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FA-70606 / GIS polygon topology / Open access

Douglas-Peucker simplification of a topology arc: first maximum tie-break · case 01

Among equally distant vertices the last one is kept, changing the simplified shape.

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

ROOT CAUSE

Using >= selects the last of several equally distant vertices.

VERIFIED REPAIR

At the first maximum tie-break step restore `if d > best:`, leaving the rest of the model unchanged.

Unsuccessful approach: The patched rule still lets the vertex just before the far endpoint override an earlier maximum.

Case contract

Input [points, tol]: an arc as integer [x, y] positions (possibly closed, first == last). Keep both endpoints; recursively (explicit stack) find the interior vertex farthest from the SEGMENT between the current endpoints (projection clamped to the segment; distance to the point itself if the endpoints coincide), taking the first maximum; keep it and split when that distance is strictly greater than tol. Return kept positions in order.

Why this case matters

Shared arcs are simplified once so adjacent polygons stay gap-free; distance and split errors change which boundary vertices survive.

1 / The failure

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    pts, tol = x
    def dist(p, a, b):
        dx, dy = b[0] - a[0], b[1] - a[1]
        if dx == 0 and dy == 0:
            return math.hypot(p[0] - a[0], p[1] - a[1])
        t = ((p[0] - a[0]) * dx + (p[1] - a[1]) * dy) / (dx * dx + dy * dy)
        t = max(0.0, min(1.0, t))
        return math.hypot(p[0] - a[0] - t * dx, p[1] - a[1] - t * dy)
    keep = [False] * len(pts)
    keep[0] = keep[-1] = True
    stack = [(0, len(pts) - 1)]
    while stack:
        i, j = stack.pop()
        best, idx = -1.0, -1
        for k in range(i + 1, j):
            d = dist(pts[k], pts[i], pts[j])
            if d >= best:
                best, idx = d, k
        if idx != -1 and best > tol:
            keep[idx] = True
            stack.append((i, idx))
            stack.append((idx, j))
    return [p for p, f in zip(pts, keep) if f]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('control #0', [[[0, 0], [3, 1], [6, -1], [9, 1], [12, 1], [15, 4], [18, 1], [21, -2], [24, 1]], 2], [[0, 0], [6, -1], [15, 4], [21, -2], [24, 1]]), ('control #1', [[[0, 3], [3, -4], [6, 1], [9, 3], [12, -4], [15, 1], [18, -1]], 1], [[0, 3], [3, -4], [9, 3], [12, -4], [15, 1], [18, -1]]), ('control #2', [[[0, -4], [3, 3], [6, -2], [9, -1], [12, 2], [15, 1], [18, 1]], 0], [[0, -4], [3, 3], [6, -2], [9, -1], [12, 2], [15, 1], [18, 1]]), ('control #3', [[[0, -3], [3, -1], [6, -3], [9, -2]], 3], [[0, -3], [9, -2]]), ('control #4', [[[0, -2], [3, -4], [6, -1], [9, -4], [12, 1], [15, 2]], 3], [[0, -2], [9, -4], [15, 2]]), ('control #5', [[[0, -2], [3, 2], [6, 2], [9, -3], [12, 3], [15, 4], [18, 2], [21, -2]], 0], [[0, -2], [3, 2], [6, 2], [9, -3], [12, 3], [15, 4], [18, 2], [21, -2]]), ('control #8', [[[0, -4], [3, -4], [6, 1], [9, 3], [12, 3], [15, -4]], 1], [[0, -4], [3, -4], [9, 3], [12, 3], [15, -4]]), ('control #10', [[[0, -4], [3, -2], [6, 1], [9, 1]], 2], [[0, -4], [9, 1]])], [('control #1', [[[0, 3], [3, -4], [6, 1], [9, 3], [12, -4], [15, 1], [18, -1]], 1], [[0, 3], [3, -4], [9, 3], [12, -4], [15, 1], [18, -1]]), ('control #4', [[[0, -2], [3, -4], [6, -1], [9, -4], [12, 1], [15, 2]], 3], [[0, -2], [9, -4], [15, 2]]), ('control #5', [[[0, -2], [3, 2], [6, 2], [9, -3], [12, 3], [15, 4], [18, 2], [21, -2]], 0], [[0, -2], [3, 2], [6, 2], [9, -3], [12, 3], [15, 4], [18, 2], [21, -2]]), ('control #6', [[[0, 4], [3, -1], [6, 2], [9, 2], [12, 2]], 3], [[0, 4], [3, -1], [12, 2]]), ('control #7', [[[0, -4], [3, 0], [6, -3], [9, 1], [12, 1], [15, 3]], 2], [[0, -4], [3, 0], [6, -3], [15, 3]]), ('control #10', [[[0, -4], [3, -2], [6, 1], [9, 1]], 2], [[0, -4], [9, 1]]), ('control #12', [[[0, 2], [3, -3], [6, 3], [9, -1]], 1], [[0, 2], [3, -3], [6, 3], [9, -1]]), ('regression #21', [[[0, 0], [2, 1], [4, 3], [6, 3], [8, 1], [10, 0]], 1], [[0, 0], [4, 3], [10, 0]])], [('control #2', [[[0, -4], [3, 3], [6, -2], [9, -1], [12, 2], [15, 1], [18, 1]], 0], [[0, -4], [3, 3], [6, -2], [9, -1], [12, 2], [15, 1], [18, 1]]), ('control #7', [[[0, -4], [3, 0], [6, -3], [9, 1], [12, 1], [15, 3]], 2], [[0, -4], [3, 0], [6, -3], [15, 3]]), ('control #8', [[[0, -4], [3, -4], [6, 1], [9, 3], [12, 3], [15, -4]], 1], [[0, -4], [3, -4], [9, 3], [12, 3], [15, -4]]), ('control #9', [[[0, -3], [3, 4], [6, 0], [9, -4], [12, 0], [15, -1], [18, 4]], 0], [[0, -3], [3, 4], [9, -4], [12, 0], [15, -1], [18, 4]]), ('control #10', [[[0, -4], [3, -2], [6, 1], [9, 1]], 2], [[0, -4], [9, 1]]), ('control #12', [[[0, 2], [3, -3], [6, 3], [9, -1]], 1], [[0, 2], [3, -3], [6, 3], [9, -1]]), ('regression #14', [[[0, 0], [10, 0], [14, 3], [20, 0]], 2], [[0, 0], [10, 0], [14, 3], [20, 0]]), ('regression #22', [[[0, 0], [3, 3], [6, 0], [9, 3], [12, 0]], 2], [[0, 0], [3, 3], [12, 0]])], [('control #4', [[[0, -2], [3, -4], [6, -1], [9, -4], [12, 