FA-70456 / GIS polygon topology / Open access
Bounding box topological relation: within operand completeness · case 01
A box poking out of the top of another is reported as within.
ROOT CAUSE
The within test omits the maxy comparison.
VERIFIED REPAIR
At the within operand completeness step restore `if b[0] <= a[0] and b[1] <= a[1] and b[2] >= a[2] and b[3] >= a[3]:`, leaving the rest of the model unchanged.
Unsuccessful approach: The maxy comparison is back but the miny comparison is now missing.
Case contract
Input [a, b], closed boxes [minx, miny, maxx, maxy] with positive width and height. Return "equals" if identical, else "disjoint" if separated with no shared point, else "contains" if a covers b (shared edges allowed), "within" if b covers a, else "touches" if the boxes share only boundary, else "overlaps".
Why this case matters
Spatial indexes and map tile filters prune candidates with envelope relations before exact geometry tests.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
a, b = x
if a == b:
return 'equals'
if a[2] < b[0] or b[2] < a[0] or a[3] < b[1] or b[3] < a[1]:
return 'disjoint'
if a[0] <= b[0] and a[1] <= b[1] and a[2] >= b[2] and a[3] >= b[3]:
return 'contains'
if b[0] <= a[0] and b[1] <= a[1] and b[2] >= a[2]:
return 'within'
if a[2] == b[0] or b[2] == a[0] or a[3] == b[1] or b[3] == a[1]:
return 'touches'
return 'overlaps'
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('control #0', [[3, 0, 9, 4], [9, 3, 13, 11]], 'touches'), ('control #1', [[6, 3, 7, 5], [3, 1, 9, 6]], 'within'), ('control #2', [[5, 9, 6, 10], [3, 9, 10, 13]], 'within'), ('control #3', [[8, 2, 9, 4], [1, 10, 4, 15]], 'disjoint'), ('control #4', [[1, 1, 7, 5], [4, 5, 9, 8]], 'touches'), ('control #5', [[9, 7, 16, 13], [1, 10, 7, 13]], 'disjoint'), ('control #7', [[1, 7, 6, 11], [0, 6, 7, 7]], 'touches'), ('boundary #18', [[0, 0, 5, 5], [0, 5, 5, 9]], 'touches')], [('control #3', [[8, 2, 9, 4], [1, 10, 4, 15]], 'disjoint'), ('control #4', [[1, 1, 7, 5], [4, 5, 9, 8]], 'touches'), ('control #5', [[9, 7, 16, 13], [1, 10, 7, 13]], 'disjoint'), ('control #6', [[3, 1, 4, 5], [8, 8, 12, 15]], 'disjoint'), ('control #7', [[1, 7, 6, 11], [0, 6, 7, 7]], 'touches'), ('control #8', [[2, 1, 4, 2], [3, 1, 6, 4]], 'overlaps'), ('control #12', [[8, 9, 9, 16], [4, 4, 11, 11]], 'overlaps'), ('boundary #18', [[0, 0, 5, 5], [0, 5, 5, 9]], 'touches')], [('control #6', [[3, 1, 4, 5], [8, 8, 12, 15]], 'disjoint'), ('control #7', [[1, 7, 6, 11], [0, 6, 7, 7]], 'touches'), ('control #8', [[2, 1, 4, 2], [3, 1, 6, 4]], 'overlaps'), ('control #9', [[7, 2, 15, 6], [8, 4, 14, 11]], 'overlaps'), ('control #10', [[7, 1, 10, 3], [7, 0, 14, 3]], 'within'), ('control #11', [[2, 7, 10, 9], [10, 8, 12, 13]], 'touches'), ('boundary #18', [[0, 0, 5, 5], [0, 5, 5, 9]], 