FA-5896 / Planar geometry / Open access
Polygon boundary lattice points · case 01
Only vertices are counted, excluding lattice points along edges.
ROOT CAUSE
Only vertices are counted, excluding lattice points along edges.
VERIFIED REPAIR
Apply the specified mathematical contract directly, preserving all terms and boundary cases: return sum(math.gcd(abs(a[0]-b[0]),abs(a[1]-b[1])) for a,b in zip(points,points[1:]+points[:1]))
Unsuccessful approach: Counting both endpoints per edge duplicates every vertex.
Case contract
Integer coordinates and lengths, with exact arithmetic except for indicated division results. Lengths are nonnegative. Rectangles are (xmin,ymin,xmax,ymax) with ordered bounds; coordinate vectors have matching dimensions. Input is the ordered integer vertices of a simple nondegenerate lattice polygon, without a repeated closing vertex. Exact operational definition: sum(math.gcd(abs(a[0]-b[0]),abs(a[1]-b[1])) for a,b in zip(points,points[1:]+points[:1]))
Why this case matters
Small exact fixtures expose this error without platform timing, external services, or probabilistic observations. Planar geometry results depend on the stated convention.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
import calendar
import statistics
import itertools
from fractions import Fraction
from datetime import date, datetime, timedelta, timezone
from decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR
N = 1
observations = []
def solve(points):
return len(points)
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: ([(0, 0), (2, 0), (2, 2), (0, 2)],)', solve(*([(0, 0), (2, 0), (2, 2), (0, 2)],)), 8)
check('fixture 2: ([(0, 0), (1, 0), (0, 1)],)', solve(*([(0, 0), (1, 0), (0, 1)],)), 3)
check('fixture 3: ([(0, 0), (3, 0), (0, 3)],)', solve(*([(0, 0), (3, 0), (0, 3)],)), 9)
check('fixture 4: ([(1, 1), (4, 1), (4, 3), (1, 3)],)', solve(*([(1, 1), (4, 1), (4, 3), (1, 3)],)), 10)
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 |
|---|---|---|---|
| fixture 1: ([(0, 0), (2, 0), (2, 2), (0, 2)],) | 4 | 8 | Failed |
| fixture 2: ([(0, 0), (1, 0), (0, 1)],) | 3 | 3 | Passed |
| fixture 3: ([(0, 0), (3, 0), (0, 3)],) | 3 | 9 | Failed |
| fixture 4: ([(1, 1), (4, 1), (4, 3), (1, 3)],) | 4 | 10 | Failed |
SHA-256 / 88bc9e4b0490664ebe3e8af8457b0e7b8029c52eebcfb8ff63f93028aad1d40b
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
import calendar
import statistics
import itertools
from fractions import Fraction
from datetime import date, datetime, timedelta, timezone
from decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR
N = 1
observations = []
def solve(points):
return sum(math.gcd(abs(a[0]-b[0]),abs(a[1]-b[1]))+1 for a,b in zip(points,points[1:]+points[:1]))
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: ([(0, 0), (2, 0), (2, 2), (0, 2)],)', solve(*([(0, 0), (2, 0), (2, 2), (0, 2)],)), 8)
check('fixture 2: ([(0, 0), (1, 0), (0, 1)],)', solve(*([(0, 0), (1, 0), (0, 1)],)), 3)
check('fixture 3: ([(0, 0), (3, 0), (0, 3)],)', solve(*([(0, 0), (3, 0), (0, 3)],)), 9)
check('fixture 4: ([(1, 1), (4, 1), (4, 3), (1, 3)],)', solve(*([(1, 1), (4, 1), (4, 3), (1, 3)],)), 10)
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 |
|---|---|---|---|
| fixture 1: ([(0, 0), (2, 0), (2, 2), (0, 2)],) | 12 | 8 | Failed |
| fixture 2: ([(0, 0), (1, 0), (0, 1)],) | 6 | 3 | Failed |
| fixture 3: ([(0, 0), (3, 0), (0, 3)],) | 12 | 9 | Failed |
| fixture 4: ([(1, 1), (4, 1), (4, 3), (1, 3)],) | 14 | 10 | Failed |
SHA-256 / dbf32b004af4ca7e53aae2acc7745b28b04fb9126a4ccef35c043db086aa84ab
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
import math
import calendar
import statistics
import itertools
from fractions import Fraction
from datetime import date, datetime, timedelta, timezone
from decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR
N = 1
observations = []
def solve(points):
return sum(math.gcd(abs(a[0]-b[0]),abs(a[1]-b[1])) for a,b in zip(points,points[1:]+points[:1]))
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: ([(0, 0), (2, 0), (2, 2), (0, 2)],)', solve(*([(0, 0), (2, 0), (2, 2), (0, 2)],)), 8)
check('fixture 2: ([(0, 0), (1, 0), (0, 1)],)', solve(*([(0, 0), (1, 0), (0, 1)],)), 3)
check('fixture 3: ([(0, 0), (3, 0), (0, 3)],)', solve(*([(0, 0), (3, 0), (0, 3)],)), 9)
check('fixture 4: ([(1, 1), (4, 1), (4, 3), (1, 3)],)', solve(*([(1, 1), (4, 1), (4, 3), (1, 3)],)), 10)
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 |
|---|---|---|---|
| fixture 1: ([(0, 0), (2, 0), (2, 2), (0, 2)],) | 8 | 8 | Passed |
| fixture 2: ([(0, 0), (1, 0), (0, 1)],) | 3 | 3 | Passed |
| fixture 3: ([(0, 0), (3, 0), (0, 3)],) | 9 | 9 | Passed |
| fixture 4: ([(1, 1), (4, 1), (4, 3), (1, 3)],) | 10 | 10 | Passed |
SHA-256 / bedaaf00d21ae57f2179797f0e7829a1ae9a0503745c2c996ac8a54fe02e1f27
Verification & scope
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 2026-09-29T14:37:55.194071+00:00.
Case digest / aa97ccbd69df724f3739b5ef06c65a12fcfce7ddafe5daceb15c14b370e56efe