1], [15, 2]], 3], [[0, -2], [9, -4], [15, 2]]), ('control #10', [[[0, -4], [3, -2], [6, 1], [9, 1]], 2], [[0, -4], [9, 1]]), ('control #11', [[[0, 4], [3, -3], [6, -2], [9, -4], [12, 4], [15, 4], [18, -1]], 2], [[0, 4], [3, -3], [9, -4], [12, 4], [18, -1]]), ('control #12', [[[0, 2], [3, -3], [6, 3], [9, -1]], 1], [[0, 2], [3, -3], [6, 3], [9, -1]]), ('control #13', [[[0, 4], [3, -1], [6, -4], [9, -2], [12, 4], [15, -3], [18, -1], [21, 0]], 3], [[0, 4], [6, -4], [12, 4], [15, -3], [21, 0]]), ('regression #14', [[[0, 0], [10, 0], [14, 3], [20, 0]], 2], [[0, 0], [10, 0], [14, 3], [20, 0]]), ('regression #15', [[[0, 0], [5, 0], [-6, 1], [10, 0]], 2], [[0, 0], [5, 0], [-6, 1], [10, 0]]), ('regression #24', [[[0, 0], [1, 5], [2, 0], [3, 5], [4, 0], [20, 0]], 3], [[0, 0], [1, 5], [2, 0], [3, 5], [4, 0], [20, 0]])], [('control #6', [[[0, 4], [3, -1], [6, 2], [9, 2], [12, 2]], 3], [[0, 4], [3, -1], [12, 2]]), ('control #8', [[[0, -4], [3, -4], [6, 1], [9, 3], [12, 3], [15, -4]], 1], [[0, -4], [3, -4], [9, 3], [12, 3], [15, -4]]), ('regression #14', [[[0, 0], [10, 0], [14, 3], [20, 0]], 2], [[0, 0], [10, 0], [14, 3], [20, 0]]), ('regression #15', [[[0, 0], [5, 0], [-6, 1], [10, 0]], 2], [[0, 0], [5, 0], [-6, 1], [10, 0]]), ('regression #16', [[[0, 0], [4, 4], [8, 0], [4, -4], [0, 0]], 1], [[0, 0], [4, 4], [8, 0], [4, -4], [0, 0]]), ('regression #17', [[[0, 0], [6, 1], [6, 7], [0, 6], [0, 0]], 2], [[0, 0], [6, 1], [6, 7], [0, 6], [0, 0]]), ('boundary #18', [[[0, 0], [5, 2], [10, 0]], 2], [[0, 0], [10, 0]]), ('boundary #19', [[[0, 0], [5, 3], [10, 0]], 2], [[0, 0], [5, 3], [10, 0]])]]
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 fixtureActualExpectedOutcome
control #0[[0, 0], [6, -1], [15, 4], [21, -2], [24, 1]][[0, 0], [6, -1], [15, 4], [21, -2], [24, 1]]Passed
control #1[[0, 3], [3, -4], [9, 3], [12, -4], [15, 1], [18, -1]][[0, 3], [3, -4], [9, 3], [12, -4], [15, 1], [18, -1]]Passed
control #2[[0, -4], [3, 3], [6, -2], [9, -1], [12, 2], [15, 1], [18, 1]][[0, -4], [3, 3], [6, -2], [9, -1], [12, 2], [15, 1], [18, 1]]Passed
control #3[[0, -3], [9, -2]][[0, -3], [9, -2]]Passed
control #4[[0, -2], [9, -4], [15, 2]][[0, -2], [9, -4], [15, 2]]Passed
control #5[[0, -2], [3, 2], [6, 2], [9, -3], [12, 3], [15, 4], [18, 2], [21, -2]][[0, -2], [3, 2], [6, 2], [9, -3], [12, 3], [15, 4], [18, 2], [21, -2]]Passed
control #8[[0, -4], [3, -4], [6, 1], [12, 3], [15, -4]][[0, -4], [3, -4], [9, 3], [12, 3], [15, -4]]Failed
control #10[[0, -4], [9, 1]][[0, -4], [9, 1]]Passed

