FA-13146 / Numerical aggregation / Open access
Frequency central scatter: Squared deviations are normalized even though the summary stores total scatter. · case 01
The reduction disagrees with its explicit aggregation oracle.
ROOT CAUSE
Squared deviations are normalized even though the summary stores total scatter.
THE FAILURE
Squared deviations are normalized even though the summary stores total scatter.
Unsuccessful approach: Sample normalization also produces a variance rather than additive scatter.
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*(x-center)**2 for x,w in rows)/total)
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 | 36/25 | 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 | 689/36 | 689/6 | Failed |
| regression 7 | 0 | 0 | Passed |
| regression 8 | 26/9 | 26/3 | Failed |
| variable replication scatter | 1 | 2 | Failed |
SHA-256 / 3e5e2b3a24ac0cff623b2c4cb638d32786183c19a069635b2fbde61d268a43b9
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(w*(x-center)**2 for x,w in rows)/max(1,total-1))
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 | 9/5 | 36/5 | Failed |
| regression 2 | 3 | 6 | Failed |
| regression 3 | 0 | 0 | Passed |
| regression 4 | None | None | Passed |
| regression 5 | None | None | Passed |
| regression 6 | 689/30 | 689/6 | Failed |
| regression 7 | 0 | 0 | Passed |
| regression 8 | 13/3 | 26/3 | Failed |
| variable replication scatter | 2 | 2 | Passed |
SHA-256 / 3b19cfd25a29af8a324519c700f35b69155b04e4d326c9cde4a14944e2d06004
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 / 4948a9ac6501913a26edb6bc19d3a816afdc457ad7095ea33192bb8d25a68b7c