FA-70586 / GIS polygon topology / Open access
Douglas-Peucker simplification of a topology arc: segment projection clamp · case 01
Vertices that overshoot the end of the base segment are dropped as if they lay on it.
ROOT CAUSE
Distance is measured to the infinite line rather than the segment.
VERIFIED REPAIR
At the segment projection clamp step restore `t = max(0.0, min(1.0, t))`, leaving the rest of the model unchanged.
Unsuccessful approach: Clamping only the lower end still measures overshoot beyond the far endpoint to the line.
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 = 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]]), ('regression #15', [[[0, 0], [5, 0], [-6, 1], [10, 0]], 2], [[0, 0], [5, 0], [-6, 1], [10, 0]]), ('regression #25', [[[0, 0], [14, 1], [10, 0]], 2], [[0, 0], [14, 1], [10, 0]])], [('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 #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 #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 #25', [[[0, 0], [14, 1], [10, 0]], 2], [[0, 0], [14, 1], [10, 0]]), ('regression #26', [[[0, 0], [5, 1], [17, 2], [12, 0]], 2], [[0, 0], [17, 2], [12, 0]])], [('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 #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 #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]]), ('regression #25', [[[0, 0], [14, 1], [10, 0]], 2], [[0, 0], [14, 1], [10, 0]]), ('regression #26', [[[0, 0], [5, 1], [17, 2], [12, 0]], 2], [[0, 0], [17, 2], [12, 0]])], [('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 #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 #26', [[[0, 0], [5, 1], [17, 2], [12, 0]], 2], [[0, 0], [17, 2], [12, 0]])], [('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 #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]]), ('regression #25', [[[0, 0], [14, 1], [10, 0]], 2], [[0, 0], [14, 1], [10, 0]]), ('regression #26', [[[0, 0], [5, 1], [17, 2], [12, 0]], 2], [[0, 0], [17, 2], [12, 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 fixture | Actual | Expected | Outcome |
|---|---|---|---|
| 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 |
| regression #15 | [[0, 0], [10, 0]] | [[0, 0], [5, 0], [-6, 1], [10, 0]] | Failed |
| regression #25 | [[0, 0], [10, 0]] | [[0, 0], [14, 1], [10, 0]] | Failed |
SHA-256 / 9a3a1692a149de1f8d7c1403b1c341b4af429f26261e849a7c626022d16bc051
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, 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]]), ('regression #15', [[[0, 0], [5, 0], [-6, 1], [10, 0]], 2], [[0, 0], [5, 0], [-6, 1], [10, 0]]), ('regression #25', [[[0, 0], [14, 1], [10, 0]], 2], [[0, 0], [14, 1], [10, 0]])], [('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 #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 #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 #25', [[[0, 0], [14, 1], [10, 0]], 2], [[0, 0], [14, 1], [10, 0]]), ('regression #26', [[[0, 0], [5, 1], [17, 2], [12, 0]], 2], [[0, 0], [17, 2], [12, 0]])], [('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 #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 #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]]), ('regression #25', [[[0, 0], [14, 1], [10, 0]], 2], [[0, 0], [14, 1], [10, 0]]), ('regression #26', [[[0, 0], [5, 1], [17, 2], [12, 0]], 2], [[0, 0], [17, 2], [12, 0]])], [('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 #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 #26', [[[0, 0], [5, 1], [17, 2], [12, 0]], 2], [[0, 0], [17, 2], [12, 0]])], [('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 #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]]), ('regression #25', [[[0, 0], [14, 1], [10, 0]], 2], [[0, 0], [14, 1], [10, 0]]), ('regression #26', [[[0, 0], [5, 1], [17, 2], [12, 0]], 2], [[0, 0], [17, 2], [12, 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 fixture | Actual | Expected | Outcome |
|---|---|---|---|
| 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 |
| regression #15 | [[0, 0], [5, 0], [-6, 1], [10, 0]] | [[0, 0], [5, 0], [-6, 1], [10, 0]] | Passed |
| regression #25 | [[0, 0], [10, 0]] | [[0, 0], [14, 1], [10, 0]] | Failed |
SHA-256 / 106c9bd6744c2af8674e7a2eba52ee6ade028895e63fd392d9906677315d8dac
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]]), ('regression #15', [[[0, 0], [5, 0], [-6, 1], [10, 0]], 2], [[0, 0], [5, 0], [-6, 1], [10, 0]]), ('regression #25', [[[0, 0], [14, 1], [10, 0]], 2], [[0, 0], [14, 1], [10, 0]])], [('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 #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 #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 #25', [[[0, 0], [14, 1], [10, 0]], 2], [[0, 0], [14, 1], [10, 0]]), ('regression #26', [[[0, 0], [5, 1], [17, 2], [12, 0]], 2], [[0, 0], [17, 2], [12, 0]])], [('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 #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 #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]]), ('regression #25', [[[0, 0], [14, 1], [10, 0]], 2], [[0, 0], [14, 1], [10, 0]]), ('regression #26', [[[0, 0], [5, 1], [17, 2], [12, 0]], 2], [[0, 0], [17, 2], [12, 0]])], [('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 #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 #26', [[[0, 0], [5, 1], [17, 2], [12, 0]], 2], [[0, 0], [17, 2], [12, 0]])], [('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 #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]]), ('regression #25', [[[0, 0], [14, 1], [10, 0]], 2], [[0, 0], [14, 1], [10, 0]]), ('regression #26', [[[0, 0], [5, 1], [17, 2], [12, 0]], 2], [[0, 0], [17, 2], [12, 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 fixture | Actual | Expected | Outcome |
|---|---|---|---|
| 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 |
| regression #15 | [[0, 0], [5, 0], [-6, 1], [10, 0]] | [[0, 0], [5, 0], [-6, 1], [10, 0]] | Passed |
| regression #25 | [[0, 0], [14, 1], [10, 0]] | [[0, 0], [14, 1], [10, 0]] | Passed |
SHA-256 / e576a23dd28aa833d6a1d5673f07348d2e8550a9705f654d2455b8251c416a1c
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 2026-09-29T14:48:22.061017+00:00.
Case digest / 75174801414695025678f9e5204321ed3630a934f4c29adb9479dc2166365fe4