SHA-256 / 30f685e76cd5b6da024c1e378bf673a8ffacee46bb571009ac3edea26da11244

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    pts, tol = x
    def dist(p, a, b):
        dx, dy = b[0] - a[0], b[1] - a[1]
        if dx == 0 and dy == 0:
            return math.hypot(p[0] - a[0], p[1] - a[1])
        t = ((p[0] - a[0]) * dx + (p[1] - a[1]) * dy) / (dx * dx + dy * dy)
        t = max(0.0, min(1.0, t))
        return math.hypot(p[0] - a[0] - t * dx, p[1] - a[1] - t * dy)
    keep = [False] * len(pts)
    keep[0] = keep[-1] = True
    stack = [(0, len(pts) - 1)]
    while stack:
        i, j = stack.pop()
        best, idx = -1.0, -1
        for k in range(i + 1, j):
            d = dist(pts[k], pts[i], pts[j])
            if d > best + 1e-9 or idx == -1 or k == j - 1:
                best, idx = d, k
        if idx != -1 and best > tol:
            keep[idx] = True
            stack.append((i, idx))
            stack.append((idx, j))
    return [p for p, f in zip(pts, keep) if f]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('control #0', [[[0, 0], [3, 1], [6, -1], [9, 1], [12, 1], [15, 4], [18, 1], [21, -2], [24, 1]], 2], [[0, 0], [6, -1], [15, 4], [21, -2], [24, 1]]), ('control #1', [[[0, 3], [3, -4], [6, 1], [9, 3], [12, -4], [15, 1], [18, -1]], 1], [[0, 3], [3, -4], [9, 3], [12, -4], [15, 1], [18, -1]]), ('control #2', [[[0, -4], [3, 3], [6, -2], [9, -1], [12, 2], [15, 1], [18, 1]], 0], [[0, -4], [3, 3], [6, -2], [9, -1], [12, 2], [15, 1], [18, 1]]), ('control #3', [[[0, -3], [3, -1], [6, -3], [9, -2]], 3], [[0, -3], [9, -2]]), ('control #4', [[[0, -2], [3, -4], [6, -1], [9, -4], [12, 1], [15, 2]], 3], [[0, -2], [9, -4], [15, 2]]), ('control #5', [[[0, -2], [3, 2], [6, 2], [9, -3], [12, 3], [15, 4], [18, 2], [21, -2]], 0], [[0, -2], [3, 2], [6, 2], [9, -3], [12, 3], [15, 4], [18, 2], [21, -2]]), ('control #8', [[[0, -4], [3, -4], [6, 1], [9, 3], [12, 3], [15, -4]], 1], [[0, -4], [3, -4], [9, 3], [12, 3], [15, -4]]), ('control #10', [[[0, -4], [3, -2], [6, 1], [9, 1]], 2], [[0, -4], [9, 1]])], [('control #1', [[[0, 3], [3, -4], [6, 1], [9, 3], [12, -4], [15, 1], [18, -1]], 1], [[0, 3], [3, -4], [9, 3], [12, -4], [15, 1], [18, -1]]), ('control #4', [[[0, -2], [3, -4], [6, -1], [9, -4], [12, 1], [15, 2]], 3], [[0, -2], [9, -4], [15, 2]]), ('control #5', [[[0, -2], [3, 2], [6, 2], [9, -3], [12, 3], [15, 4], [18, 2], [21, -2]], 0], [[0, -2], [3, 2], [6, 2], [9, -3], [12, 3], [15, 4], [18, 2], [21, -2]]), ('control #6', [[[0, 4], [3, -1], [6, 2], [9, 2], [12, 2]], 3], [[0, 4], [3, -1], [12, 2]]), ('control #7', [[[0, -4], [3, 0], [6, -3], [9, 1], [12, 1], [15, 3]], 2], [[0, -4], [3, 0], [6, -3], [15, 3]]), ('control #10', [[[0, -4], [3, -2], [6, 1], [9, 1]], 2], [[0, -4], [9, 1]]), ('control #12', [[[0, 2], [3, -3], [6, 3], [9, -1]], 1], [[0, 2], [3, -3], [6, 3], [9, -1]]), ('regression #21', [[[0, 0], [2, 1], [4, 3], [6, 3], [8, 1], [10, 0]], 1], [[0, 0], [4, 3], [10, 0]])], [('control #2', [[[0, -4], [3, 3], [6, -2], [9, -1], [12, 2], [15, 1], [18, 1]], 0], [[0, -4], [3, 3], [6, -2], [9, -1], [12, 2], [15, 1], [18, 1]]), ('control #7', [[[0, -4], [3, 0], [6, -3], [9, 1], [12, 1], [15, 3]], 2], [[0, -4], [3, 0], [6, -3], [15, 