], 'repeated_point'), ('regression #11', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 5], [0, 12], [0, 0]], 'spike'), ('regression #12', [[0, 5], [0, 0], [10, 0], [10, 10], [0, 10], [0, 12], [0, 5]], 'spike'), ('regression #13', [[0, 0], [4, 0], [4, 4], [8, 4], [8, 8], [4, 8], [4, 4], [0, 4], [0, 0]], 'self_intersection'), ('regression #14', [[0, 0], [10, 0], [10, 10], [5, 0], [0, 10], [0, 0]], 'self_intersection'), ('regression #15', [[0, 0], [10, 0], [10, 5], [2, 5], [6, 5], [6, 8], [0, 8], [0, 0]], 'spike'), ('control #16', [[0, 0], [6, 0], [6, 6], [3, 3], [0, 6], [0, 0]], 'valid')], [('regression #10', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 0], [0, 0]], 'repeated_point'), ('regression #13', [[0, 0], [4, 0], [4, 4], [8, 4], [8, 8], [4, 8], [4, 4], [0, 4], [0, 0]], 'self_intersection'), ('regression #14', [[0, 0], [10, 0], [10, 10], [5, 0], [0, 10], [0, 0]], 'self_intersection'), ('regression #15', [[0, 0], [10, 0], [10, 5], [2, 5], [6, 5], [6, 8], [0, 8], [0, 0]], 'spike'), ('control #16', [[0, 0], [6, 0], [6, 6], [3, 3], [0, 6], [0, 0]], 'valid'), ('regression #17', [[0, 0], [10, 0], [10, 10], [0, 10], [4, 10], [0, 0]], 'spike'), ('control #18', [[1, 1], [9, 2], [8, 9], [2, 7], [1, 1]], 'valid'), ('regression #19', [[0, 0], [8, 0], [8, 8], [0, 8], [0, 4], [8, 4], [0, 0]], 'self_intersection')]]
for label, args, expected in fixtures[N-1]:
    check(label, 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
control #0	`valid`	`valid`	Passed
control #1	`valid`	`valid`	Passed
control #2	`valid`	`valid`	Passed
regression #3	`self_intersection`	`self_intersection`	Passed
regression #4	`spike`	`spike`	Passed
regression #5	`not_closed`	`not_closed`	Passed
regression #10	`repeated_point`	`repeated_point`	Passed
regression #13	`self_intersection`	`self_intersection`	Passed

SHA-256 / 18cb4b546760935da4507d4250b0bbedda4f33f003fc29c1723be6cd40b66bcf

Verification & scope

Stipulated deterministic toy contract on a bounded input domain; results are rounded as stated and no conformance with any published standard or library is claimed. 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 2026-09-29T14:48:21.643195+00:00.

Case digest / f37b571f7ad645914751c00560d6afe4924b47da28d98b970276f77e54ac9818