'touches'), ('boundary #28', [[0, 6, 5, 9], [0, 0, 5, 6]], 'touches')], [('control #7', [[1, 7, 6, 11], [0, 6, 7, 7]], 'touches'), ('control #10', [[7, 1, 10, 3], [7, 0, 14, 3]], 'within'), ('control #11', [[2, 7, 10, 9], [10, 8, 12, 13]], 'touches'), ('control #12', [[8, 9, 9, 16], [4, 4, 11, 11]], 'overlaps'), ('control #13', [[5, 3, 9, 9], [7, 8, 8, 15]], 'overlaps'), ('control #14', [[3, 2, 10, 3], [8, 5, 14, 7]], 'disjoint'), ('control #15', [[3, 5, 7, 12], [9, 2, 16, 3]], 'disjoint'), ('boundary #18', [[0, 0, 5, 5], [0, 5, 5, 9]], 'touches')], [('control #12', [[8, 9, 9, 16], [4, 4, 11, 11]], 'overlaps'), ('control #13', [[5, 3, 9, 9], [7, 8, 8, 15]], 'overlaps'), ('control #14', [[3, 2, 10, 3], [8, 5, 14, 7]], 'disjoint'), ('control #15', [[3, 5, 7, 12], [9, 2, 16, 3]], 'disjoint'), ('boundary #16', [[0, 0, 5, 5], [5, 0, 9, 5]], 'touches'), ('boundary #17', [[0, 0, 5, 5], [5, 5, 9, 9]], 'touches'), ('boundary #18', [[0, 0, 5, 5], [0, 5, 5, 9]], 'touches'), ('boundary #19', [[0, 0, 10, 10], [0, 0, 5, 5]], 'contains')]]
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 | touches | touches | Passed |
| control #1 | within | within | Passed |
| control #2 | within | within | Passed |
| control #3 | disjoint | disjoint | Passed |
| control #4 | touches | touches | Passed |
| control #5 | disjoint | disjoint | Passed |
| control #7 | within | touches | Failed |
| boundary #18 | touches | touches | Passed |
SHA-256 / 815dc0f6053d5d32329fda2a63889ca7cc166cf9f476ed0f0c7ba522fb74a7e2
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
a, b = x
if a == b:
return 'equals'
if a[2] < b[0] or b[2] < a[0] or a[3] < b[1] or b[3] < a[1]:
return 'disjoint'
if a[0] <= b[0] and a[1] <= b[1] and a[2] >= b[2] and a[3] >= b[3]:
return 'contains'
if b[0] <= a[0] and b[2] >= a[2] and b[3] >= a[3]:
return 'within'
if a[2] == b[0] or b[2] == a[0] or a[3] == b[1] or b[3] == a[1]:
return 'touches'
return 'overlaps'
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('control #0', [[3, 0, 9, 4], [9, 3, 13, 11]], 'touches'), ('control #1', [[6, 3, 7, 5], [3, 1, 9, 6]], 'within'), ('control #2', [[5, 9, 6, 10], [3, 9, 10, 13]], 'within'), ('control #3', [[8, 2, 9, 4], [1, 10, 4, 15]], 'disjoint'), ('control #4', [[1, 1, 7, 5], [4, 5, 9, 8]], 'touches'), ('control #5', [[9, 7, 16, 13], [1, 10, 7, 13]], 'disjoint'), ('control #7', [[1, 7, 6, 11], [0, 6, 7, 7]], 'touches'), ('boundary #18', [[0, 0, 5, 5], [0, 5, 5, 9]], 'touches')], [('control #3', [[8, 2, 9, 4], [1, 10, 4, 15]], 'disjoint'), ('control #4', [[1, 1, 7, 5], [4, 5, 9, 8]], 'touches'), ('control #5', [[9, 7, 16, 13], [1, 10, 7, 13]], 'disjoint'), ('control #6', [[3, 1, 4, 5], [8, 8, 12, 15]], 'disjoint'), ('control #7', [[1, 7, 6, 11], [0, 6, 7, 7]], 'touches'), ('control #8', [[2, 1, 4, 2], [3, 1, 6, 