FA-50906 / Raster clipping / Open access
Clip mask morphology: gradient union · case 01
Morphological clip gradient retains the eroded interior.
ROOT CAUSE
Morphological clip gradient retains the eroded interior.
VERIFIED REPAIR
Apply the documented state transition at gradient union. A binary sample mask supports dilation/erosion by an explicit signed structuring element. Out-of-target samples are uncovered; empty structuring elements yield empty output. Open erodes then dilates; close dilates then erodes. Gradient is dilated minus eroded; boundary is original minus eroded; exterior boundary is dilated minus original. Iterations use complete prior masks.
Unsuccessful approach: Subtracting the source omits the inner half of the morphological gradient.
Case contract
A binary sample mask supports dilation/erosion by an explicit signed structuring element. Out-of-target samples are uncovered; empty structuring elements yield empty output. Open erodes then dilates; close dilates then erodes. Gradient is dilated minus eroded; boundary is original minus eroded; exterior boundary is dilated minus original. Iterations use complete prior masks.
Why this case matters
Raster clip state can leak coverage across draws even when every individual region is valid.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(commands, size):
full=set(range(size))
out=[]
for cmd in commands:
source,kernel,mode,iterations=cmd
source=set(source)&full
kernel=set(kernel)
def dilate(s): return {x for x in full if any(x-k in s for k in kernel)}
def erode(s): return {x for x in full if kernel and all(x+k in s for k in kernel)}
result=set(source)
for _ in range(max(0,iterations)):
prior=set(result)
if mode=='dilate': result=dilate(prior)
elif mode=='erode': result=erode(prior)
elif mode=='open': result=dilate(erode(prior))
elif mode=='close': result=erode(dilate(prior))
elif mode=='gradient': result=dilate(prior)|erode(prior)
elif mode=='inner': result=prior-erode(prior)
else: result=dilate(prior)-prior
out.append(sorted(result))
return out
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
if N == 1:
check('explicit sequence 0', solve([[[1], [0, 1], 'dilate', 1]], 4), [[1, 2]])
check('explicit sequence 1', solve([[[0, 1, 2, 3, 4, 5, 6, 7], [-1, 0, 1], 'erode', 1]], 4), [[1, 2]])
check('explicit sequence 2', solve([[[1], [], 'erode', 1]], 4), [[]])
check('explicit sequence 3', solve([[[1], [0, 1], 'open', 1]], 4), [[]])
check('explicit sequence 4', solve([[[0, 2], [0, 1], 'close', 1]], 4), [[0, 1, 2]])
check('explicit sequence 5', solve([[[0, 1, 2], [0, 1], 'gradient', 1]], 4), [[2, 3]])
check('explicit sequence 6', solve([[[0, 1, 2], [0, 1], 'inner', 1]], 4), [[2]])
check('explicit sequence 7', solve([[[1], [0, 1], 'outer', 1]], 4), [[2]])
check('explicit sequence 8', solve([[[0], [0, 1], 'dilate', 2]], 4), [[0, 1, 2]])
check('explicit sequence 9', solve([[[1], [0, 1], 'dilate', 0]], 4), [[1]])
check('explicit sequence 10', solve([[[2], [-1, 0], 'dilate', 1]], 4), [[1, 2]])
check('explicit sequence 11', solve([[[0, 1, 2], [0, 1], 'open', 1]], 4), [[0, 1, 2]])