3]]), ('control #8', [[[0, -4], [3, -4], [6, 1], [9, 3], [12, 3], [15, -4]], 1], [[0, -4], [3, -4], [9, 3], [12, 3], [15, -4]]), ('control #9', [[[0, -3], [3, 4], [6, 0], [9, -4], [12, 0], [15, -1], [18, 4]], 0], [[0, -3], [3, 4], [9, -4], [12, 0], [15, -1], [18, 4]]), ('control #10', [[[0, -4], [3, -2], [6, 1], [9, 1]], 2], [[0, -4], [9, 1]]), ('control #12', [[[0, 2], [3, -3], [6, 3], [9, -1]], 1], [[0, 2], [3, -3], [6, 3], [9, -1]]), ('regression #14', [[[0, 0], [10, 0], [14, 3], [20, 0]], 2], [[0, 0], [10, 0], [14, 3], [20, 0]]), ('regression #22', [[[0, 0], [3, 3], [6, 0], [9, 3], [12, 0]], 2], [[0, 0], [3, 3], [12, 0]])], [('control #4', [[[0, -2], [3, -4], [6, -1], [9, -4], [12, 1], [15, 2]], 3], [[0, -2], [9, -4], [15, 2]]), ('control #10', [[[0, -4], [3, -2], [6, 1], [9, 1]], 2], [[0, -4], [9, 1]]), ('control #11', [[[0, 4], [3, -3], [6, -2], [9, -4], [12, 4], [15, 4], [18, -1]], 2], [[0, 4], [3, -3], [9, -4], [12, 4], [18, -1]]), ('control #12', [[[0, 2], [3, -3], [6, 3], [9, -1]], 1], [[0, 2], [3, -3], [6, 3], [9, -1]]), ('control #13', [[[0, 4], [3, -1], [6, -4], [9, -2], [12, 4], [15, -3], [18, -1], [21, 0]], 3], [[0, 4], [6, -4], [12, 4], [15, -3], [21, 0]]), ('regression #14', [[[0, 0], [10, 0], [14, 3], [20, 0]], 2], [[0, 0], [10, 0], [14, 3], [20, 0]]), ('regression #15', [[[0, 0], [5, 0], [-6, 1], [10, 0]], 2], [[0, 0], [5, 0], [-6, 1], [10, 0]]), ('regression #24', [[[0, 0], [1, 5], [2, 0], [3, 5], [4, 0], [20, 0]], 3], [[0, 0], [1, 5], [2, 0], [3, 5], [4, 0], [20, 0]])], [('control #6', [[[0, 4], [3, -1], [6, 2], [9, 2], [12, 2]], 3], [[0, 4], [3, -1], [12, 2]]), ('control #8', [[[0, -4], [3, -4], [6, 1], [9, 3], [12, 3], [15, -4]], 1], [[0, -4], [3, -4], [9, 3], [12, 3], [15, -4]]), ('regression #14', [[[0, 0], [10, 0], [14, 3], [20, 0]], 2], [[0, 0], [10, 0], [14, 3], [20, 0]]), ('regression #15', [[[0, 0], [5, 0], [-6, 1], [10, 0]], 2], [[0, 0], [5, 0], [-6, 1], [10, 0]]), ('regression #16', [[[0, 0], [4, 4], [8, 0], [4, -4], [0, 0]], 1], [[0, 0], [4, 4], [8, 0], [4, -4], [0, 0]]), ('regression #17', [[[0, 0], [6, 1], [6, 7], [0, 6], [0, 0]], 2], [[0, 0], [6, 1], [6, 7], [0, 6], [0, 0]]), ('boundary #18', [[[0, 0], [5, 2], [10, 0]], 2], [[0, 0], [10, 0]]), ('boundary #19', [[[0, 0], [5, 3], [10, 0]], 2], [[0, 0], [5, 3], [10, 0]])]]
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 fixtureActualExpectedOutcome
control #0[[0, 0], [12, 1], [15, 4], [18, 1], [21, -2], [24, 1]][[0, 0], [6, -1], [15, 4], [21, -2], [24, 1]]Failed
control #1[[0, 3], [3, -4], [6, 1], [9, 3], [12, -4], [15, 1], [18, -1]][[0, 3], [3, -4], [9, 3], [12, -4], [15, 1], [18, -1]]Failed
control #2[[0, -4], [9, -1], [12, 2], [15, 1], [18, 1]][[0, -4], [3, 3], [6, -2], [9, -1], [12, 2], [15, 1], [18, 1]]Failed
control #3[[0, -3], [9, -2]][[0, -3], [9, -2]]Passed
control #4[[0, -2], [15, 2]][[0, -2], [9, -4], [15, 2]]Failed
control #5[[0, -2], [3, 2], [6, 2], [9, -3], [12, 3], [15, 4], [18, 2], [21, -2]][[0, -2], [3, 2], [6, 2], [9, -3], [12, 3], [15, 4], [18, 2], [21, -2]]Passed
control #8[[0, -4], [9, 3], [12, 3], [15, -4]][[0, -4], [3, -4], [9, 3], [12, 3], [15, -4]]Failed
control #10[[0, -4], [9, 1]][[0, -4], [9, 1]]Passed