4]], 'overlaps'), ('control #12', [[8, 9, 9, 16], [4, 4, 11, 11]], 'overlaps'), ('boundary #18', [[0, 0, 5, 5], [0, 5, 5, 9]], 'touches')], [('control #6', [[3, 1, 4, 5], [8, 8, 12, 15]], 'disjoint'), ('control #7', [[1, 7, 6, 11], [0, 6, 7, 7]], 'touches'), ('control #8', [[2, 1, 4, 2], [3, 1, 6, 4]], 'overlaps'), ('control #9', [[7, 2, 15, 6], [8, 4, 14, 11]], 'overlaps'), ('control #10', [[7, 1, 10, 3], [7, 0, 14, 3]], 'within'), ('control #11', [[2, 7, 10, 9], [10, 8, 12, 13]], 'touches'), ('boundary #18', [[0, 0, 5, 5], [0, 5, 5, 9]], 'touches'), ('boundary #28', [[0, 6, 5, 9], [0, 0, 5, 6]], 'touches')], [('control #7', [[1, 7, 6, 11], [0, 6, 7, 7]], 'touches'), ('control #10', [[7, 1, 10, 3], [7, 0, 14, 3]], 'within'), ('control #11', [[2, 7, 10, 9], [10, 8, 12, 13]], 'touches'), ('control #12', [[8, 9, 9, 16], [4, 4, 11, 11]], 'overlaps'), ('control #13', [[5, 3, 9, 9], [7, 8, 8, 15]], 'overlaps'), ('control #14', [[3, 2, 10, 3], [8, 5, 14, 7]], 'disjoint'), ('control #15', [[3, 5, 7, 12], [9, 2, 16, 3]], 'disjoint'), ('boundary #18', [[0, 0, 5, 5], [0, 5, 5, 9]], 'touches')], [('control #12', [[8, 9, 9, 16], [4, 4, 11, 11]], 'overlaps'), ('control #13', [[5, 3, 9, 9], [7, 8, 8, 15]], 'overlaps'), ('control #14', [[3, 2, 10, 3], [8, 5, 14, 7]], 'disjoint'), ('control #15', [[3, 5, 7, 12], [9, 2, 16, 3]], 'disjoint'), ('boundary #16', [[0, 0, 5, 5], [5, 0, 9, 5]], 'touches'), ('boundary #17', [[0, 0, 5, 5], [5, 5, 9, 9]], 'touches'), ('boundary #18', [[0, 0, 5, 5], [0, 5, 5, 9]], 'touches'), ('boundary #19', [[0, 0, 10, 10], [0, 0, 5, 5]], 'contains')]]
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 | touches | touches | Passed |
| control #1 | within | within | Passed |
| control #2 | within | within | Passed |
| control #3 | disjoint | disjoint | Passed |
| control #4 | touches | touches | Passed |
| control #5 | disjoint | disjoint | Passed |
| control #7 | touches | touches | Passed |
| boundary #18 | within | touches | Failed |
SHA-256 / 80471e20fa6bf46a1c348f8cef5c48d3774a5ee386d07e489acd0480909ffc4e
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
a, b = x
if a == b:
return 'equals'
if a[2] < b[0] or b[2] < a[0] or a[3] < b[1] or b[3] < a[1]:
return 'disjoint'
if a[0] <= b[0] and a[1] <= b[1] and a[2] >= b[2] and a[3] >= b[3]:
return 'contains'
if b[0] <= a[0] and b[1] <= a[1] and b[2] >= a[2] and b[3] >= a[3]:
return 'within'
if a[2] == b[0] or b[2] == a[0] or a[3] == b[1] or b[3] == a[1]:
return 'touches'
return 'overlaps'
