FAILURE MAP
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FA-12886 / Numerical aggregation / Open access

Absolute deviation about anchor: Only extreme observations contribute to total deviation. · case 01

The reduction disagrees with its explicit aggregation oracle.

Verified by executionVariant 1 · 6 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Only extreme observations contribute to total deviation.

THE FAILURE

Only extreme observations contribute to total deviation.

Unsuccessful approach: Multiplying the range by count cannot recover interior deviations.

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(min(xs)-anchor)+abs(max(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 fixtureActualExpectedOutcome
regression 188Passed
regression 200Passed
regression 300Passed
regression 488Passed
regression 567Failed
variable anchor57Failed

SHA-256 / 6eed501a93c5263cb1a1a1cba491619e40f74c0899591a6bc6efa6c3085352cd

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 (max(xs)-min(xs))*len(xs) 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 fixtureActualExpectedOutcome
regression 1248Failed
regression 200Passed
regression 300Passed
regression 448Failed
regression 5187Failed
variable anchor157Failed

SHA-256 / b04fbdddbb22f6242960e5344b028d6656d4c4c2c94ae640a3110e871c88eb41

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 6 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

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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 2026-09-29T14:39:01.250375+00:00.

Case digest / 85b4ac9c3d33af7771c3daab9748110c3bed4aa748bc122606362e094e17d480