SHA-256 / 0130466c25422e13b37c4d12f74af826fe65a2c32e36b031b15756f315fc3176

3 / The verified repair

Exit 0
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    pts, tol = x
    def dist(p, a, b):
        dx, dy = b[0] - a[0], b[1] - a[1]
        if dx == 0 and dy == 0:
            return math.hypot(p[0] - a[0], p[1] - a[1])
        t = ((p[0] - a[0]) * dx + (p[1] - a[1]) * dy) / (dx * dx + dy * dy)
        t = max(0.0, min(1.0, t))
        return math.hypot(p[0] - a[0] - t * dx, p[1] - a[1] - t * dy)
    keep = [False] * len(pts)
    keep[0] = keep[-1] = True
    stack = [(0, len(pts) - 1)]
    while stack:
        i, j = stack.pop()
        best, idx = -1.0, -1
        for k in range(i + 1, j):
            d = dist(pts[k], pts[i], pts[j])
            if d > best:
                best, idx = d, k
        if idx != -1 and best > tol:
            keep[idx] = True
            stack.append((i, idx))
            stack.append((idx, j))
    return [p for p, f in zip(pts, keep) if f]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('control #0', [[[0, 0], [3, 1], [6, -1], [9, 1], [12, 1], [15, 4], [18, 1], [21, -2], [24, 1]], 2], [[0, 0], [6, -1], [15, 4], [21, -2], [24, 1]]), ('control #1', [[[0, 3], [3, -4], [6, 1], [9, 3], [12, -4], [15, 1], [18, -1]], 1], [[0, 3], [3, -4], [9, 3], [12, -4], [15, 1], [18, -1]]), ('control #2', [[[0, -4], [3, 3], [6, -2], [9, -1], [12, 2], [15, 1], [18, 1]], 0], [[0, -4], [3, 3], [6, -2], [9, -1], [12, 2], [15, 1], [18, 1]]), ('control #3', [[[0, -3], [3, -1], [6, -3], [9, -2]], 3], [[0, -3], [9, -2]]), ('control #4', [[[0, -2], [3, -4], [6, -1], [9, -4], [12, 1], [15, 2]], 3], [[0, -2], [9, -4], [15, 2]]), ('control #5', [[[0, -2], [3, 2], [6, 2], [9, -3], [12, 3], [15, 4], [18, 2], [21, -2]], 0], [[0, -2], [3, 2], [6, 2], [9, -3], [12, 3], [15, 4], [18, 2], [21, -2]]), ('control #8', [[[0, -4], [3, -4], [6, 1], [9, 3], [12, 3], [15, -4]], 1], [[0, -4], [3, -4], [9, 3], [12, 3], [15, -4]]), ('control #10', [[[0, -4], [3, -2], [6, 1], [9, 1]], 2], [[0, -4], [9, 1]])], [('control #1', [[[0, 3], [3, -4], [6, 1], [9, 3], [12, -4], [15, 1], [18, -1]], 1], [[0, 3], [3, -4], [9, 3], [12, -4], [15, 1], [18, -1]]), ('control #4', [[[0, -2], [3, -4], [6, -1], [9, -4], [12, 1], [15, 2]], 3], [[0, -2], [9, -4], [15, 2]]), ('control #5', [[[0, -2], [3, 2], [6, 2], [9, -3], [12, 3], [15, 4], [18, 2], [21, -2]], 0], [[0, -2], [3, 2], [6, 2], [9, -3], [12, 3], [15, 4], [18, 2], [21, -2]]), ('control #6', [[[0, 4], [3, -1], [6, 2], [9, 2], [12, 2]], 3], [[0, 4], [3, -1], [12, 2]]), ('control #7', [[[0, -4], [3, 0], [6, -3], [9, 1], [12, 1], [15, 3]], 2], [[0, -4], [3, 0], [6, -3], [15, 3]]), ('control #10', [[[0, -4], [3, -2], [6, 1], [9, 1]], 2], [[0, -4], [9, 1]]), ('control #12', [[[0, 2], [3, -3], [6, 3], [9, -1]], 1], [[0, 2], [3, -3], [6, 3], [9, -1]]), ('regression #21', [[[0, 0], [2, 1], [4, 3], [6, 3], [8, 1], [10, 0]], 1], [[0, 0], [4, 3], [10, 0]])], [('control #2', [[[0, -4], [3, 3], [6, -2], [9, -1], [12, 2], [15, 1], [18, 1]], 0], [[0, -4], [3, 3], [6, -2], [9, -1], [12, 2], [15, 1], [18, 1]]), ('control #7', [[[0, -4], [3, 0], [6, -3], [9, 1], [12, 1], [15, 3]], 2], [[0, -4], [3, 0], [6, -3], [15, 3]]), ('control #8', [[[0, -4], [3, -4], [6, 1], [9, 3], [12, 3], [15, -4]], 1], [[0, -4], [3, -4], [9, 3], [12, 3], [15, -4]]), ('control #9', [[[0, -3], [3, 4], [6, 0], [9, -4], [12, 0], [15, -1], [18, 4]], 0], [[0, -3], [3, 4], [9, -4], [12, 0], [15, -1], [18, 4]]), ('control #10', [[[0, -4], [3, -2], [6, 1], [9, 1]], 2], [[0, -4], [9, 1]]), ('control #12', [[[0, 2], [3, -3], [6, 3], [9, -1]], 1], [[0, 2], [3, -3], [6, 3], [9, -1]]), ('regression #14', [[[0, 0], [10, 0], [14, 3], [20, 0]], 2], [[0, 0], [10, 0], [14, 3], [20, 0]]), ('regression #22', [[[0, 0], [3, 3], [6, 0], [9, 3], [12, 0]], 2], [[0, 0], [3, 3], [12, 0]])], [('control #4', [[[0, -2], [3, -4], [6, -1], [9, -4], [12, 1], [15, 2]], 3], [[0, -2], [9, -4], [15, 2]]), ('control #10', [[[0, -4], [3, -2], [6, 1], [9, 1]], 2], [[0, -4], [9, 1]]), ('control #11', [[[0, 4], [3, -3], [6, -2], [9, -4], [12, 4], [15, 4], [18, -1]], 2], [[0, 4], [3, -3], [9, -4], [12, 4], [18, -1]]), ('control #12', [[[0, 2], [3, -3], [6, 3], [9, -1]], 1], [[0, 2], [3, -3], [6, 3], [9, -1]]), ('control #13', [[[0, 4], [3, -1], [6, -4], [9, -2], [12, 4], [15, -3], [18, -1], [21, 0]], 3], [[0, 4], [6, -4], [12, 4], [15, -3], [21, 0]]), ('regression #14', [[[0, 0], [10, 