if N == 2:
check('explicit sequence 0', solve([[[1], [0, 1], 'dilate', 1]], 5), [[1, 2]])
check('explicit sequence 1', solve([[[0, 1, 2, 3, 4, 5, 6, 7], [-1, 0, 1], 'erode', 1]], 5), [[1, 2, 3]])
check('explicit sequence 2', solve([[[1], [], 'erode', 1]], 5), [[]])
check('explicit sequence 3', solve([[[1], [0, 1], 'open', 1]], 5), [[]])
check('explicit sequence 4', solve([[[0, 2], [0, 1], 'close', 1]], 5), [[0, 1, 2]])
check('explicit sequence 5', solve([[[0, 1, 2], [0, 1], 'gradient', 1]], 5), [[2, 3]])
check('explicit sequence 6', solve([[[0, 1, 2], [0, 1], 'inner', 1]], 5), [[2]])
check('explicit sequence 7', solve([[[1], [0, 1], 'outer', 1]], 5), [[2]])
check('explicit sequence 8', solve([[[0], [0, 1], 'dilate', 2]], 5), [[0, 1, 2]])
check('explicit sequence 9', solve([[[1], [0, 1], 'dilate', 0]], 5), [[1]])
check('explicit sequence 10', solve([[[2], [-1, 0], 'dilate', 1]], 5), [[1, 2]])
check('explicit sequence 11', solve([[[0, 1, 2], [0, 1], 'open', 1]], 5), [[0, 1, 2]])
if N == 3:
check('explicit sequence 0', solve([[[1], [0, 1], 'dilate', 1]], 6), [[1, 2]])
check('explicit sequence 1', solve([[[0, 1, 2, 3, 4, 5, 6, 7], [-1, 0, 1], 'erode', 1]], 6), [[1, 2, 3, 4]])
check('explicit sequence 2', solve([[[1], [], 'erode', 1]], 6), [[]])
check('explicit sequence 3', solve([[[1], [0, 1], 'open', 1]], 6), [[]])
check('explicit sequence 4', solve([[[0, 2], [0, 1], 'close', 1]], 6), [[0, 1, 2]])
check('explicit sequence 5', solve([[[0, 1, 2], [0, 1], 'gradient', 1]], 6), [[2, 3]])
check('explicit sequence 6', solve([[[0, 1, 2], [0, 1], 'inner', 1]], 6), [[2]])
check('explicit sequence 7', solve([[[1], [0, 1], 'outer', 1]], 6), [[2]])
check('explicit sequence 8', solve([[[0], [0, 1], 'dilate', 2]], 6), [[0, 1, 2]])
check('explicit sequence 9', solve([[[1], [0, 1], 'dilate', 0]], 6), [[1]])
check('explicit sequence 10', solve([[[2], [-1, 0], 'dilate', 1]], 6), [[1, 2]])
check('explicit sequence 11', solve([[[0, 1, 2], [0, 1], 'open', 1]], 6), [[0, 1, 2]])
if N == 4:
check('explicit sequence 0', solve([[[1], [0, 1], 'dilate', 1]], 7), [[1, 2]])
check('explicit sequence 1', solve([[[0, 1, 2, 3, 4, 5, 6, 7], [-1, 0, 1], 'erode', 1]], 7), [[1, 2, 3, 4, 5]])
check('explicit sequence 2', solve([[[1], [], 'erode', 1]], 7), [[]])
check('explicit sequence 3', solve([[[1], [0, 1], 'open', 1]], 7), [[]])
check('explicit sequence 4', solve([[[0, 2], [0, 1], 'close', 1]], 7), [[0, 1, 2]])
check('explicit sequence 5', solve([[[0, 1, 2], [0, 1], 'gradient', 1]], 7), [[2, 3]])
check('explicit sequence 6', solve([[[0, 1, 2], [0, 1], 'inner', 1]], 7), [[2]])
check('explicit sequence 7', solve([[[1], [0, 1], 'outer', 1]], 7), [[2]])
check('explicit sequence 8', solve([[[0], [0, 1], 'dilate', 2]], 7), [[0, 1, 2]])
check('explicit sequence 9', solve([[[1], [0, 1], 'dilate', 0]], 7), [[1]])
check('explicit sequence 10', solve([[[2], [-1, 0], 'dilate', 1]], 7), [[1, 2]])
check('explicit sequence 11', solve([[[0, 1, 2], [0, 1], 'open', 1]], 7), [[0, 1, 2]])
if N == 5:
check('explicit sequence 0', solve([[[1], [0, 1], 'dilate', 1]], 8), [[1, 2]])
check('explicit sequence 1', solve([[[0, 1, 2, 3, 4, 5, 6, 7], [-1, 0, 1], 'erode', 1]], 8), [[1, 2, 3, 4, 5, 6]])
check('explicit sequence 2', solve([[[1], [], 'erode', 1]], 8), [[]])
check('explicit sequence 3', solve([[[1], [0, 1], 'open', 1]], 8), [[]])
check('explicit sequence 4', solve([[[0, 2], [0, 1], 'close', 1]], 8), [[0, 1, 2]])
check('explicit sequence 5', solve([[[0, 1, 2], [0, 1], 'gradient', 1]], 8), [[2, 3]])
check('explicit sequence 6', solve([[[0, 1, 2], [0, 1], 'inner', 1]], 8), [[2]])
check('explicit sequence 7', solve([[[1], [0, 1], 'outer', 1]], 8), [[2]])
check('explicit sequence 8', solve([[[0], [0, 1], 'dilate', 2]], 8), [[0, 1, 2]])
check('explicit sequence 9', solve([[[1], [0, 1], 'dilate', 0]], 8), [[1]])
check('explicit sequence 10', solve([[[2], [-1, 0], 'dilate', 1]], 8), [[1, 2]])
check('explicit sequence 11', solve([[[0, 1, 2], [0, 1], 'open', 1]], 8), [[0, 1, 2]])
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 |
|---|---|---|---|
| explicit sequence 0 | [[1, 2]] | [[1, 2]] | Passed |
| explicit sequence 1 | [[1, 2]] | [[1, 2]] | Passed |
| explicit sequence 2 | [[]] | [[]] | Passed |
| explicit sequence 3 | [[]] | [[]] | Passed |
| explicit sequence 4 | [[0, 1, 2]] | [[0, 1, 2]] | Passed |
| explicit sequence 5 | [[0, 1, 2, 3]] | [[2, 3]] | Failed |
| explicit sequence 6 | [[2]] | [[2]] | Passed |
| explicit sequence 7 | [[2]] | [[2]] | Passed |
| explicit sequence 8 | [[0, 1, 2]] | [[0, 1, 2]] | Passed |
| explicit sequence 9 | [[1]] | [[1]] | Passed |
| explicit sequence 10 | [[1, 2]] | [[1, 2]] | Passed |
| explicit sequence 11 | [[0, 1, 2]] | [[0, 1, 2]] | Passed |
SHA-256 / 27ce4d5ac90277558c89d027455c9530ece6f86abda40d11fbc244dedf7adb80
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(commands, size):
full=set(range(size))
out=[]
for cmd in commands:
source,kernel,mode,iterations=cmd
source=set(source)&full
kernel=set(kernel)
def dilate(s): return {x for x in full if any(x-k in s for k in kernel)}
def erode(s): return {x for x in full if kernel and all(x+k in s for k in kernel)}
result=set(source)
for _ in range(max(0,iterations)):
prior=set(result)
if mode=='dilate': result=dilate(prior)
elif mode=='erode': result=erode(prior)
elif mode=='open': result=dilate(erode(prior))
elif mode=='close': result=erode(dilate(prior))
elif mode=='gradient': result=dilate(prior)-prior
elif mode=='inner': result=prior-erode(prior)
else: result=dilate(prior)-prior
out.append(sorted(result))
return out
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
if N == 1:
check('explicit sequence 0', solve([[[1], [0, 1], 'dilate', 1]], 4), [[1, 2]])
check('explicit sequence 1', solve([[[0, 1, 2, 3, 4, 5, 6, 7], [-1, 0, 1], 'erode', 1]], 4), [[1, 2]])
check('explicit sequence 2', solve([[[1], [], 'erode', 1]], 4), [[]])
check('explicit sequence 3', solve([[[1], [0, 1], 'open', 1]], 4), [[]])
check('explicit sequence 4', solve([[[0, 2], [0, 1], 'close', 1]], 4), [[0, 1, 2]])
check('explicit sequence 5', solve([[[0, 1, 2], [0, 1], 'gradient', 1]], 4), [[2, 3]])
