FA-70451 / GIS polygon topology / Open access
Bounding box topological relation: containment with shared edges · case 01
A box flush against the inside of another is not reported as contained.
ROOT CAUSE
Containment demands strict inequalities, excluding boxes that share an edge with the container.
VERIFIED REPAIR
At the containment with shared edges step restore `if a[0] <= b[0] and a[1] <= b[1] and a[2] >= b[2] and a[3] >= b[3]:`, leaving the rest of the model unchanged.
Unsuccessful approach: Only the minimum sides accept shared edges; flush maximum sides still fail.
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] 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'), ('boundary #19', [[0, 0, 10, 10], [0, 0, 5, 5]], 'contains'), ('boundary #21', [[0, 0, 10, 10], [2, 2, 8, 10]], 'contains')], [('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'), ('boundary #21', [[0, 0, 10, 10], [2, 2, 8, 10]], 'contains'), ('regression #24', [[0, 0, 4, 9], [0, 1, 4, 9]], 'contains')], [('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'), ('regression #23', [[0, 0, 4, 9], [0, 0, 4, 3]], 'contains'), ('regression #31', [[0, 0, 3, 3], [1, 1, 3, 3]], 'contains')], [('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'), ('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'), ('boundary #21', [[0, 0, 10, 10], [2, 2, 8, 10]], 'contains'), ('regression #24', [[0, 0, 4, 9], [0, 1, 4, 9]], 'contains')], [('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'), ('regression #23', [[0, 0, 4, 9], [0, 0, 4, 3]], 'contains'), ('regression #31', [[0, 0, 3, 3], [1, 1, 3, 3]], '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 |
| boundary #19 | overlaps | contains | Failed |
| boundary #21 | overlaps | contains | Failed |
SHA-256 / 4f7e428300b09db5a708ec42e091a7f2eb244355beef57682272faabfbe99734
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[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'), ('boundary #19', [[0, 0, 10, 10], [0, 0, 5, 5]], 'contains'), ('boundary #21', [[0, 0, 10, 10], [2, 2, 8, 10]], 'contains')], [('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'), ('boundary #21', [[0, 0, 10, 10], [2, 2, 8, 10]], 'contains'), ('regression #24', [[0, 0, 4, 9], [0, 1, 4, 9]], 'contains')], [('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'), ('regression #23', [[0, 0, 4, 9], [0, 0, 4, 3]], 'contains'), ('regression #31', [[0, 0, 3, 3], [1, 1, 3, 3]], 'contains')], [('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'), ('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'), ('boundary #21', [[0, 0, 10, 10], [2, 2, 8, 10]], 'contains'), ('regression #24', [[0, 0, 4, 9], [0, 1, 4, 9]], 'contains')], [('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'), ('regression #23', [[0, 0, 4, 9], [0, 0, 4, 3]], 'contains'), ('regression #31', [[0, 0, 3, 3], [1, 1, 3, 3]], '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 |
| boundary #19 | contains | contains | Passed |
| boundary #21 | overlaps | contains | Failed |
SHA-256 / 39634b07988f15ca716ca9359df2de96d60270cd7aa8483340d8ead4f30b6d29
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'), ('boundary #19', [[0, 0, 10, 10], [0, 0, 5, 5]], 'contains'), ('boundary #21', [[0, 0, 10, 10], [2, 2, 8, 10]], 'contains')], [('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'), ('boundary #21', [[0, 0, 10, 10], [2, 2, 8, 10]], 'contains'), ('regression #24', [[0, 0, 4, 9], [0, 1, 4, 9]], 'contains')], [('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'), ('regression #23', [[0, 0, 4, 9], [0, 0, 4, 3]], 'contains'), ('regression #31', [[0, 0, 3, 3], [1, 1, 3, 3]], 'contains')], [('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'), ('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'), ('boundary #21', [[0, 0, 10, 10], [2, 2, 8, 10]], 'contains'), ('regression #24', [[0, 0, 4, 9], [0, 1, 4, 9]], 'contains')], [('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'), ('regression #23', [[0, 0, 4, 9], [0, 0, 4, 3]], 'contains'), ('regression #31', [[0, 0, 3, 3], [1, 1, 3, 3]], '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 |
| boundary #19 | contains | contains | Passed |
| boundary #21 | contains | contains | Passed |
SHA-256 / 4b1e232a573a19f98cd961d60c55fd36505f701bcb415027c63e61d115d6d788
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 2026-09-29T14:48:20.957591+00:00.
Case digest / 354b680c554f6ec7d1c9c0a3127edcbb9620e5bac9b442e373cb03fb9e8cbcf6