0], [14, 3], [20, 0]], 2], [[0, 0], [10, 0], [14, 3], [20, 0]]), ('regression #15', [[[0, 0], [5, 0], [-6, 1], [10, 0]], 2], [[0, 0], [5, 0], [-6, 1], [10, 0]]), ('regression #24', [[[0, 0], [1, 5], [2, 0], [3, 5], [4, 0], [20, 0]], 3], [[0, 0], [1, 5], [2, 0], [3, 5], [4, 0], [20, 0]])], [('control #6', [[[0, 4], [3, -1], [6, 2], [9, 2], [12, 2]], 3], [[0, 4], [3, -1], [12, 2]]), ('control #8', [[[0, -4], [3, -4], [6, 1], [9, 3], [12, 3], [15, -4]], 1], [[0, -4], [3, -4], [9, 3], [12, 3], [15, -4]]), ('regression #14', [[[0, 0], [10, 0], [14, 3], [20, 0]], 2], [[0, 0], [10, 0], [14, 3], [20, 0]]), ('regression #15', [[[0, 0], [5, 0], [-6, 1], [10, 0]], 2], [[0, 0], [5, 0], [-6, 1], [10, 0]]), ('regression #16', [[[0, 0], [4, 4], [8, 0], [4, -4], [0, 0]], 1], [[0, 0], [4, 4], [8, 0], [4, -4], [0, 0]]), ('regression #17', [[[0, 0], [6, 1], [6, 7], [0, 6], [0, 0]], 2], [[0, 0], [6, 1], [6, 7], [0, 6], [0, 0]]), ('boundary #18', [[[0, 0], [5, 2], [10, 0]], 2], [[0, 0], [10, 0]]), ('boundary #19', [[[0, 0], [5, 3], [10, 0]], 2], [[0, 0], [5, 3], [10, 0]])]]
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 fixtureActualExpectedOutcome
control #0[[0, 0], [6, -1], [15, 4], [21, -2], [24, 1]][[0, 0], [6, -1], [15, 4], [21, -2], [24, 1]]Passed
control #1[[0, 3], [3, -4], [9, 3], [12, -4], [15, 1], [18, -1]][[0, 3], [3, -4], [9, 3], [12, -4], [15, 1], [18, -1]]Passed
control #2[[0, -4], [3, 3], [6, -2], [9, -1], [12, 2], [15, 1], [18, 1]][[0, -4], [3, 3], [6, -2], [9, -1], [12, 2], [15, 1], [18, 1]]Passed
control #3[[0, -3], [9, -2]][[0, -3], [9, -2]]Passed
control #4[[0, -2], [9, -4], [15, 2]][[0, -2], [9, -4], [15, 2]]Passed
control #5[[0, -2], [3, 2], [6, 2], [9, -3], [12, 3], [15, 4], [18, 2], [21, -2]][[0, -2], [3, 2], [6, 2], [9, -3], [12, 3], [15, 4], [18, 2], [21, -2]]Passed
control #8[[0, -4], [3, -4], [9, 3], [12, 3], [15, -4]][[0, -4], [3, -4], [9, 3], [12, 3], [15, -4]]Passed
control #10[[0, -4], [9, 1]][[0, -4], [9, 1]]Passed

SHA-256 / 5828769e3c4f93578d343d3c15e2e3b03f05b30c1171c83c6b2e98970d691baa

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 2026-09-29T14:48:22.318019+00:00.

Case digest / a623e0670bdcd497b3e9d5c8b32f6502630d0fbd88482e851338f5196e491d41