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('control #0', [[3, 0, 9, 4], [9, 3, 13, 11]], 'touches'), ('control #1', [[6, 3, 7, 5], [3, 1, 9, 6]], 'within'), ('control #2', [[5, 9, 6, 10], [3, 9, 10, 13]], 'within'), ('control #3', [[8, 2, 9, 4], [1, 10, 4, 15]], 'disjoint'), ('control #4', [[1, 1, 7, 5], [4, 5, 9, 8]], 'touches'), ('control #5', [[9, 7, 16, 13], [1, 10, 7, 13]], 'disjoint'), ('control #7', [[1, 7, 6, 11], [0, 6, 7, 7]], 'touches'), ('boundary #18', [[0, 0, 5, 5], [0, 5, 5, 9]], 'touches')], [('control #3', [[8, 2, 9, 4], [1, 10, 4, 15]], 'disjoint'), ('control #4', [[1, 1, 7, 5], [4, 5, 9, 8]], 'touches'), ('control #5', [[9, 7, 16, 13], [1, 10, 7, 13]], 'disjoint'), ('control #6', [[3, 1, 4, 5], [8, 8, 12, 15]], 'disjoint'), ('control #7', [[1, 7, 6, 11], [0, 6, 7, 7]], 'touches'), ('control #8', [[2, 1, 4, 2], [3, 1, 6, 4]], 'overlaps'), ('control #12', [[8, 9, 9, 16], [4, 4, 11, 11]], 'overlaps'), ('boundary #18', [[0, 0, 5, 5], [0, 5, 5, 9]], 'touches')], [('control #6', [[3, 1, 4, 5], [8, 8, 12, 15]], 'disjoint'), ('control #7', [[1, 7, 6, 11], [0, 6, 7, 7]], 'touches'), ('control #8', [[2, 1, 4, 2], [3, 1, 6, 4]], 'overlaps'), ('control #9', [[7, 2, 15, 6], [8, 4, 14, 11]], 'overlaps'), ('control #10', [[7, 1, 10, 3], [7, 0, 14, 3]], 'within'), ('control #11', [[2, 7, 10, 9], [10, 8, 12, 13]], 'touches'), ('boundary #18', [[0, 0, 5, 5], [0, 5, 5, 9]], 'touches'), ('boundary #28', [[0, 6, 5, 9], [0, 0, 5, 6]], 'touches')], [('control #7', [[1, 7, 6, 11], [0, 6, 7, 7]], 'touches'), ('control #10', [[7, 1, 10, 3], [7, 0, 14, 3]], 'within'), ('control #11', [[2, 7, 10, 9], [10, 8, 12, 13]], 'touches'), ('control #12', [[8, 9, 9, 16], [4, 4, 11, 11]], 'overlaps'), ('control #13', [[5, 3, 9, 9], [7, 8, 8, 15]], 'overlaps'), ('control #14', [[3, 2, 10, 3], [8, 5, 14, 7]], 'disjoint'), ('control #15', [[3, 5, 7, 12], [9, 2, 16, 3]], 'disjoint'), ('boundary #18', [[0, 0, 5, 5], [0, 5, 5, 9]], 'touches')], [('control #12', [[8, 9, 9, 16], [4, 4, 11, 11]], 'overlaps'), ('control #13', [[5, 3, 9, 9], [7, 8, 8, 15]], 'overlaps'), ('control #14', [[3, 2, 10, 3], [8, 5, 14, 7]], 'disjoint'), ('control #15', [[3, 5, 7, 12], [9, 2, 16, 3]], 'disjoint'), ('boundary #16', [[0, 0, 5, 5], [5, 0, 9, 5]], 'touches'), ('boundary #17', [[0, 0, 5, 5], [5, 5, 9, 9]], 'touches'), ('boundary #18', [[0, 0, 5, 5], [0, 5, 5, 9]], 'touches'), ('boundary #19', [[0, 0, 10, 10], [0, 0, 5, 5]], 'contains')]]
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 | touches | touches | Passed |
| control #1 | within | within | Passed |
| control #2 | within | within | Passed |
| control #3 | disjoint | disjoint | Passed |
| control #4 | touches | touches | Passed |
| control #5 | disjoint | disjoint | Passed |
| control #7 | touches | touches | Passed |
| boundary #18 | touches | touches | Passed |
SHA-256 / 4c95b18aa0ee998fefb75930aea5e3c40e1abb226f5713132e2e1b3287ed845b
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 2026-09-29T14:48:21.008410+00:00.
Case digest / 215b23700284a2718026567fc5938bd9a4578439421646057f5649f7e2c4f5dc