check('explicit sequence 6', solve([[[0, 1, 2], [0, 1], 'inner', 1]], 4), [[2]])
check('explicit sequence 7', solve([[[1], [0, 1], 'outer', 1]], 4), [[2]])
check('explicit sequence 8', solve([[[0], [0, 1], 'dilate', 2]], 4), [[0, 1, 2]])
check('explicit sequence 9', solve([[[1], [0, 1], 'dilate', 0]], 4), [[1]])
check('explicit sequence 10', solve([[[2], [-1, 0], 'dilate', 1]], 4), [[1, 2]])
check('explicit sequence 11', solve([[[0, 1, 2], [0, 1], 'open', 1]], 4), [[0, 1, 2]])
if N == 2:
check('explicit sequence 0', solve([[[1], [0, 1], 'dilate', 1]], 5), [[1, 2]])
check('explicit sequence 1', solve([[[0, 1, 2, 3, 4, 5, 6, 7], [-1, 0, 1], 'erode', 1]], 5), [[1, 2, 3]])
check('explicit sequence 2', solve([[[1], [], 'erode', 1]], 5), [[]])
check('explicit sequence 3', solve([[[1], [0, 1], 'open', 1]], 5), [[]])
check('explicit sequence 4', solve([[[0, 2], [0, 1], 'close', 1]], 5), [[0, 1, 2]])
check('explicit sequence 5', solve([[[0, 1, 2], [0, 1], 'gradient', 1]], 5), [[2, 3]])
check('explicit sequence 6', solve([[[0, 1, 2], [0, 1], 'inner', 1]], 5), [[2]])
check('explicit sequence 7', solve([[[1], [0, 1], 'outer', 1]], 5), [[2]])
check('explicit sequence 8', solve([[[0], [0, 1], 'dilate', 2]], 5), [[0, 1, 2]])
check('explicit sequence 9', solve([[[1], [0, 1], 'dilate', 0]], 5), [[1]])
check('explicit sequence 10', solve([[[2], [-1, 0], 'dilate', 1]], 5), [[1, 2]])
check('explicit sequence 11', solve([[[0, 1, 2], [0, 1], 'open', 1]], 5), [[0, 1, 2]])
if N == 3:
check('explicit sequence 0', solve([[[1], [0, 1], 'dilate', 1]], 6), [[1, 2]])
check('explicit sequence 1', solve([[[0, 1, 2, 3, 4, 5, 6, 7], [-1, 0, 1], 'erode', 1]], 6), [[1, 2, 3, 4]])
check('explicit sequence 2', solve([[[1], [], 'erode', 1]], 6), [[]])
check('explicit sequence 3', solve([[[1], [0, 1], 'open', 1]], 6), [[]])
check('explicit sequence 4', solve([[[0, 2], [0, 1], 'close', 1]], 6), [[0, 1, 2]])
check('explicit sequence 5', solve([[[0, 1, 2], [0, 1], 'gradient', 1]], 6), [[2, 3]])
check('explicit sequence 6', solve([[[0, 1, 2], [0, 1], 'inner', 1]], 6), [[2]])
check('explicit sequence 7', solve([[[1], [0, 1], 'outer', 1]], 6), [[2]])
check('explicit sequence 8', solve([[[0], [0, 1], 'dilate', 2]], 6), [[0, 1, 2]])
check('explicit sequence 9', solve([[[1], [0, 1], 'dilate', 0]], 6), [[1]])
check('explicit sequence 10', solve([[[2], [-1, 0], 'dilate', 1]], 6), [[1, 2]])
check('explicit sequence 11', solve([[[0, 1, 2], [0, 1], 'open', 1]], 6), [[0, 1, 2]])
if N == 4:
check('explicit sequence 0', solve([[[1], [0, 1], 'dilate', 1]], 7), [[1, 2]])
check('explicit sequence 1', solve([[[0, 1, 2, 3, 4, 5, 6, 7], [-1, 0, 1], 'erode', 1]], 7), [[1, 2, 3, 4, 5]])
check('explicit sequence 2', solve([[[1], [], 'erode', 1]], 7), [[]])
check('explicit sequence 3', solve([[[1], [0, 1], 'open', 1]], 7), [[]])
check('explicit sequence 4', solve([[[0, 2], [0, 1], 'close', 1]], 7), [[0, 1, 2]])
check('explicit sequence 5', solve([[[0, 1, 2], [0, 1], 'gradient', 1]], 7), [[2, 3]])
