FA-70416 / GIS polygon topology / Open access
DE-9IM matrix named predicate evaluation: touches alternatives · case 01
Geometries that meet only boundary-to-boundary are not reported as touching.
ROOT CAUSE
The boundary/boundary alternative F***T**** is missing from touches.
VERIFIED REPAIR
At the touches alternatives step restore `(match('FT*******') or match('F**T*****') or match('F***T****'))`, leaving the rest of the model unchanged.
Unsuccessful approach: The patched version restores boundary/boundary but drops the boundary/interior alternative F**T*****.
Case contract
Input [matrix, predicate, dimA, dimB] with a 9-character intersection matrix over "F012" (row-major II, IB, IE, BI, BB, BE, EI, EB, EE). Pattern characters: "*" anything, "T" any non-F value, "F" only F, "0"/"1"/"2" that exact dimension. disjoint = FF*FF****; intersects = not disjoint; touches (not both points) = FT******* or F**T***** or F***T****; within = T*F**F***; contains = T*****FF*; covers = any of T*****FF*, *T****FF*, ***T**FF*, ****T*FF*; overlaps needs equal dimensions and 1*T***T** for lines else T*T***T**; crosses = T*T****** if dimA < dimB, T*****T** if dimA > dimB, 0******** for two lines, otherwise false; equals = T*F**FFF*. Unknown predicates return None.
Why this case matters
Spatial SQL predicates, topology rules and QA checks are expressed as DE-9IM patterns; a wrong pattern changes join results silently.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
matrix, pred, da, db = x
def match(pattern):
for m, p in zip(matrix, pattern):
if p == '*':
continue
if p == 'T' and m == 'F':
return False
if p == 'F' and m != 'F':
return False
if p in '012' and m != p:
return False
return True
if pred == 'disjoint':
return match('FF*FF****')
if pred == 'intersects':
return not match('FF*FF****')
if pred == 'touches':
return (da, db) != (0, 0) and (match('FT*******') or match('F**T*****'))
if pred == 'within':
return match('T*F**F***')
if pred == 'contains':
return match('T*****FF*')
if pred == 'covers':
return any(match(p) for p in ('T*****FF*', '*T****FF*', '***T**FF*', '****T*FF*'))
if pred == 'overlaps':
if da != db:
return False
return match('1*T***T**') if da == 1 else match('T*T***T**')
if pred == 'crosses':
if da < db:
return match('T*T******')
if da > db:
return match('T*****T**')
return da == 1 and match('0********')
if pred == 'equals':
return match('T*F**FFF*')
return None
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('control #0', ['FF2F11212', 'crosses', 2, 2], False), ('control #1', ['FF2F11212', 'intersects', 2, 2], True), ('control #2', ['FF2F11212', 'within', 2, 2], False), ('control #3', ['FF2F11212', 'touches', 2, 2], True), ('control #4', ['212101212', 'overlaps', 2, 2], True), ('control #5', ['212101212', 'crosses', 2, 2], False), ('control #6', ['212101212', 'touches', 2, 2], False), ('regression #119', ['FF21F1212', 'touches', 2, 1], True)], [('control #3', ['FF2F11212', 'touches', 2, 2], True), ('control #4', ['212101212', 'overlaps', 2, 2], True), ('control #5', ['212101212', 'crosses', 2, 2], False), ('control #6', ['212101212', 'touches', 2, 2], False), ('control #7', ['212101212', 'intersects', 2, 2], True), ('control #8', ['2FF1FF212', 'contains', 2, 2], False), ('regression #92', ['FF2F11212', 'touches', 2, 2], True), ('regression #119', ['FF21F1212', 'touches', 2, 1], True)], [('control #6', ['212101212', 'touches', 2, 2], False), ('control #7', ['212101212', 'intersects', 2, 2], True), ('control #8', ['2FF1FF212', 'contains', 2, 2], False), ('control #9', ['2FF1FF212', 'crosses', 2, 2], False), ('control #10', ['2FF1FF212', 'intersects', 2, 2], True), ('control #11', ['2FF1FF212', 'disjoint', 2, 2], False), ('regression #94', ['FF1F00212', 'touches', 1, 2], True), ('regression #119', ['FF21F1212', 'touches', 2, 1], True)], [('control #3', ['FF2F11212', 'touches', 2, 2], True), ('control #10', ['2FF1FF212', 'intersects', 2, 2], True), ('control #11', ['2FF1FF212', 'disjoint', 2, 2], False), ('control #12', ['212FF1FF2', 'intersects', 2, 2], True), ('control #13', ['212FF1FF2', 'contains', 2, 2], True), ('control #14', ['212FF1FF2', 'covers', 2, 2], True), ('control #15', ['212FF1FF2', 'disjoint', 2, 2], False), ('regression #119', ['FF21F1212', 'touches', 2, 1], True)], [('control #12', ['212FF1FF2', 'intersects', 2, 2], True), ('control #13', ['212FF1FF2', 'contains', 2, 2], True), ('control #14', ['212FF1FF2', 'covers', 2, 2], True), ('control #15', ['212FF1FF2', 'disjoint', 2, 2], False), ('control #16', ['2FF1FF2F2', 'equals', 2, 2], False), ('control #17', ['2FF1FF2F2', 'disjoint', 2, 2], False), ('regression #92', ['FF2F11212', 'touches', 2, 2], True), ('regression #119', ['FF21F1212', 'touches', 2, 1], True)]]
