FA-13156 / Numerical aggregation / Open access
Frequency central scatter: Absolute deviations are substituted for squared deviations. · case 01
The reduction disagrees with its explicit aggregation oracle.
ROOT CAUSE
Absolute deviations are substituted for squared deviations.
THE FAILURE
Absolute deviations are substituted for squared deviations.
Unsuccessful approach: Subtracting the center after squaring has no centering interpretation.
Case contract
Rows [integer value, nonnegative frequency] represent replicated observations. Return unnormalised sum of squared deviations from their exact replicated mean as a Fraction string; zero total frequency returns None.
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(rows):
total=sum(w for x,w in rows)
if total==0: return None
center=Fraction(sum(x*w for x,w in rows),total)
return str(sum(w*abs(x-center) for x,w in rows))
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([(1, 2), (1, 2), (4, 1)],)), '36/5')
check('regression 2', solve(*([(1, 2), (4, 1)],)), '6')
check('regression 3', solve(*([(0, 1), (0, 3)],)), '0')
check('regression 4', solve(*([],)), None)
check('regression 5', solve(*([(3, 0), (8, 0)],)), None)
check('regression 6', solve(*([(9, 1), (-2, 3), (5, 2)],)), '689/6')
check('regression 7', solve(*([(7, 3), (1, 0)],)), '0')
check('regression 8', solve(*([(1, 1), (2, 1), (5, 1)],)), '26/3')
check("variable replication scatter",solve([(0,N),(2,N)]),str(2*N))
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 | 24/5 | 36/5 | Failed |
| regression 2 | 4 | 6 | Failed |
| regression 3 | 0 | 0 | Passed |
| regression 4 | None | None | Passed |
| regression 5 | None | None | Passed |
| regression 6 | 25 | 689/6 | Failed |
| regression 7 | 0 | 0 | Passed |
| regression 8 | 14/3 | 26/3 | Failed |
| variable replication scatter | 2 | 2 | Passed |
SHA-256 / ace8ce7930f172e2f0e459ad92f0f31ee557604c2b8fcd694faa8877bb42bd88
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(rows):
total=sum(w for x,w in rows)
if total==0: return None
center=Fraction(sum(x*w for x,w in rows),total)
return str(sum(abs(w*(x-center)**2-center) for x,w in rows))
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([(1, 2), (1, 2), (4, 1)],)), '36/5')
check('regression 2', solve(*([(1, 2), (4, 1)],)), '6')
check('regression 3', solve(*([(0, 1), (0, 3)],)), '0')
check('regression 4', solve(*([],)), None)
check('regression 5', solve(*([(3, 0), (8, 0)],)), None)
check('regression 6', solve(*([(9, 1), (-2, 3), (5, 2)],)), '689/6')
check('regression 7', solve(*([(7, 3), (1, 0)],)), '0')
check('regression 8', solve(*([(1, 1), (2, 1), (5, 1)],)), '26/3')
check("variable replication scatter",solve([(0,N),(2,N)]),str(2*N))
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 | 148/25 | 36/5 | Failed |
| regression 2 | 2 | 6 | Failed |
| regression 3 | 0 | 0 | Passed |
| regression 4 | None | None | Passed |
| regression 5 | None | None | Passed |
| regression 6 | 325/3 | 689/6 | Failed |
| regression 7 | 14 | 0 | Failed |
| regression 8 | 46/9 | 26/3 | Failed |
| variable replication scatter | 0 | 2 | Failed |
SHA-256 / b9f95e681831fe072d8063265efcfce97b7803b6a974768782db3a3cc5b76818
HELD IN THE MEMBER ARCHIVE
The verified repair and its recorded checks are member-only.
This mechanism has 9 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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Sign in to the archive ↗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 2026-09-29T14:39:04.229740+00:00.
Case digest / 5658433368b539948f14fd8de26c35b82c7a064d7dc989ca6d3e3deb879015ca