check('explicit sequence 6', solve([[[0, 1, 2], [0, 1], 'inner', 1]], 7), [[2]])
check('explicit sequence 7', solve([[[1], [0, 1], 'outer', 1]], 7), [[2]])
check('explicit sequence 8', solve([[[0], [0, 1], 'dilate', 2]], 7), [[0, 1, 2]])
check('explicit sequence 9', solve([[[1], [0, 1], 'dilate', 0]], 7), [[1]])
check('explicit sequence 10', solve([[[2], [-1, 0], 'dilate', 1]], 7), [[1, 2]])
check('explicit sequence 11', solve([[[0, 1, 2], [0, 1], 'open', 1]], 7), [[0, 1, 2]])
if N == 5:
check('explicit sequence 0', solve([[[1], [0, 1], 'dilate', 1]], 8), [[1, 2]])
check('explicit sequence 1', solve([[[0, 1, 2, 3, 4, 5, 6, 7], [-1, 0, 1], 'erode', 1]], 8), [[1, 2, 3, 4, 5, 6]])
check('explicit sequence 2', solve([[[1], [], 'erode', 1]], 8), [[]])
check('explicit sequence 3', solve([[[1], [0, 1], 'open', 1]], 8), [[]])
check('explicit sequence 4', solve([[[0, 2], [0, 1], 'close', 1]], 8), [[0, 1, 2]])
check('explicit sequence 5', solve([[[0, 1, 2], [0, 1], 'gradient', 1]], 8), [[2, 3]])
check('explicit sequence 6', solve([[[0, 1, 2], [0, 1], 'inner', 1]], 8), [[2]])
check('explicit sequence 7', solve([[[1], [0, 1], 'outer', 1]], 8), [[2]])
check('explicit sequence 8', solve([[[0], [0, 1], 'dilate', 2]], 8), [[0, 1, 2]])
check('explicit sequence 9', solve([[[1], [0, 1], 'dilate', 0]], 8), [[1]])
check('explicit sequence 10', solve([[[2], [-1, 0], 'dilate', 1]], 8), [[1, 2]])
check('explicit sequence 11', solve([[[0, 1, 2], [0, 1], 'open', 1]], 8), [[0, 1, 2]])
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 |
|---|---|---|---|
| explicit sequence 0 | [[1, 2]] | [[1, 2]] | Passed |
| explicit sequence 1 | [[1, 2]] | [[1, 2]] | Passed |
| explicit sequence 2 | [[]] | [[]] | Passed |
| explicit sequence 3 | [[]] | [[]] | Passed |
| explicit sequence 4 | [[0, 1, 2]] | [[0, 1, 2]] | Passed |
| explicit sequence 5 | [[3]] | [[2, 3]] | Failed |
| explicit sequence 6 | [[2]] | [[2]] | Passed |
| explicit sequence 7 | [[2]] | [[2]] | Passed |
| explicit sequence 8 | [[0, 1, 2]] | [[0, 1, 2]] | Passed |
| explicit sequence 9 | [[1]] | [[1]] | Passed |
| explicit sequence 10 | [[1, 2]] | [[1, 2]] | Passed |
| explicit sequence 11 | [[0, 1, 2]] | [[0, 1, 2]] | Passed |
SHA-256 / 28d3290922f28c27d8c87e41cff73d5aaed533772345b21024e02eb700fa3ab7
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(commands, size):
full=set(range(size))
out=[]
for cmd in commands:
source,kernel,mode,iterations=cmd
source=set(source)&full
kernel=set(kernel)
def dilate(s): return {x for x in full if any(x-k in s for k in kernel)}
def erode(s): return {x for x in full if kernel and all(x+k in s for k in kernel)}
result=set(source)
for _ in range(max(0,iterations)):
prior=set(result)
if mode=='dilate': result=dilate(prior)
elif mode=='erode': result=erode(prior)
elif mode=='open': result=dilate(erode(prior))
elif mode=='close': result=erode(dilate(prior))
elif mode=='gradient': result=dilate(prior)-erode(prior)
elif mode=='inner': result=prior-erode(prior)
else: result=dilate(prior)-prior
out.append(sorted(result))
return out
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