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 | False | False | Passed |
| control #1 | True | True | Passed |
| control #2 | False | False | Passed |
| control #3 | False | True | Failed |
| control #4 | True | True | Passed |
| control #5 | False | False | Passed |
| control #6 | False | False | Passed |
| regression #119 | True | True | Passed |
SHA-256 / 4cd8364aa412a850947af9cb497692879b9cfb59ef2c7973bc2f769c5bed588e
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
matrix, pred, da, db = x
def match(pattern):
for m, p in zip(matrix, pattern):
if p == '*':
continue
if p == 'T' and m == 'F':
return False
if p == 'F' and m != 'F':
return False
if p in '012' and m != p:
return False
return True
if pred == 'disjoint':
return match('FF*FF****')
if pred == 'intersects':
return not match('FF*FF****')
if pred == 'touches':
return (da, db) != (0, 0) and (match('FT*******') or match('F***T****'))
if pred == 'within':
return match('T*F**F***')
if pred == 'contains':
return match('T*****FF*')
if pred == 'covers':
return any(match(p) for p in ('T*****FF*', '*T****FF*', '***T**FF*', '****T*FF*'))
if pred == 'overlaps':
if da != db:
return False
return match('1*T***T**') if da == 1 else match('T*T***T**')
if pred == 'crosses':
if da < db:
return match('T*T******')
if da > db:
return match('T*****T**')
return da == 1 and match('0********')
if pred == 'equals':
return match('T*F**FFF*')
return None
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('control #0', ['FF2F11212', 'crosses', 2, 2], False), ('control #1', ['FF2F11212', 'intersects', 2, 2], True), ('control #2', ['FF2F11212', 'within', 2, 2], False), ('control #3', ['FF2F11212', 'touches', 2, 2], True), ('control #4', ['212101212', 'overlaps', 2, 2], True), ('control #5', ['212101212', 'crosses', 2, 2], False), ('control #6', ['212101212', 'touches', 2, 2], False), ('regression #119', ['FF21F1212', 'touches', 2, 1], True)], [('control #3', ['FF2F11212', 'touches', 2, 2], True), ('control #4', ['212101212', 'overlaps', 2, 2], True), ('control #5', ['212101212', 'crosses', 2, 2], False), ('control #6', ['212101212', 'touches', 2, 2], False), ('control #7', ['212101212', 'intersects', 2, 2], True), ('control #8', ['2FF1FF212', 'contains', 2, 2], False), ('regression #92', ['FF2F11212', 'touches', 2, 2], True), ('regression #119', ['FF21F1212', 'touches', 2, 1], True)], [('control #6', ['212101212', 'touches', 2, 2], False), ('control #7', ['212101212', 'intersects', 2, 2], True), ('control #8', ['2FF1FF212', 'contains', 2, 2], False), ('control #9', ['2FF1FF212', 'crosses', 2, 2], False), ('control #10', ['2FF1FF212', 'intersects', 2, 2], True), ('control #11', ['2FF1FF212', 'disjoint', 2, 2], False), ('regression #94', ['FF1F00212', 'touches', 1, 2], True), ('regression #119', ['FF21F1212', 'touches', 2, 1], True)], [('control #3', ['FF2F11212', 'touches', 2, 2], True), ('control #10', ['2FF1FF212', 'intersects', 2, 2], True), ('control #11', ['2FF1FF212', 'disjoint', 2, 2], False), ('control #12', ['212FF1FF2', 'intersects', 2, 2], True), ('control #13', ['212FF1FF2', 'contains', 2, 2], True), ('control #14', ['212FF1FF2', 'covers', 2, 2], True), ('control #15', ['212FF1FF2', 'disjoint', 2, 2], False), ('regression #119', ['FF21F1212', 'touches', 2, 1], True)], [('control #12', ['212FF1FF2', 'intersects', 2, 2], True), ('control #13', ['212FF1FF2', 'contains', 2, 2], True), ('control #14', ['212FF1FF2', 'covers', 2, 2], True), ('control #15', ['212FF1FF2', 'disjoint', 2, 2], False), ('control #16', ['2FF1FF2F2', 'equals', 2, 2], False), ('control #17', ['2FF1FF2F2', 'disjoint', 2, 2], False), ('regression #92', ['FF2F11212', 'touches', 2, 2], True), ('regression #119', ['FF21F1212', 'touches', 2, 1], True)]]
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 | False | False | Passed |
