FA-13136 / Numerical aggregation / Open access
Frequency central scatter: Frequency affects the center but not the squared deviations. · case 01
The reduction disagrees with its explicit aggregation oracle.
ROOT CAUSE
Frequency affects the center but not the squared deviations.
VERIFIED REPAIR
Preserve the frequency central scatter contract at the identified reduction decision.
Unsuccessful approach: Squaring weighted residuals squares their frequency as well.
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((x-center)**2 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 | 162/25 | 36/5 | Failed |
| regression 2 | 5 | 6 | Failed |
| regression 3 | 0 | 0 | Passed |
| regression 4 | None | None | Passed |
| regression 5 | None | None | Passed |
| regression 6 | 865/12 | 689/6 | Failed |
| regression 7 | 36 | 0 | Failed |
| regression 8 | 26/3 | 26/3 | Passed |
| variable replication scatter | 2 | 2 | Passed |
SHA-256 / c442dcbc104f034c3db425e68efd600a7d58cfc3d075a93d80c864ed74bb5b8d
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))
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 | 216/25 | 36/5 | Failed |
| regression 2 | 8 | 6 | Failed |
| regression 3 | 0 | 0 | Passed |
| regression 4 | None | None | Passed |
| regression 5 | None | None | Passed |
| regression 6 | 4231/18 | 689/6 | Failed |
| regression 7 | 0 | 0 | Passed |
| regression 8 | 26/3 | 26/3 | Passed |
| variable replication scatter | 2 | 2 | Passed |
SHA-256 / 7d94383df057c78aab25d006e239cf1bf904b3fb33f8278e1fa362d8627a2342
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(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))
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 | 36/5 | 36/5 | Passed |
| regression 2 | 6 | 6 | Passed |
| regression 3 | 0 | 0 | Passed |
| regression 4 | None | None | Passed |
| regression 5 | None | None | Passed |
| regression 6 | 689/6 | 689/6 | Passed |
| regression 7 | 0 | 0 | Passed |
| regression 8 | 26/3 | 26/3 | Passed |
| variable replication scatter | 2 | 2 | Passed |
SHA-256 / a2838721c019788801efdb6c42d3c979c563bb33fdf9b10978e250cc6c3625e7
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 2026-09-29T14:39:03.888385+00:00.
Case digest / c944f566260ef3c60fbc8d7d39e7f4cb3a0cadd1a0a4de4ad2127dc17645a5ae