FA-12871 / Numerical aggregation / Open access
Absolute deviation about anchor: The anchor is subtracted once from the total instead of once per observation. · case 01
The reduction disagrees with its explicit aggregation oracle.
ROOT CAUSE
The anchor is subtracted once from the total instead of once per observation.
VERIFIED REPAIR
Preserve the absolute deviation about anchor contract at the identified reduction decision.
Unsuccessful approach: Scaling the anchor still permits cancellation.
Case contract
Return sum(abs(x-anchor)); empty input returns zero. Anchor is supplied, not estimated.
Why this case matters
Exact bounded examples isolate a reduction defect without floating-point or external-service effects.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
from collections import Counter, defaultdict
import math
import itertools
N = 1
observations = []
def solve(xs, anchor):
return abs(sum(xs)-anchor) if xs else 0
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([1, 5, 9], 5)), 8)
check('regression 2', solve(*([], 4)), 0)
check('regression 3', solve(*([4, 4], 4)), 0)
check('regression 4', solve(*([-3, -1], 2)), 8)
check('regression 5', solve(*([0, 0, 6], 1)), 7)
check("variable anchor", solve([N-3,N+2,N+2],N),7)
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 |
|---|---|---|---|
| regression 1 | 10 | 8 | Failed |
| regression 2 | 0 | 0 | Passed |
| regression 3 | 4 | 0 | Failed |
| regression 4 | 6 | 8 | Failed |
| regression 5 | 5 | 7 | Failed |
| variable anchor | 3 | 7 | Failed |
SHA-256 / ef62e497021a97545ff8a6607fe57ab70b9ea6a7ae5547b66fd62a4c3e879814
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
from collections import Counter, defaultdict
import math
import itertools
N = 1
observations = []
def solve(xs, anchor):
return abs(sum(xs)-anchor*len(xs))
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([1, 5, 9], 5)), 8)
check('regression 2', solve(*([], 4)), 0)
check('regression 3', solve(*([4, 4], 4)), 0)
check('regression 4', solve(*([-3, -1], 2)), 8)
check('regression 5', solve(*([0, 0, 6], 1)), 7)
check("variable anchor", solve([N-3,N+2,N+2],N),7)
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 |
|---|---|---|---|
| regression 1 | 0 | 8 | Failed |
| regression 2 | 0 | 0 | Passed |
| regression 3 | 0 | 0 | Passed |
| regression 4 | 8 | 8 | Passed |
| regression 5 | 3 | 7 | Failed |
| variable anchor | 1 | 7 | Failed |
SHA-256 / 98f46b10be780c16add8d6052bf54f6687f6088d8a5f2c27435c6f2b4c3c52fb
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
from collections import Counter, defaultdict
import math
import itertools
N = 1
observations = []
def solve(xs, anchor):
return sum(abs(x-anchor) for x in xs)
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([1, 5, 9], 5)), 8)
check('regression 2', solve(*([], 4)), 0)
check('regression 3', solve(*([4, 4], 4)), 0)
check('regression 4', solve(*([-3, -1], 2)), 8)
check('regression 5', solve(*([0, 0, 6], 1)), 7)
check("variable anchor", solve([N-3,N+2,N+2],N),7)
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 |
|---|---|---|---|
| regression 1 | 8 | 8 | Passed |
| regression 2 | 0 | 0 | Passed |
| regression 3 | 0 | 0 | Passed |
| regression 4 | 8 | 8 | Passed |
| regression 5 | 7 | 7 | Passed |
| variable anchor | 7 | 7 | Passed |
SHA-256 / fdf32ae20efa0796e6f0e4a7625899e2afdf6315c10f56c9ba996a64f78c8aa0
Verification & scope
Small offline integer/rational inputs only; no performance, statistical inference, or production-library conformance claim. 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 2026-09-29T14:39:00.890246+00:00.
Case digest / 5f672f043b109832d1862a527763ae9449c433ab877dd2126c6f4b07eb75c96f