FA-5781 / Planar geometry / Open access
Squared point distance · case 01
Manhattan distance replaces squared Euclidean distance.
ROOT CAUSE
Manhattan distance replaces squared Euclidean distance.
VERIFIED REPAIR
Apply the specified mathematical contract directly, preserving all terms and boundary cases: return sum((x-y)**2 for x,y in zip(a,b))
Unsuccessful approach: Squaring the sum introduces cross terms and cancellation.
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. Squared point distance. Exact operational definition: sum((x-y)**2 for x,y in zip(a,b))
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(a, b):
return sum(abs(x-y) for x,y in zip(a,b))
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: ((0, 0), (3, 4))', solve(*((0, 0), (3, 4))), 25)
check('fixture 2: ((1, 2), (1, 2))', solve(*((1, 2), (1, 2))), 0)
check('fixture 3: ((0, 0), (1, -1))', solve(*((0, 0), (1, -1))), 2)
check('fixture 4: ((-2, 0), (2, 0))', solve(*((-2, 0), (2, 0))), 16)
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), (3, 4)) | 7 | 25 | Failed |
| fixture 2: ((1, 2), (1, 2)) | 0 | 0 | Passed |
| fixture 3: ((0, 0), (1, -1)) | 2 | 2 | Passed |
| fixture 4: ((-2, 0), (2, 0)) | 4 | 16 | Failed |
SHA-256 / fb776eacedca275cd58f636e61f0d930709f0f108c708e18e989e54e96104ac6
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(a, b):
return sum(x-y for x,y in zip(a,b))**2
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: ((0, 0), (3, 4))', solve(*((0, 0), (3, 4))), 25)
check('fixture 2: ((1, 2), (1, 2))', solve(*((1, 2), (1, 2))), 0)
check('fixture 3: ((0, 0), (1, -1))', solve(*((0, 0), (1, -1))), 2)
check('fixture 4: ((-2, 0), (2, 0))', solve(*((-2, 0), (2, 0))), 16)
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), (3, 4)) | 49 | 25 | Failed |
| fixture 2: ((1, 2), (1, 2)) | 0 | 0 | Passed |
| fixture 3: ((0, 0), (1, -1)) | 0 | 2 | Failed |
| fixture 4: ((-2, 0), (2, 0)) | 16 | 16 | Passed |
SHA-256 / b00ce21369ae2f13944eba9811902b4e1d380ac6cf5dec1f099e8d178c823807
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(a, b):
return sum((x-y)**2 for x,y in zip(a,b))
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: ((0, 0), (3, 4))', solve(*((0, 0), (3, 4))), 25)
check('fixture 2: ((1, 2), (1, 2))', solve(*((1, 2), (1, 2))), 0)
check('fixture 3: ((0, 0), (1, -1))', solve(*((0, 0), (1, -1))), 2)
check('fixture 4: ((-2, 0), (2, 0))', solve(*((-2, 0), (2, 0))), 16)
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), (3, 4)) | 25 | 25 | Passed |
| fixture 2: ((1, 2), (1, 2)) | 0 | 0 | Passed |
| fixture 3: ((0, 0), (1, -1)) | 2 | 2 | Passed |
| fixture 4: ((-2, 0), (2, 0)) | 16 | 16 | Passed |
SHA-256 / c2cb9d3b008c956983d2249f706c9f1cd9a190251c94ac2946bbc590d1b5a3db
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 2026-09-29T14:37:53.638062+00:00.
Case digest / 15f2cfaeb7f8a4859c0efe46f377c9d39861eaba00f55f3c37262c4040d0bac8