FA-13161 / Numerical aggregation / Open access
Frequency central scatter: Equal-frequency observations are collapsed by their weight. · case 01
The reduction disagrees with its explicit aggregation oracle.
ROOT CAUSE
Equal-frequency observations are collapsed by their weight.
VERIFIED REPAIR
Preserve the frequency central scatter contract at the identified reduction decision.
Unsuccessful approach: Deduplicating identical compressed rows also removes independent frequency mass.
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):
rows=list({w:(x,w) for x,w in rows}.values())
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 | 6 | 36/5 | Failed |
| 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 | 0 | 26/3 | Failed |
| variable replication scatter | 0 | 2 | Failed |
SHA-256 / 13c0ebe3f1b4ca35ebdd2f8b32a1e5f76711f8189792d4e0cdb9d3c3345e2ee9
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):
rows=list(set(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 | 6 | 36/5 | Failed |
| 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 / 976201e49630c7cf0079afbf1a75edd5aa2172a78ddeba2e51e46239ae8defb6
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 2026-09-29T14:39:04.220243+00:00.
Case digest / 660fc9c6e2381743f20c56b0d51b6a60c667ff674faed1b4f5c228b0c5e5f3fa