if N == 1:
check('explicit sequence 0', solve([[[1], [0, 1], 'dilate', 1]], 4), [[1, 2]])
check('explicit sequence 1', solve([[[0, 1, 2, 3, 4, 5, 6, 7], [-1, 0, 1], 'erode', 1]], 4), [[1, 2]])
check('explicit sequence 2', solve([[[1], [], 'erode', 1]], 4), [[]])
check('explicit sequence 3', solve([[[1], [0, 1], 'open', 1]], 4), [[]])
check('explicit sequence 4', solve([[[0, 2], [0, 1], 'close', 1]], 4), [[0, 1, 2]])
check('explicit sequence 5', solve([[[0, 1, 2], [0, 1], 'gradient', 1]], 4), [[2, 3]])
check('explicit sequence 6', solve([[[0, 1, 2], [0, 1], 'inner', 1]], 4), [[2]])
check('explicit sequence 7', solve([[[1], [0, 1], 'outer', 1]], 4), [[2]])
check('explicit sequence 8', solve([[[0], [0, 1], 'dilate', 2]], 4), [[0, 1, 2]])
check('explicit sequence 9', solve([[[1], [0, 1], 'dilate', 0]], 4), [[1]])
check('explicit sequence 10', solve([[[2], [-1, 0], 'dilate', 1]], 4), [[1, 2]])
check('explicit sequence 11', solve([[[0, 1, 2], [0, 1], 'open', 1]], 4), [[0, 1, 2]])
if N == 2:
check('explicit sequence 0', solve([[[1], [0, 1], 'dilate', 1]], 5), [[1, 2]])
check('explicit sequence 1', solve([[[0, 1, 2, 3, 4, 5, 6, 7], [-1, 0, 1], 'erode', 1]], 5), [[1, 2, 3]])
check('explicit sequence 2', solve([[[1], [], 'erode', 1]], 5), [[]])
check('explicit sequence 3', solve([[[1], [0, 1], 'open', 1]], 5), [[]])
check('explicit sequence 4', solve([[[0, 2], [0, 1], 'close', 1]], 5), [[0, 1, 2]])
check('explicit sequence 5', solve([[[0, 1, 2], [0, 1], 'gradient', 1]], 5), [[2, 3]])
check('explicit sequence 6', solve([[[0, 1, 2], [0, 1], 'inner', 1]], 5), [[2]])
check('explicit sequence 7', solve([[[1], [0, 1], 'outer', 1]], 5), [[2]])
check('explicit sequence 8', solve([[[0], [0, 1], 'dilate', 2]], 5), [[0, 1, 2]])
check('explicit sequence 9', solve([[[1], [0, 1], 'dilate', 0]], 5), [[1]])
check('explicit sequence 10', solve([[[2], [-1, 0], 'dilate', 1]], 5), [[1, 2]])
check('explicit sequence 11', solve([[[0, 1, 2], [0, 1], 'open', 1]], 5), [[0, 1, 2]])
if N == 3:
check('explicit sequence 0', solve([[[1], [0, 1], 'dilate', 1]], 6), [[1, 2]])
check('explicit sequence 1', solve([[[0, 1, 2, 3, 4, 5, 6, 7], [-1, 0, 1], 'erode', 1]], 6), [[1, 2, 3, 4]])
check('explicit sequence 2', solve([[[1], [], 'erode', 1]], 6), [[]])
check('explicit sequence 3', solve([[[1], [0, 1], 'open', 1]], 6), [[]])
check('explicit sequence 4', solve([[[0, 2], [0, 1], 'close', 1]], 6), [[0, 1, 2]])
check('explicit sequence 5', solve([[[0, 1, 2], [0, 1], 'gradient', 1]], 6), [[2, 3]])
check('explicit sequence 6', solve([[[0, 1, 2], [0, 1], 'inner', 1]], 6), [[2]])
check('explicit sequence 7', solve([[[1], [0, 1], 'outer', 1]], 6), [[2]])
check('explicit sequence 8', solve([[[0], [0, 1], 'dilate', 2]], 6), [[0, 1, 2]])
check('explicit sequence 9', solve([[[1], [0, 1], 'dilate', 0]], 6), [[1]])
check('explicit sequence 10', solve([[[2], [-1, 0], 'dilate', 1]], 6), [[1, 2]])
check('explicit sequence 11', solve([[[0, 1, 2], [0, 1], 'open', 1]], 6), [[0, 1, 2]])
if N == 4:
check('explicit sequence 0', solve([[[1], [0, 1], 'dilate', 1]], 7), [[1, 2]])