| control #1 | True | True | Passed |
| control #2 | False | False | Passed |
| control #3 | True | True | Passed |
| control #4 | True | True | Passed |
| control #5 | False | False | Passed |
| control #6 | False | False | Passed |
| regression #119 | False | True | Failed |
SHA-256 / 3e1d66b2f5dc8d67abc4c2689868033d8f14910ac5c896871fd9a64bafe75d66
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
matrix, pred, da, db = x
def match(pattern):
for m, p in zip(matrix, pattern):
if p == '*':
continue
if p == 'T' and m == 'F':
return False
if p == 'F' and m != 'F':
return False
if p in '012' and m != p:
return False
return True
if pred == 'disjoint':
return match('FF*FF****')
if pred == 'intersects':
return not match('FF*FF****')
if pred == 'touches':
return (da, db) != (0, 0) and (match('FT*******') or match('F**T*****') or match('F***T****'))
if pred == 'within':
return match('T*F**F***')
if pred == 'contains':
return match('T*****FF*')
if pred == 'covers':
return any(match(p) for p in ('T*****FF*', '*T****FF*', '***T**FF*', '****T*FF*'))
if pred == 'overlaps':
if da != db:
return False
return match('1*T***T**') if da == 1 else match('T*T***T**')
if pred == 'crosses':
if da < db:
return match('T*T******')
if da > db:
return match('T*****T**')
return da == 1 and match('0********')
if pred == 'equals':
return match('T*F**FFF*')
return None
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('control #0', ['FF2F11212', 'crosses', 2, 2], False), ('control #1', ['FF2F11212', 'intersects', 2, 2], True), ('control #2', ['FF2F11212', 'within', 2, 2], False), ('control #3', ['FF2F11212', 'touches', 2, 2], True), ('control #4', ['212101212', 'overlaps', 2, 2], True), ('control #5', ['212101212', 'crosses', 2, 2], False), ('control #6', ['212101212', 'touches', 2, 2], False), ('regression #119', ['FF21F1212', 'touches', 2, 1], True)], [('control #3', ['FF2F11212', 'touches', 2, 2], True), ('control #4', ['212101212', 'overlaps', 2, 2], True), ('control #5', ['212101212', 'crosses', 2, 2], False), ('control #6', ['212101212', 'touches', 2, 2], False), ('control #7', ['212101212', 'intersects', 2, 2], True), ('control #8', ['2FF1FF212', 'contains', 2, 2], False), ('regression #92', ['FF2F11212', 'touches', 2, 2], True), ('regression #119', ['FF21F1212', 'touches', 2, 1], True)], [('control #6', ['212101212', 'touches', 2, 2], False), ('control #7', ['212101212', 'intersects', 2, 2], True), ('control #8', ['2FF1FF212', 'contains', 2, 2], False), ('control #9', ['2FF1FF212', 'crosses', 2, 2], False), ('control #10', ['2FF1FF212', 'intersects', 2, 2], True), ('control #11', ['2FF1FF212', 'disjoint', 2, 2], False), ('regression #94', ['FF1F00212', 'touches', 1, 2], True), ('regression #119', ['FF21F1212', 'touches', 2, 1], True)], [('control #3', ['FF2F11212', 'touches', 2, 2], True), ('control #10', ['2FF1FF212', 'intersects', 2, 2], True), ('control #11', ['2FF1FF212', 'disjoint', 2, 2], False), ('control #12', ['212FF1FF2', 'intersects', 2, 2], True), ('control #13', ['212FF1FF2', 'contains', 2, 2], True), ('control #14', ['212FF1FF2', 'covers', 2, 2], True), ('control #15', ['212FF1FF2', 'disjoint', 2, 2], False), ('regression #119', ['FF21F1212', 'touches', 2, 1], True)], [('control #12', ['212FF1FF2', 'intersects', 2, 2], True), ('control #13', ['212FF1FF2', 'contains', 2, 2], True), ('control #14', ['212FF1FF2', 'covers', 2, 2], True), ('control #15', ['212FF1FF2', 'disjoint', 2, 2], False), ('control #16', ['2FF1FF2F2', 'equals', 2, 2], False), ('control #17', ['2FF1FF2F2', 'disjoint', 2, 2], False), ('regression #92', ['FF2F11212', 'touches', 2, 2], True), ('regression #119', ['FF21F1212', 'touches', 2, 1], True)]]
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 | False | False | Passed |
| control #1 | True | True | Passed |
| control #2 | False | False | Passed |
| control #3 | True | True | Passed |
| control #4 | True | True | Passed |
| control #5 | False | False | Passed |
| control #6 | False | False | Passed |
| regression #119 | True | True | Passed |
SHA-256 / 94073d7df999d134449add08cc01fdb69c5d508e91f5cc122044c78799f44e06
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 2026-09-29T14:48:20.531286+00:00.
Case digest / c80392116a7763993db214f18b73b215242dc261677b2509624f84bca43fe887