check('explicit sequence 1', solve([[[0, 1, 2, 3, 4, 5, 6, 7], [-1, 0, 1], 'erode', 1]], 7), [[1, 2, 3, 4, 5]])
check('explicit sequence 2', solve([[[1], [], 'erode', 1]], 7), [[]])
check('explicit sequence 3', solve([[[1], [0, 1], 'open', 1]], 7), [[]])
check('explicit sequence 4', solve([[[0, 2], [0, 1], 'close', 1]], 7), [[0, 1, 2]])
check('explicit sequence 5', solve([[[0, 1, 2], [0, 1], 'gradient', 1]], 7), [[2, 3]])
check('explicit sequence 6', solve([[[0, 1, 2], [0, 1], 'inner', 1]], 7), [[2]])
check('explicit sequence 7', solve([[[1], [0, 1], 'outer', 1]], 7), [[2]])
check('explicit sequence 8', solve([[[0], [0, 1], 'dilate', 2]], 7), [[0, 1, 2]])
check('explicit sequence 9', solve([[[1], [0, 1], 'dilate', 0]], 7), [[1]])
check('explicit sequence 10', solve([[[2], [-1, 0], 'dilate', 1]], 7), [[1, 2]])
check('explicit sequence 11', solve([[[0, 1, 2], [0, 1], 'open', 1]], 7), [[0, 1, 2]])
if N == 5:
check('explicit sequence 0', solve([[[1], [0, 1], 'dilate', 1]], 8), [[1, 2]])
check('explicit sequence 1', solve([[[0, 1, 2, 3, 4, 5, 6, 7], [-1, 0, 1], 'erode', 1]], 8), [[1, 2, 3, 4, 5, 6]])
check('explicit sequence 2', solve([[[1], [], 'erode', 1]], 8), [[]])
check('explicit sequence 3', solve([[[1], [0, 1], 'open', 1]], 8), [[]])
check('explicit sequence 4', solve([[[0, 2], [0, 1], 'close', 1]], 8), [[0, 1, 2]])
check('explicit sequence 5', solve([[[0, 1, 2], [0, 1], 'gradient', 1]], 8), [[2, 3]])
check('explicit sequence 6', solve([[[0, 1, 2], [0, 1], 'inner', 1]], 8), [[2]])
check('explicit sequence 7', solve([[[1], [0, 1], 'outer', 1]], 8), [[2]])
check('explicit sequence 8', solve([[[0], [0, 1], 'dilate', 2]], 8), [[0, 1, 2]])
check('explicit sequence 9', solve([[[1], [0, 1], 'dilate', 0]], 8), [[1]])
check('explicit sequence 10', solve([[[2], [-1, 0], 'dilate', 1]], 8), [[1, 2]])
check('explicit sequence 11', solve([[[0, 1, 2], [0, 1], 'open', 1]], 8), [[0, 1, 2]])
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 |
|---|---|---|---|
| explicit sequence 0 | [[1, 2]] | [[1, 2]] | Passed |
| explicit sequence 1 | [[1, 2]] | [[1, 2]] | Passed |
| explicit sequence 2 | [[]] | [[]] | Passed |
| explicit sequence 3 | [[]] | [[]] | Passed |
| explicit sequence 4 | [[0, 1, 2]] | [[0, 1, 2]] | Passed |
| explicit sequence 5 | [[2, 3]] | [[2, 3]] | Passed |
| explicit sequence 6 | [[2]] | [[2]] | Passed |
| explicit sequence 7 | [[2]] | [[2]] | Passed |
| explicit sequence 8 | [[0, 1, 2]] | [[0, 1, 2]] | Passed |
| explicit sequence 9 | [[1]] | [[1]] | Passed |
| explicit sequence 10 | [[1, 2]] | [[1, 2]] | Passed |
| explicit sequence 11 | [[0, 1, 2]] | [[0, 1, 2]] | Passed |
SHA-256 / 8a2613ae3697d095c1bd08bfb42b0127397ecaa5322af6aaa2cd68387f4f6171
Verification & scope
Finite one-dimensional integer sample sets model coverage state only; no geometric intersection, memory layout, GPU or graphics-standard conformance 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 2026-09-29T14:45:13.589320+00:00.
Case digest / 2967fb2f0581f15c29739f351fc0de4da24002d808c235b120a8318e7114051d